A B S T R A C T THE SMW TRIO AND THE MEASUREMENT OF PROTON-IRON INELASTIC CROSS SECTION ABOVE 70 GeV by Billy Wei-yu Loo Co-chairmen: Lawrence W. Jones, David R. Bach The Streamer chamber, Marx generator, amd Widegap spark chamber form an intimate trio that support and complement each other as detectors for ultra-high energy charged particles. A research program covering the feasibility study and actual incorporation of such devices in a high altitude cosmic ray experiment is reported. Design philosophies and optimization procedures are also presented. The program resulted in the successful development of (1) the first streamer chamber in the U.S. and demonstrated the practicality of recording streamers of arbitrary length along trhe electric field when coupled to an image intensifier system, and (2) a compact 10-stage Marx generator with a total capacitance of 0.08 of and a capability of delivering a

voltage pulse of 50-300 kV amplitude with both the risetime and delay-time to be in the neighborhood of two nanoseconds, and (3) a high precision multi-wide-gap spark chamber with an intrinsic angular resolution of 0.1 mr per gap; and two such chambers are employed in conjunction with a superconducting magnet of 13 kilogauss-meters to form a spectrometer which has a maximum detectable momentum of about 5 TeV/c. Concurrent with the magnetic spectrometer development, the energy dependence of proton-iron inelastic cross section was studied with a total absorption ionization calorimeter of 1200 gm/cm2 of iron interleaved with 10 plastic scintillation layers. Systematic effects were thoroughly investigated. It was found that between 20 and 1500 GeV the cross section was best represented by a flat 710 mb with a slope uncertainty of 3.5% per decade change in energy.

UM HE 72-12 THE SMW TRIO AND THE MEASUREMENT OF PROTON-IRON INELASTIC CROSS SECTION ABOVE 70 GeV by Billy Wei-yu Loo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics and Nuclear Engineering) in The University of Michigan 1972 Doctoral Committee: Professor Lawrence W. Jones, Co-chairman Professor David R. Bach, Co-chairman Professor Wayne E. Hazen Professor John S. King Associate Professor Glenn F. Knoll

ACKNOWLEDGEMENT I must first of all thank my parents whose sacrificial love and earnest quest for reality and wisdom have always been a sustaining and motivating force for me. I would like to express my respect and gratitude to Prof. Lawrence Jones, true gentleman and scholar, for his most intellegent and considerate guidance throughout my graduate career. I would like to thank Prof. David Bach for his counselling and coordinational effort which made the joint degree in physics and nuclear engineering possible. I am indebted to Orman Haas for his kind and ingenious mechanical assistance in all phases of the work; to Fritz Bausch for his expert help on wide-gap spark chambers and surveying instruments; to Paul Holloway and the entire staff of the physics instrument shop, Glenn Edict and Jim Pluta of the electronics shop for many years of uncommon cooperation; to Dick Worland and his surveying staff at the Argonne National Laboratory for their excellent fiducial measurements; to Tom McCorreston for helpful theoretical discussions; to the University of Denver for the hospitality at its High Altitude Lab; to the Lawrence Berkeley Lab for the use of film measuring facilities in the early phase of the experiment; to the Argonne National Lab for the film -ii

processing and computing facilities; and to all who have participated in the construction, execution, film measurement, and data reduction of the Echo Lake experiment; their pleasant coorporation is collectively but gratefully acknowledged. -iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS.................................. ii TABLE OF CONTES................................iv LIST OF TAB LES................................vi LIST OF FIGURES..........vii CHAPTER I. BACKGROUND...................1....... A. Introduction............................ 1 B. High Energy Particle Detector Research... 2 C. Relative Merit..................... 8 D. The Emergence of the SMW Trio........ 12 E. Theory of Gas Discharge.................. 16 F. Cosmic Ray Experiment............ 21 CHAPTER II. STREAMER CHAMBER................ 27 A. The Ideal................................ 27 B. Design Principles....................... 28 C. Description........................ 32 D. Performance................. 32 E. Conclusion...................... 42 CHAPTER III. MARX GENERATORS...................... 43 A. The Idea l............................... 43 B. Design Principles................43 C. Marx Generator Development............... 48 D. Performance........................... 62 E. Conclusion............................. 67

Page CHAPTER IV. WIDE GAP SPARK CHAMBERS..... 68 A. The Ideal................................ 68 B. Preliminary Investigations.............. 69 C. Thin Foil Chambers...................... 83 D. High Precision Multi-Wide-Gap Spark Chambers........................... 91 (1) Design Principles................... 91 (2) Chamber Construction................ 99 (3) Fiducial System..................... 105 (4I) Surveying............................ 107 (5) Performance..................... 113 (6) Conclusion.......................... 121 CHAPTER V. PROTON-IRON INELASTIC CROSS SECTIONS. 124 A. Theorectical Considerations......... 124 B. Description of Experiment................ 130 C. Data Acquisition and Processing. 134 D. Method.................................. 137 E. Systematic Problems and Solutions........ 139 F. Corrections............................. 166 G. Results............................. 170 H. Conclusion.............................. 175 CHAPTER VI. EPILOGUE............................. 176 LIST OF REFERENCES...................... 178

LIST OF TABLES TABLE PAGE 1 Some Detector Properties 9 2 Some Noble Gas Properties 18 3 Locations and Sizes of Scintillators in the 132 Calorimeter 4 Systematic Problems and Solutions 141 5 Persistence Cut Matrix 151 6 XFe Matrix 157 7 AXFe Matrix 158 8 AN2 Matrix 159 9 AN3 Matrix 160 10 Correlation Matrix 165 11 Muon Corrections 167 12 Final Experimental Results on Proton Iron Inelastic Interactions 171 13 Results of Energy Dependent Curve Fittings 174 -vi

LIST OF FIGURES FIGURE PAGE 1 Growth of Spark Chamber Research 13 2 The Evolution of a Spark Channel 19 3 Spark Formation Time 22 4 Echo Lake Laboratory 24 5 Front View of Experimental Arrangement 25 6 Variation of Brightness with Streamer Length and Electric Field 29 7 Arrangement of Apparatus with Light Tight Walls Removed 33 8 Details of the Streamer Chamber and Marx Generator 34 9 Full Length Streamers 36 10 1.5 mm Streamers at f: 4.5 36 11 2.0 mm Streamers at f: 4.5 37 12 2.5 mm Streamers at f: 5.6 37 13 3.0 mm Streamers at f: 5.6 38 14 3.5 mm Streamers at f: 8 38 15 4.0 mm Streamers at f: 11 39 16 4.5 mm Streamers at f: 11 39 17 5.0 mm Streamers at f: 16 40 -vii

FIGURE PAGE 18 5.5 mm Streamers at f: 16 40 19 Streamer Length Fluctuations at a Given Setting 41 20 Marx Circuit for Generating a Negative Pulse 46 21 Marx Circuit for Generating a Positive Pulse 46 22 Marx Circuit with Coupling Capacitors 46 23 Side View of Model B Marx Generator 50 24 End View of Model B Marx Generator 51 25 Partial Assembly Drawing of Marx Generator 57 26 Details of Trigger Assembly of Model C Marx Generator 58 27 Complete Components of Model C Marx Generator 59 28 Side View of Model C Marx Generator 63 29 End View of Model C Marx Generator 64 30 Variation of Delaytime with Trigger and Bias Voltages at Constant Pressure 66 31 Arrangement for Testing of a Wide-gap Spark Chamber 70 32 Schematics of Chamber Testing Facilities 71 33 Typical Muon Test Tracks 73 -viii

FIGURE PAGE 34 Distribution of Angular Errors in Test Chambers 74 35 Distribution of Position Errors in Test Chambers 75 36 Variations of Digitized Points Along a Spark 77 37 Uniformity of Small Angle Tracks 79 38 Appearance of Large Angle Tracks 80 39 Effects of Wire Electrodes on Discharge 81 40 Effects of C2H50H on Spark Discharge 82 41 Effects of Dielectric Layers on Discharge 84 42 Partial Assembly Drawing of a Thin Foil Chamber 85 43 A 2x2 m2 Thin Foil Wide-Gap Spark Chamber 88 44 Strength of the Thin Foil Window 89 45 The Modified Echo Lake Cosmic Ray Experiment 93 46 Construction Details of Multi-Wide-Gap Spark Chamber 100 47 Chamber Glass Plates Before Assembling 102 48 Base Frame of Multi-Wide-Gap Spark Chamber 103 49 Assembly Procedures of Multi-Wide-Gap Spark Chamber 104 -ix

FIGURE PAGE 50 Fan Connections to the Marx Generator 106 51 Precisions of the Fiducial Marks 108 52 A Completed Chamber Mounted with Surveying Instruments 110 53 Details of the Cathatometer Mount 111 54 Spark Characteristics at 120 kV 114 55 Spark Characteristics at 140 kV 115 56 Spark Characteristics at 160 kV 116 57 Spark Characteristics at 180 kV 117 58 Spark Characteristics at 200 kV 118 59 The Intrinsic Angular Resolution of a Single Spark 120 60 An Air Shower of Over 90 Resolved Tracks 122 61 Theoretical Predictions of Proton-Iron 129 Cross Sections 62 Front View of the Ionization Calorimeter 131 63 A Proton Interacted in the Carbon Target 133 64 Electronic Block Diagram of the Echo Lake Cosmic Ray Experiment 135 65 Comparison of the Average Shower Curves with the Monte Carlo Results of W.V. Jones 143

FIGURE PAGE 66 Behavior of Hadronic and Electromagnetic Cascades in the Calorimeter 148 67 A Typical Persistence Distribution 149 68 Illustration of Formation Zone by Qualitative Average Shower Curves 152 69 Effects of Formation Zone 154 70 Characteristic Dependence of XFe on D 161 71 Number of Detected Interactions in Layer 162 2 vs. D 72 Error Contributions to AN2 163 73 Variation of XpFe with Energy 172 74 Variation of UpFe with Energy 173 -xi

CHAPTER I BACKGROUND A. INTRODUCTION In the course of a few decades, man has witnessed the phenomenal growth of particle accelerator technology and the resulting population explosion of elementary or subnuclear particles. At the same time he could no longer comfortably account for the physical universe in terms of gravitational and electromagnetic interactions. Yet in spite of vast volumes of experimental data accumulated and efforts of thorough theoretical scrutiny, the true nature of strong and weak interactions remains a mystery. From the few pieces of the puzzle assembled so far, physicists are convinced that there will not be enough clues available from the data of present day accelerator energy of 70 GeV. (1) It is further believed that due to the wave nature of matter, large momentum and energy transfer is only possible in small regions of space and time, and the short deBroglie wave lengths of particles of hundreds or thousands of GeV will be necessary to probe spacial structures below 10 15 cm and time intervals under 10-25 sec. It is hoped that life will be simpler in the smaller world. Just as larger accelerators are essential to the production of high energy particles, more sophisticated instruments are needed to detect or analyze them. Only -1

-2through advanced and precision instruments can man extend his realm of physical observations. The 200 GeV accelerator will soon be operational and other accelerators of up to 5000 GeV are under consideration.(2) Superconducting or even cold aluminum magnets will undoubtedly make them economically feasible someday and new detectors will be sought to meet those demands. B. HIGH ENERGY PARTICLE DETECTOR RESEARCH We shall consider here only charged particle detectors although neutral particles and energetic photons are always detected through the production of charged particles. Thus all particles, whether they are strong or weak interacting, are eventually detected via electromagnetic interactions in the detection medium. Gravitons and neutrinos are of course exceptions. There is a whole army of particle detectors ranging from the old Geiger Muller counter to solid state detectors; but we shall only consider those which would yield momentum or energy information in the ultra-relativistic range. That is, when the energy of a particle is much larger than its rest mass or y >> 1 where V 1$2 and E = ymoc2 ~ pc

-3Energy measurements may generally be carried out under the following five categories: (1) Velocity Selection (a) Time of flight measurement: This is the simplest and most direct measurement but its effectiveness is rather limited at high energies. For instance, the best time resolution of counters is about 10 10 sec. For a flight path of say 10 m, the velocity resolution dp f c = 3x10. Since p tdE -= y 2d y2dp the maximum detectable y is 18.3 or the maximum detectable momentum is under 20 GeV/c for protons. (b) Cerenkov detectors: When the velocity of a charged particle exceeds the velocity of light in the medium with index of refraction n, continuous spectrum of Cerenkov radiation will be emitted at an angle e with respect to the particle trajectory according to cos = and the number of photons N produced by a particle of charge Ze along the track length x in the wave length region of X to ~2 is N = 2rr 2 x J2 ( ) It is thus possible to operate a Cerenkov detec

-4tor as a threshold counter or a differential counter for Pn >1 and AP, corresponding to the range of A accepted in the detector, respectively. Making use of the previous equation, it is also possible to operate a multichannel Cerenkov counter in which the detected light intensity is related to the momentum of the particle. Recent development has pushed the resolution to AP = 6x10-7 (3) or a maximum detectable y of 1290. (2) Magnetic Bending Unlike in an electric field, a charged particle experiences no energy change while traversing a constant magnetic field. But more relavent is the fact that the largest practically attainable magnetic force is some hundred times higher than the electric force. In the case of magnetic bending, the particles energy for unit charge in GeV is equal to the magnetic rigidity E = 30 BR where B is the magnetic field in kilogauss and R is the radius of curvature in kilometers and and R v 1 L2 8S' where L is the path length in the magnetic field and S is the sagitta. It is seen that dE S and the spacial resolution of the detector in the magnetic field will be of

-5prime importance. Bubble chambers and wide-gap spark chambers have spacial resolution of about 0.1 mm, while that of cloud chambers and streamer chambers is about 0.2 mm. On the other hand, if detectors are placed outside of the magnetic field and the deflection angle e is measured, E=-8 BdL Given the same magnetic field strength and region and given the same spacial resolution of the detectors, it is seen from simple geometrical consideration that one can achieve an energy resolution of a factor of four better with the detectors outside of the magnetic field region. Spacial resolution of 2 iam can be achieved with emulsions(4) while those of wire spark chambers and counter hodoscope are about 0.3 mm and a few mm respectively. (3) Relativistic Rise in Energy Loss The rate of energy loss of a particle of charge ze in a medium of atomic number Z by excitation and ionization along its trajectory is given by dE 4e4z2N [ 2mv2 2 ln(l-2) 2 where N is the number of absorber atoms per cm3 and

-6I is the mean excitation and ionization potential of the absorbing atoms. dE In general, a- decreases rapidly as E is increased and a characteristic minimum is reached at about twice the rest mass energy of the particle. It then increases logarithmicly with E. Such a rise is reduced in denser materials or at ultra-relativistic energies due to the screening of the Coulomb field by the close packing of the atoms. But such density effect is found to be absent in the case of thin ( 0 0-5cm) films. Thus a measure of dE is a measure of log y. Streamer chambers,(5) proportional counter arrays (6) are suitable for this type of measurements. Collecting secondary electrons from thin film solid state detector slabs is also a promissing approach.(7) Transition Radiation When a charged particle traverses a boundary of two media of different dielectric constants, a continuous spectrum of transition radiation in the optical region is proportional to log y while in the x-ray region it is linearly proportional to y. When foils of thickness just thicker than the formation zone (<20 pm) of such radiation are stacked with appropriate spacing (<1 mm), sufficient x-ray photons will be generated and can be detected by proportional counters or solid

-7state detector arrays. The total length of the detector needed is much less than that of a corresponding threshold Cerenkov counter whose length increases proportionally to y2. (9) (5) Total Absorption Spectrometers (a) Calorimeters: Usually the particle and its reaction products, excepting muons and neutrinos, are completely contained within the bulk of a stack of iron. Its energy is proportional to the total ionization that is sampled by layers of plastic or liquid scintillation counters. Corrections must be made for undetected energy of nuclear disintegration and the estimation of energy loss in iron by the measurement of ionization in the scintillators. The best energy resolution is about 10-20%, depending on design parameters. (b) Total absorption nuclear cascade counters: In contrast to the sampling nature of the calorimeter, all of the particle energy which finally appears in the form of collision loss to the atomic electrons in large slabs of scintillation crystals is detected. Since the absorption mean free path is at most slowly varying at extremely high energies, there is virtually no limit to the highest energy detectable. Besides, energy resolution of close to 1% can be achieved.(lO)

-8C. RELATIVE MERIT There are at least a dozen properties that an ideal detector should have. The most crucial ones are of course high detection efficiency, high energy resolution and possible particle identification. It would also be extremely helpful to have high multiparticle efficiency and a large dynamic range of energy measurement. Furthermore, it would be nice if the particle will survive the measurement. When events are very frequent, one would like it to have good time resolution and repetition rate. And when events are very infrequent or when background rate is high, one would like it to have large acceptance and capability for external triggering. Other important features concern the speed of data reduction and possible on-line operation or decision making. Finally there is the inescapable question of cost. The ideal tool does not exist. In order to choose the proper weapon for a specific situation, it may be helpful to list some of the long and short ends of the alternatives:

-9Table 1 Some Detector Properties DETECTOR ADVANTAGE DISADVANTAGE Time of Fast and simple. Low maximum detectaFlight ble momentum. Cerenkov Good velocity selector Can be excessively Counter and particle identifier long. at moderate energies. Low admittance. Bubble Excellent spacial reso- Non -t r igge rab le. Chamber lution. Ionization in- Expensive. formation. Detection Long dead time medium can also serve as ( ~1 sec ) target. Excellent vertex detections. Isotropic. Wide-gap Excellent angular reso- Non-isotropic. No Spark lution. Easy to build ionization informaChamber very large and simple tion. Moderate time systems. High multiple resolution (~1 psec) track efficiency. and dead time ( NO.1 sec ) Cloud Ionization Information. Very long dead time Chamber ( ~lO sec )

- 10Table 1 ( continued ) DETECTOR A DVANTAGE DISADVANTAGE Streamer Ionization information. Low light output. Chamber Isotropic. High multi- Moderate time resolu pile track efficiency. tion and dead time. Emulsion Unsurpassed spacial Serious background resolution. loading problem. Awkward to use. Wire Spark On line analysis. No ionization inforChambers High repetition rate. mation. Low multiple Large system possible. track efficiency. Moderate spacial resolution. Counter On line analysis. Very Poor spacial resoluHodoscope high repetition rate. tion. Propor- Particle identification Limited by density tional effect and ionizaCounter tion fluctuations.

-11Table 1 ( continued ) DETECTOR ADVANTAGE DISADVANTAGE Thin Film True log y measurement. Limited size, thus Secondary admittance and Electron efficiency. Detector Transition Linearly Proportional Limited size. Radiation to y. Large dynamic Non-isotropic. Detector range. Calori- Good energy threshold Destructive measuremeter triggering device. ment. Non-isotropic. Moderate energy resolution. Bulky, thus limited admittance to diverging particles. Total Excellent energy reso- Destructive measureAbsorption lution. Homogeneous. ment. Limited admitNuclear Particle identification. tance. Expensive. Cascade Unsurpassed dynamic Detector range.

-12D. THE EMERGENCE OF THE SMW TRIO Since all radiations eventually lose a significant fraction of their energies through ionization of the medium, gas filled detectors form the oldest and most reliable family of nuclear workhorses. The ionization chamber, proportional counter and Geiger-MUller counter differ little more than different voltage regions of operation. They indeed formed the first trio of nuclear detectors. The early spark chamber was actually a transformation of the G-M tube with plane electrodes. But when its reliability was improved by voltage pulsing and noble gas filling, it had possessed the outstanding capability of displaying spacial information. This fact, together with its good time resolution and intrinsic simplicity, had enabled it to blossom into a field of its own. The depth and diversity of its development was phenomenal. One measure of its growth is the number of pages per review article that was devoted to it in the decade of the Sixties as shown in Figure 1. It is not necessary to mention here the various possibilities and modes of operation of spark chambers. They can be found in the review articles (11-16). Charpak also has a good summary of spark chambers with automatic filmless readout or data recordings in ref. (17). But even with such a large spectrum of spark chamber types they

-13260 240 (15) 0 220 w 200 -J t 180 3 160 140 w 120 g 100 _ (14) 80 (13) 60 0 40 (12) 0 20 I I I'61'62'63'64'65'66'67'68'69 YEAR Fig.1 Growth of Spark Chamber Research

-14generally fall under two catagories, i.e. wide-gap and narrow-gap chambers. The electrode spacings of narrow-gap chambers are typically under 1 cm and the voltage pulse required is usually under 15 kV, which can be easily provided by the switching of a thyratron or a single spark-gap. With the application of clearing field or quench gas, the time resolution can be made very short, and together with digitized readout they are particularly suited for rapid on-line analysis in intense particle beams. However, the spark in a narrow-gap chamber generally follows the electric field line rather than the actual trajectory of the particle. Therefore one can get only one set of 2-dimensional spacial information, which is accurate to about 0.2 mm, from each gap. In other words, the information density is not high for narrow-gap chambers. and unless one is at liberty to place chambers arbitrarily far apart, with the correspondingly low detection solid angle, narrow-gap chambers are not the best choice as far as the question of maximum detectable momentum is concerned. Furthermore, multiple-particle and large-angle (with respect to electric field) detection efficiencies are moderate. Ionization information is not available either. On the other hand, the electrode spacings of widegap spark chambers are usually tens of centimeters and voltage pulses of hundreds of kilovolts are required. If

-15the high voltage pulse width is sufficiently large to allow the development of a full spark channel, the spark will follow the trajectory of the particle (except at regions of within 1 cm from the electrodes) up to about 40~. Beyond that point, tracks are more diffused and finally disappear at about 600 with respect to the electric field. But if the pulse width is shortened to under about tens of nanoseconds, the development of each ion pair will be limited and generally prevented from coalescing with their neighbors. The resulting track of truncated streamers not only registers almost isotropic 3-dimensional spacial information about the particle trajectory, it may also provide ionization information for relativistic rise measurements. Whether it is operated in streamer mode or in spark mode, multiple track efficiencies are extremely high. It is the combination of high information density (up to the reciprocal of ion density along the track), high efficiency, intrinsic simplicity (hence practicality for large and precise systems) and the capability for post event triggering that makes them most attractive for ultra-high energy applications. As we have seen that wide-gap chambers while enJoying certain advantages as a class by themselves also bear more stringent requirements. In order to achieve optimum operations, they need high voltage pulses of hundreds of kilovolts with fast rise-times and minimum delays. But

as far as voltage availability is concerned, there seems to be a natural barrier at about 30-50 kV, beyond which general insulating problems become rapidly more difficult. Common electronic components and switching by thyratrons or single spark-gaps have reached their practical limits. Here is where the Marx generator comes to the rescue. Marx generators work on the simple principle of charge conservation. If n capacitors charged in parallel to a d.c. supply voltage of Vo are rapidly switched by spark gaps to series connections, and if all capacitors are isolated from each other by large enough resistors such that the RC time constant of any part of the circuit is much larger than the switching time, a voltage of nVo will be developed across the series. The optimization procedures to meet the demands of wide-gap chambers will be the subject of chapter III. It is thus clear that Streamer chambers, Marx generators and Wide-gap spark chambers intimately support and complement each other to form a unique family of detectors for ultra-high energy physics. Indeed, they are the SMW trio. E. THEORY OF GAS DISCHARGE Gas discharge is the basic mechanism that is common to all members of the SMW trio. The beauty of the SMW Trio is their intrinsic simplicity; and they can be made operational without a detailed knowledge of the gas dis

-17charge mechanism. However a brief description of several pertinent aspects may clarify some of the optimization procedures involved. Table 2 lists some of the commonly used chamber gas properties under typical operational condition of electric field E=10 kV/cm and at one atmosphere. More complete data on the variation of these properties with various parameters are available; but these may serve as guide lines. When a charged particle passes through the chamber fill gas, a trail of ions will be left along its trajectory (Fig.2A). The diffusion constants of positive ions are a few orders of magnitude smaller than those of electrons, so one only needs to be concerned with electron motions. Upon the arrival of the uniform high voltage gradient E, each electron will initiate a cascade of ionizations, called an avalanche, towards the anode as illustrated in Fig.2B. The multiplication factor is described by eax where a is known as the first Townsend coefficient of ionization, and x is the distance from the original ion. The drift velocity v for E > 10 is (22) v = 2.6 x 106 J Ep_ 1.5 cm/sec where E is in V/cm and P is in torrOrdinarily the avalanche will propagate with a velocity of 107 cm/sec until the external electric field is

-18TABLE 2 Some Noble Gas Properties at E=10 kV/cm and P=760 torr He lium Neon Argon REF. First Townsend Ionization Coefficient 60 70 10 (19) a ( cm1 ) Electron Diffusion 4400 8100 1100 (20) Coefficient 310* 2000* 370* D ( cm2/sec ) Electron Mean Free Path 2.7 1.8 1.2 (15) X ( Pm ) Ionization Potential ( eV ) 2421.5 15.7 (19) Metastable States 20.7 16.7 11.7 ( eV ) 19.8 16.6 11.5 (19) Primary Specific Ionization 6.6 15 30 (21) ( ion pairs per cm ) * Diffusion coefficient with E = 0

IauU'qMO X:ds F jo uo$FnToA, GIT, ZD'2d H 3 / /~~~~~ /~~~~~/ // // / / AtZ/~ I~~~/ / I I/ / V~~ Pg 99 / / / PV ~ = // / I ~/ / i,~~~~~/ - /!~ /~~, // z~~~~~~~~~~~~/! / /x ~~~~~~~~~//! //~~~~~~~/'~~~~i / -.~~~~~~~~~~~~~~~~~~ / j/i

-20locally cancelled by the roughly dipole field of the space charges; this is known as the Meek condition (Fig.2C). At this point multiplication by collision will cease. But if it has reached such a magnitude that ax = 20 (or an ion density of about 7x111cm-3) sufficient energetic photons will have been produced to induce photoionization.(23) Photoionizations cause secondary avalanches to form near the head and the tail of the avalanche, where the electric field is most intense (Fig.2D). Electrons are expelled away from the negative head of the original avalanche and are drawn into the positive tail. These secondary streamers coalesce and transform into positive and negative streamers (Fig.2E). They grow in opposite directions along the electric field lines at about 108 cm/sec. If the voltage is sharply switched off at this stage, as in the case of streamer chamber operation, the streamers will be "frozen" in space to yield spacial information about the particle. The avalanches are not visible and the empirical relation for the young streamers to become sufficiently bright for photographic recording is (for neon) (24) E2 T p. - 9.1 i 1.5 where E is in kV/cm T is the pulse width in nanoseconds, and P is in torr. If the pulse width is made longer, streamers will continue to grow, and branching may take place along adjacent field

-21lines. The coalescence of secondary streamers will result in a highly conductive channel of plasma. The chamber will be called a projection chamber or a wide-gap spark chamber, depending whether the conducting columns are formed out of independent primary ion pairs (Fig.2F), or out of the linkage of neighboring streamers (Fig.2G) along the trajectory of the particle to form a rather uniform spark (Fig.2H). In either case, voltage is terminated by the spark channels themselves. Such a spark formation time TF is shown to be primarily depending on the Townsend coefficient a and electron drift velocity v, and only mildly varying with chamber size and circuit parameters: T 29.5 ~ 0.5 ( e ) Measurements by Fisher and Zorn are shown in Fig.3. (25) The performance of the wide-gap chambers are heavily dependent on the nature of the working gas. The questions of proper choice, the control of impurities and, in particular, the effects on space and time resolutions will be explored further in Chapter IV. F. COSMIC RAY EXPERIMENT Particle accelerators in nature existed long before artificial ones. Cosmic rays, which are mainly protons with a decreasingly small percentage of heavier nuclei, rain on the earth from all directions. Some are prevented

10 I I I I I I I I I I iw<0.1 I 0.01 Io l- I I I I I > > I I I I I I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 ELECTRIC FIELD E (kV/cm) Fig.3 Spark Forrmation Time

-23from reaching the surface due to the deflection in the earth's magnetic field and by the attenuation of the atmosphere. Taking 0.31 gauss as the equatorial magnetic field and 6.38 x108 cm as the earth's radius, any particle with a magnetic rigidity of greater than 59.3 GeV can always reach the earth. The atmosphere being 1030 gm/cm2 thick provides about eight absorption mean free paths of shielding against energetic protons. The integral spectrum of primary cosmic rays above 1GeV is roughly 0.3 cm-2 sec-1 sterad-1 while the flux above energy E is proportional to E-1.7. Some particles had been recorded with energy exceeding 1020 ev. Thus by setting up an experiment as high above the atmosphere and with as large a detector as is practical, one could get a preview of ultra-high energy interactions before the arrival of super accelerators in the hundreds or even thousands of GeV range. This is what we have done at Echo Lake, Colorado which is at an altitude of 3230 m or above one third of the atmosphere. Fig.4 shows Sigma Hall, the building which houses the main apparatus and the fast logics. The adjacent 40 foot trailer houses other electronic control and recording systems. Fig.5 is a schematic of the experimental set up. A coincidence of pulses from the top counter, the second layer of the calorimeter, the sum pulse of the entire calorimeter exceeding a preset threshold of 36 or 90 GeV, and

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-25Total Cross Section Experiment Front View o 10 20 30 40 inche s Top counter Thin foil wide gap spark chamber Stainless steel Flask Shower Counter LIQUID HYDROGEN AntiAluminum Coincidence jacket Coincidenc Thin foil wide gap spark chamber 20 gm/cm2 F _....:__ Iron plate each gap _F Narrow gap spark chamber 2 ~-_~- _2... >:.!:-....... I(10 gaps) 120 gm/cm2 120 gm/cm2 absorption 120 gm/cme2 I-...i-. -iii.. "calor-imeter 10 layers of ~'120 gm/cm2' -...... ~'counters in 120 gm/cm2 1120 gm/cm2 160 gm/cm2 of iron 160 gm/cm2 Fig.5 Front View of Experimental Arrangement

-26no signal from the anti-coincidence shower counter guard ring would constitute a trigger. The thin foil wide-gap chambers which straddled the target would record the incident and out-going particles through two 900 stereo cameras. All of the layer information from the calorimeter was recorded either on magnetic tape or by an array of binary neon lights photographed together with the spark chambers. The apparatus has an effective admittance of 0.94 m2 sr through layer 8 of the calorimeter, and the trigger rate for charged hadrons of greater than 90 GeV was about 20 per hour. Besides liquid hydrogen, other targets of carbon, aluminum, iron, tin and lead had also been used. The arrangement was basically a transmission experiment to measure the proton inelastic cross-sections above 70 GeV, together with studies of angular distributions and average multiplicities with various targets and energies. A bonus of this experiment was the precise measurement of energy dependence of proton-iron inelastic cross-section by studying the interaction of the transmitted proton flux in the calorimeter. A detailed analysis of this measurement will be the subject of chapter V.

CHAPTER II STREAMER CHAMBER A. THE IDEAL The ideal streamer chamber is not intended to be a detector for all occasions. A detector will be considered ideal if all its unique properties are abundantly realized. The very fact that the discharges are decoupled almost guarentees that a streamer chamber will have 100% multiple track efficiency when lateral track spacings are smaller than streamer lengths. This decoupled nature of streamer development undoubtedly allows relative if not absolute ionization measurements. The near isotropic property of the chamber was well demonstrated by Chikovani et al. (26) when spiral tracks were observed in the magnetic field. Due to the low density of the gas medium, the chamber is well suited to observe low energy recoil or short lived decaying particles. A 4n detection geometry is possible when targets are inserted into the active volume if the gas is not served as target itself. All of these good characteristics can be realized if the streamers will produce sufficient light for recording. -27

-28B. DESIGN PRINCIPLES (1) Electrical Requirements: To achieve the best spacial resolution, it is important that the high voltage pulse be delivered with minimum delay such that electron diffusion will be kept to a minimum. For the sake of achieving isotropy as well as spacial resolution and dense shower efficiency, it is desirable to keep the streamer lengths to a minimum. Furthermore, the streamer brightness at a given length will increase with electric field E, as shown in Fig.6, up to about 15 kV/cm. (27) All these constraints point to the requirement that the voltage pulse must not only be of large amplitude but the rise-time must be extremely short in order to reach the optimum voltage level before the pulse is sharply turned off to limit the streamer length. Such a requirement can be best realized in small chambers with Marx generator pulsing and crowbar (shunting spark gap) switching. But for a large chamber whose transit dimension is comparable to the pulse width, it should be treated as a terminated transmission line and be pulsed by a Blumlein with impedence matching. In any case, a Marx generator is involved and its development will be the subject of the next

-29toL \ \ RB= RELATIVE BRIGHTNESS E -J, 6 w 00 4 2 I I I l I! J I_. 6 7 8 9 10 11 12 13 14 15 16 E (kV/cm) Fig.6 Variation of Brightness with Streamer Length and Electric Field

-30chapter. (2) Optical Requirements: The minimum photon density required to register an image on a very fast photographic film (ASA > 1000) is about 2x106 photons/mm2. (28) In Fig.6, the curve labled with relative brightness = 1 corresponds to the case where 50% of the streamers will be recorded at f:l.5 and film speed of ASA 1500. Thus it is seen that tracks of less than 2 or 3 mm can hardly be recorded by direct photography. The other aspect of the optical requirement has to do with the depth of field. This is particularly serious with large volume chambers. Consider a simple lens that is focused at infinity. A point source at a distance H from the lens of focal length F will form an image at a distance q behind the lens. But in the film plane, it will have a circle of confusion of CF. From geometrical consideration it is seen that F2 H _ = -hyperfocal distance fCF where f is the usual F to aperture ratio. If the lens is focused on a point at distance p from the lens, there will be far and near planes p1 and p2 in which the circles of confusion CO are the

-31same: Co = D CF where D is the demagnification F p F Explicitly, P HpF Hp Pl = H-(p-F) H-p' P2 H+(p-F) H+p Thus the depth of field - P1-P2 H2-p2 To see the relations between Ap, D, f and Co, we note that Ap = 2D2fCF 2D2fCF = 2DfC This shows that the depth of field ap is directly proportional to f, D, and Co, but the maximum value of each is not without constraint. If N denotes the total number of photons and A the area normal to the optical axis, NF _ No 1 1 AF Ao 31 —f' therefore the maximum value of f is limited by object brightness and film sensitivity. Co must also be limited to be smaller than the object size in order that the object brightness will not be significantly diminished. Finally, D is limited by film resolution, hence when demagnification is high, space resolution will be correspondingly low. It is towards the goal of breaking the aforemen

-32tioned constraints and the goal of achieving an ideal detector that the following feasibility study of the use of image intensifier with streamer chamber was initiated. C. DESCRIPTION A detailed description of the experiment can be found in reference (29). It is intended here to briefly review some general features of that study. Fig.7 shows the experimental arrangement. The chamber of 23x15x6 cm3 active volume was viewed directly by a 3-stage image intensifier. A 900 stereo view parallel to the electric field was photographed by means of a mirror looking through the transparent screen electrode. The streamer chamber was pulsed by a simple 5stage Marx generator as shown in Fig.8 and the crowbar shunting spark gap was pre-triggered by a pulse from the first stage of the generator to reduce time-jitters in the switching action. The size of the crowbar gap controled the duration of the pulse hence the length of the streamers. D. PERFORMANCE Streamers of any length can be obtained just by a dial of the crowbar. Fig.9 is an overexposed picture of a full length streamer track showing the field of view covered by the image tube and the extent of distortion in

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B~~~~~~~~~ -14 Fig.8 Details of the Streamer Chamber and Marx Generator

-35volved. Samples of scattering from chamber walls or in chamber gas at various streamer length settings are illustrated in Fig.lO-18. They correspond to streamers of about 1.5 mm to 5.5 mm in 0.5 mm increments with f-stops ranging from 4.5 to 16. The control of average streamer length at a given setting is shown in Fig.19. All the pictures were taken at the same voltage gradient of 17 kV/cm (assuming peak voltage is reached) and comparisons indicate that there is approximately a factor of 2.5 increase in brightness for every mm increase in streamer length. Some 3 mm streamers have been photographed directly with a 76 mm lens at f:0.87. Assuming that 2X106 photons/mm are needed for recording, and taking an effective streamer width to be about 0.5 mm, the number of photons liberated is estimated to be 3.6x107. The observed streamer density along a track was about 6 per cm in a 85-15 nelium (or neon-helium) mixture at one atmosphere. This is less than the primary ion density, but due to fluctuation in avalanche development, not all avalanches are expected to turn into visible streamers within a given time. Unless the gas density is low, there is also a finite probability for avalanches to merge with their close neighbors.

Fig.9 Full Length Streamers Fig.lO 1.5 mm Streamers at f:4.5

I _ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Fig.ll 2.0 mm Streamers at f-14.5 Fig.12 2.5 mm Streamers at f':5.6

I~~~~~ _ _r I l_ Oo3 Fig.13 3.0 rmm Strewhers at f'5.6 Fig.14C 3.5 mm Streamers at f:8

Fig.15 4.0 mm Streamers at foll Fig.16 4.5 mm Streamers.St, f. l I Fig.15 4. mSraesa ~lFg1.5 mm Streamers at f:ll

I~~~ _l~ At FIg~~l7 __.0 mm Streames at f:16 ig~l8 5.5mm Stream10 Fig.17 5.0 mm Streamers at f:16 Fig.18 5.5 mm Streamers at f:16

-4140 30 U) 0 r 20 z 10 1 4 2162242833640I | I 2 I 4 0.4.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 AVERAGE STREAMER LENGTH (mm.) Fig.19 Streamer Length Fluctuations at a Given Setting

-42E. CONCLUSION It is concluded that this experiment even in its unsophisticated form has demonstrated the immense potential of the streamer chamber as a research tool. The coupling of the image intensifier certainly has overcome the light output and depth of field weaknesses and paves the way towards automatic digitization. Needless to say the Marx generator and image intensifier used in 1964-5 were primitive by today's standard. The voltage characteristics were not optimized, which could account for the apparently low light output compared to the observed 108 photons for a 1 mm streamer; (30) and the image tube distortion was excessive. But far superior instrumentation is now available, and the intrinsic advantages of the streamer chamber have been realized. Its growing popularity as a detector in experiments at several major accelerators attests to this fact.

CHAPTER III MARX GENERATORS A. THE IDEAL It is clear from the discussion of the previous chapters that an ideal Marx generator must have minimum delay-time and rise-time (< 10-9 sec if possible) besides the capability of delivering a peak voltage of hundreds of kilovolts. If the load impedance is low, the generator's internal impedance must be correspondingly low. If the capacitive load is high, its output capacitance must be correspondingly high. Often, the amount of stored energy, compactness and reliability are of concern. Thus there may be many variation of the ideal generator depending on specific applications. Unlike the optical problems encountered with streamer chambers, there is no sharp exclusive nature among the desirable features. It is a question of optimization to attain them all. B. DESIGN PRINCIPLES The basic element in the operation of a Marx generator is the switching action by spark-gaps. Sparkgaps are preferred because of their unsurpassed simplicity, speed, and high-current handling capability. The risetime T of the voltage pulse (10-90%)

switched by a spark-gap can be expressed as (31) T = 2.2 ( TL + TR ) where TL is the exponential risetime due to the inductance of the sparks and circuit elements while TR is the exponential risetime associated with the formation of a plasma in a spark channel. More explicitly TL =, where L is the inductance and Z is the load impedance. For a conducting column of length z and radius r (typically 0.1 mm) (32) L 2x ( n 2x _ 0.75) [ in nanohenry ] On the other hand, TR 200 pl/2 nsec TR - 1/3 E4/3 [ nse ] where E is the electric field in kV/mm, Z is the impedance across the gap in ohms, and P is the density ratio of the gas to standard air. Therefore, the risetime can be minimized by keeping circuit inductance and spark lengths to a minimum. Statically, Vo = Ex is to be set on the verge of the spontaneous breakdown voltage of a gap and is proportional to px; hence TR is proportional to p-5/6, and density in turn is proportional to pressure. Thus high pressure operation will reduce both TL and TR.

-45The final risetime of the output pulse may be further sharpened by a spark gap in series. The overall delay is of course very much related to the risetime of individual gaps. Under a given set of Vo and x, the breakdown time is determined by the amount of overvoltage and the presence of free electrons. Free electrons may be provided by a continuous discharge from a corona needle or by ionization with UV photons. Suppose the DC supply voltage is positive, then a Marx generator of n stages can be used to generate a negative pulse or a positive pulse depending whether it is triggered by shorting the high voltage electrode of the first capacitor to the ground (Fig.20), or to the DC ground electrode of the second capacitor (Fig.21) respectively. In either case an overvoltage of magnitude Vo is applied to the remainder of the circuit. As far as fast pulses are concerned, the circuit to the right of the first gap is an alternate series of (n-l) storage capacitors CO's and interelectrode capacitance Cg's. Since Co>>Cg an overvoltage of will appear across each gap. When the second gap is n-l 2Vo shorted, an overvoltage of n-2 will appear across the remaining gaps, and so on. Thus when n is large, the delay will be long due to the small overvoltage. This difficulty is overcome by the introduction of coupling capacitors Cc as shown in Fig.22.(33) If Co>>Cc>>Cg then almost the full

+vo Trigger. Fig.20 Marx Circuit for Generating a Negative Pulse +Vo V0~b~ __o+ vI -Trigger Fig.21 Marx Circuit for Generating a Positive Pulse cc Cc tcO -c 00-0 -o4 --- C Cg Co - Cc cc Figo22 Marx Circuit with Coupling Capacitors

-47overvoltage will appear across the next gap to be broken down because Cc provides a relatively low impedance path to the ground. In short, best results can be achieved with small gaps, high pressure, corona source, and coupling capacitors. Topologically, the components should be arranged with minimum circuit inductance and the gaps should "see" each other such that they are linked by UV radiation for fastest action. When a Marx generator fires into a chamber of load capacitance CL the voltage across the chamber V is a damped oscillation of frequency uW) = 1 R2 LC 4L2 where L, R and C are the series combination of the load and generator circuit parameters. When the damping is small or for the initial part of the wave, V behaves approximately as V = nV C/n ( t ) + CL ( 1 - cos wt ) Thus the actual gain in peak voltage of V will be leveling off with increasing n when Co/n becomes comparable with CL. Again, it is seen that small L lead to high w hence fast risetime. Sometimes it is also necessary to keep Co large if too high a voltage is undesirable but sufficient total energy n Co V2 must be provided, such as to support very

-48high multi-particle events in wide gap spark chambers. For compactness, capacitors are usually made of ferroelectric materials such as barium titanate which has a dielectric constant of about 4000. Since most capacitors have a height to diameter ratio H of less than unity and since all the capacitors eventually will have to discharge in series, the most compact Marx generator will be the size of a cylinder of length L = nH and diameter D. The minimum L is determined by the highest voltage required and the dielectric strength of the material. For instance, if a pulse of 300 kV is needed and if a convenient 30 kV power supply is available, then n will be 10, and H will be determined by the dielectric strength (for common Sprague door-knob capacitors it is about 15 kV per cm at which field the capacitance will also drop down to 60% of the field free value), and Co will be determined by D. Note that for a given D, output capacitance and voltage are rather unaffected by variations of n and Vo as long as nVo is constant. But switching will be faster for large n (within practical limits) because the overvoltage will be large compared to Vo in each gap. C. MARX GENERATOR DEVELOPMENT (1) Model A This simplest version of a five stage generator

-49is shown in Fig.8 and the circuit was that of Fig.21. Each capacitor (Type 715C, Sprague Electric Co.) has a capacitance of 2500 pf and is rated at 30 KVDC. Copper electrodes were fastened directly to each screw terminal and the gap spacings were adjustable. The trigger electrode had a trumpet shape with a peripheral gap of 0.1 mm at the center and flush with the cup electrode. A 7 kV trigger pulse would break down this gap rapidly, producing sufficient photoelectrons to break down the main gap. The gaps were not pressurized. Neither were they optically or capacitively coupled. Nevertheless, it was able to pulse the small streamer chamber reliably with a delay-time of about 70 nsec. (2) Model B This generator was designed to drive the (2m)2 thin foil wide-gap spark chambers used in the Echo Lake Cosmic Ray Experiment. Its circuit was similar to that beautiful design by Gygi and Schneider.(33) A two-column arrangement effectively realized the circuits of Fig.21 and 22 with all the gaps seeing each other. Figs.23 and 24 are the side view and end view of the generator with the pressure vessel removed. The principles mentioned earlier can be visualized as follows: Imagine a vertical long cylinder of bare BaTiO3

iiii -— c:i:::::::i::_:i:i ii::i::_:i-i::::i::::::j:::::: a-:::::::::j::::.:-::-::j~:::':::':'::':'::::::::::~:::::a:_:l:8-:i: —::::::-:,:~:~:i,:k:ii:i:::::::i::::i:i::::-:-:i:-:::::::::::::::::: 1 ( f:'iL1`:isji"'':'::'::li::'::::::(:::::'::::: c:s~-: izli,'::i;'".l:i:::::i:::;i:i:ii:;-: i::~c: ii:-a~ ~~ii:~::ii;:: f;L,:::?::: I7'B:-aii i-::::::_:l::i:::i:I::::::,::-:::::;;1::: i::-::::::-::i;:::::::::..:_::::: sL:-":"::i: ifa- BJ -i::I i T,: a::, Sj;" 1-:::::::':::"::':::-::i:i: - 1 ~ i II.:: i i,, VI i a — j::~g ar*ar;.\uaap,.p i~t'~i:i4asl ds O -iir:i:i:: i:::::: i:::(ii:i;ii(::::i::.:::::::il r: L-:: I::-:j::::i:::i::i.::: R(:,::i: ii j -:ii -::-:: i iii r I::i i::i::_ ii:d'-iiii:ii:i:~::::::i:i " a ~ i: i:::I-a; r a -ii:i: c:::::1:si:i::i::.iil s:i -:li'~&:l E3i: I:i'i:i'i'.::i:l=i:::::::::l:::'i:iliC "i:::::ii::::i:lic:.:i-iiii:: :::::'::',y~:~::~:::::::::_::-::_i:::ii~:: -::-::i:: iiii::::::i::.:::.'::::i: aXB Fig.23 Side Clew of Model B Marx Generator

-51Figoa';~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P _ _~~~"....j;... a:.. Fig.24 End View of Model B Marx Generator

-52sliced into eight equal short cylinders. If every other piece is moved sideways and the spaces created are filled with nylon cylinders, there will be two side by side columns. Disc stainless steel electrodes are then inserted between each cylinder to turn them into columns of alternating capacitors whose values are determined by C = 0.885 C A H where e is the dielectric constant and A and H are the circular area (cm2) and height (mm) of the cylinder. The white cylinders are nylon (Cc C 5 pf) and the grey ones are BaTiO3 (Co F 3900 pf). The top electrode of each Co is charged to Vo through the zig-zag resistor string while the bottom ones remain at dc ground but are isolated from each other. The isolated resistor strings are chosen such that the nth ground electrode from the bottom will see n.100 kn to the bottom ground plate. All resistors are connected to electrodes with miniature banana plugs for easy disassembly. It is seen then a voltage Vo appears across each gap of the two columns. When all the gaps are short-circuited by sparks, all the Co's will be connected in series and a pulse of 8'Vo is generated at the top output electrode. Since all RC time constants are much longer than the switching time, the resistors play no part during the switching moment and behave just like open circuits. And since all the interelectrode capacitance Cg's are only a fraction of a

-53pf, the condition Co>>Cc>>Cg is satisfied and full overvoltages are developed across each gap and full amplification is achieved over each column. Unlike the circuit shown in Fig.21 there is actually no internal trigger electrode. The switching is initiated by applying a negative trigger pulse, which is generated by an external spark gap (15 kV) and amplified by a 3:1 auto-transformer, to overvoltage the first gap. Not shown in the figures is a sharp 1.6 mm tungsten corona needle between the first and second gap. No significant difference was found between electron libration by positive ion bombardment on the cathode and from plain field emission. The corona current was limited by 22 megohms of resistance. The BaTiO3 cylinders (cores of Type 715C, Sprague Electric Co.) are bare slugs with silver plating on the flat faces and without the usual epoxy encapsulation and screw terminals for compact low inductance assembly. Since their dimensions are not precisely controlled by the manufacturer, teflon rings were press-fitted on each end, then machined to be truly round and concentric in order to fit the recesses in the disc electrodes. 0.25 mm thick indium foil sandwichs were used to ensure uniform disc-silverplating contacts. In order to achieve optimum performance, all the gap spacings must be well controlled. Since the amount of

-54overvoltage is lowest at the lowest stages, the breakdown voltage should be determined by the first gap. This is accomplished by fixing the end electrodes of the columns so that the gap spacings are exactly 1.52 mm. The lowest nylon cylinder in each column has an ecentricity of 0.25 mm between the end circles such that, by controlled rotation, the first gap can be set at 1.45 mm and the second gap at 1.47 mm. Thus there will be a taper of 0.05 mm from the second to the top gap. The generator has a 9.5 mm aluminum cylindrical pressure vessel with a plexiglas lining of the same thickness and a 7.6 cm opaque nylon window at the HV end. It is pressurized with nitrogen and a pressure relief valve is set at 16 atmospheres. Usually the pressure is adjusted to give a spontaneous breakdown voltage of a few hundred volts above the operating voltage Vo which has a range of 5-30 kV. (3) Model C A large volume multi-wide-gap spark chamber presents a larger capacitive load to a Marx generator. Thus a correspondingly larger output capacitance is needed to achieve a required peak voltage. More important is the energy storage requirement when a high peak voltage is not desired. For example, the two new high-precision chambers of the Echo Lake Experiment each has four 20.5 cm gaps and

-55a total capacitance of 700 and 800 pf. For such gaps filled with 90-10 nelium at 2/3 atm. the threshold voltage for track formation is about 55 kV. Photographing at f:16, the energy required per spark to register a marginal track on Tri-X film is 0.1 joule. However, 0.5 joule per spark is preferred in actual data taking. This is the motivation for designing the new ten-stage Marx generator with a total capacitance of 0.08 pf. This means that it can produce high quality single particle tracks, at f:16 and 7 kV per stage, or marginally support a dense shower of 250 particles, at f:8 and 25 kV per stage, in all four gaps. Single tracks in pure helium have been photographed at 20 kV per stage and f:90. The optimum arrangement is a four column design. It is somewhat similar to placing two Model B generators side by side with all 22 spark gaps "seeing" each other and all mirror image electrodes synchronized. The main difference is that there are internal tungsten trigger electrodes with BaTiO3 sleeves in the first gaps of each column and they utilize lower and faster trigger pulses. The builtin redundancy cuts inductance and time-jitter by halves besides improving on the reliability factor. Unlike Model B, a negative pulse is generated because the circuit is similar to the combination of Figs.20 and 22. Light weight aluminum electrodes all with long wearing elkonite inserts are also incorporated.

-56Fig.25 is a scaled assembly drawing showing half of the mirror image columns and partial construction details. The electrical circuit is also schematically superimposed. Details of the trigger assembly are shown in Fig.26. Fig.27 shows all the components of a Model C Marx Generator. The enumerated components are described below: (for convenience, dimensions are given in inches) (1) Pressure Vessel: 3/8" aluminum cylinder 18 3/4" long with 12" ID and welded to end flanges. (2) Base Plate: 1 1/21 aluminum plate, 14" in diameter. (3) Plexiglas Liner: 3/4" cylinder, 17 3/4" long with 12" OD. It also helps to compress the 0ring in the nylon window. (4) Nylon Window: Black 3" thick nylon insulator. It can withstand at least 20 atmospheres of pressure. (5) Output Electrode: 1" aluminum rod with banana plug connections to other rods. (6) Pressure Control: Safety relief valve is set at 16 atmospheres. (7) Bolts: 1/4-20 holochrome bolts, 2 1/2; long. The base plate is fastened to the pressure vessel by 24 of these. (8) Trigger Cables: RG-8 cables with banana plug connections. They bring triggers from the Science

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-60Accessory Spark Gap Pulser. (9) Trigger Components: As it can be seen in Fig.26 the brass plug which receives the trigger cable is being pushed outwards by the inside nitrogen pressure, thus good contact is maintained with the screw head of the trigger pin. The tip of the 1/32" tungsten rod has a thin BaTiO3 sleeve and fits snuggly into the center hole of the first ground electrode. The high dielectric constant of the sleeve causes a very intense field concentration at the thin air space, resulting in a rapid discharge at the tip of the trigger eTlctrode. A 1.2 kV trigger is needed in an unpressurized gap. With the gap pressurized, there is no significant reduction in delay-time beyond a few kV. (10) Trigger Electrodes: 1/21 aluminum discs with 3/8" elkonite inserts. (11) Nylon Capacitors: 2 3/8" diameter, 0.850" high. They serve as coupling capacitors of, 5 pf, ensuring full overvoltages be developed across each gap. The lowest two in the column have a 0.010" eccentricity between the two ends so that gap spacings can be precisely controlled by their relative rotations. (12) Tie Rods: 1/2" nylon rods with threaded ends and nuts, 14 1/211 long. (13) Barium Titanate Capacitors: 20 capacitors of silver end platings. The sides were painted with glyptal

-61resin. Since they are not perfectly round, they are made to sit loosely in plexiglas rings that are machined to be truly concentric cylinders to fit the recesses in the electrodes. The vertical spacings are maintained by the BaTiO3 with 0.010" indium foils sandwiched between electrodes. It was necessary to sort these capacitors according to their varying thickness such that the four columns will be equally tall. (14) Electrodes: 3/8" aluminum discs with 5/16" elkonite inserts. They are 3" in diameter and recesses of 1/16"? deep are machined into both sides for alignment purposes. (15) Top Electrodes: They fit the top plate to locate the four columns. 1/8" thick rubber gaskets are used to assure even compression in each column. (16) Top Plate: 1" plexiglas disc, 9 1/4ll diameter. It maintains the top electrode spacings and holds the columns in position by means of four tie rods. (17) Connecting Plate and Rod: It unites the outputs of both columns into the output electrode. (18) High Voltage Inlet: Plexiglas insulation with brass plug at the center to receive banana plug connection from the dc power supply. (19) Charging Resistors: Four 1 megohm resistors to match the current capacity of the power supply.

-62(20) Isolation Resistors: All 100 kQ 2W resistors. They play no part in the switching circuit except to isolate the stages during the discharge and allow them to return to equilibrium afterwards. Miniature banana plug connections are for easy disassembling. (21) Synchronization Wires: They connect all mirror image electrodes even though they are only 0.010" apart. Figures 28 and 29 illustrate the two views of an assembled generator. D. PERFORMANCE Three Model B generators were built for the Echo Lake Experiment. One had survived four years of continuous operation without any servicing. Another one, due to a faulty HV connector from the triggering spark gap, had been suspected and had its electrodes cleaned twice. The spare third was never needed. Two Model C generators were built to drive the ne;imulti-wide-gap spark chambers and are currently in operation with 100% efficiency even when Vo is set at 30% below the breakdown voltage. Two of the Model B generators will be triggered in parallel to drive a two (2x2x0.18 m3) gap chamber, whose middle electrode has a 6.35 mm lead sandwich for studying neutral particle production in energetic interactions.

-i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 Fig. 28 Side View of Model C -Marx Generator * ~~~~~~~'~~~~~~~~~~*~~~~~4 ~~~~~: *~~~~~~~~~~~~~~~~: c~ ~ ~~i:iii:~A:::I~ 9~~~~~~~~::'I:'':i~-in::::,:::' i: 9:k ~ ~ ~ ~ ~ ~ ~~~~:::~~~~~~~~~~~:~U Fi.2 id Ve o odl ar Gnrao

LI: ~~~~~~~:~:3~~~~ Fig.29 End View of Model C Marx Generator

-65A cylindrical transmission line with gold plated capacitive divider probe and liquid teminating resistors was constructed to measure the risetime of the generators. But due to conflicting schedules, it was never completed. Instead, the risetime was crudely estimated from the signal tapped off the voltage dividing resistor string at the corner of a thin foil chamber. If one could take the risetime as one half the period of the ringing frequency, then it would be 4 i 4 nsec. The error reflects the uncertainty in the oscilloscope trace. The delaytime of the Model C generator has been measured as a function of trigger voltage. It was done by placing a pickup coil directly next to the Science Accessory Pulser, which was triggered by muon coincidence, such that the signal from the firing of the Marx generator will have an opposite polarity to the signal from the firing of the spark gap. This eliminated any cable corrections and the zero crossover point was markedly distinct. The zero-delay position was varified by turning off the HV supply to the Marx Generator. The pressure of the generator was set such that spontaneous firing will occur at 12.8 kV per stage. At this level, no attenuators or change of scale was necessary because the two pickup signals had about the same magnitude. The result of the measurement is shown in Fig.30. It is observed that operating at 300 volts below spontaneous firing, the delaytime was zero with a 3 nsec uncer

140'G SPONTANEOUS FIRING AT 12.8 kV CONSTANT NITROGEN PRESSURE O I 2 120'55' w A, ~~~~IOO /~~~~~~~~~~ o/ / o 00 / -V) a=O / cc 80/ w z / w / 060 A' x~~~~~~~~~ M. 40 - - /~~~~~~~~~~~~~4 d~~~~~~~~~~~~~~~~~~~~~~~oo X / ~ I QI~~~~~~~ s Z: /1 ~~~,/ 20 0O ~,,'""~c 12.8 12 II 10 9 8 VOLTAGE PER STAGE (kV) Fig.3C0 Variation of Delaytirme with Trigger and Bias Voltages at Constant Pressure

-67tainty of the oscilloscope trace; time jitter was only observable for Vo's at a considerable (N 20%) margin below breakdown. E. CONCLUSION It is seen that based on simple design principles, Model C has reached a fairly high degree of optimization in fulfilling the goals of supporting other members of the Trio. If subnanosecond risetimes are really desired, one has to be much more concerned with impedance matching and special care in preparing for the output gap.(34) Another feature that may be desirable in other applications is that of rapid cycling. But this is usually done by proper energy storage and switching external to the Marx generator.

CHAPTER IV WIDE-GAP SPARK CHAMBERS A. THE IDEAL As we have noted in chapter I, a wide-gap spark chamber has some distinct advantages and disadvantages. In the first place, the formation of a spark channel virtually wipes out all ionization information except perhaps allowing crude estimates by spark width measurements. Secondly, the formation of a spark channel depends on the linkage of neighboring streamers; since streamers propagate in the direction of the local electric field, isotropy cannot be expected. For particle trajectories at large angles to the applied electric field, neighboring streamers may fail to link, and detection efficiency will be necessarily low. The actual cutoff point depends on the strength and width of the voltage pulse or actually on its closeness to the streamer mode operation. Typically one can count on 100% detection efficiency up to 30~ and 0% at about 600~. The long memory time which enables post-event triggering is, from another point of view, a handicap in high flux operations. Due to their limited mobility, electrons cannot be effectively swept out of the large gap by a clearing field. However, small amounts of electronega-68

-69tive quench gas such as 0.1% CH4 or 10-5% CC14 may reduce the memory time by an order of magnitude to about 1 psec.(35) Thus all these limitations are to be expected and tolerated even for the ideal wide-gap spark chamber. The real question lies with how to exploit its good characteristics, how to take the full advantage of its simplicity and high multiple-track efficiency, and how to press for the ultimate precision that its high information density tracks have to offer. B. PRELIMINARY INVESTIGATIONS A test chamber with two 127x76x20 cm3 gaps was constructed to gain a feeling of the spacial and angular resolutions that one might obtain with this type of chamber. Much of the construction was similar to the thin foil chambers which will be described in section C of this chapter. The experimental arrangement is shown in Fig.31, and schematically illustrated in Fig.32. The two fiducial crosses were in line with the zenith. The two smaller 5.1 cm gap chambers placed above and below the wide-gap chamber were to define a reference trajectory of zenith angle e3 and intercept of x3 with the center electrode. Similar e1, x1 and e2, x2 were to be determined by the upper and lower sparks of the wide-gap chamber respectively. The system was triggered by cosmic ray muon coincidence from two count

-70* ~~~~~~~~~~~~~~- -......... I.CO.r E43 4fff E iiiki"||iti000lit11 X i; g-1 ct.!Adinr ~a lg! L 0_~, -, C;!_-_ — I *xb

-7125 20 I/ 10 / /7 I -10 _ I + >-~I..4~~~~~~~I'1 -15 - / / -20 i, -25'

-72ers with 23 cm of lead between them. Fig.33 shows a typical muon test track. Note that because the wide-gap chamber was pulsed by a Model B Marx Generator which had a positive output, the sparks show a coherent drift of about 5 mm towards the center electrode. The opposite effect is seen in the end chambers which were driven by a -25 kV pulse from a single spark gap. The test pictures were taken with 30:1 demagnification and were measured on a 3 Pm least count film-plane digitizer. The recording density was two digitization points per cm of track length. First order pin-cushion distortion of the lens was corrected through photographing tungsten plumb lines that were electrically heated to glow by means of mercury pool contacts. The angular and spacial resolutions were measured by Ae = e3 - 2 (e1 + e2) and Ax = x3 - 2 (XI + X2) respectively, and their distributions were plotted in Figs. 34 and 35. The rms spread of ae was observed to be 0.88 mr while that of Ax was 0.23 mm. Unfortunately a calorimeter was not available to trigger on very energetic particles and the 23 cm of lead provided essentially a 300 MeV/c muon trigger. The pro

-73Fi~g.33 Typical Muon Test Tracks

a e = 3 - (81 + e2) CORRECTED FOR OPTICAL DISTORTION 11 1 - 7 5 I 4. -3.6 -3.2 -2.8 -2.0 -1.6 -12 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 -4.0 -3.6 -3.2 -2.8 -2.4 -2.0 -1.6 -1.2 -o.8 -o.4 o c.4 o.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 A (mr) F'ig.34 Distribution of Angular Errors in Test Charrbers

A X = X3 - j (X1 + X2) AT Y = O 12 CORRECTED FOR OPTICAL DISTORTION 0 8 6 2 -1.2 -1.0 -v.0 -o.4 -u.2 0 0.2 0.4 J. 1.0 1.2,X ( m.m. ) - Fig.35 oDistrri;1ior: of Position Errors -in Test Chambers

jected rms multiple scattering of such a particle in a 50 am aluminum electrode is 1.2 mr, and in a.75 mm electrode of the end chamber, it is 4.6 mr. Therefore the observed Ae and Ax above were completely accountable by multiple scattering. Comparing just the tracks in the wide-gap chamber, the spread of (el-02)rms was 0.9 mr. Thus we might conclude that the accuracy of the chamber was surely superior to the observed values. On the other hand, there was additional information in the variation of the digitized points along the best fitted straight line to a single spark. Fig.36 is a typical example. It shows that the points were randomly distributed with a rms spread e of about 100 Am in real space. If L is the spark length and N is the total number of uniformly spaced digitizations, the rms angular uncertainty due to the point uncertainty e is e (26N 1 L L2 (2N2+1) Therefore when N >> 1 As % e 3 J and for the test tracks cited above, (e = 0.1 mm, L = 180 mm, N = 40) the angular resolution for a single spark was 0.15 mr.

(cm) 2 4C 6 8 10 12 14 16 i8 20 12 0.3 VARIATIONS OF DIGITIZED POINTS ALONG A SPARK 10 (CORRECTED FOR OPTICAL DISTORTIONS) 8 0.2 6 41 0.1 0 ~~~~~~~~~~~~~~~~~~~~~~~0 0 2~~~~~~~~~~~~~~~~~~~~~~~~. 4 ~~~~~~~~~~~~~~~~~~~~~~~0.2 8 ~~~NE DIGITIZED UNIT (0.0001" ON FILM)02 10 12 0.3 4t ~~~I I I\ I I n1d I I~ 0 1 2 3 4 5 6 7 8 (inches) Fig.36 Variat.I~ons of DJigitized Points A-long a, Spark

-78Other properties of wide-gap spark chambers are best displayed by the following figures: Fig.37 is a superposition of eight triggers to illustrate the degree of isotropy for small angle tracks. The apparent curves in the ends of the sparks are reflections from the upper and lower electrodes. The actual amount of deviation from a straight track can be seen near the center electrode. Such deviations are generally contained within one cm from the electrodes, thus a 20 cm gap will have a useful region of about 18 cm. Fig.38 is a track at 420 with respect to the electric field. It typifies the increased flaring at the ends of larger angle sparks where the formation of plasma channels directly to the electrode is becoming more competitive to the linkage of neighboring streamers. Fig.39 shows the effect of replacing the center electrode with wires of 1 cm spacing in a small 15 cm gap test chamber. Wire electrodes have significant constructional advantages when considering building chambers of ~ 10 m long. It is seen that much of the track length is wasted by the flaring in the non-uniform electric field. However, when the same chamber was filled by 85-15 nelium with 10% saturated C2H5OH vapor, the flaring was drastically reduced as shown in Fig.40. This again illustrates the dominant roll of photo-ionization in the streamer formation process.

Fig.37 Uniformity of Small Angle Tracks

Iig.38 ppeaanc of arg Ange Tac0 Fig. 38 Appearance of Large Angle Tracks

_~~~~~~~~~~~~~~~~..........! i I ~$~;: I::...::::i~:::::::...........:ig-39 Effects of Wir. Elec.rodes on'Discha'.. s::':'::E:;:'::',,':;E; —:: i T,#':. E ":: j.::::::::.' s'. ","'':.8.''~::i:;V _::''s~ i'::,'%E,,, i.;. ~.~;-i ~.:...........;..:.....:''. _ i..''S I:. E;?.,;'REE::. i. " Ei' V _- _ *.... _ __ l _ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::::::: _X2D A; CESSA Eii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::.~i:~: i:";:i~~ii::::ir: I 11 | S~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iii~-i.::~:':::'-~-i~ai _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ir6:: I~:::~~: _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::~.ii::xii:i-ii:::~ ii~:fiij:~jii~ii: iiii:::i-i..iii:ii.......... a::::"":::'~c~ii\'ii:~i:: 1' om;' k w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i Fig.39 Effects of Wire Electrodes on Discharge~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:ii:::

Fig.40 Effects of C2H5OH on Spark Discharge

-83A quick test was also done on the feasibility of placing chamber gas within boxes of dielectrics and inserting them between separate plane electrodes. As it can be seen in Fig.41, extensive distortions were developed, evidently from the transient surface charge distribution on the dielectrics. Such effect was not observed in streamer chambers since little current flow was allowed. C. THIN FOIL CHAMBERS Two thin foil wide-gap spark chambers were constructed for the Echo Lake Cosmic Ray Experiment. As shown in Fig.5, they were to detect the incident and emerging particles from the target. Wide-gap chambers were chosen because of their high multiple-track efficiency, ease of photographic recording and low chamber capacitance. In a cosmic ray background of about one unacompanied particle per 4 m2 detector area per 250 usec, the 10 psec memory time of the chamber was not a handicap. Thin foil electrodes and windows were used so that angular distributions and multiplicities may be studied with a minimum amount of multiple Coulomb scattering and delta ray productions. Fig.42 is a partial assembly drawing of one of the thin foil chambers. The chamber walls were made of 1.26 cm plate glass for good optical quality and minimum

92JavDSTG UO SlateR 0TIma40TGTGG JO S409Jna T8 i7.,: w m:.::::::i::i:::::: -::::::.~i::~-::ii:_:ii$;i'r:"i:::::-:::::i.::::: ~.. ( -...j.:-:....... H~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i cO _!' _i:?!; i!.'....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.... l!::::I::::::::::::~:::::::ii::::I.:' ~-:iiii~i~.:!i -- ------....~ ~~~~~~~~~~~~~~~~~~~~~:::::,i:::ii~-iiiii:~:::::i:~~~~~~~~~~~~~~~~~~~~~~~~~~,~~~~~~~~~~~~~"Pa~ ~~~~~~~~~~~~~~~~~~~~~~~~'lrsl~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%~~~~~~~~~~~~~~ar~~~~~~~~~~~~~.....

THIN FOIL WIDE GAP SPARK CHAMBER 71- - --- I I O.002"ALUMINUM THIN FOIL ELECTRODES 80 I - FAN ELECTRODES 96" II OPTICAL AXIS_ _ I I i I I 1 GENERATOR O0ALUM. BASE FRAME a.. 0 GLASS FRAMES 8"e J80" _- - 244 I <7 Fig. 42 Partial Assembly Drawing of a Thin Foil Chamber

-86out-gassing. There were two 20.5 cm active gaps and two outer 5.1 cm dummy gaps whose functions were to shield the RF radiation and to insure that active electrode positions were unaffected by ambient pressure changes. The electrodes were 50 am hardened aluminum foils. Each piece was spliced from two sheets in the middle with 25 pm mylar tapes. It was slightly but uniformly stretched over a flat surface, then cemented to a 2x2 m2 glass frame with Dow Corning 891 RTV to form a section of the chamber. There was also a peripheral layer of 0.25 mm thick by 12.7 cm wide mylar tape between each foil and glass, to prevent surface breakdowns which might result from dielectric discontinuities and minor surface flaws. Wires were stretched over the external surface at 1.27 cm intervals and interconnected by 1.5 kQ 2W resistors at all four corners to reduce the non-uniform fringe fields. With the chamber capacitance at 360 pf, this arrangement produced a 1.1 asec decay constant as well. Pairs of fiducial crosses 1 mm wide by 2.5 cm long and 162.56 cm apart were sand blasted onto the glass frames such that one pair would be on the front and back planes in each view of each chamber. These crosses were only lit for calibration purposes. During a normal run, four external fiducials designed for automatic scanning were used in each view. The inner surfaces of the glass frames at the far sides of the cameras were sand blasted

to eliminate reflections. Fig.43 shows one of the two large volume thin foil chambers which was assembled and tested at the University of Michigan. It was then completely disassembled for shipment to Echo Lake, Colorado. The thin foil window which faced the target had a 125 Am thick protective mylar lining, and its strength was being tested while disassembling as shown in Fig.44. The static pressure in the chamber was monitored by a Mercoid Type PQ sensor which would actuate a solenoid valve to let in gas from the supply bottle whenever the chamber gauge pressure dropped below 0.2 torr. A safety bubbler set at 0.4 torr would bleed off any excess pressure. The gas was also slowly recirculated at about one chamber volume per day through a purifier which consisted of a cartridge of type 13X Linde Molecular Sieves followed by a cartridge of calcium chips maintained at about 3500C. The former removed all molecules with large electric dipole moments electrostatically while the latter removed oxygen and some nitrogen chemically. Each chamber was driven by a Model B Marx generator at typically 14 kV per stage, and had been continuously operational for four years. Photography was done by two 90~ stereo cameras (Flight Research Model 207) at f:8 and a demagnification of 65:1. Each light ray would encounter two mirror reflections before reaching the camera

OWN~~~~~~~~~~~~~~~~~~~~~~~~O Fig.43 A 2x2 m2 Thin Foil Wide-Gap Spark Chamber

i~~~~~~~~i~~~~~~~~: _- i::::ii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l:::::~~~~~~~~~~~~~~~~~~~ i::.:::~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~O -:::.::,:i~~~~~~~~~~~~~~~~~~~~~ -:i-i~~~~~~~~~~~~~iii~~~~~~ F~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ig.44 S trenj~gtho h Ti ol Window

-90such that all spark chamber information was folded into a single 35 mm film format. The rather low f-stop used was to ensure that all secondaries emerging from the target would be recorded. The single gap detection efficiency was defined as the ratio of the number of tracks resolved in the gap to the maximum number of tracks resolved in any view of any gap. This efficiency was observed to be 96% for large multiplicity tracks with angles of less than 35~. The missing tracks were partly due to some local intensity differences between the two gaps and partly due to shadowing effects among the tracks themselves. Thus the combined detection efficiency for both gaps was virtually 100% and rather independent of multiplicity. The smallest angle observed between two very close tracks near a vertex was 2 mr. This means their separation at the far ends was about 0.8 mm. Considering the mechanism of spark formation, two tracks are expected to be resolvable as soon as their lateral spacing is comparable with the reciprocal of the ion density along the tracks. For neon at two thirds of an atmosphere, this is about 1.0 mm. The angular resolution determined through comparisons of tracks in the two chambers was 2 mr. This was quite adequate for all the data analysis that were intended excepting elastic scattering measurements. But it fell far

-91short of the intrinsic resolution of such chambers. One of the major sources of error was the lack of sufficient number of fiducial marks and the knowledge of the precise locations of the existing marks, whose positions in real space were not known to better than 0.5 mm. Another complication was the compound distortions in the mirrors; even with the aid of a fiducial grid, it was not possible to untangle all the distortions down to 0.1 mm. A third possibility was the distortion of sparks in a non-uniform electric field. Each electrode had the same maximum sag of about 1.3 cm at the center; but some small unmatched ripples of about one mm were present over surface lengths of several centimeters. The fringe field correction by voltage dividing wire planes was perhaps only partially effective. D. HIGH PRECISION MULTI-WIDE-GAP SPARK CHAMBERS (1) DESIGN PRINCIPLES Unlike many other processes, the momentum analysis by magnetic deflection is a direct and absolute measurement. The most accurate determination, as it was pointed out in chapter I, is to have detectors placed before and after a deflection magnet. At relativistic energies, the momentum p in GeV/c of a singly charged particle is

-92p = 300 B dl where e, the deflection angle, is in mr and the magnetic field integral is in Tesla-meters. Therefore, for a given magnet, the momentum resolution is equal to the angular resolution. A 1.3 Tesla-meter superconducting magnet which was originally designed for a balloon-borne cosmic ray experiment was on loan from Alvarez et al. to the Echo Lake Experiment. Two spark chambers of four 20.5 cm gaps each were designed to match the magnet. The incorporation of this spectrometer to the original Echo Lake Experiment is illustrated in Fig.45. The sole purpose of the chambers is to measure as accurately as possible the deflection angle e. An angular resolution Ae of 0.1 mr will correspond to a maximum detectable momentum M.D.M. of 3.9 TeV/c. The chambers were designed for making direct angular measurements rather than deducing angles from spacial determinations for several reasons: First, long leverage arms cannot be utilized in order to maintain a sufficiently large admittance of the apparatus. Second, the zenith or the level provides the most convenient common reference; thus no complicated chamber to chamber and view to view correlations are necessary for angular measurements. Third, angular errors due to non

-9338CO at.., * -''',' ".. I, I "', t,, " _ I I \ - I - ~~ 66'x660cMAMF#?R -2~~~~ ~~HAPPE SUPERCONDUCTI NG MAGNET FZ3 = \ _ = 2 -______ _.. /40X.___ IHYDR06EN TAR6ET SHOWER AirI. /20 — DROGL~V _ ~~/04 | | l i | 8c;sx8o'CHAMHEAWe 80 80 00/ P/ATE CHA4IB8ER /40L- - -- L~ -i.'sido - ---- - i — CA L O 8 /ME ER -i0 I III IIZi Fig.45 The Modified Echo Lake Cosmic Ray Experiment

-94uniform fringe field tend to cancel in mirror image gaps but position errors do not. Last but most significantly, lateral mechanical stability of the apparatus is far worse than rotational or level stability. Besides, the latter can be easily monitored throughout the experiment. Having decided on the type and modes of operation of the chamber, the remaining question was how to assure that sparks would faithfully reproduce the particle's angle in the critical view parallel to the magnetic field lines. The deciding factors are summarized as follows: (a) Electron Diffusion: Prior to the arrival of the voltage pulse, the electrons diffuse away from the original column. This one dimensional projected rms spread Ar is given by Ar = 2Dt where D is the diffusion constant and t is the diffusion period or voltage delay-time. It is a priori that delaytime should be kept to a minimum. (b) Electric Field: An ion column will drift a few mm along the electric field before a spark channel is formed. If the field lines are not parallel along all portions of a track, a rotation of the spark will result. Assuming the drift of a track is 5 mm, then the directional field uniformity must be better than 0.4% along

-95the track for a rotation to be less than 0.1 mr. The maximum zenith angle of a track within the fiducial volume of the apparatus is 13~ corresponding to a lateral displacement of 6.6 cm in a 20 cm gap. If this displacement is allowed to subtend an angle of 4 mr with the center of curvature of the electrode, then the maximum allowable sag in the electrode of a 168 cm span will be 2.14 cm. Similarly, surface bumps of 1 mm high should not have a wavelength of less than 36 cm. In practice, electrodes with maximum sags of less than 1 mm and surface waves of less than 0.5 mm over distances longer than 30 cm have been achieved. On the other hand small bumps over distances much smaller than the gap spacing will not have much effect. Due to geometrical constraints the zenith angle distribution of the actual flux is rather vertically peaked, and the probability of a large angle track passing through consecutive bumpy regions in all the gaps is small indeed. A fluid mapping was done to study the fringe fields between thick electrodes and near by shieldings. A careful tracing with a digital voltmeter could chart the field lines to ~0.2% accuracy. No observable field non-uniformity was found at regions over one gap width inside from the edges. One of the reasons for choosing four 20 cm gaps instead of two 40 cm gaps was

-96to maintain a large useful fraction of the chamber volume. The use of 25 cm overhangs for 20 cm gaps was a simple and effective solution to the fringe field problem. (c) Magnetic Field: The trajectory of an electron in vacuum under a cross field of E (along +z axis) and B (along -y axis) is x = w2 ( wt - sin wt ) z = a ( 1 - cos wt ) eE eB where a = and w = eB In a noble gas medium and under the condition of strong electric field E and weak magnetic field B. the cycloidal radius a2 will be much larger than the electron mean free path X, and motion may be approximated by successive small angle scatterings nearly along the electric field. The resultant angle is then Ax X or AZ a/w2 AzXe B2 Ax= mc Taking the column drift as Az = 5 mm, X = 2.17 Am in neon at 500 torr and E = 5 kV/cm, the lateral displacement will be 0.38 Am at B = 100 gauss or 38 Am at B =

-971,000 gauss, The highest stray field in the nearest gap to the Echo Lake magnet is about 350 gauss and the effect is completely negligible. Again, it is seen that angular measurements, which are sensitive only to the gradient of magnetic field, is inherently less vulnerable than position determinations. (d) Information Density: The ultimate limitation on the amount of information a spark has to offer is the primary ion density along the track. Since to increase this density by pressurization is not feasible for large volume chambers, some improvement may be gained by taking advantage of the gas properties. Among the common noble gases used for spark chambers, argon will give the highest ion density but the threshold voltages for forming a spark in a 20 cm gap in He, Ne and Ar are 55, 100 and over 250 kV respectively. Thus Ne is generally chosen as the fill gas. The ionization potentials of noble gases are large but the excitationlevels are also quite high. Many atoms will be in the excited state from soft collisions with the ionizing particle, thus only a small amount of energy is required to ionize them. The energy locked up in a metastable state will not be available for further ionization except when there are inpurity atoms present whose ionization potential is close to and below that level. This increase in ion

-98ization from impurities is known as the Penning effect. It is seen from Table 2 that argon will be a suitable impurity to produce this effect in neon. A parctical amount to use is about 0.5%. (e) Multiple Scattering: The amount of multiple scattering is a constant fraction of magnetic deflection since they have the same momentum dependence. This fraction is 1.7% in the entire spectrometer of the Echo Lake Experiment. (f) Optics: Worse results usually arise from compounding errors; thus optics must be kept as simple as possible. This means direct photography without mirrors is essential. In making measurements, it means the use of film-plane digitizers without inherent non-linearities. High quality glass is needed for chamber wall construction. The radius of curvature of good plate glass is typically 0.5 km. The error from such a gross bending of a 1.27 cm glass is less than 1 Am hence completely negligible. More serious is any local lens effects. A local flatness of 2 fringes per 2.45 cm (5893 A light source) will lead to an average error of 20 pm at 85 cm behind the glass if known fiducial marks are spaced 10 cm apart on the glass. (g) Fiducial Marks: We have learned from the mistakes of the thin foil chambers that positions of reference

-99marks must be known as precisely as possible. There should be a sufficiently dense map of marks on the front glass of the chamber to correct lens distortions and similarly on the back glass to correct errors introduced by the front glass. (2) CHAMBER CONSTRUCTION Fig.46 shows the details of the multi-wide-gap chamber. The special electrodes made by the Met-L-Wood Corporation had a 1.27 cm thick balsa wood core and 0.625 mm aluminum skins. The combination was designed for high strength to weight ratio. The maximum sag at the middle of the plate was less than 1 mm when supported on a 168x168 cn2 glass frame with 25 cm overhangs. Square aluminum rods were imbedded beneath the glass to carry the compressive load, and on the perimeters for smooth edges. Surfaces not parallel to the optical axes were scrubbled to reduce reflections, although it was not most effective at such small angles. On the other hand reflections from the back surfaces of the chamber were eliminated by tacking 1.6 mm sand blasted black plexiglas sheets to the glass. Holes were cut to uncover the back fiducial marks. The glass plates were made by a twin ground process for good parallelism on the surfaces. The quality control figure for local distortion indicated a standard deviation of 2 fringes per radial 2.54 cm or a radius of

-100INCHES l I I I I I l 0 1 2 3 4 5 6 7 8 MYLAR INSULATION 0.010'' Thick, 5"Wide IMBEDDED ALUMINUM RODS 1/2" x1/2" TWIN GROUND GLASS 1/2"x8" RTV CEMENT 0.030"Thick MET- L-WOOD 0.025" ALUMINUM SKIN / 0. 500" BALSA WOOD CORE MET-L-WOODi 0.025" ALUMINUM SKIN 0.250" PLY WOOD CORE I" x 3" ALUMINUM BASE FRAME Fig.46 Construction Details of MultiWide-Gap Spark Chamber

-101curvature of 547 m. The long edges of each plate were ground to be parallel to within 0.25 mm, while the short edges were polished to facilitate edge illuminations of the fiducial marks. 1.0 cm holes were drilled for gas connections. Fig.47 shows the chamber glass plates before assemblying. Fig.48 shows the base frame of the smaller chamber constructed out of selected aluminum bars with minimum twists. It was supported on four fine leveling screws. The level of the chamber could be checked by using a special 2.44 m long leveling bar across the four corner pads on the base frame. The idea was to assemble the chamber on a perfectly leveled frame such that after transportation, it could be releveled on the experimental stack to relieve mechanical strains. The chamber could be consistantly leveled to + 12 or; this formed the basis for angular correlations. The layer by layer construction of the chamber is illustrated in Fig.49. With the aid of a 2.4 m vernier calipers and a sensitive level, the glass plates were held by jigs while they were cemented with Dow Corning 891 Silastic RTV. The vertical tip of the frames were held to be under a fraction of a mr. Small 1 mm thick spacers were placed under the glass to assure a minimum glue thickness for secure bonding. The anti-reflection sheets were tacked to the back surface with minimum optical contact areas so

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I Fg.48 Base Frame of Multi-Wide-ap Spark Chamber Fig.k8 Base Frame of' Multi-Wide-Gap Spark Chamber

I I i? i IAs bP e e MtiG S k a Fig.49. Assembly Procedures of Multi-Wide-Gap Spark Chamber

-105as not to interfere with the lighting of the fiducial marks by total internal reflections. Fig.50 shows the fan connections from the chamber electrodes to a Model C Marx Generator. Part of a crude version of a gas control and purification system is also visible. The two chambers were constructed and tested at the University of Michigan, then trucked intact to the Echo Lake Laboratory. (3) FIDUCIAL SYSTEM There were two rows of fiducial crosses with approximately 10 cm horizontal spacings and 15 cm vertical spacings on every piece of glass, except those for the 5 cm dummy gaps. Each cross consisted of lines 0.8 mm wide by 2.5 cm long and was sand blasted with number 180 silicone carbide grits. The depth of the crosses was about 70 4m. The key to simple reconstruction from film to real space was to produce an identical pattern on all 32 pieces of glass such that only one set of relative positions of the crosses was needed. This was achieved by using a single 1.6 mm thick stainless steel mask with the fiducial pattern carefully cut into it with a fine circular saw on a milling machine. With the proper combination of pressure and flow rate in the sand blasting jet, sharp and consistant crosses were obtained. To achieve reproducability, the glass and mask were uniformly clamped to a flat

-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ii~~~~~~~~~~~~~~~~~~~~~? a: ala: Fig.50 Fan Connections to the Marx Generator,i~iii~i,~i,~!:i,,~! —-.......... F~~~~ig5FnConcintoteMrGeeto

-107table, and the mask's surface was shielded by 0.5 mm thick polyethylene tapes to prevent it from undergoing plastic deformation. Eight pieces of the glass sand blasted on different days and representing the front windows of the critical view were taken to Argonne National Laboratory for surveying. A self-checking three-transit system travelling on two perpendicular 2.5 m tooling bars was employed to measure the relative x-z positions of the 38 fiducial crosses. With careful measurements, the rms point setting accuracy on the center of a cross was as high as + 6.5 vm. Fig.51 shows the distribution of individual x measurements from the values averaged over all glasses and all measurements. The standard deviation of 16 pm reflects both the measurement accuracy and the reproducability of the patterns. (4) SURVEYING After obtaining the relative coordinates of the fiducials on a single glass, the final question was to interrelate the glass positions in three dimensions. A 0.15 mm phorsphor bronze wire stretched to 75% of its tensile strength by a 2 kg plumb bulb damped by mineral oil will form a very stable vertical reference. Four such lines were hung from the top of the upper chamber

-107table, and the mask's surface was shielded by 0.5 mm thick polyethylene tapes to prevent it from undergoing plastic deformation. Eight pieces of the glass sand blasted on different days and representing the front windows of the critical view were taken to Argonne National Laboratory for surveying. A self-checking three-transit system travelling on two perpendicular 2.5 m tooling bars was employed to measure the relative x-z positions of the 38 fiducial crosses. With careful measurements, the rms point setting accuracy on the center of a cross was as high as + 6.5 im. Fig.51 shows the distribution of individual x measurements from the values averaged over all glasses and all measurements. The standard deviation of 16 4m reflects both the measurement accuracy and the reproducability of the patterns. (4) SURVEYING After obtaining the relative coordinates of the fiducials on a single glass, the final question was to interrelate the glass positions in three dimensions. A 0.15 mm phorsphor bronze wire stretched to 75% of its tensile strength by a 2 kg plumb bulb damped by mineral oil will form a very stable vertical reference. Four such lines were hung from the top of the upper chamber

-lo870 60 l_ 482 MEASUREMENTS o' = 0.64 x 10-3 INCH 50 O) z w at D40 iL 0 10 O 2 3 DEVIATION FROM THE MEAN (10-3 Inch) Fig.1 PrecVisions of the FiducialN Marks

-109through 1.9 cm holes in the electrodes of both chambers. The lines were adjusted to fall on the exact corners of a true rectangle (+ 50 m diagonal errors), hence constituting a set of master reference lines for x-y measurements. Fig.52 portrays a completed chamber mounted with surveying instruments. Basically, measurements were made by recording position changes in the optical axis of a cathetometer when it was moved between a reference line and a fiducial mark. Of the four degrees of freedom associated with a line in space, the two rotations must be constrained in order to record the two translations consistantly. In practice, it must be adjusted to be parallel to a level line in a plane defined by two of the reference plumb lines. Fig.53 is a close-up look of the cathetometer mount. The dark disc at the lower middle of the picture is the cathetometer eye-piece. The horizontal adjustment was monitored by the sensitive (48 4r/div) level directly above while the left right adjustment confined the optical axis to be in the plane of the near and far plumb lines. A "noplay" micrometer translational stage was used to make fine horizontal displacement measurements. The sliding of this stage on the vertical bar with a precision vernier scale allowed z measurements. Supported on two pivots, the vertical bar in turn could slide on the upper square frame and

Fig.52 A Comnpleted Chamber Mounted with Surveying Instruments

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-112its orientation could be monitored by the two perpendicular levels near its top. The leveling bar at the very top had been calibrated at the Argonne National Laboratory for deflections of various relevant spans. Its surface was also charted to 5 pm accuracy. It is seen that the micrometer at the very top could make a one-step z correction for the sag of the apparatus by measuring to the load-free leveling bar. The effectiveness of the design was realized by purposefully locating the plumb wires near a set of fiducial marks, such that the critical x measurement could be made by a small smooth movement of the micrometer translational stage without touching other adjustments. Thus this measurement would be insensitive to any mechanical defect of the structures. The depth informations were recorded by measuring the small distance between the glass and the plumb wire. A micrometer depth gauge was connected to an ohmmeter such that precise contact positions could be located without displacing the wire. Errors of less than 12 im were typical. Armed with the relative fiducial positions on a glass, one could deduce all fiducial coordinates from a simple measurement of the curvature of the glass when the corner fiducials were known.

-113Results of on site surveying had shown that the rms error was 19 pm for x measurements and about 40 pm for y and z measurements. Sensitive levels were mounted on all four sides of the chambers for continuous post-survey monitoring. (5) PERFORMANCE The multi-wide-gap chambers were test fired with helium filling at one atmosphere before being shipped to Colorado. The threshold voltage for the development of sparks in helium was 101 kV. Above 110 kV, the track forming efficiency was virtually 100%. Resistor strings could be plugged in near the corners to give a RC time constants of 1-10 psec, although voltage was usually terminated by tracks themselves. When the gas conditions were equally good in all the gaps, there was little intensity difference among the sparks. On the other hand, any inbalance in track intensity could be easily corrected by inserting relative amounts of series resistances of 1-20 ohms in the current return loops at the fan connections. Figures 54-58 show the characteristics of helium tracks from 120 to 200 kV in 20 kV increments. Note the gradual transition from very smoo.th spark channels at low voltages to very lumpy ones at high voltages. This behavior

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,: < Of A, A; S.:..!.y i..?? i; S C i. Hi..:.:.... ~~~~p:- ~ ~ ii:::.................................................................................................. Fig.55 Spark Characteristics at 140 kV

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Fig.58 Spark Characteristics at 200 kV~~~~~~~~~~~~~~~Aercan.. _~~~~~~~~~~~~~~~~~~~~~~~~~~NW... 0..........._7.... ~.... ~..... ~u!/!11ili~~~~~~ ~ ~.......? j() ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.......... lig -I Spar — i a * 11 _ Ad |~~~~~~~~~~~~~~~~~~~~~~~~~~~~O i= i_' W a" "'-"_..:..4.............................................................. _..._~~....................................................................................................................................._.......i X~~~~Fg 58 Spr Chrctrs t c at 20 kVJ _

-119is expected from the known process of spark formation. The Townsend coefficient a increases with the field strength E thus the Meek condition is satisfied at a shorter distance. This means that the linkage between neighboring streamers will be less effective and spark development will show more local characteristics. Furthermore, while the growth of a streamer along the electric field is heavily field dependent, the transverse growth is primarily a diffusion process. Thus when the spark formation time becomes shorter at higher fields, the transverse linkage with neighbors is even more difficult in an inclined track, and isolated developments become more prominent. It is clear that operating a wide-gap chamber very much above its threshold voltage is not desirable as far as obtaining the best spacial resolution is concerned. The most accurate spark will be developed if plenty of time is allowed for streamers to socialize with their neighbors and smooth out any local fluctuations. Fig.59 shows the result of digitizations of single sparks in neon at 500 torr and the advantage of low voltage operation is evident. The intrinsic angular resolution was estimated according to 2~ Ae - e LiN where e is the rms deviation of the digitization points

-1201.0 0.8 0.6 0.4 (D X' O-.'"..+; I 0.2I 10 20 30 40 50 60 708090 NUMBER OF DIGITIZATION PER SPARK Fig.59 The Intrinsic Angular Resolultion of a Single Spark

-121from a straight line fit, L the useful spark length and N the number of digitizations. This estimate is slightly more conservative than the expression developed on page 76. The addition of C2H5OH was also known to be able to reduce local spark fluctuations,(36) but a factor of two in resolution is gained at the expense of over a factor of 50 loss in spark brightness. Fig.60 is an air shower accidently detected during the testing of the chamber. Unfortunately the camera was then focused on the front glass, and the film was Kodak Panatomic X. Nevertheless, over 90 tracks were resolved. (6) CONCLUSION The performance of the multi-wide-gap chamber has demonstrated that large and precise detectors are entirely practical. With some care in design and construction systematic sources of error can be kept smaller than the intrinsic resolution in the spark whose ultimate precision depends on the optimum mode of operation that is possible in a given situation. So far we have only considered problems at the source. In practice, equivalent attention must be given to the other links in the chain of information transmission. The questions of lens distortion, film flatness, and digitization if not properly handled all may contribute to the

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-123degradation of the intrinsic resolution which was seen to be about 100 or at N = 100 in one gap, or 50 pr in four gaps. Thus the M.D.M. for the Echo Lake magnetic spectrometer could be as high as 5.5 TeV/c.

CHAPTER V PROTON-IRON INELASTIC CROSS SECTIONS A. THEORETICAL CONSIDERATIONS The p-p inelastic cross section exhibits little energy dependence between 70 and 1,000 GeV.(37) Recent observations on attenuation of primary proton flux by air nuclei indicated at least an 8% rise in cross section between 70 and 3x104 GeV.(38) It is of interest to see if energy dependence of p-nucleus cross section can nevertheless be compatible with a flat p-p cross section. The theoretical approach to this problem is usually to seek a way of calculating the elastic scattering amplitude F(t), where t is the square of the four momentum transfer to the target nucleus, and is related to the angular differential cross section by da _y - F(t) F*(t) dltl P2l b djtj p2 lab The total cross section uT is then deduced from the optical theorem aT = bla Im F(O) lab and inelastic cross section is taken as the difference be-124

-125tween total and elastic cross sections. At very high energies and heavy nuclei, the real part of the scattering amplitude is assumed to be negligible. The simplest description of the scattering process is the optical model in which the nucleus presents itself collectively as an optical potential V(r). The wave equation is (v2 + k2)! (r) = V(r) y(r) Using the eikonal approximation!(r) = eikz cp(r) and the fact that scattering is forward-peaked at high energies, the wave equation is reduced to Odz (Ir) - 2k V(r) p (r) and cp(r) = exp [2ik i V(r') dz'] For a heavy nucleus of mass number A, V(r) can be approximated by V(r) = -4LA f(O) p(r) where f(q) is the nucleon-nucleon scattering amplitude, p(r) the nuclear density distribution, and q = /~T is the momentum transfer. Finally, F(q) is calculated by an impact parameter expansion iF(q) k Jo(qb)[l - p(b,z)]b db F(q) =r o~

-126with r = b+z and Jo is the zeroth order Bessel Function. Therefore given the nuclear density distribution nucleon-nucleon cross sections, the optical model can be used to calculate nucleon-nucleus cross sections. If p(r) is constant for r<ro or a Gaussian function, there will be analytical solutions. But it is more realistic to use the Woods-Saxon form of p(r) = P0o 1+ expL4.4(r-a)] For iron the half-density radius a and the 90-10% skin depth b are about 4.0 f and 2.4 f respectively.(39) Note that for the optical model this calculation would lead to no energy dependence for the cross section as long as f is independent of energy and V is very small compared to the particle energy. Glauber has developed a model in which a proton undergoes multiple diffractive reactions with the nucleons. (40,41) It may lead to similar results as the optical model but it could also display in the form of a series the contributions to the scattering amplitude from single nucleon interactions and increasingly higher order processes in which internuclear shadowing and the correlation of intranuclear coordinates play a role. Thus the model also requires two input functions; the nucleon-nucleon amplitude f(q) and the nuclear form factor S(q) which is the Fourier

-127transform of the density distribution p(r) S(q) =fe'ig p(r) dr. Trefil has incorported the effect of inelastic intermediate states, first proposed by Abers et al., to the Glauber calculation. (42,L43) The nucleon-nucleus elastic scattering amplitude is written as F = Fo+L Fi where Fo is the amplitude calculated according to the normal Glauber theory and Fi represents the contribution to the elastic scattering from an intermediate N* if the ith kind and the summation is taken over all N* which can participate in the reaction according to w v t Pr-ie without violating the coherency requirement mq2 -i2 where q = momentum transfer t mi m,m and D is a charac2p teristic distance of the order of the nuclear diameter. The p-N* coupling is assumed to be of the form Gi(mi) = P(x) e-X where x = mi and P(x) is a polynomail in x. It was also assumed that except for the coupling factor N*,production cross sections are similar to that

-128for the N*(1480) which has an energy independent cross section of 0.8 mb. Thus i * 0.8 7 IGi(mi)12 < 30 mb I G(1480)12 I The last inequality is a condition imposed to assure that P(x) will sensibly behave since the total p-p inelastic cross section is approximately 30 mb. The results of Trefil's calculation is shown in Fig.61 for energy independent p-p cross sections. The solid lines are the Glauber model results. The dotted and the dashed curves represent,respectively, the choices P(x) = l+x+; /. = 19 mb and P(x) = l+x-x2; ai = 28 mb It is seen that the shadowing effects of inelastic intermediate states on total and elastic crosssections are of comparable magnitude and saturate at about 400 GeV, leaving the inelastic cross section rather insensitive to energy.

-129TOTAL 1000 0, ELASTIC 500 100 P(GeVfc) Fig.61 Theoretical Predictions of Proton-Iron Cross Sections

-130B. DESCRIPTION OF EXPERIMENT The experimental set-up is already illustrated in Fig.5 and briefly described in chapter I, section F. More comprehensive and detailed descriptions are given in References (44) and (37). We shall only mention some features that are essential for the discussion for this phase of the experiment. The thin foil wide-gap spark chambers as described in chapter IV were to define the trajectory of the incident particle. The anticoincidence guard ring and a visual scan of the photographic film assured that no more than one particle had traversed the fiducial volume of the system, particularly into the calorimeter. The ionization calorimeter is shown in Fig.62. It is about 100 tons of iron interleaved by 10 scintillation layers which are viewed by 80 photomultiplier tubes. The details of placement and size of scintillators are summaried in table 3. The top section (above layer 3) also contain 10 narrow-gap (19 mm) spark chamber modules for visual study of cascade developments. All chambers were photographed by a single camera through strip mirrors in each of the two 900 stereo views. Fig.63 is an illustration of an "unfolded" event by proper magnifications of different segments of the film in order to restore the approximate real space relationships. Note that the cas

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Table 3 Locations and Sizes of Scintillators in the Calorimeter Depth of Iron Type of from top of Area of one Thickness of PhotoScintillator z -Coordinate Calorimeter Half Layer Scintillator multiplier Layer ( cm gm/cm2 ( m2 ) ( cm ) Tubes Top Counter 120.13 O.914x1.829 1.91 RCA 6810 Layer 1 -131.3 40 0.914x1.829 1.91 RCA 6810 Layer 2 -155.7 120 o.9 14x 1.829 1.91 RCA 6810 Layer 3 -184.9 210 l.219x 2.438 3.81 EMI 9816 Layer 4 -205.8 330 l.219x 2.438 3.81 EMI 9816 Layer 5 -226.4 450 l.219x 2.438 3.81 EMI 9816 Layer 6 -247.6 570 1.219x 2.438 3.81 EMI 9816 Layer 7 -267.6 690 1.219x2.438 3.81 EMI 9816 Layer 8 -287.9 810 l.219x 2.438 3.81 EMI 9816 Layer 9 -313.7 970 1.219x2.438 3.81 EMI 9816 Layer 10 -338.8 1130 1.219x2.438 1.91 EMI 9816

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-134cade development in the narrow-gap chamber also helps to identify the incident proton from the particle which back scattered from the target. C. DATA ACQUISTION AND PROCESSING Fig.64 shows the block diagram of the triggering and recording electronics. It is seen that the top counter, layer 2 and the sum of layers 1 through 9 of the calorimeter constituted a charged hadron coincidence trigger. On occasions, the top counter, layer 1 and layer 10 combination was used as a muon coincidence trigger. The shower counter guard-ring (7.68 m2 total area) was of course in anticoincidence for both triggers. The outputs of eight photomultipliers of each layer were summed passively. The pulse area, which was more representative than the time gittering pulse height of such a sum signal was then recorded by a logarethmic analog to digital converter (LADC). The 128 channels of each LADC covered a dynamic range of about 60 db and they were calibrated every few days for linearity and compared with the mean muon pulse area which was recorded at the same time as a standard reference of a minimum ionizing particle. The spark chamber films and the magnetic tape containing the calorimeter data together with LADC and muon

-135ECHO LAKE COSMIC RAY EXPERMENT ELECTRONICS BLOCK DIAGRAM EXP ELECTRONICS AREA I TRALER COTINTER HAL)~RON~S ~SCAAER E SHOWER COUNTERS L — MO7E COTROL AND}CL LTS TEST SWITCHES S. SHOWER oOUNTERS L NORTH VIEW W. SHOW_ I J CAM. CIAERA w. SHOWDYNIXESI LII)WEST VEW COUNTERSL LAYERS 2 I LAYER 3f.....C "S 34 GeVl__IJ I FANLOCK LIGHT GATESE LAYER 4 1'(DJ TYPE TYPEWRITER.AYER | r I1 I N O.FOR THRESHOLDS ES |BELOWA 84 CONDENCE UNTGeV LAYER 6 I ELECTRO NICS OI FOR TRL NLY SINGLER LAYER *~ I I I EX P AREA UII - MUL TIPLE INE Lake Cosmic Ray Experiment DYMDE33 i iDGA CHAMBERS! E I #mAOD L KEY: LAVER!: tN ACTIVE FAN-IN LAYER I PASSIVE FAN-OUT *m WITH CA"N N LAYER 4 OISCRIMI DSSRRMNATOR WITH ua'tr-"A OR.1 F -~, u -,-A+ 8 Fig.64 El~~~~~~ctroni~~cv Blc ~-~mo teEh Laire Cosmic Ray ExperWITH ~

-136calibrations were then the raw recorded data of the experiment. The films were developed at the Argonne National Laboratory and then forwarded to the University of Michigan for prescanning and measuring. The calorimeter tape was first edited at the National Center for Atmospheric Research in Boulder, Colorado and sent to the University of Wisconsin for energy evaluation. The film pre-scanning sorted out those events with interactions in targets from the "straight throughs", which are the transmitted flux, and rejected all inefficient or contaminated events. All the interactions were analyzed with the Wisconsin 1 am least count manual measuring microscope and all the straight throughs were measured with the Michigan Automatic Scanning System (MASS). MASS is a programmed-spot digitizer controlled by a DDP 124 computer. It digitizes 13 points per spark and has an effective resolution of 5 Pm on the film. The two MASS output tapes for the North and West orthogonal views were then merged at ANL with records paired according to event numbers. Reconstructions were accomplished by the program named Cosmic which included correction for optical distortions, rejection of some out-of-geometry events, and compution of the intersection of a particle's trajectory with the x-y plane and the directional cosines. In the real space coordinates, the x-y plane lies in the mid-plane of

-137the hydrogen target, with the x axis pointing north, and z is the line of symmetry along the zenith. Finally, the proccessed calorimeter data in terms of number of equivalent muons in each layer was added to each event which had been successfully processed by Cosmic. A similar output tape was generated from interacting events for further analyses. The seemingly scattered effort was only the result of making maximum use of all available computing, film processing and measuring facilities. A condensed tape of 50,000 straight through events was the basis for the following analysis. D. METHOD Assume a particle comes within the fiducial volume of the apparatus and is stopped in the calorimeter without making an interaction in the target. Let its zenith angle be measured by the spark chambers and its energy determined by the calorimeter and sorted into a particular energy bin. The layer in which the first inelastic interaction occurs is detected by the subsequent scintillation counter which shows an anomalously large pulse (greater than some detection threshold D in terms of equivalent number of muons). The interaction mean free path XFe can then be determined from its reciprocal YFe by a maximum likelihood calculation. The likelihood function is of the form

-138N L (' k ) - fi (e o k) i=l where fi (O,j,k,Y) is the normalized probability that the ith particle with incident zenith angle 8 in the kth energy bin would interact inelastically in the jth layer of the calorimeter. Its explicit form is exp[-Yz(ji-l) sec ei] -exp[-Yz(ji)sec ei] 1 - exp[-Yzm (ki) sec ei] where z(j) is the vertical depth of the jth scintillator in gm/cm2 of iron and zm(k) is the verticle depth of the last scintillator used in the calculation for the kth energy bin. YFe is then determined by W wf where W = In L If we call A = z (ji-l) sec Bi B = z (ji) sec 8i C = Zm (k) sec ei and summations are over all particles in any energy bin, then W= -YA + n (l-eYB)- l n (l-eYC) = v - A + )= eY -~ L ~ -B

-139The equation aW - 0 has no analytical solution. So - is aY aY called the residue and a numerical calculation by iteration technique is performed. The zero-crossing point may be determined to an arbitrary degree of precision. In practice, the convergence is rather rapid and linear. Three iterations will usually give an error of less than 10-4 in Y. Concurrently an evaluation is also done on a 2w v B2 eYB 1 C2 eYC ~y2 -L (eYB _1)2 L (eYC _1)2 and the experimental uncertainty is represented by AYFe = F_ 2W _-1/2 which is exactly one standard deviation if W is normally distributed. Ideally, XFe is determined for each energy bin and a least square fit of the experimental points will yield the energy behavior of cross section desired. Almost no experiment is ideal and this one is no exception. E. SYSTEMATIC PROBLEMS AND SOLUTIONS There were over a dozen systematic problems that might either prevent a correct determination of AFe or introduce an energy biased effect. Many were expected at the

-140outset but others became apparent or were isolated only after extensive searches and cross-checking. Fortunately many effects, once recognized, could be dealt with quite effectively simply by restricting data inclusion through imposing various boundary conditions. As a result, of the 50,000 original events, only 6588 survived the wield of the axes. The principle of parsimony was adhered to at the expense of badly needed statistics; but the otherwise compounding of numerous correction uncertainties could be overwhelming. Table 4 is a summary of the 15 problems and their treatments. Some problems may have arisen out of physical processes, but since the effects are distinct, they will be labled and discussed separately: (1) Time Variation of LADC Setting: This was only a problem in the early portion of the data where the attenuation was set too high for layer 1 of the calorimeter. Thus low energy events that did interact in layer 1 usually did not give an output signal until deeper down --- XFe would appear to be too high. This situation was avoided by skipping all events with energy less than 211 GeV for the first 10406 events. (2) Energy Trigger Threshold: Many problems were associated with the statistical nature of the nuclear cascade development which itself reflected collectively the

-141PROTON IRON I N ELASTIC CROSS SECTION ABOVE 70 GeV LAMBDA TOO SYSTEMATIC PROBLEMS EFFECTS SOLUTION PROCEDURES HIGH LOW 1i Time Variation of LADC Setting. Attenuation too high on layer 1 in initial, J..DATA,SAMPLE Skip over 10406 events for ES211 GeV portion of data SELECTION 2 Energy Trigger Threshold, Energy overestimated and flux supreseed for / ENERGYCUT70 GeV for 36 GeV triggers near threshold events 211 GeV for 90 GeV triggers 3.Side.Leakage,Energy underestimated.-Detection Efficiency reduced GEOMETRY CUT Top counter layer Guided byZXmin,Final layer 10 size (260cm 2 4 NonUniform Scintillator Response'nacturateenergyevaluation 5 -Bottom Leakage'. Energy underestimated ENERGY ~ Start LADC summation one layer ahead of EVALUATION layer of interactionasdetectedatgivenlevel. ~~~~~~.. I'' IInclude correction functions for bottom 6 Delta Rays.. Deep interacting event shiftedto highe bin leakage and positionvariationof scintillator response 7 Energy Bin Shifting Moreelastic events shifted to lower bin 8 Decreasing Layer Detection Efficiency Deep interacting events suppressed LAST Last layer included LAYER CUT with cascade fluctuation and persistance cut 9' Muon Contamination' Muon interactions independent of depth. PERSISTENCE Apply maximum cut CUT 700 gm/cm2'or 5% ofdatarejection 10 Formation Zone Detection deferred to deeper depth. FIRST Ignore interactions in layer 1 which suffers Deplete events from early layers. LAYER CUT from primary formationzoneeffect Most serious at low energy, Varies with log D 11; Relative Low Signal LADC Settings. Some LADC require a min signal DETECTION There is no region c for output. LEVEL all four systematic effectssimultaneously. ISELECTION Nor can each effect be corrected independently. 12 Landau Fluctuation Landau tail causes premature detection Thus shoud seek region where all effects Ladu a I Thus shol sekregio whre alleffects I./.~11.~ Iare small and where residue effects have first order cancellations among themselves. 13 I Degree of Inelasticity More elastic events suppressed to deeper I _X layers at high GuidedbyAmin. Resulting uncertainty indicated by range of AN2 max Final D = 10 + 2. 3. Average system. error = 29% statistical error. 14 J Residue Muons More serious at Iowenergy4Aiso photonuclear eventsJ CORRECTION Monte Carlo correct AFTER persistence cut..ApplymodifiedRossicalculation MAX IMUM'with ~'30oWHM assumption. With w —p flux 15 Pion Contamination Effective cross section lowered MAXIMUM with 30 FWHM assumption. With -p flux LIKELIHOOD ratio = 0.3, crFe = 596mb(Allaby: A0 743 FITS;interpolation.) e|a ( - cu. 625, T(A) = crA213 (Bellettini), ~Tabl~e 4L Systematic Problems ~~and~ Solutions |T(n-c~U= 1262mb (J~o~esX- cu L

-142fluctuation in the fraction of unsampled nuclear fragments and the Landau fluctuation of individual energy losses, particularly in the beginning and the end of the cascade. It is unnecessary at this point to review in detail the calculation of energy determination from the raw LADC signals except to note that proper weighting has been given to each layer and corrections have been allowed for the unseen nuclear disintegration and scintillation response. The average behavior of cascades are shown in Fig.65 and compared with Monte Carlo calculations of W.V. Jones.(37) The uncertainty associated with any single event was estimated to be about 20% and sampled ionization at any given depth may vary wildly about the average values. This was the major source of error in determining the first interaction site and will be discussed forther later on. Due to the width of energy resolution, the edge of the energy spectrum near the trigger threshold appears diffused and depressed. Those marginal events which did trigger the system were- those which developed on the average, longer and flatter cascades, hence were less vulnerable to the truncation effect of discrete sampling. This means that, on the average, their first interaction sites would be detected deeper down, or XFe would be too high for the lower energy bins. The solution to this problem was to make an energy cut, such that only events in the region with a constant slope of the energy spectrum would be

I I I I i I...I' I " I I 1000 o ~0['~ + 0. 0+.. 0 0 o ~ ~ 0+0% + 0+0 +'/ T~ O ~10c ~+ 1000 GeV 100 4 %,0o- 0 + o LLJ + 0+ 0 0+ + 300 GeV ~~~~~~~~~~~~~~~~~+ 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0I 1 LiJ IL. 0 -0- W.. JONES' MONTE CARLO o0 + + ECHO LAKE CALORIMETER I I I I I I I I I +.,Ie~- _ o 200 400 600 800 1000 1200 DEPTH IN CALORIMETER (gm/cm2) Fig. 65 Comparison of the Average Shower Curves with the Monte Carlo Resiilts of W.V. Jones

accepted. This corresponds to a 70 GeV and 211 GeV cut for the nominally 36 GeV and 90 GeV triggers respectively. (3) Side Leakage: Due to the finite size of the calorimeter some fraction of the cascades, particularly at large zenith angles, may escape. Not mentioning the energy underestimation, the more serious effect was to have a trigger bias against those which interacted at deeper layers, resulting in an underestimation of XFe. This effect was avoided by making a geometry cut. The trajectory of the incident particle as determined by the spark chamber was extrapolated beyond the interaction site and this ray was required to pass through the top counter (182.8 cm)2, layer 2 (180.0 cm )2 and an imaginary square at the level of layer 10. The size of this square was used as a parameter and as it was increased from some nominally small dimension, A Fe was noted to decrease due to the increase in statistics. However beyond a certain area, AXFe was reached and further acceptance of events actually led to a larger AXFe. This provided evidence for the onset of systematic errors. The optimum size used was (260 cm)2. For comparison, the actual size of layer 10 was (244 cm)2. (4) Non-uniform Scintillator Response: The edgecenter relative response of the scintillators was about 2.3 for the thick layers (layers 3 through 9) compared to about ulity for the other thin layers. For the former cases, a

-145well fitted quadratic correction function was applied in the energy calculation. In any case the geometry cut would prevent any incident tracks from coming too close to the edge of the scintillators and be mistaken as an interaction. (5) Bottom Leakage: Based on the average cascade development, a correction function was applied to those cascades which leak through the last layer. (6) Delta Rays: There may be energetic delta ray production before the particle makes the first strong interaction. This effect will be discussed in the next section. (7) Energy Bin Shifting: The measurement of energy dependency of cross-sections requires events to be sorted into the same unique energy bins reguardless how the measurements be made. Since the hadron flux of energy greater than E (GeV) is N (>E) = 3x10-3 E-2 (cm-2 sr1 sec-1) the fractional change in the bin statistics is roughly proportional to E-1 for a constant shift of energy AE in the energy evaluation. This would introduce an energy bias if the events that move across the bin boundaries are not typical of their binmates. The procedure of energy evaluation therefore must be done with more care. Normally energy was calculated for the hadronic cascade and no attempt was made to evaluate the small but

uncertain contribution from the ionization and energetic delta ray production before the first strong interaction. If the first interaction was detected in layer j, the LADC outputs of the layers previous to layer j were excluded in order to avoid the delta ray confusion. But since interactions have various degree of inelasticity, the apparent layer of first interaction (LFI) depended on the detection threshold D and so would the energy determination and binning. It was observed that for reasonable increase in D, LFI was down shifted by no more than a layer. Thus a compromise was to include the LADC of the (j-i) layer in the energy calculation. (8) Decreasing Layer Detection Efficiency: Energy leakage also contributed to decreasing triggering efficiency for deeper interactions. This difficulty was easily overcome by terminating the maximum likelihood calculation at layer 6. It would leave over 700 gm/cm2 for cascade development and was entirely consistant with the persistance cut question discussed later. Examinations of the attenuation curves indicated that no energy dependent last layer cut was necessary. (9) Muon Contamination: If a very energetic muon decays in the calorimeter, it will initiate an electromagnetic cascade. A muon may also initiate a hadronic cascade through photonuclear interaction. This will constitute a

-147small uniform background at any depth, but the fractional effect is more serious for deeper layers and XFe will be too high. Fortunately the photonuclear interaction is a small (about 3% in emulsions) (45) fraction of the total muon background. Thus it seems possible to exclude the muon events by "pulse shape discrimination". Electromagnetic cascades are characteristically sharper than hadronic cascades of the same detected energy. This means that their persistence is shorter and consequently less sensitive to the change of D. The persistence of an event was taken as the vertical distance between the z coordinates of the first and last layer which had outputs greater than D equivalent muons plus the mean thicknesses of the end layers. The zenith angle effect was also corrected for. Fig.66 shows the behavior of persistence (gm/cm2) with D. The hadronic curves were obtained from the mean persistences of the two energy bins with high statistics. The dashed curves are EM cascades based on the calculation by Rossi (46) and the experimental EM curves were obtained from those energy bins where there was a clear separation of the two groups (Fig.67). The comparitatively lower values experimental curves were probably due to the discrete sampling nature of the calorimeter.

1400'\[L~(m~ III.. —- ROSSI CALCULATION 1200 - -— THIS EXPERIMENT 0 1000 3 800 w HADRONIC U)v,~~~~ ~CASCADES cn 600 600- 512GeV -249 Gev " CAS - 2 4 6 8 10 20 30 50 100 D (EQUIVALENT MUONS) Fig. 66 Behavior of' Hadronic and Electromagnetic Cascades in the Calorimeter

90 MEAN ENERGY= 512 GeV D= 10 EQUIVALENT MUONS 80 70 60 ELECTROMAGNETIC HADRONIC GO CASCADES CASCADES z w Fd u 50 C)_ _ _ _ _ __ _ _ _ _ _ _ cr tL w~~~~~~~~~~~~~ ct 0 40 ~ CD 2 30 H. 30 ct H. a I 0 ~~~~~ROSSI 1 CALCULATION 100 200 300 400 500 600 700 800 900 1000 1100 1200 PERSISTENCE (gm/cm2)

-150The FWHM of the experimental hadronic cascades was about 30%. It is obvious in Fig.66 that in regions of high D's and low energies, the two types of cascades may no longer be distinguished. Following as closely as possible to the principle of exclusion rather than correction, it was decided to make a maximum cut not exceeding 700 gm/cm2 (never necessary to be so high) or 5% of data rejection (such that statistics is not appreciably affected). The persistence cut matrix used is shown in Table 5 ~ The muon contamination was estimated from a count of the short persistence events in those energy bins and at a level of D where there was clear separation of the hadron and EM groups. It was determined to be 1.7 + 0.4% before the persistence cut. (10) Formation Zone: Fig.68 is a schematic of an exaggerated initial portion of average shower curves. It is clear that on the average there is always a minimum distance zF (called formation zone) in order that the cascade be developed to a particular detection level D. The size of zF depends both on energy E and D. The effect of the formation zone is that interactions occuring near the lower edge of a layer may not be detected until the subsequent layer. This down shifting of events ordinarily will not affect the slope of the attenuation curve except at the first layer where there is no com

MEAN ENERGY D=4 D=6 D=8 D=10 D=12 D=14 D= D=16 D=18 D=20 D=25 D=30 (GeV) 84 385 360 330 310 300 290 280 270 260 240 220 120 420 385 360 335 320 310 300 290 280 265 245 173 480 440 410 380 360 345 335 330 320 300 285 249 580 540 510 480 460 435 420 410 400 375 310 354 690 655 630 600 580 560 545 530 520 490 470 41 512 700 700 700 700 700 680 650 665 655 625 605 742 700 700 700 700 700 700 700 700 700 700 700 1488 700 700 700 700 700 700 700 700 700 700 700 Table 5 Persistence Cut Matrix

-152100 E3>E2 E2>EI z i, 0 10 z -J I I IDI I I I I Z F2 -— "_ I DEPTH FROM FIRST INTERACTION Fig.68 Illustration of' Formation Zone by Qualitative Average Shower Curves

-153pensating events sliding down from above. Fig.69 illustrates the effect of the formation zone on the shape of the attenuation curve, hence XFe also. It is also seen that zF can be evaluated by making a fit to the lower portion of the attenuation curve. This has been done for all combinations of E and D. For example, at D = 10, zF ranges from 18.4 gm/cm2 at 84 GeV to 1.6 gm/cm2 at 1500 GeV. The dependence of zF on D was approximately logarithmic as expected. An alternative of dealing with the ZF's is to incorporate them in the maximum likelihood calculation by replacing each z with an appropriate (Z-zF). However, it was again preferred to keep a smaller but cleaner data sample by rejecting all events from layer 1. It will be seen that the ZF's estimated above are only average values and individual events may fluctuate greatly. This means that the effect of zF will be primarily in layer 1, but there will also be a small secondary effect in layer 2 and a neglegibly small tertiary effect in layer 3. (11) Relative Low Signal LADC Setting: There was a pedestal in each LADC calibration in that a minimum signal of several equivalent muons was needed to give an output of one digit greater than no signal. The purpose of the pedestal was mainly to discriminate against noise and the set

-154ZF\ LL W \ \ \ 0\ z \ z A -i DEPTH IN CALORIMETER Fig o69 Effects of Formation Zone

-155tings were somewhat different for each layer, depending on the expected dynamic range. Thus for low values of D, XFe depended strongly on the relative pedestal settings. The net effect was that XFe would be too high if one used D to be less than seven or eight. (12) Landau Fluctuation in Ionization: The ionization loss of a single particle typically has a Landau distribution in a sampling detector. The Landau tail can then be mistaken for an interaction and leads to too low a XFe. It is expected that this effect is more serious at the lower values of D. (13) Degree of Inelasticity: At increasing high values of D, the events of lower inelasticity are supressed to the deeper layers resulting in XFe being too high. Normally, this problem could be handled by making a series of measurements at different D's and then extrapolate XFe to the value corresponding to D = 1. Such a technique was not possible here due to the dominance of other systematic effects at low D's. Indeed, at any energy, the variation of XFe with D reflected collectively all systematic effects of problems 10-13. There was no region of D that was free from all four systematic effects simultaneously. Nor could each effect be corrected independently. The optimum solution was to seek a region where all effects were small and where

-156residual effects had first order cancellations among themselves. When such an optimum D was determined, a quantitative uncertainty may then be evaluated for the combined contributing sources. With all of the forementioned data cuts, XFe and AXFe were calculated by the maximum likelihood method for all combinations of E and D. The results are listed in tables 6 and 7 as XFe and AXFe matrices. The total number of interactions detected in layers 2 and-3 are called AN2 and AN3 respectively; and they are recorded in tables 8 and 9 as AN2 and AN3 matrices. The general behavior of XFe with D is illustrated in Fig.70. Regions of dominance by various effects are also indicated. Similarly the general behavior of AN2 is illustrated in Fig.71, and the contributing factors that created this characteristic shape is illustrated if Fig.72. At low values of D, events were detected prematurely due to Landau fluctuations, hence the low values of AN2. As D was increased, AN2 recovers rapidly. In the mean time, the secondary effect of formation zone was building up as log D (more events were lost to layer 3 than gained from layer 1) so a peak was reached. Eventually, this logarithmic decrease would be superceded by the effect of inelasticity (gaining more events from layer 1 than losing to layer 2) at very high values of D. Of course these characteristic shapes were energy dependent and examinations of the pat

MEAN ENERGY D —4 D=6 D=8 D=10 D=12 D=14 D=16 D=18 D=20 D=25 D=30 (GeV) 84 141.1 140.0 138.1 136.8 137.1 137.7 139.2 142.3 146.1 160.1 163.8 120 127.0 124.1 125.1 127.0 126.7 126.6 126.8 127.8 128.9 133.6 141.9 173 137.5 130.9 131.2 134.4 138.2 139.6 139.7 140.1 136.6 136.4 137.0 249 139.4 133.1 130.9 132.0 132.2 131.0 132.2 133.3 135.1 139.0 137.3 354 135.3 129.5 127.1 126.1 127.9 127.2 130.4 133.2 133.2 134.4 133.8 512 141.7 134.8 129.6 131.4 135.4 135.0 138.3 138.4 140.3 141.1 139.1 742 134.3 128.4 127.5 125.4 124.1 125.6 129.8 129.7 133.8 134.8 140.5 1488 172.1 142.4 136.5 138.8 148.2 148.6 148.9 149.1 144.5 144.7 141.0 Table 6 XFe Matrix

MEAN ENERGY D=4 D=6 D=8 D=10 D=12 D=14 D=16 D=18 D=20 D=25 D=30 (GeV) 84 4.43 4.20 4.o6 3.98 4.00 4.04 4.11 4.26 4.42 5.00 5.17 120 5.28 4.83 4.80 4.89 4.83 4.84 4.87 4.91 4.95 5.23 5.69 173 8.70 7.72 7.66 7.87 8.16 8.29 8.28 8.30 7.88 7.87 7.87 249 4.36 3.84 3.65 3.64 3.63 3.56 3.63 3.67 3.74 3.88 3.75 354 6.51 5.67 5.41 5.25 5.32 5.25 5.44 5.54 5.60 5.62 5.56 H 512 10.90 9.46 8.63 8.76 9.12 9.10 9.33 9.36 9.51 9.58 9.35 742 15.18 13.66 13.17 12.77 12.37 12.53 13.26 13.30 13.90 14.14 14.96 1488 33.34 22.84 20.80 20.99 23.14 22.92 23.05 22.93 22.19 22.24 20.81 Table 7 A XFe Matrix

MEAN ENERGY D=4 D=6 D=8 D=10 D=12 D=14 D=16 D=18 D=20 D=25 D=30 (GeV) 84 736 798 831 849 837 833 820 810 803 778 748 120 426 490 505 500 511 505 505 500 501 494 481 173 170 202 207 205 201 199 201 202 216 215 217 249 717 875 954 973 979 996 986 986 971 953 999 354 304 374 401 422 422 429 423 425 424 427 434 uk 512 123 151 173 172 172 170 172 171 171 170 171 742 52 59 64 65 68 69 67 67 65 64 62 1488 21 29 33 33 31 33 33 34 34 35 38 Table 8 AN2 Matrix

MEAN ENERGY D=4 D=6 D=8 D=10 D=12 D=14 D=16 D=18 D=20 D=25 D=30 (GeV) 84 459 499 507 511 513 506 497 490 48y 509 546 120 210 222 231 235 238 238 237 243 242 235 239 173 111 113 116 118 121 121 123 123 121 121 121 249 475 482 480 486 488 499 500 495 503 512 522 354 189 206 203 205 212 214 217 213 211 217 215 512 76 78 76 77 75 77 77 78 78 78 81 742 40 43 43 44 45 44 43 42 42 41 43 1488 13 16 16 17 18 16 16 15 15 13 14 Table 9 AN3 Matrix

ll L L REL IES L DC LAND4u PEDESTAL TAIL SECO DARY FOR/MATION DEG.rEE OF INELASTICiTy I0 D (EQUIVALENT MUONs) 2030 Characteri -iCepe J-l-ependenc, orr.

('u LANDAU SECONDARY DEGREE OF FLUCTUATION FORMATION ZONE I NELASTICITY 10 20 30 D (EQUIVALENT MUONS) g_ -.'1 T-h'~.o Ov'; t'ed int e acStions in Layer 2 vs. D

z 0 z:R> | TRUE AN2 01 0 SECONDARy FORMATION ZONE I ANDAU FLUCTUATION 10 20 30 D (EQUIVALENT MUONS) Fig.72 Error Contributions to AN2

terns of variation of XFe, AN2 and AN3 with E and D were entirely consistant with the above descriptions. Table 10 is a "correlation matrix". It is to facilitate the choice of an optimum D and the evaluation of the resulting systematic uncertainty. For every energy bin, the letter A is to mark the value of D at which XFe is minimum, B is to mark the value of D at which AXFe is minimum, C is to mark the value of D at which AN2 is maximum, X is to mark the value of D at which AN3 is maximum. All systematic effects tend to distort the attenuation curve from being a pure exponential, and AkFe reflects this fact besides estimating pure statistical uncertainties. Therefore it is natural to choose the values of D at which AXFe are minimum. As table 10 shows, there is no significant energy dependence of the location of B. Thus the mean value of D = 10 was chosen as the optimum for all energy bins. Note that there was a remarkably strong correlation of B and C. Since the location of C depended on the combination of systematic effects, it was in a way a marker on the specific combination process. The strong correlation could then be interpreted as a consistant and effective cancellation of systematic errors. The remaining systematic uncertainty was represented by the spread of B or C. This r.m.s. spread in D was ~ 2.3. The correspond

MEAN ENERGY D=4 D=6 D=8 D=10 D=12 D=14 D=16 D=18 D=20 D=25 D=30 (GeV) 84 ABC X 120 A B C X 173 A BC X 249 A BC X 354 A BC X 512 ABCX 742 ABX C 1488 ABC X Table 10 Correlation Matrix

ing uncertainty in XFe was then seen to be, on the average, 29% of the statistical uncertainty, or less than 5% of the total error. Note also that all the locations of A's were to the left (lower values of D) of B's. This assured that the cancellation process was not overwhelmed by a dominant source, namely the relative LADC pedestal settings. The facts that almost all the X's were on the right of C's and that dips in the AN3 curves were almost non-existant were consistant with the expectation that formation zone effects occured only in the top layers. F. CORRECTIONS So far, the solutions to systematic problems were to seek optimum data cuts rather than to make numerous corrections. Cross sections were determined with the appropriate cuts incorporated into the maximum likelihood calculations. However there were two remaining effects that must be corrected. (1) First was the residual muon contamination which survived the persistence cut. As it was noted, the overlapping of EM and hadronic cascades was more serious in the lower energy regions. Table 11 summarizes the correction process. First it was assumed that the EM cascades were normally distri

MEAN PERSISTANCE MEAN STANDARD RESIDUAL RESIDUAL CORRECTION ENERGY CUT PERSISTANCE DEVIATION MUONS MUON FACTOR FOR (GeV) (gm/cm2) (gm/cm2) (gm/cm2 ) ) BACKGROUND XFe _(%) I I 84 310 273 69 29.5 0.50.g980 120 335 286 73 25.1 0.42 0.984 173 380 300 76 14.5 0.24 0.992 249 480 312 79 1.7 0.03 1.000 354 600 324 82 0.1 0 1.000 512 700 337 86 0 0 1.000 742 700 350 89 0 0 1.000 1488 700 367 93 0 0 1.000 Table 11 Muon Corrections

buted about a mean persistence which was taken to be 0.67 of the Rosse calculation. This assumption was of course not true, but it was approximately correct for practical purposes. The distribution was taken to have a spread of 30% FWHM, as was the case for hadrons, or a standard deviation of 25.4%. The percentage of muon which survived the persistent cut and the actual muon background in the hadron flux was then easily evaluated for each energy bin. The effect of muon contamination was evaluated by an approximate Monte Carlo calculation. The primary hadron flux was attenuated exponentially in the calorimeter while muon interactions were distributed uniformly with depth. The surviving flux was then simulated at each layer of the calorimeter for appropriate values of XFe and various percentages of muon contamination. Least square fits were then performed to obtain an apparent XFe for each case and a direct comparison would give the correction factors needed. (2) Among the incident charged hadrons there is a significant pion component. Pion cross sections are believed to be lower than proton's, thus the measured XFe will be higher than the desired proton-iron interaction length XpFe. The pion-proton flux ratio was determined to be approximately 0.3 (37). The ratio of pion-proton inelastic cross sectiqn in iron was estimated from accelerator data at 20 GeV. In the cases where direct data on iron targets

were not available, interpolations were done from copper according to the dependence on mass number A. Proton data were also deduced from neutron data. Specifically, A for iron is 55.85 and for copper, it is 63.54. The relation between interaction length X and cross section a is A NopX where No is the Avogadro's number and p is the density. Thus for iron 92679 (mb) X(gm/cm2) From Allaby's data,(47) the pion inelastic or absorption cross section is arFe = 30.0 x (55.85)0'743 = 595.9 mb From Jones' data,(48) the neutron copper total cross section is aT (n-Cu) = 1262 mb From Belletini's data,(49) the ratio of absorption to total cross section for copper is 0.625 and UT is proportional to A2/3. The proton iron absorption cross section was then determined to be apFe 1.0424 UFe

-170or XpFe = 0.9593 X Fe G. RESULTS The results of corrections after the maximum likelihood calculation for D = 10 are listed in table 12. Separate plots of XpFe and apFe vs. energy are shown in Figs.73 and 74. The 20 GeV point was deduced form the accelerator data of reference (48). The final results have been fitted to both a flat constant A and to a two parameter function of the form A+B log10 E. Separate fittings were tried for both the inclusion and exclusion of the accelerator point. The complete results are listed in table 13.

Table 12 Final Experimental Results on Proton-Iron Inelastic Interations Energy (GeV) Number A A X,, Z of 2 2 Bin Size Mean ents (gm/c ) (gmm ) (mb) (mb) Bin Size Mean Events 70 - 101 84 1828 136. 1 4.0 681 20 101-146 120 979 126.8 4.9 731 28 146 - 211 173 444 135.3 7. 9 685 40 211 - 303 249 1965 134. 0 3. 7 692 19 303 - 437 354 831 128.0 5.3 724 30 437 - 629 512 335 133. 3 8. 9 695 46 629 - 905 742 138 127. 3 13. 0 728 74 > 905 1488 68 140.9 21.3 658 100

160 150 E u 140 E I a. 30e a I30 120 110. I I I I I I I 10 20 40 100 200 400 1000 2000 ENERGY (GeV) Fig.73 Variation of XpFe with Energy

900 800 3 700 - -- E. b 600 500 10 20 40 100 200 400 1000 2000 ENERGY (GeV) Fig.74 Variation of CpFe with Energy

-174Table 13 Results of Energy Dependent Curve Fittings _ApFe = A + B log10 E Data A B | 21 Deg. Freedom This Expt. Only 139. 8 ~ 16. 4 -3. 24 ~ 7. 16 0.55 This Expt. + Accel. 129. 0 ~ 9.9 1. 35 i 4.53 0. 57 a pFe A + B log10 E Data A B.2/Deg. Freedom This Expt. Only 660 ~ 85 17. 0 ~ 37. 3 0. 53 This Expt. + Accel. 716 ~ 54 -7.1 ~ 24.7 0. 56 A =A pFe Data A /,21Deg. Freedom This Expt. Only 132. 4 ~ 2. 0 0.58 This Expt. + Accel. 131. 9 ~ 1. 9 0. 58 apFe A Data A X2Deg. Freedom This Expt. Only 698 ~ 10 0. 57 This Expt. + Accel. 701 ~ 10 0. 57

-175H. CONCLUSION From the fits to the experimental points we conclude that, between 20 and 1500 GeV, XpFe is best represented by 131.9 +1.9 gm/cm2 independent of energy; although a slope of 3.5% change per decade change in energy is not ruled out. Comparing to results of other similar cosmic ray experiments, we note that Andronikashvilli et al.(50) reported XFe= 130 + 6 gm/cm between 50 and 800 GeV, and Bashindjhagyan et al.(51) reported X 132~ 5 gm/cm2at pFe 400 GeV. None of the groups found any significant energy dependency. Since we have better p-Fe data than p-p data, we may conclude that according to Trefil's calculation, ap is also independent of energy. By the same token, the rising inelastic cross section in air can be attributed to a rising p-p total cross section.

CHAPTER VI EPILOGUE We have described the emergence of the SMW Trio from the world of high energy particle detectors. We have seen, through their basic operational mechanisms, their limitations, and some means of realizing their maximum characteristic potentials. We have also witnessed their incorportion into physics experiments, the touchstones for real effective performances. Innovations are continuously being made on alleviating their shortcomings. To achieve isotropy in wide-gap chambers the application of a rotating electric field has been attempted.(52) To take advantage of the on line analysis capabilities of wire chambers, it is necessary to improve their spacial resolutions. This can be done by limiting lateral diffusion of the sparks and delta ray productions. A double barrel approach is to minimize gap width and going either to low temperature (53) or high pressure (54'55) operations. An even more radical attempt is to use liquid argon in the electron multiplication medium.(56) If cost is not of prime concern, multiwire proportional chambers can offer tremendous advantages in time resolution,repetition rate and multi-track effi-176 -

-177ciencies.(17) If a streamer chamber is driven by a short voltage pulse such that avalanches are not permitted to develop into streamers, metastable atoms may persist for preliminary analysis by auxiliary equipment to decide whether to re-pulse the chamber to record a possible rare event.(57) Another unique variation is the discharge-condensation chamber which is a hybrid of streamer and cloud chamber. (58) The dense column of ions developed from the initial short voltage pulse renders the chamber insensitive to other minimum ionizing tracks upon expansion, thus achieving good time resolutions (~1 4sec). The very long memory time ( 0.01 sec) also allows auxiliary decision making instruments to trigger on rare events in a high flux background. The addition of the magnetic spectrometer to the Echo Lake Experiment will permit an absolute calibration of a calorimeter at high energy for the first time, and a good correction to the systematic effects of the calorimeter to the transmission experiments will be possible. Also possible will be a much more definitive measurement of the -p flux ratio which is an important correction factor in extracting the proton cross sections from the charged hadron cross sections.

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