AEDC 02792-1-T THE UNIVERSITY OF MICHIGAN INTERIM REPORT ON TRANSIENT, HIGH CURRENT ARCS IN EXTREMELY DENSE AIR Hb- C'. ]Early, Under Contract with Arnold Engineering Development Center Air Research and Development Command United States Air Force Arnold Air Force Station, Tennessee Contract No. AF 40(600)-733, Task No. 89101 November, 1960

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TABLE OF CONTENTS Page ABSTRACT INTRODUCTION 1 POWER SUPPLY 3 INSTRUMENTATION 4 ARC CHAMBE No. 1 5 EEmCTRODE EROSION 7 EROSION REDUCTION BY MAGNETICALLY DRIVEN ARCS 13 MOTION OF ARCS DUE TO SELF-MAGNETIC FIELD 16 BLOW-OUT ARCS 16 CHAMBER GEOMETRIES 18 POSSIBILITY OF PRODUCING A HOMOGENEOUS, HIGH DENSITY PLASMA 19 FOR SCIENTIFIC MEASUREMENTS ARC CHAMBER No. 2 21 PRESENT STATUS OF INVESTIGATION 25 APPENDIX A. TRANSIENT TEMPERATURE RISE IN A METAL AT 26 HIGH CURRENT DENSITY 28 REFERENCES

ABSTRACT The objective of the study of quarter-il2ion-ampere, high pressure arcs is to obtain information useful in the design of arc chambers for hypersonic wind tunnels. Initial experiments indicated that the are properties were dominated by gas contamination due to electrode erosion, This interim report describes exploratory studies in which magnetically driven arcs were used to minimize electrode erosion. The use of a controllable, externally applied magnetic field to drive an arc inside a chamber is experimentally very convenient for the scientific study of low contamination plasmas at high pressures and temperatures. For wind tunnel usage the desired motion of the are spots can apparently be produced by utilizing the inherent instability of the arc column due to its self-magnetic field. The experiments described in this report used a 200,000-joule inductive energy storage power supply which was capable of producing 250,000 amperes with a maximum potential limitation of 800 volts. Future: experiments will be made with a 6-megaJoule power supply designed for voltages up to 20 kv at currents of 300,000 amperes,

INTRODUCTION This study of transient electric arcs at currents up to 300,000 amperes and high gas pressures is directed towards the engineering problems associated with heating air for a Hot-Shot type of hypersonic wind tunnel. The objective is to obtain a better understanding of arc characteristics at high temperature and pressure in order to assist in the design and improvement of wind-tunnel arc chambers and power supplies. The work is thus a combination of both basic and applied science. This interim report discusses an exploratory investigation of methods of producing a low contamination, homogeneous plasma at very high temperature and pressure. The miscellaneous topics herein discussed are all related to the general objective of producing and measuring the characteristics of such a plasma and correlating experimental data with theory. The initial experiments on this contract at currents of 300,000 amperese indicated that the rate of erosion from the electrodes was so large that the' properties of the arc were dominated by the properties of the metal vapor present. The work, so far, has been directed primarily towards exploring methods of reducing air contamination which is important to both the wind tunnel objective and the basic science objective, One approach to the erosion problem is to study the erosion process in detail from a quantitative, energy balance standpoint, and another approach is to consider only the gross, qualitative phenomena and explore various methods of using moving arc spots to reduce the erosion. This project has proceeded in both directions, but the emphasis has been on the exploratory work of finding effective methods of reducing erosion. The experiments have been performed with an energy-storage power supply which will deliver half-meganmpere current pulses, but the available voltage has been a limiting factor. A much larger, 6BmegaSoule power supply, I

financed by the University of Michigan Institute of Science and Technology, has been under construction for the past years, It is estimated that this new power supply will be in operation by January, 19619 and future experiments on this contract will be conducted at substantially higher energy levels.

POWER SUPPLY The transient arcs discussed in this report were produced by means of a transformer type of energy-storage inductance coil. The high impedance primary winding of the coil was energized by a dic current of 5000 amperes from an ignitron rectifier, and approximately 200,000 joules of energy could be stored in the magnetic field. The secondary consisted of a twos turn winding of aluminum sheets which was tightly coupled to the primarye With the two secondary turns connected in parallel, the power supply would deliver pulses of current at 500,000 amperes (maximum) at 400 volts maximum. By reconnecting the two secondary turns in series, the load current was reduced to 250,000 amperes and the voltage was doubled. The maximum available voltage was limited by a protector spark gap across the primary winding. Typical discharge time constants were 1 to 3 milliseconds, A general description of the power supply and switching technique will be found in References 1 and 2. A related discussion of inductive energy storage is given in Ref. 33

INSTRUMENTATION All experimental data were recorded by means of oscilloscopes and Polaroid cameras which were located about 200 feet from the arc chamber in order to reduce extraneous interference. Triggering of the scopes was accomplished by a special triggering switch which was attached to the fast mechanical switch which opened the prinary circuit of the energy-storage coilo Voltage curves were obtained by resistive voltage dividers, and arc current curves were obtained by integrating the L voltage curves dt of the voltage across the energy storage coil. Pressure curves were obtained with an Atlantic Research Corporation lead zinconate pressure transducer which was calibrated against a dead weight tester, The calibration appeared reliable for pressures up to 7000 psi, Above this pressure the response became somewhat non-linear, and the calibration was not considered reliable,

ARC CHAMBER No. 1 For this investigation, it was not necessary that the arc chamber be equipped with the rupture diaphragm and dump valve associated with wind tunnel usage, and therefore a closed chamber was used. The first high current arc tests were made with the chamber arrangement shown in Fig. 1 which was designed to withstand 1000 atmospheres. An axial electrode geometry was chosen so that there would be no magnetic force on the arc column tending to deflect it sidewise, The wall of the beryllium copper chamber acted as a symmetrical return path for the current so that the self-magnetic field of the arc was also symmetrical. It was believed that if a stationary are column could be obtained in this manner, such factors as column diameter, temperature distribution, and pinch pressures could be measured more satisfactorily than if the arc were unstable and fluctuating. The electrodes consisted of tungsten tips attached to the ends of l-inch diameter beryllium copper rods, The lower rod was electrically connected to the chamber, while the upper rod was free to slide inside a guide which was electrically insulated from the chamber, At the beginning of the current pulse, the air cylinder held the electrodes in contact with a loading force of 600 pounds. Having the electrodes in solid contact at the beginning of the current pulse was desirable in that the load impedance on the secondary of the energy storage coil was low during the switchingo Without this low value of load impedance the switching process in the primary of the col' was difficult. A gasbtight seal around the sliding electrode was achieved by means of a combination of an motoring seal and a packing of viscous grease between the electrode and the electrode guide, The "O" ring was adequate

to withstand the pre-firing pressure in the chamber, but it might have extruded if subjected to the high-transient pressure during the firingo To prevent possible extrusion and binding, the O"0 ring was placed very close to the outside end of the electrode guide. The retraction of the electrode after arc initiation moved this."0O ring outside the guide. During the remainder of the transient pulse, the viscous grease was adequate to prevent leakage. Electrical contact to the moving electrode was obtained by 4 flexible braided copper straps similar to the braided copper strap used for the ground connection to a car battery0 These braided straps were connected to the edge of a s-inch diameter beryllium copper plate attached to the moving electrode as shown in the figure0 The geometry of the braid and plate is such that the magnetic field of the current acts on the plate and retracts the electrode. At a current of 300,000 amperes, the magnetic force tending to retract the upper electrode was calculated to be approximately 5000 pounds. This force was adequate to separate the electrodes a distance of 10oO inch in 3 milliseconds, The electrode motion was arrested after approximately 1 inch of travel when it hit a massive iron plate, Wood and rubber shock absorbers were used to cushion the blow when the electrode struck the iron plate. The cross-sectional drawing in Fig. 1 shows the quartz pressure window designed to withstand 1,000 atmospheres which was located in the chamber walls the window had a useful diameter of 1/2 inch. By using a special lens adjacent to the surface of this window, a photographic field of view was obtainable inside the chamber representing a solid angle of 35 degrees, 6

ELECTRODE EROSION All attempts to obtain a satisfactory light sample from the Noo 1 chamber failed, At the very beginning of each current pulse, the window was rendered completely opaque by metallic tungsten which was sprayed about the chamber, The inside walls of the chamber were also coated with a red-brown powder which was tentatively identified as a mixture of cupric oxide, CuO, and tungsten dioxide, W02, Tungsten trioxide, W03, a yellow-green powder, was also found but only when the arc duration was accidentally cut very short because of a flash-over in the protective — system of the power supply, The powdery dust was deposited almost uniformly throughout the chamber and probably did not settle out until later in the cycle. The metallic tungsten was deposited so quickly that no useful light sample was obtainable through the window, The deposits on the chamber walls indicated that, while the maximum amount of tungsten traveled radially outward from the point of contact of the two electrodes, the tungsten was sprayed in virtually all directions, There was little to be gained by moving the window to sonie other position. In trasent arcs having lower currents and/or shorter duration, most of the material is lost by evaporation. Also in low current steady state arcs, most of the material is lost as vapor. Under such conditions, an approximate energy balance can be obtained by equating the power delivered to the cathode or anode fall of potential to the power expended in melting and vaporizing the eroded metalo4' 5 As the current level (or pulse length) is increased part of the metal leaves the electrode as droplets of at molten liquid, as in the case of a welding arc in which the filler metal for the weld is provided by consuming the electrode, When the temperature of the electrode tip exceeds the bowiing point, the expanding gas bubbles

spatter the droplets of molten metal away from the electrode tip. The production of molten metal is a combination of joule heating (which is greatly accentuated by the high resistance of the hot metal) and the energy delivered to the surface by ion and electron bombardmentAn analytical explanation of the transient energy balance under these conditions is being prepared, but will need experimental verifications The importance of joule heating is indicated by the curves of Figsio 2 and 3, which illustrate the fast temperature rise in tungsten and copper for current densities comparable to the conditions in the electrodes of 1/3-megampere arcs. These curves were calculated (Appendix A), using handbook data for the resistivity of copper and tungsten as a function of temperature and assuming a constant specific heat which actually varies less than 5 per cent. The curves are useful in determining the upper limit of pulse handling capacity for these metals. With the No. 1 are chamber, a test was made in which the electrodes were clamped together under a heavy clamping pressure and the metal erosion per coulomb at the junction of the two electrodes was comparable to the conditions where the electrode separation was 1/2 to 1 inch and an arc was known to be present0 If the actual area of intimate and complete contact of the clamped electrodes was 0-5 cm2, a 300,000(3aampere arc would have theoretically brought the tungsten at the interface to the boiling temperature in 300 microseconds0 With an area of lO cm2, the melting point would be reached in 1.2 milliseconds. In several tests, the initial contact resistance between the electrodes was reduced by a very thin "shim4 of deformable, soft metal between the electrode tips which increased the area of contact, The resulting benefit, if any, was not large and the results were inconclusive0 Fig0 Lt is a photograph of a pair of' 3f/1iinch diameter tungsten electrodes after one firing at 300,000 amnperes. This photograph does not

provide information as to the actual diameter of the are spot except (in this case) to indicate that it was smaller than the 3/b-nch diameter of the tungsten. Fluctuations in the voltage trace (Fig. 5) suggest the possibility that the arc column and are spots may have been undergoing rapid changes due to "sausage" and/or "kinkK instabilities, Fig. 6 is a photograph of two i-l/2-inch diameter tungsten electrodes which illustrates the explosive pressure of the gas from the vaporizing tungsten. As the electrodes pulled apart, molten or plastic metal was blasted out in a radial direction and flow lines were left in the remaining metal on the electrode surface. A listing of data from 12 tests is given in tabular form in Table 1, and a brief description of these tests is given below. No. 1 and NQo. 2, Tungsten electrodes 1.5 inches and 0*75 inch in diameter were used. The faces were slightly covex for No. 1 and flat for test Nao 2, and in order to increase the area of initial contact and decrease contact resistance, a thin shim 0,01 inch thick of soft solder was placed between the electrodes. No, 3. At the time this test was made, it was believed that the principal cause of erosion was the energy delivered to the surface of the anode and cathode spots and the imnportance of ohmic heating of the metal was not appreciated. It was reasoned that if the erosion were related to the gaseous conduction mechanism at the anode and cathode spot, then the presence of a metal vapor having a very low ionization potential, as comEpared to tungsten, would have a significant effect on the rate of erosion. Tungsten has an ionization potential of 8.1 volts as compared to 5,96 volts for aluminum and 5.19 volts for barium, A special insert was placed between the electrodes which consisted of barium held in place by an aluminum retainer. The electrode loading pressure (previous to the current flow) was approximately 600 pounds. The are voltage exceeded the h00-volt 9

Table 1. Erosion Datao No. Diameter Peak Cathode Anode No o f Total Initial of current erosion erosion coulombs grams pressure Remarks electrodes eroded (inches) (amps) (grams) (grams) per 100 coul. Initial contact area 1 1,5 325,000 2.3 2.7 500 1,00 600 increased by.14 gmi shim of soft solder. Discharge arrested by 2 0~75 300,000 1.8 1o5 300 1.10 600 arc-over across primary (~es-t)~ ~overvoltage protector gap after 1.8 ms. 0.14 gm. solder shim used. Discharge arrested by 3 0.75 150,000 0,4 0.6 100 1.00 600 flashyover. (est.) Shim of barium and soft aluminum~ As'ymmetric electrode 4 0o75 1.5 1.5 400 to produce magnetic blow-out. Asymmetric electrode 5 0.75 300,000 0.8 0.9 200 085 600 to produce magnetic blow-out. Parallel arcs, only one 6 0.75 300,000 1.2 3.9 400 1.27 600 carried current. 7 0~75 325,000 1.9 1.6 500 0O70 600 Same as above, 8 0.75 250,000 5.8 3.2 1100 0.85 600 Clamped electrodes Concentric copper 9 - 300,000 -1,6 2~5 400 0.22 600 electrodes. Spoke arc moving in z directiono 10 0.75 2759000 0.7 1.1o 360 0.50 600 Mallory G14i tipso 11 0,75 300,000 0o8 1o2 1400 O50 600 Same as above. 12 0~75 3009000 1,6 2.3 400 0,95 600 Mallory G-12 tipso

limitation when the current reached a value of only 1509000 amperes. No. 4 and No. 5. The axial symmetry of the magnetic field inside the arc chamber was destroyed by machining the support to one electrode so as to put a NkinkK in the current path. The lack of symmetry caused a radially directed blow-out force and increased the voltage in the are column, This increase caused a larger proportion of the total energy to go into heating the gas and a smaller portion to go into melting the electrodes. However, even a relatively small deviation in axial symmetry caused such a pronounced increase in the voltage requirement that the are could not be maintained with the available power sources No. 6 and No, 7. Since the electrode erosion per coulomb for very large arc currents was very much larger than for smaller are currents, it appeared that the total erosion for a given total arc current would be reduced if two or more arcs could be operated in parallel. Familiar types of arcs have a negative slope on the volt-ampere characteristics and operation of two arcs in parallel requires stabilizing resistances or balancing reactors In this particular cases there appeared to be a theoretical argument that the volt-ampere characteristic might have a positive slope and parallel operation might be possible. The experiments indicated that this theory was wrong and that one or the other of the arcs would take all of the current and the other arc would extinguish. Noo 8. The electrodes were clamped together under heavy pressure to prevent the formation of an arc column9 The duration of the current pulse wasE 7 milliseconds9 The results of this test seemed to indicate that the erosion is primarily due to ohmic heating of the electrode metal, The tabulated data indicates that the erosion per 100 coulombs for this test is consistent with other tests using tungsten electrodes. No, 9, This was an experiment to determinLe if an arc spot moving 11

rapidly over the surface of an electrode would significantly reduce erosion0 The arc was driven between the parallel surfaces of copper electrodes spaced 0~25 inch apart. The electrodes were made of copper because of the difficult machining problem with tungsten0 The geometry and magnetic force configuration are rather complicated to explain without going into considerable detail, The arc moved in an axial direction and the driving force was less violent than if a straight rail geometry had been used. The erosion measurement, based on loss of electrode weight. is misleading9 since most of the material lost by the anode was collected by the surrounding cathode. The arc traces9 however9 indicated that erosion was probably reduced by the moving arc. No 109 No. 11, and No. 12o The electrodes were tipped with 0.75inch diameter Elkonite discs, 0o125 inch thick. This material produced by Mallsory, is sintered tungsten and tungsten carbide with the interstitial voids filled with silver0 The G-12 material has more silver, higher conductivity and lower strength properties than the GrL material0 The tests indicate that the Gal14 Elkonite is significantly better than pure tungsten0 12

EROSION REDUCTION BY MAGNETICALLY DRIVEN ARCS Experimental information from various sources indicates that an effective method of reducing erosion is to magnetically drive the arc spot along or across the electrode surface0 When this is done, the arc will dwell on any one area only a very short time, and therefore the thermal capacity of the metal surface layer will be sufficient to minimize heating and melting, This method has been utilized for many years in the design of circuit breakers and more recently in the design of are air heaters for plasma research. The advantage of reducing the dwell time of the are spot on any one area is also illustrated by thermonuclear research apparatus where spark gaps are operated repetitively with very high current sparks in the microsecond range and the electrode erosion is unimportant. The amount of electrode erosion per coulomb produced by very high current sparks is small if the individual current pulses are short enough. Since both the amount and rate of erosion increase very rapidly with pulse duration, the thermal capacity of the metal surface layer appears to be the important factor in the low erosion caused by sparks in the microsecond range. The rate at which an arc spot must move to sufficiently limit the erosion in a high pressure are chamber is not known, but let us assume that an'exwposuret time of 5O pbseconds does not cause excessive erosion, If an arc spot is assumed to have a diameter of I em, and if it moves one diameter in 50 mieroseconds, the resultant velocity is 20,9000 cm/sec, or approximately 660 feet/sec. Velocities of this order are presumably attainable even at very high air densities, although published data as to the velocities of magnetically driven arcs seem to be lPimited mostly to observations at atmospheric pressure. 13

The calculation of the are velocity n a magnetic field is not a simple task. The force on the arc column can be calculated, and it might seem, at first thought, that a knowledge of the gas properties and the column diameter would enable the velocity to be approximately calculated0 This has been done with some success with arcs at current levels low enough so that heat convection forces are the predominant forces on the arc columno However, the motion of a magnetically driven arc through a gas is not the motion of a solid cylinder through a viscous fluid, but is much more complex. The mobility of electrons is greater than the mobility of ions, so that electrons are displaced slightly out of the are column on one sides, causing new ionization into which the column will move. The column motion involves both the creation of new charged particles and the small, but significant, motion of the charged particles in the direction of the arc motion0 The rate of motion is difficult to predict quantitatively. Walker and Early6 measured the velocity of magnetically driven arcs in air at 30 atmospheres pressure. A 6000=gauss field moved a 2-ampere arc along rail electrodes at 200 feet/second0 The rate of motion is very dependent on the gas density and temperature. Fig. 7(a), reproduced from Refo 6, illustrates an experiment (at atmospheric pressure) with a rotating arc. One electrode was a 1/4Winch~ diameter, copper rod located in the center of a l13/41inch-diameter hole in a copper sheet which served as the other electrode. The axial magnetic field was 5600 gauss, and the current was 12 amperes. The arc column did not rotate like a radial spoke in a wheel, but was bent into a spiral because the angular velocity was greater near the center electrode. This spiral effect presumably also exists under conditions where both the air density and the current density are scaled up by large factors. Fig. 7(b) is a single frame of a Fastex motion picture taken with the 4l

center electrode as the anode. The rate of rotation, as measured from the Fastex film, was 2700 revolutions per second. The arc voltage was 1400 volts. Fig. 7(c) was taken under identical conditions, except that the center electrode was the cathode. The arc voltage was 1200 volts, and the rate of rotation was 2000 revolutions per second. The velocity of air motions as observed by smoke tests, was at least one or two orders of magnitude slower than the velocity of the are, The electrode erosion, after 15 minutes of operation, was too small to be noticed by visual inspection, although the power into the arc was 15 kwo

MOTION OF ARCS DUE TO SELF-MAGNETIC FIELD At high currents, the forces on the arc column due to its self-magnetic field become very important. In any loop of current, the forces from the self-magnetic field of the current in the loop are in such a direction that the loop will tend to enlarge or stretch in a direction which will increase its inductance. At arc currents of many thousands of amperes, the effects of the self-magnetic field of the arc will completely overshadow the thermal convection effects. For example, even if an arc column were assumed to be straight and the self-magnetic field were symmetrical, and the magnetic forces were balanced, a small perturbation would tend to grow forming kink (sidewise movement) and sausage (pinching) instabilities. Blow-Out Arcs An arc across the ends of two parallel electrodes or across the end of a coaxial line can be termed a blow-out arc because the self-magnetic field of the arc current forces the arc to expand outward into a loop until the voltage becomes high enough to cause the arc to re-ignite near the electrodes. If the arc is free to expand in all directions with no convection or wall effects, the arc column will tend to blow out into a circle. Where there are metal chamber walls present, the arc current induces image currents in the metal wall which tend to repulse the arc from moving towards the wall. This effect is well described in the literature pertaining to thermonuclear research where a copper tmirrors is used outside dielectric cylinders and toroids to help keep the "pinch" stabilized.7'8 This image current thus acts to reduce "kink" instabilities. At currents of hundreds of thousands of amperes, a dominant effect associated with a blow-out arc is the huge magnretohydrodynamic force which causes convection air flow in the gas and increases the rate of heat tr$as16

fer to the walls of the arc chamber. To illustrate the magnitude of this "pumping force" in the gas and the resultant acceleration of the air, a numerical example is of interest. Assume that the electrode tips are relatively close together, and that the magnetic forces are such as to blow the arc out into a loopo Since the actual effect of the tips is not significant, it can be assumed for s impEcity that the are is in the shape of a toroid and the force is expanding the toroid in a radial direction, If it is assumed that the minor diameter remains constant as the major diameter expands, the total radial force outward on the circle is given by the relation9 1 ii dL where F = force in newtons I - current in amperes L = inductance in henrys R = major radius of toroid in meters. The inductance of a toroid as a function of the major and minor diameters is given in Ref, 10. If the calculation is carried out for a million-ampere arc having a major diameter of 16 cm and a minor diameter of 3 cm, the total MHD force on the gas is 1.7 x 106 newtons, or approximately 380,000 pounds. An orderof-magnitude conception of the effectiveness of this force in accelerating air can be obtained by assuming that the force is acting to accelerate 6.4 pounds of mass in a linear, non-viscous manner. After 20 milliseconds, the mass would attain a final velocity of 12,000 meters/sec and would travel a distance of 120 meters, Even if allowances are made for the fact that the motion is reduced by a large factor inside an are chamber, and for the tapering off of the current pulse, there is a significant circulation which 17

pumps the hot plasma from the arc against the far end of the chamber and circulates it back along the walls of the chamber as illustrated in Fig. 8(a). Suggested Chamber Geometries The chamber design illustrated in Fig. 8(b) uses the end of the chamber for one electrode and the chamber wall for the other electrode. This appears to have a reduced pumping action and the systematic circulation of plasma from the center of the chamber to the walls would be expected to be greatly reduced. Fig. 8(c) is similar to Fig. 8(b), except that the current is brought into the chamber on parallel plates instead of a coaxial line, and hence it is easier to locate the dump valve opening in the end of the chamber. Fig, 8(d) is a chamber design which uses half of the copper chamber liner for the cathode and the other half for the anode, This design has been tested at a current level of 400 amperes at atmospheric pressure, and the results support the theory that the arc and the arc spots move continuously due to the inherent instability of the arc column~ Also, there is apparently no pumping action in this design. There is, however, a great deal of small scale turbulence in the gas which causes the gas to mix more rapidly. A further investigation of the relative merits of the design of Fig. 8(c) as compared to Fig. 8(d) is planned on this contract. 18

POSSIBILITY OF PRODUCING A HOMOGENEOUSg HIGH DENSITY PLASMA FOR SCIENTIFIC MFASURENETS If the properties of a very high density plasma are to be experimentally measured9 it seems essential to be able to produce a small volume of the plasma which is in thermal equilibrium and at a uniform temperature. The conducetivity of such a plasma as obtained by theoretical calculations is only an approximation and may represent substantial error ll Measurements on such an "ideal" plasma would assist in predicting the arc impedance under various conditions in arc chambers for Hotshot wind tunnelso Such a plasma can possibly be produced inside an arc chamber by a rotating arco It is logical to assume that if a rotating arc is in a closed chamber, and if the rate of heat loss from the chamber is low enough9 the cooling and deionlzation of the gas between successive passes of the are column become insignificant9 and the plasma tends to assume uniform temperature and conductivityo This assumption is also consistent with the behavior of a stationary arc column operating on alternating current where the temperature fluctuation may be thousands of degrees at 60 cycles but gradually decreases at higher currents and frequencies.1213 The cyclic temperature fluctuation of an are arc is always reduced at high currents where the arc column diameter is larger and the volume-to-surface ratio of the plasma is greater0 Likewise9 the temperature fluctuations produced by a rotating arc inside a large are chamber would be less than in the case of a small chamber. In the large chambers the ratio of heat stored to the heat lost per second may be much greater than in a small chambero Hence9 the thermal time constant is longer. Refo 14 describes a rotating arc at high current levels used for thermonuclear research0 A discussion with the authors of this paper indicated that they found no evidence of a spoke-like arc column0 19

The heat loss due to convection currents set up in the gas by a 1/3-megampere rotating arc can be made very small in comparison with a blow-out arc at the same current, As described in the next section of this report, an external magnetic field of a few hundred gauss is sufficient to cause the are to move rapidly, and yet the magnetic force on the gas is one or two orders of magnitude less than in a blow-out arc at a comparable current level. An alternative method of producing a low contamination, homogeneous plasma is the system shown in Fig. 8(d), which requires no external magnetic field. The attractiveness of using the split chamber design was not fully appreciated at the time the decision was made to design chamber No. 2 for a rotating arc. 20

ARC CHAMBER No. 2 The design of the No. 2 arc chamber was chosen with two objectives in mindo (1) To demonstrate that rapidly moving arc spots greatly reduce electrode erosion even at current levels of hundreds of thousands of amperes. (2) To obtain a plasma of high density gas, a portion of which would be homogeneous as to temperature and current density, or at least determine the size of the chamber and the energy level necessary to achieve this condition~ It was believed that a chamber which used an externally applied magnetic field to rotate an arc at a controllable rate would offer the best probability of meeting the above objectives. It also appeared that experiments with a blow-out arc would yield empirical data applicable to a particular piece of apparatus but would not be amenable to scaling or similitude relationships or interpretation in terms of gaseous conduction theory. Various considerations led to the prediction that the production of a plasma of uniform current density and temperature by a blow-out arc geometry would be so difficult that measurements with such a chamber would probably be limited to the conditions of a transient "odying plasma" after the current had been turned off. Measurements in a dying plasma would be of basics science interest, but the most important measurement of all, plasma conductivity, to be directly useful in an engineering application, should be made under conditions where the plasma has a high uniform current density. Although the use of an externally supplied magnetic field is attractive from a basicsscience point of view, there is a disadvantage of major significance in that the design is not easily adapted to the requirements of a Hotshot wind tunlel. 21

Fig. 9 is a cut-away drawing of the No. 2 are chamber. The total volume was 41.0 cubic inches. Because of the limitations of the power supply, the energy density in the chamber was increased by filling the ends of the chamber with ceramic inserts which decreased the volume to 18 cubic inches. The chamber was made of beryllium copper and designed for 15,000 psi. An axial magnetic field was produced by a winding of copper cable around the chamber which would supply fields up to 8000 gauss inside the chamber for periods of several seconds without overheating the cable. The part of the chamber wall which served as the anode was protected by two replaceable metal rings which were held in place by a press fit. In order to prevent the blow-out effects caused by the self-magnetic field of the arc current from overshadowing the effect of the applied field, the current was brought into the chamber symmetrically from both ends as illustrated in Fig. 10. With this arrangement there was no average net blowout force on the arc towards either end of the chamber, and the dominant magnetic effect was the rotation caused by the reaction of the arc current on the axial magnetic field. If a 300,000-ampere arc column is assumed to be 1 cm in diameter, the self-magnetic field at the surface of the column is approximately 100,000 B2 gauss. Since the magnetic pressure is (in cgs units), and thus varies as the square of the field strength, the addition of an externally supplied magnetic field of a few thousand gauss has little effect unless the forces on the arc column caused by the self-magnetic field are approximately balanced. Otherwise, the effect of the self-magnetic field will predominate over the effect of the externally applied field, The limited voltage obtainable from the power supply required that the spacing between the concentric electrodes be kept small. With the inductive storage transformer reconnected so that the two secondary turns were in 22

series, the maximum available voltage was 800 volts, which seemed to be more than enough to sustain the arc, once it was established~ The average arc voltage was 250 to 500 volts, depending on current and air density, but short voltage "spikes" occurred when the required voltage would exceed the available voltage, and the arc would extinguish. The voltage spikes were apparently caused by some form of arc instability~ Arc initiation was accomplished by a small third electrode inside the chamber which was connected to the high voltage primary winding of the coil through a resistance. About 50 amperes of current would flow to this third electrode throughout the discharge, and this current not only initiated the main discharge but also helped somewhat to prevent extinguishing when transient "tspikes" occurred in the arc voltage. Tests at 250,000 amperes indicated that the erosion was greatly reduced. The anode rings could be weighed before and after each tests and the amount of material lost was usually too small to measure, certainly temperature are probably possible by this method. Fig~ 11 illustrates typical curves of voltage, current, power and pressire which were obtained on several successful firings at approximately in the primary circuit of the inductance coil, and good, repeatable results were obtained at peak currents of 2000 to 12,000 amperes, but these results are not particularly relevant to the objective of this contracto Repeatable operation could also be obtained at 1/ megampere when the magnetic 23

field was very low, but with a magnetic field of about 1000 gauss which was required to move the arc fast enough to control the erosion, the power supply peak voltage limitation was seriouso Theory showed that a considerable amount of energy was lost in the switching operation whenever the secondary arc voltage was high at the instant of switchingo Since the arc voltage was rapidly fluctuating, the energy lost in switching and the energy into the chamber would vary considerably from one experiment to the next. In addition, the arc voltage requirement was not met with a satisfactory safety factor, and the value of 800 volts on the secondary, which corresponded to 50,000 volts on the primary, was not enough to consistently maintain the arc, Each time there was a severe transient in the arc, the primary voltage would exceed the allowable voltage, and the protective spark gap on the primary of the coil would arc over, shorting out the system. The operation was not reproducible, nor scientifically satisfactory. 2h

PRESENT STATUS OF INVESTIGATION In July, 19599 the University of Michigan Department of Aeronautical and Astronautical Engineering negotiated a contract with the Office of Naval Research to build a Hotshot wind tunnel. The tunnel was to be constructed and operated under the Office of Naval Research contract, and the energy storage power supply was to be financed by the University of Michigan Institute of Science and Technology, The power supply, now nearly completed, is to be an interdepartmental facility and will be used for arc and plasma studies by the Departnient of Electrical Engineering, for thermonuclear work by the Department of Nuclear Engineering, and for hypersonic wind tunnel work by the Department of Aeronautical and Astronautical Engineering. This energy storage supply will use a unipolar generator and flywheel in conjunction with a larige inductance coil similar to Hotshot II at AEDCo The flywheel will store 20 megajoules of kinetic energy, and 6 megajoules will be stored in the inductance coil at peak current. Fig. 12 is a photograph of the inductance coil. Since the high current arc investigation sponsored by AEDC required a better power supply, it was decided to suspend the experimental program approximately one year, until approximately June, 19609 when the new power source was scheduled to be completed. Delivery of the unipolar generator was originally scheduled for April, 1960, but the delivery date was subset quently moved up to August, 1960, by mutual agreement. This unit has not yet been received. The supplier reports that the time extension was used to incorporate improvements Into the system, based on information obtained from similar generator units, It is reported that the generator is nearly completed (as of Novembers, 1960), and will be shipped in the very near ffutureo

APPENDIX A Transient Temperature Rise in a Metal at High Current Density The power dissipated per unit volume in a metal is given by the formula P j v - =J2? where J = current density e= resistivity. When the current density is uniform and the temperature rise is sufficiently rapid so that thermal diffusion effects can be neglected, the following relationship holds: J2pdt = C m dT where C = specific heat m = density. Since the resistivity and specific heat are functions of temperature, by separating variables, dt = mC(T) dT J0 {(T) Solving this equation by integration yields the temperature implicitly as a function of time. = m C(T) dT + constant j J2 (T) Values of specific heat and resistivity at various temperatures are available in handbooks, and integration may be carried out numerically. An approximate empirical equation for to(T) for tungsten derived from handbook data is (0= 4.16(T2 + 5T),uohm-cm, where T is in kilodegrees Kelvin. The specific heat of tungsten varies less than 5 per cent over the range from room temperature to 1800 0K, and in the curves plotted in Figures 2 and 3 it was assumed to be constant. 26

An interesting closed form solution may be obtained by making two simplifying approximations. First, assume that the specific heat is a constant. Next, assume that the resistivity varies linearly with absolute temperature. This is inferred by the Wiedemann-Franz law for all metals. For tungsten, this is quite reasonable an assumption, since the resistivity rises only slightly more rapidly than linearly. The resistivity can be written as where eo/TO is merely a constant, but the use of this notation maintains the dimensions. The term (o/To may be interpreted as the slope of a straight line that is used to approximate the resistivity-vs.-temperature curve. The advantage of these latter assumptions can now be shown, since m C dT m C TOdT m C To dT 1 0 2 T 10 0_ go J 0 T mCTT ort =m Co IlnT + constant, This can be re-arranged, and if To is defined as room temperature, T = To [e mTo The temperature rises exponentially with time. 27

REFERENCES 1. "Half-iegampere Magnetic-Energy-Storage Pulse Generator," R. C. Walker and H. C. Early, The Review of Scientific Instruments, Volo 29, No. 11 (November, 1958), p-p 1-02 —1b20. 2. "Inductive Energy Storage —A Tool for High Temperature Research," Ho C. Early and R. C. Walker, Conference on Extremely High Temperatures, New York: John Wiley and Sons, 1958, ppT.6-i70'.. 3. "Economics of Multimillion-Joule Inductive Energy Storage," H. C. Early and R. C. Walker, American Institute of Electrical Engineers, Transactions, Vol. 76, Part I, No 31 (July, 1957) pp. 320-324, 4. "Analysis of Electrode Phenomena in the High-Current Arc," J. D. Cobine and Eo E. Burger, Journal of Applied Physics, Vol. 26, No. 7 (July, 1955) ppo 895-900o 50 "High-Current Arc Erosion of Electric Contact Materials," W. R. Wilson, American Institute of Electrical Engineers, Transactions, Vol. 74, Part III Powepparatus and Systems), No 19 (August, 1955), P 657664. 6. "Velocities of Magnetically Driven Arcs in Air and Helium Up to 30 Atmospheres," R. C. Walker and H. C. Early, Conference Paper at AIEE Winter Meeting, February, 1955. 7. Conference on Thermonuclear Reactions, J. L. Tuck, Radiation Laboratory-, University? Californ'ia, U S. Atomic Energy. Commission Report WASH-146. 8. An Introduction to Thermonuclear Research, Albert Simon, London: rergamon Press, 1959, pO 116o 9. Electrical Coils and Conductors, H. B. Dwight, New York: McGraw-Hill Book Company, 7pST, P-299. 10. Radio Engineersv Handbook, F. E. Terman, New York: McGraw-Hill Book Company,,1943, po-2F 11. "Experimental Investigation of a High-Energy Density, High-Pressure Arc Plasma," Edward Ao Martin, Journal of Applied.Physics, Volo 31, No. 2 (February, 1960), pp. 255 27o — 120 "The Thermal Mechanism in the Column of the Electric Arc," L. S. Ornstein and H. Brinkman, Physica, Vol I, 1934, p. 797. 13. Gaseous Conductors, J. D. Cobine, New York: McGraw-Hill Book Company, 19tl, Chapter 1o. 14. "A Hydromagnetic Capacitor," Anderson et alo, Journal of Applied Psics, Vol. 30, Noo 2 (February, 1959), pp. 188-196. 28

LIMIT MPISTONROD OF SWMITC AIR CYLINDEH ST /, /P I /B.. ~.V L'"., / I T Y, R,,C,,E RUBBER —,RV ELOCIT~''" CFDU ZO"~ ~~~ RIGS.. \'z \\ t__.:_ 3'..:z3~ _,t $ E DR DISKS FLEXIBLE COPPER SHOC O C K A BSORBlr~A P $ C! H.B E BRAID e eeC P~~ ~ SKDS:o "O" RI NGS < 0 0 -~~~~~~~~I \~~~~~~~~~~~~~~~c = \<- L\\' i\ \\t F \,\'\L \~ %x,. INSULATION / 1/2 COPPER PLATES rNN 9 AX lA L+CONNECTING TO.RES,.R TRANSFORMER QUARTZ I A FROM CHAMBER. CA E H N I SM \h!~~~~~~~~ ~~~~~ I E Z 0 E L C T R I FIG. I ARC CHAMBER AND ELECTRODE ATUATINGT LETOD T a,', -"-0"RINGS"'"; -— ~~~~~~~~~~~~~~~~~~ —I.~~~~~~~~~~~~~I' CO~~~x(AL,~~ (_A:HIVE,.. ~_ECH I ~~~~~H ~ ~ ~SEEYUE I~NSDULAED i:C..~/,,~ - TNGSE ELECTRODE ACUTIPS MECHANISMi ~+"...

MELTING POINT OF TUNGSTEN (36230K or 33500C) 3500 0 0 3000 - 0 aJ 2500 - 2500 300,000 DUI I 1 200,000 2000 rU 150,000 AMPERES/CM2 < 1500 F- 1000 500 300 L 0 1 2 3 4 5 6 7 8 9 10 I 1 12 13 14 15 16 TIME (MILLISECONDS) FIG. 2. THE TEMPERATURE RISE IN TUNGSTEN FROM OHMIC HEATING AT CONSTANT CURRENT DENSITY

1400 l I IMELTING POINT OF COPPER (153~K or 1080;C) I 1300 z 1200 w 1100 Lr o, 900 600,000.800 400,000 D 700 /300,000 AMPERES/CM2 Lu 600 200,000 Hi 500 400 300 0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 TIME (MILLISECONDS) FIG. 3. THE TEMPERATURE RISE IN COPPER FROM OHMIC HEATING AT CONSTANT CURRENT DENSITY

FIG. 4. TUNGSTEN ELECTRODE TIPS, 0.75 INCH DIALMETER, AFTER ONE FIRING AT 300 KILOAIPRES. Molten tungsten flowed away from the flat end surfaces of the electrodes and solidified on the sides. Arc spot diameter was evidently less than the 0.75 inch diameter of the end surface.

500 2 50o 5 2ooC _D CURRENT 3oo -150 3 c. ooo 100 100 2 io. 2.0 3.0 TIME (MILLISECONDS) FIG. 5. TYPICAL DISCHARGE CHARACTERISTICS FOR ARC CHAMBER NO. 1.

FIG. 6. EROSION OF 1i-INCE DIVERTER FIAT TENGSTBN 3CORODI:S.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i l11n"e makasilsrt h lo ie fmle ea casdbihevprbat hl h letoe ee eaaig

DIRECT jot4 O M AGt4E-Tj FIELD............~~~...........~~ ~~ ~~~~~~ ~~~~~,~ R O T A T I N G.....................................~~~~ ~~~~r~........................~~r~~~r~....................~~~~~~~~~~~~~~~~~~~ ARC...............:.....................~~~~~~~~~~~~~~~~~......................................... r~~~~r~~............ L A~~~~~~~~....................... C O P P E R P~~~r......... RODE~~~,~~~~,~~,~~~~~~~.~~~~~~~~~~....... ELECT~~~~~~...................................,~ R07AT\NG~~~~~~~~~~~....................~~ ~~ ~ ~~ ~~~ ~~ ~~ ~..........::::: 1 3/41' DIA, ~~~~~~~~~~~~.................~~~~~ ~~~~~~~...........................................~~ ~ ARC~~~~~~~O COPPERLIT ~~r~~~~,~~~r~~ -~~,,r~~r~~r~/4 ~~~ i~,c~~~~~~~r~~rr~~~,ELECTRODEELC TO D + 5000 4r~~~~~~~~~~~~~r~~~~~~~~~~~~~, VOLTS -TA-TMG ARC~~~~~~~~~~~~~,C~~~~~~~,~ 5~~~~~~~~~~~~~-~~R~~~~C T~~ ~~~~E FO R R~~~~~~~~~~~~ TROIA SSURE~~~,~~~~~~~~~~~ I~~~~iG. 7(o) ELEC HERIC PRE~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~ AT AT M OSP ~~L~~~~~~~~~,~~~~~~~~

Arc Positions Plasma /, S F/o w FIG. 8(a) BLOW-OUT ARC CHAMBER WITH BOTH ELECTRODES INSULATED FROM CHAMBER. STRONG CONVECTION COOLING OF PLASMA. Arc Positions +xx_ / //////// _ ///,///// -— (, / %.1.. / FIG. 8(b) ARC CHAMBER DESIGN WITH COAXIAL INPUT. LESS "PUMPING" AND CONVECTION EFFECTS THAN IN FlG.-(a). to PUMPING" AND CONVECTION EFFECTS THAN IN FIG.-W.)

Arc Positions Insulation _ / FIG. 8(c) DESIGN WITH ELECTRICAL INPUT ON PARALLEL PLATES, TO FACILITATE USE OF DUMP VALVE. ARC ACTION SIMILAR TO FIG.- (b) C-' \ \ _ a- 1\1 Arc Positions FIG. 8(d) SPLIT CHAMBER DESIGN. ARC DOES NOT EXTINGUISH AND REIGNTE AS IN ALTERNATE DESIGNS ABOVE. NO PUMPING ACT ION. NO PUMPING ACTION.

COPPER RING ANODE STAINLESS STEEL RING COPPER RING CATHODE BERYLLIUM COPPER CHAMBER-6" DIAM O - RING PRESSURE SEAL. ~..:. LUCITE INSULATOR FIG.9. CHAMBER #2. THE ARC ROTATION WAS PRODUCED BY AN EXTERNAL MAGNETIC FIELD

INSULATOR FIG. 10. ELECTRICAL CONNECTIONS TO ARC CHAMBER NO. 2. CURRENT WAS BROUGHT INTO CHAMBER ON PARALLEL COPPER PLATES AT BOTH ENDS OF CHAMBER TO CANCEL THE BLOW -OUT FORCE ON ARC COLUMN.

400 U LV 000 1 2 a 4 TIME MILLISECONDS FIG. II. TYPICAL DISCHARGE CHARACTERISTICS FOR ARC CHAMBER #2

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UNIVERSITY OF MICHIGAN lIIII III I I 11111111 llI 3 9015 02086 6615 THE UNIVERSITY OF -MICHIGAN DATE DUE