THE UN IVERS I TY OF MI CHI GAN COLLEGE OF ENGINEERING Department of Electrical Engineering Space Physics Research Laboratory Final Report'HEMISPHERICAL?LANGMUIR PROBE MEASUREMENTS IN THE LOWER IONOSPHERE Y So Hsu Ao F. Nagy ORA Project 07084 under contract with: DEPARTMENT OF THE ARMY BALLISTIC RESEARCH LABORATORIES CONTRACT NOo DA-20-O18-AMC-1765 (x) ABERDEEN PROVING GROUND, MARYLAND administered through OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR August 1967

TABLE OF CONTENTS Page LIST OF TABLES iv LIST OF FIGURES v I. INTRODUCTION 1 II. ENGINEERING ASPECTS 2 A. General Description 2 B. Langmuir Probe Mechanical Construction 7 C. System Electronics 7 Do Current Detector 12 E. Sweep Voltage Generator 15 III THEORETICAL BACKGROUND 17 A. Review of Probe Theory in the Lower Ionosphere 17 Bo General Ion Current Equation 18 C. Sheath Model 20 D. Ion Current Equation for Density Calculations 22 IVo DATA REDUCTION AND RESULTS 25 A. Flight Information and Telemetry Data 25 B. Ion Density Calculations 26 C. Electron Temperature 30 V. DISCUSSIONS AND CONCLUSIONS 35 ACKNOWLEDGMENTS 38 REFERENCES 39 APPENDIX: ELECTRONIC SYSTEM TEST AND EVALUATION DATA 42 iii

LIST OF TABLES Table Page I. Langmuir Probe Ion Current, Positive Ion Density vs. Altitude 31 II. Electron Temperature vs. Altitude 34 III. Positive Ion Density, Sheath Thickness, Sheath Radius, and Mean Free Path vs. Altitude 36 iv

LIST OF FIGURES Figure Page 1. Black Brant AC 17.604. Payload layout and sensor locations. 3 2. Nose tip Langmuir probe system completely assembled. 4 3. Front and back view of the Langmuir probe system electronics with housing removed. 5 4. Simplified Langmuir probe system block diagram. 6 5. System timing and flags. The top segment is the generator voltage wave form. 8 6. System interface, showing pin connections to the rocket telemetry system and power supplies. 9 7. Langmuir probe system mechanical drawings and parts specifications. 10 8. Langmuir probe system electronics schematic. 11 9. Single range current detector schematic. 13 10. Sweep voltage generator schematic. 16 11. Effects of probe velocity on the random ion current to a moving spherical Langmuir probe. 21 12. Graphical illustration of sheath thickness as a function of probe potentials for the two sheath models sl and s2. 23 13. Section of Langmuir probe telemetry data. 27 14. Average of measured ion current to the hemispherical Langmuir probe vs. altitude. 28 15. Final positive ion density vs. altitude. 32 16. Comparison of charged particle density results. 33 v

I. INTRODUCTION This is the final report on the Langmuir probe system which was developed and built by this Laboratory for the Ballistic Research Laboratory under Contract No. DA-20-018-AMC-1765(x), and was carried aboard Black Brant AC 17.604 launched from Fort Churchill at 12:16 PM., on September 28, 1966, during a PCA event of about 1o5 db. The rocket reached an altitude of approximately 116 km. The primary mission of this experiment was to measure charged particle parameters in the D and lower E regions of the ionosphere during an auroral absorption event. The first part of this report deals with the engineering aspect of the probe system. In the next section the lack of an appropriate theory for supersonic D-region probes is discussed and the somewhat empirical approach used for the data reduction is outlined. In Section IV the data obtained from the probe results are shown and compared with the results of other experiments flown on the same rocket. 1

II. ENGINEERING ASPECTS A. GENERAL DESCRIPTION The Langmuir probe is but one of many experiments carried aboard the Black Brant Rocket AC 17.604 for making measurements in the D and lower E regions of the earth's ionosphere. The general payload layout and location of the various sensors is shown in Fig. 1. A more detailed description of the complete instrumentation of AC 17o604 was given by Burt.1 The velocity of the rocket is expected to be supersonic, resulting in the formation of a bow shock wave; therefore, it is important to locate the probe outside the influence of the shock cone of the rocket. The nose tip location was selected because of the technical advantages over a boom supported probe. Choice of a hemispherical over a conical configuration was influenced by the following considerations: (a) the effective collection area is not very sensitive to small changes in the angle of attack as would be the case for a conical nose tip and (b) the current collection theory for spherical collectors for long mean free path is well established. Figures 2 and 3 show, respectively, the completely assembled Langmuir probe system and the system electronics with the housing removed. The Langmuir probe system used two VCO channels at 30 and 40 KHz and the system block diagram is shown in Fig. 4. The Langmuir probe current is measured alternately by the two channels, such that during the time when one channel is making current measurements the other channel performs inflight calibration and records other pertinent system parameters. The system logic timing and flags are shown 2

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Fig. 3. Front and back view of the Langmuir probe system electronics with housing removed. 5

HEMISPHERICAL CYLINDRICAL GUARD COLLECTOR a(1~ | ROCKET NOSE CONE +2.5VJL I l -2.5v l RANGE CHANGE LOGIC.008 /L.A. 0.1 O.I.A. and and I.O0.A. 15.0 t.. A. CURRENT CURRENT DETECTOR DETECTOR TO 40 KHz TO 30 KHz VCO VCO Fig. 4. Simplified Langmuir probe system block diagram. 6

in Figo 5 while Fig. 6 shows the interface connections to the FM-FM telemetry system and power supply aboard the rocket. As usual, the rocket body serves as the voltage reference to the entire system. B. LANGMUIR PROBE MECHANICAL CONSTRUCTION The solid hemispherical nose tip Langmuir probe has a diameter of 2.5 in. and was machined from 303 stainless steel. The guard ring and housing tube were made of 304 stainless steelo Ceramic insulations separate the guard ring from the nose tip and the housing tubeo The entire system is attached to the rocket nose cone tube via a 303 stainless steel adaptoro Figure 7 shows the complete mechanical drawings and parts specifications; section CC shows the location of the electronic support assembly. The completed system was vibration tested for mechanical and electrical integrity prior to integration with the rest of the payload. Co SYSTEM ELECTRONICS The Langmuir probe electronic system schematic is shown in Fig. 8. Briefly, the probe and guard are driven by the same voltage generator with the voltage format shown in the top segment of Fig. 5o The probe current is alternately measured by the two current detectors which are characterized by the two operational amplifiers AMP1 and AMP 2 in Fig. 80 Each detector has two current ranges. The output of the oOo08 pA current range of detector 1 and the 0.1 pA current range of detector 2 are biased positively by approximately 2.5 v with respect to the system ground. AMP 3 is the operational amplifier used to generate the saw-tooth segment of the generator voltage. R1 (25 megohms) and R2 7

K&E 19-1153 1-6S. — 25 MSEC 50 —- 0 MSEC + 2.5V +2V OV (FF I 0) -2.5V OV -- — 50 M SEC RANGE FLAG + 2V (J I-2) (F F 2 0) OV OV + 2V -1 MEASURE +2 SYSTEM FLAG IU2 MEASURE J14 2 CALIBRATE (FF3 0) (JI s -4) -I CALIBRATE OV OV OO MODE +2V CONTROL | (FF4) SQ. WAVE AV RAMP AV SO. WAVE AV (FF4 Q) OV SYNC TO IOSEC SYNC TIER SEC (TIMER FIRES AT 10 SEC INTERVALS OPERATINS FF4) ~oQ TIMER ~~, II SYSTEM RANGE |FLAG |FLAG 2 DETECTOR I DETECTOR 2 ZV OV M EASURE.006 O V |COM. MODE CHECK AND 2V OV MEASURE.00& L~ CALIBRATE RI (25M)- Q UA RANGE COM. MODE CHECK AND CALIBRATE R2 (2M ) 15 A RANGE COMMON MODE CHECK AND OV OV CALIBRATE RI (25M)-.008 UA RANGE EASURE. |0 ~ V l 2V COMMON MODE CHECK AND DV 2V MEASURE 15 HA CALIBRATE R2 ( 21 )- 1.0 UA RANGE ENGINEER TBL DRAFTSMAN JRP SPACE PHYSICS RESEARCH LABORATORY TIMING AND FLAGS DEPARTMENT OF ELECTRICAL ENGINEERING LANGMUIR PROBE AC 17.604 10-20-65 UNIVERSITY OF MICHIGAN I. 10-5-65 ANN ARBOR, MICHIGAN B-356 D Fig. 5. System timing and flags. The top segment is the generator voltage wave form.

K IE 19- II3 1-65. POWER REQUIRED: AVERAGE POWER INPUT: 2.8 WATTS 28VDC AT IOOMA CANNON DEM-9S CANNON DEM - 9P + *S Q 22 —, —+728 POWER +,DIm < 8 9 9 28 V.D.C. IOOMA 7 7 DATA SIGNAL 2 XTMR 2, CHANNEL 14, DATA SIGNAL 6 6 DATA SIGNAL I ELECTRODE PROBE \ #26 XTMR I, CHANNEL 14, DATA SIGNAL ^ —-- 5 5 POWER RETURN 4 4 SYSTEM FLAG \ I I 1 R3 3 AV MONITOR 2 2 RANGE FLAG ~22 _ SIGNAL RETURN AND CHASSIS GROUND - 1 SIGNAL AND CHASSIS GND NOTE NO PULLOFF REQUIRED ENGINEER TBL DRAFTSMAN JRP SPACE PHYSICS RESEARCH LABORATORY LANGMUIR PROBE INTERFACE DEPARTMENT OF ELECTRICAL ENGINEERING AC 17.604 10-20-65 UNIVERSITY OF MICHIGAN 8-26-65 ANN ARBOR, MICHIGAN B- E345 DATE Fig. 6. System interface, showing pin connections to the rocket telemetry system and power supplies.

A -0/ - 005 -eOCKET TUSBE WAS/E~ g — /5 —4 N. ST Z- JAM viUr 30.3 S7T1vN ST7 T'V. ST. 7- -Ea -. - C -/1 - 01 7 I/ - 0/j - OC / 8 0/55 -0 2 OBSE qioqEPCe / - SC EW i IULLi RTOe CE-/TEe /VSurq Toe 30 3 ST/ V / TL O / / — TE TBKE UP SC E_ \ -NIOSE T/P \ \PT (/4- F.,TYV.. / / \ 303 ST r. S TI'i'I/VG 0P E 0'. vi TON -.,C:IE8 SE,-L grp/~~~~~~~~~~~~~~~~~~~~~~~ / \ | __-\e oo \ \w BDe G Z' 5 A/T-o /a ---— e —o w — ---- B\C VI \-0/S -- 5E~cCo~N B. B nE -— OV C C c-o/5-sF | | g| =-0,5-0 /-' CP/Ish - / 0/ = = _ __ __. 0 —---— i —-- ----------------- --------—. — _______ 1y'~s~^. ^ /- - __..... ~04 STfN - At B -0/5 -0/9 Fig. 7. Langmuiir pro'be system mechanical drawings and-ls- parts/i- EZ sp3cn ST0 F.T 8speCTIfoiatios-05 - 00-F 304 STIVS7-.i, - -Tv,, A 8- ~L=A -E/IV1C - -5 A_ _ T 9_ _ _ /N N7E7;: /1 o-. _g/L__ - - __ __7-0_ F 50 0.0 0 /.1- i- iv _ _ WASOq/l?' C6~TION BE SC~TIONCC A-O/SIV TOa 7R=V/ TCO/s-OST / -0/5 - CE/V Te ULT ___ ELAECT/OT/CS PPORT ASY. -0/5-0 o-o116 - 01~ TIN B LA,-~ECTING, C Fig. 7. Langmuir probe system mechanical drawings and parts specifications.

lOG 04.. EMISPHrERICAL I 13 3- - ------ - i ElO~t 2.0K 2.7K GUARO.-,. R7 RCANNON DEM-9P ELECTRODE IooKK[ W 3M } ~Al3 f-3 NOT USED R32 R33 13i0 1.2K 250 124 PP I R ____.41004 3 v40K v-'U A5' U.o M + 210.50 20V2 F I 0 01 RII^" ~ ~ ~ ~3 DI? oil NTUE 013.5 N4T RI R 92 D1 03 o 40K 1F 41004 G OK 23V 680K 004- 47K R5 R29A _ I I IJ...... —'- I' —1 ],~., ___ S,- -, FF2 0 B_ 01 R 4 0 + 3V RW FF 13 F 323V _L_ F M IZII -25 3 ^ ~ y Jr * [~0*! *I L M1a-35 4 (3V G23V 1/3I 15 K2. c$ C4 0300M d 4 ~ 2.2K -: 2.2K ~~~~475 475 rI 82~K303 9 030 R35 92 -6 3 3 I 30.9K9 1.21 20 41004 -3- I-E!. ~ ^) -'" ]W RIG rW ^M - -r |8> —---------— 0 —3 —W-i- _04''.0OI NOR2s~~3 -100 FR.I -~ T ______'__f 2.2K' FOO R83 I IK 7 7Cj 7 -3GATES I 4K i-7 23 I.9 > O-' iK I3/1 83P 054 S C2S' l5 l 24 IS R ie R37 6.1E4 R41 - C20 2.72045 L_~__,,,,b.~vv'-3I 2040 1112.30...31 Io 4.o,-.-,-V R, " _ UNI/ERSITY OFAMP M I CHANNEL 2 47K - 007ANN ARORMI44H C-34 DAT.001 E Fig. 8, M R4. 3angrui prob sysm — erons s T.. -23V R4ZA DI l 49 R21 R2 FMI711 IN645 FMI711 IG45 I1/[ 5 V +23 1 1/35 2.2K QI lJDI 2.2K 0..,33 2 100 2 771 | R71 W 2V RT4 a-rR40!44 R49 R50 0 __ ~I ~ _ VH.'~-'7- - - -- o [ 47K e 2.72 1 L__J,_, AAA,,,' I o,, K 2.2K ~F [i --- 4 I I " — I4...'1, 4v'S- S' " ~ cJ ~f -... 3,. ^ p... J -.:.,R A 44 SNR5IIII 5SNR51 0'~ IN 4 1- O 2N2193A I 3 W_8 3 35 FDIOO'". 15 ^ ^^ 4J 1 _FI rI":;9'v R70 _!.....'L.J K'~ i:':. ~:.,P r -~1 /'r?' o - -- - c - +.....O. - > 10.5V 2N34a-,J27 | 64 2|7K 2.;-' +N 1 36V N2 D61:44 D47 3 e _ 6_ 02 0 I Q21 023 _ 04 5 ~~6K -1.5C 1/ 335 FD OO - Fig. 8. v0 SOURC s e e L__ - [ oD2 Q20 r0,21 223 /_ - SOURc CE I' I _ I I PHSC R/PE.SEARCH LABORATORY LANGMU PROBE.K - I.K UNIVERSITY OF MICHIGAN -- 6 R-"67 - ANN ARBOR, MICHIGAN C-E~ DATE LAST USED: C35,,D49,028,T2,14,R86 Fig. 8. Langmuir probe system electronics schematic.

(2 megohms) are the calibration resistors. The system logic made generous use of micromodules because of reliability in performance and ease of construction. The lower right hand corner section of Fig. 8 shows the system power regulator. During the calibration phase, the detector input is first shorted together to simulate zero probe current (common mode check); this is followed by applying the generator voltage successively to the two calibration resistors and measuring the resulting current. The use of operational amplifiers for sweep voltage generation and current detection enhances both reliability in performance and reduction in construction time. D. CURRENT DETECTOR The current detectors used in the Langmuir probe system consisted of two Philbrick PP25A operational amplifiers and:.four sets of matched range resistors. A single range detector schematic is shown in Fig. 9. The resistance pairs designated R1 and R2 are separately matched to 0.1% and track each other to within 25 parts per million (ppm) over the expected temperature range of -25~C to +50~C. For purposes of analysis, the Langmuir probe is represented by an equivalent resistance Rp. The open loop gain of the amplifiers has a value greater than 20,000, and an input impedance of about 1012 ohms. For all practical purposes, the current flowing into terminals (1) and (2) are zero and so we can write the following equations: e) - e2 A= (1) il = if + ip (2) 12

\~ Langmuir Probe R2 I\RP I _ R2 ip if I AIN0N ~| R0 Fig. 9. Single range current detector schematic. 15

el-Eo if = R2 (3) R1+R2 Substituting for the numerical value of A (the open loop gain) into Eq. (1) we find that Eo/A is negligible compared with either e1 or e2, and so we get e- l e2. By eliminating il, if, ip, el, and e2 from the above equations we get the final result: Eo = Ein +R2 R (7) EoR2 (R1+R2, Rp Since el and e2 are equal we may substitute Eq. (6) for el, in Eq. (4) and use the result in Eq. (7) to give: Eo = Rip. (8) The last equation shows that the detector output voltage is directly proportional to the probe current with R2 the proportionality factor. Therefore, different current ranges are obtained by changing the value of R2. From the overall performance of the detector, it was found that range change is best accomplished by changing the resistors R1 along with R2, but keeping the resistance ratio R2/R1 constant. In order to achieve a high signal to noise 14

ratio and adequate common mode rejection, the optimum value for the ratio R2 to R1 was found to be 100 for this particular design configuration. E. SWEEP VOLTAGE GENERATOR The sweep voltage generator employed a Fairchild ADO-3 operational amplifier and a low leakage silver-dip-mica capacitor. The schmatic for the generator is shown in Figo 10. R1 and R2 serve as a voltage divider and set the starting level of each sweep. Following the general analysis method of the previous section we get the following relation: eo = e2 + (eg-e2)dt. (9) The system logic and timing determines the period of each sweep and the slope of the ramp is determined by the RC product. In practice the available space dictates the value of C, so that any slope change is best accomplished by varying the resistor R as was done in the present system. 15

C I' AI +9i RI A 1. 2 Re Fig. 10. Sweep voltage generator schematic. l6

III. THEORETICAL BACKGROUND A. REVIEW OF PROBE THEORY IN THE LOWER IONOSPHERE The theory of electrostatic probes carried by supersonic rockets in the Dand lower E-regions of the ionosphere, where the neutral particle density is high, has not been developed adequately enough for any practical application. Pearl2 conducted an extensive review of the work done in this area, but found no satisfactory theory applicable to a moving spherical Langmuir probe. He further concluded that it is unlikely that an analytic solution of the problem can be obtained in the near future. He then attempted to solve the problem of a hemispherical probe moving at supersonic speeds by a numerical method. Unfortunately there was no tangible conclusion, nor specific results that can apply to an actual experiment in the D-region of the ionosphere. Smith3 avoids this difficulty by using electron density values from propagation experiments to calibrate the probe current to his Langmuir probe in terms of ambient electron densityo This method appears reliable, provided the effects of vehicle speed and other dynamic parameters, which affect the probe current, are properly accounted foro Balmain4 considered a spherical probe at high pressures, assuming the probe to be stationary. He suggests that the effects of vehicle speed can be overcome by operating the probe at high negative voltages. The Langmuir probe system described in this report has a potential of ~2,5 v with respect to the rocket body, and therefore Balmain's conditions are not met. In a very recent article, Su and Sonin5 considered the case of a moderately ionized gas, but here again the condition of a stationary probe renders this 17

work inapplicable to the present system. B. GENERAL ION CURRENT EQUATION In view of the lack of an adequate:working theory which is applicable in the D- and lower E-regions of the ionosphere, the authors adopted an empirical procedure by using various collisionless theories that are directly applicable only to the upper portions of this flight, but which are being used for reducing the data for all the region above 80 km. The collisionless theory of moving spherical collectors has been discussed by various authors (Medicus,6 Kanal,7 Sagalyn et al 8 Nagy et alo,9 and Laframboise10). They derived the current collection characteristics of such moving probes by making a number of simplifying assumptionso The assumptions made by Kanal were as follows: 1o The sheath surrounding the moving spherical collector remains spherical; 2,. The velocity distribution of the ambient particles is Maxwellian;,. Electrons and positive ions are present in equal numbers; 4o The mean free path of the particles is large compared to the dimensions of the collector and the sheath; and 5o All ions reaching the collector are collected. A discussion of the above assumptions as related to our experiment will be given later. For now we present the equation of the general ion current to a moving spherical collector as given by Kanal7: Ii = JioA ( F(x) - ar2 H(i/2,x)] (10) 18

where ___1 1 F(x) = (X (x2 + )erf(xp(-) 2x 2 p(-x) -2H(yni/2,x) = erf(y2-x2 ( /2) erf(yy2+x) - erf( ) (+ yl/ x) exp {-(yl/2+x)2 (Y7/2+x) exp -(i/2-x)2 2 x 2x 2 r2 Y - a2-r2 a = sheath radius r = collector radius qV - kT A = collector area Jio = qNi 4kTi/2icmi is the random ion current density w 2 X = Co ~7 c0 = 48kTi/jmi is the average thermal speed of the ions w = vehicle or probe speed V = probe potential with respect to the ambient ionosphere Ti = ion temperature mi = mean ion mass k = Boltzmann's constant q = electronic charge Ni = ion number density The limits of F(x) and H(y71/2,x) as x - 0 are given by Eqs. (11) and (12), respectively; 19

Lim F(x) = 1 (11) x+0 Lim HE(yl/2,x ) = e72. (12) x+0 Substituting the results of Eqs. (11) and (12) into Eq, (10), the classical Langmuir1 equation for a stationary probe is obtained: Lim Ii = Jio A r)2 - a2ri exp(2 )j. (13) x+0 r2 e~p(-r', ~ (E3 Using the following typical daytime E-region parameters (Ti = 3000K, mi = 30) and taking the probe to'be at -4 v with respect to the ambient ionosphere a value of 154 is obtained for r. Since a is comparable in magnitude to r, we conclude that for the values of x encountered in flight, the second term in Eq. (10) is negligible compared to the first term, and so we can write Ii Jio A ) F(x).(14) The effect of the probe motion is accounted for by the term F(x) which is plotted in Fig. 11, C. SHEATH MODEL In order to calculate the ion density from Eq. (14) one needs to know the relationship between the sheath radius and the probe potential. For the condition when the dimension of the probe is much greater than the sheath thickness Bettinger and Walker12 obtained the following relations 1t/4 = () h/. (15) The above form was also derived by Hoegy and Brace5l3 with a somewhat different 20

VELOCITY CORRECTION FOR RANDOM ION CURRENT 100 10 1.0 2 fak8fkTj kT~ x = c= Io AqN 0 = — 0.1 1.0 10 100 /Co Fig. 11. Effects of probe velocity on the random ion current to a moving spherical Langmuir probe. 21

coefficient. Bettinger and Walker12 obtained the following relationship for the case when the sheath thickness is much greater than the radius of the collector. s2= o.8 r)/ h1/2 (16) where s = a-r is the sheath thickness h = 4/okT/q2N = 68.6 T/N is the Debye length Figure 12 is a graphical comparison of Eqs. (15) and (16) for N = 3x1011 particles per cubic meter and Ti = 300~K. The radius of the probe r, is 3.17 cm. From Fig. 12 at 4 v sl is 8.6 cm thus contradicting the requirement that s1 ~ r. The requirement that s2 be much greater than r is partially met. s2 was chosen as the appropriate sheath model for reasons to be discussed later. D. ION CURRENT EQUATION FOR DENSITY CALCULATIONS In the previous section we adopted s2 as the most appropriate sheath model. This sheath relation will be used in the rest of this report, so the subscript will be dropped from now on to simplify the notation. We defined, s = a-r, therefore, a = + 1. Substituting this to Eq. (14) we get: Ii = Jio A ( + ) F(x) (17) Employing the definition of h, Jio and the sheath model from Eq. (16) we can write: 22

u 20I I I Ti =300 K Nj =3X 101 (#/m3) SI 15 I 10 2 - -S2 V) Fig. 12. Graphical illustration of sheath thickness as a function of probe potentials for the two sheath models s1 and s2* 235

Ii = qA /kTi/2rTmi Ni 83 r11/2 68.6 TINi 68.6 4 Ti) + 1' F(x) (18) Introducing new symbols to denote the constants in Eq. (18) we obtain the ion current equation in its final form. = uNi [l + BNi 1/]2 F(x) (19) where = qA JkTji/'2mi = OO8f/2/r2/3 (eokTi/q2)1/324 24

IV. DATA REDUCTION AND RESULTS Ao FLIGHT INFORMATION AND TELEMETRY DATA The Langmuir probe system was launched at 12:16 PM CST on September 28, 1966 aboard Black Brant AC 17.604. The rocket reached an altitude of about 116 km. The system utilized two VCO channels operating at 30 KHz and 40 KHz as outlined in Section II-A. The entire system operated satifactorily after take-off; however, when the 30-in. boom and the radiometer doors were ejected, the signal from the 40 KHz channel became extremely noisy and intermittent. Common to both channels was a square wave modulation of the detector output with a period of 200 ms, which corresponds to the switching time of the standing wave impedance probe experiment. It was determined that this modulation was due to changes in the rocket equilibrium potential when the standing wave impedance probe switched from 3 MHz to 7 MHz at 100-ms intervals. The net result of the loss of data from the 40 KHz channel means that the 0.008 pA and 1.0 MA detectors provided no useful datao This is particularly unfortunate since reliable electron temperature information is contained in the 1.0 pA range detector. As it turns out from the data available, that this range also would have provided the most reliable ion current information for the entire flight with the exception of a 15-km interval centering around the 100-km level, This is because the 0.1 pA range suffered ion current saturation while the 15 pA range had poor resolution in the lower altitudes. The ion current saturation in the 0.1 pA range detector also introduces errors in the electron temperature derived from its output. The combination of telemetry interference 25

and ion current saturation resulted in only four electron temperature values being obtained, and even these the authors consider to be questionable. Figure 13 is a section of the telemetry data corresponding to the altitude of 109.5 km. In most circumstances the electron current is used to deduce the ambient charged particle density, because it is much less sensitive to probe orientation and velocity than the ion current, and also no assumption on the ion composition is needed. However, in this particular flight, the positive voltage of 2.5 v with respect to the rocket skin was not sufficient to drive the probe into the electron accelerating mode. Nagyl4 reported this to be due to the fact that the rocket body somehow assumed a more negative potential than anticipatedo The net result is that only positive ion saturation current, at -2.5 v with respect to the rocket skin, was measured, Figure 14 shows the average ion current as a function of altitude and the horizontal bars represent twice the standard deviation for the upleg data points. Because of increasing angle of attack past the apogee, the interpretation of downleg ion current in terms of positive ion density becomes very difficult; therefore, the downleg ion density is likely to contain significant errors. Bo ION DENSITY CALCULATIONS This section describes the calculation of ion density from measured ion current utilizing Eq. (19) and the velocity correction of random ion current from Fig. 11o The procedure of ion density reduction is given below..lo The measured ion current was first corrected for probe velocity effects using Eq. (19) and Fig. 11. This was dohe by recording the 26

CALR1 CALR r rbt ~~MRle MRle 30 KHz Channel CMR1 CMR CALR i; pz MR2e P1-I CMR2 rALR CMR2 / I J MR MR MR2i MRli MRli 109.5 km. JJJ IJ! IT IJJ^^^ 0.1 IA: Range 1; 15 PA: Range 2 CMR1: Range 1 common mode check CMR2: Range 2 common mode check CALR1: Range 1 calibration CALR2: Range 2 calibration MRli: Range 1 ion current measurement MR2i: Range 2 ion current measurement MRle: Range 1 electron current measurement MR2e: Range 2 electron current measurement Fig. 13. Section of Langmuir probe telemetry data. 27

AC 17-604 Fort Churchill,Canada 12:16 C.S.T. 110 September 28,1966 Down-leg-\ -- Up-leg 100 LdJ Q 90 80 0 0.1 0.2 0.3 0.4 0.5 0.6 ION CURRENT (MLA) Fig. 14. Average of measured ion current to the hemisphereical Langmuir probe vs. altitude. 28

value of I/Io for specified values of x and then dividing the measured ion current by this ratio to give an "expected true" ion current. This corresponds to dividing Eq. (19) by F(x). 2. Using the "expected true" ion current (measured ion current corrected for probe velocity effects) and denoted by Iit, and Eq. (19 we get: lit = aNi[1 + N/3]2 (20) The ion density was calculated by an iterative method. We first assume an ion density and evaluate the right hand side of Eq. (20). The result is compared with Iit and the value of the ion density Ni was considered acceptable when the two sides of Eq. (20) agree to within 1.0%. The ion temperature in the region 85-115 km is expected to be the same as the neutral particle temperature. Using the information given in the CIRA 1965 Model Atmosphere, 500~K was selected as an appropriate average value for the ion temperature, and was used throughout all the calculations. An ion mass of 30 was chosen for this region following the ion composition measurements of Narcisi and Bailey15 who reported the predominance of ions of mass 30+ and 32+ above 82 km. Using the chosen ion temperature of 300~K and mean ion mass of 30, we get a = 1.161x1019 and p = 1.155x104. Here we have taken the probe voltage to be -4 v with respect to the ambient ionosphere. This choice is supported by the rocket equilibrium potential measurements of Bettinger* employing the Hot Probe and Ulwick* using the Ion Trap, which showed that the vehicle *Private communications. 29

potential fluctuated about an average of -1.5 v with respect to the ambient ionosphere. For ion current measurement, the Langmuir probe potential was at -2.5 v with respect to the rocket. Therefore, the Langmuir probe potential is -4 v with respect to the ambient ionosphere. Table I shows the measured and expected true ion current and final ion density as a function of altitude. Figure 15 is a plot of ion density vs. altitude. Figure 16 is a comparison with the preliminary electron density profile obtained by Bowhill* from the CW Propagation experiment, and the electron density profile obtained by Ulwick et al.,6 with the standing wave impedance probe (SWIP). Note the change in density scale with reference to the Langmuir probe profile; this separation of the curves affords a better comparison of the three density results. C. ELECTRON TEMPERATURE As indicated in Section IV-A, the available data provided very little.information from which to determine the electron temperature. However, it was found that electron temperature reduction was possible from four probe characteristics. Reduction of the electron temperature follows the standard method by extrapolating the ion current and subtracting this from the total current. The resulting portion is the electron current. In the retarding region the electron current is governed by Eq. (21) Ie = Ieo exp qlV (21) The electron temperature Te is therefore given by: Te (V-Vi) (22) Te - k In(I2/I1) (22) *Private communications. 50

TABLE I LANGMUIR PROBE ION CURRENT, POSITIVE ION DENSITY VSo ALTITUDE (AC 17o6o4) Alt. Ii i it Ii Ni Ni (km) Up Down Up Down Up Down 76 oo004 Oo00179 1. 45x106 78 Oo008 Oo00376 L.29xo07 80 o 015 o 00711 8 95xlo7 82 Oo050 0o0146 5.55xlo8 84 Oo072 0o036o 5047x109 86 o.142 Oo078 0,o0736 0oo044 2 75x1010 7 x109 88 O~ 215 o0o98 Oo1120 Oo0510 6045xl10 1_2 xl1010 90 Oo290 0o125 Oo1576 Oo0679 1,22x1011 2 26x10 92 03590 Ool55 o21i79 o0o866 2.21xo011 5377x1010 94 o 48o 0 202 o 2759 Oo161 35 2x10 60 80x10o 96 Oo442 Oo255 o02600 Oo1500 5.02xlO11 1 15xlO11 98 Oo432 Oo303 0.2650 o1859 3,12xlO11 1.67x1011 100 0o455 03352 Oo2862 O.2088 3,555x011 2.06x011 102 O~o467 Oo345 o 3072 0 o2270 4005xl011 2 40xl011 104 Oo425 0.323 Oo2872 Oo2182 3559x1011 2.21xlO11 106 Oo580 0o312 Oo2714 0o2229 3526x1011 2o3 xl011 108 - 34o Oo5.33 Oo2500 O 2449 2o82xl011 2o 74x101 1 110 0o305 Oo328 025383 Oo2563 2.60x1l11 2,96x1011 112 0o286 0.510 0o25383 Oo 2583 2 69x1011.OOx1011 114 Oo274 o0285 0.2425 O.2522 2~67x1011 2~87x1011 115 0270 Oo 27O Oo 2512 Oo2512 2. 85x1011 2 85x1011 Ii = measured ion current (CpA) Iit ion current corrected for velocity effects (piA) o Ni = number of ions per cubic meter, 51

120 111111 I I I I III" I I I, III[ I I I, III,, I I I II'I[, I I i 1, AC 17-604 Fort Churchill, Canada I I0 12:16 C.S.T. September 28,1966 E 100 / Down o - H- 90 / h]~~ <"^^^ ^-~~~~Up 80 70 106 107 108 109 i00 1012 ION DENSITY(PER M3) Fig. 15. Final positive ion density vs. altitude.

115 AC 17-604 0 0 0 LANGMUI 0 P Fort Churchill,Canado o \ PROBE 110 12:16 C.S.T. 000 I S.W.I.P. Up-leg September 28,1966 o (Electron 00o \ Density) 00 0 0 105 0 - o \- I __ ~~~~~~~~~~0 PROPAGATION 0 o ~Up-leg 0 100^~~~~,^Electron Density\ 00 Down-leg 100 k Up-leg 00 Q Preliminary 0 1- 0 h- 95 o \00 i - DENSITY SCALE CHANGE 0 (S.W.I.P))XIO o10 0 (PROPOGATION) X 10 0 o I 90 0 0 0 0 doo^ ^^ 85 0 GO 0 80 108 109 10 ~ 10" 12 ION DENSITY (PER M3) Fig. 16. Comparison of charged particle density results.

The four electron temperatures are listed in Table II TABLE II ELECTRON TEMPERATURE VS. ALTITUDE (AC 17.604) Altitude (km) 109 105 100.3 94.5 Temperature (~K) 1007 1226 1553 1510 The above values compare favorably with the electron temperatures obtained by Ulwick et al.1 54

V. DISCUSSIONS AND CONCLUSIONS The result of the ion density calculation depends on the proper choice of a sheath model for the hemispherical Langmuir probe. At -4 v the sheath thickness s1 is greater than the probe radius; this clearly violates the assumption for this model which requires that r be much greater than a. On the other hand, at -4 v S2 partially meets the requirement that a be much greater than r. The final ion density using s2 as the sheath model, shows general agreement with the electron density profile from the Standing Wave Impedance Probe and the CW Propagation experiment above about 90 km. This indicates that s2 is the more appropriate sheath model for the hemispherical Langmuir probe described in this report. The region of applicability of the collisionless theory and the assumptions made by Kanal to obtain his equations will now be briefly discussed. The assumption of a spherical sheath for a sphere moving at supersonic speeds in a medium of relatively high neutral particle density is certainly questionable for the general case; however, the sheath distortion around a moving hemisphere should not be too severe for small angles of attack. Assumptions (2) and (3) given in Section III-B are believed to be satisfied at altitudes above about 85-90 km. The most significant assumption which establishes the low altitude limit for the equations used is the requirement that the mean free path be large compared to the sheath dimension. The mean free path (L) in Table III is for neutral particles and was taken from the U.S. Standard Atmosphere 1962; although the ion-neutral collision frequency differs from that of the neutral35

neutral collision frequency, the latter is sufficient to provide an approximate indication of the region where the collisionless theory is applicable. The variation of the sheath dimension is also given in Table III, and it shows that the sheath is about the same length as the mean free path around 96 km. Shulz and Brown17 used the criterion of "ten collisions" in the sheath for a collision dominated probe; this condition occurs just above 85 km. Table III further shows that above 100 km the collisionless theory is applicable. It seems therefore the equations obtained from the collisionless theory could be used down to about 95 km. TABLE III POSITIVE ION DENSITY, SHEATH THICKNESS, SHEATH RADIUS, AND MEAN FREE PATH VS. ALTITUDE Alt. (km) Ni(#/m3) s(cm) a(cm) L(cm) L/a 80 9x7 x107 80.0 83.17 0.407 0.0049 85 1,44x001 15.1 18.27 1.201 0.0657 90 1.23x1011 7.4 10.57 2.563 0.242 95 3.40xlOll 5.27 8.44 6.705 0.794 100 3.55x1011 5.19 8.36 16.29 1.950 105 3.52xl01 5.20 8.37 38.10 4.550 110 2.60x1011 5.76 8.93 81.5 9.130 115 2.85x011 5.58 8.75 171.9 19.65 The charged particle density results obtained from the various experiments were compared in Fig. 16. Above 92 km, there is reasonable general agreement; however specific differences as great as a factor of 1.5 up to about the 110km level are present. Above 110 km the SWIP results decreased while the electron density from the propagation experiment shows an apparent increase. It is interesting to point out that the Langmuir probe ion density profile fall in 56

between the two electron density results above 92 km. The rapid decrease in the positive ion density below 92 km suggests the breakdown of the collisionless theory from which the results were obtained. The few electron temperature values obtained from the Langmuir probe also show reasonable agreement with those obtained by Ulwick et al. We therefore believe that such a hemispherical nose tip Langmuir probe is capable of providing reliable electron temperature, electron and ion density information above about 95 km. Below this altitude the Langmuir probe can be used to obtain an indication of the charged particle density variation with altitude. 37

ACKNOWLEDGMENTS The authors wish to extend their appreciation especially to T. B. Lee and Don Crosby for their work in the design, construction, and testing of the Langmuir probe system; J. C. Pearl and Dr. E. G. Fontheim for valuable discussions on the theoretical aspects. 38

REFERENCES 1. Burt, Do Ao "Rocket Instrumentation for Auroral Measurement —-Black Brant AC 17,604," Scientific Report No, 7, Contract No, AF 19(628)4995, AFCRL 67-0295, University of Utah, March 1967. 2. Pearl, Jo Ca "Studies Toward Development of a D-Region Probe," Final Report, ORA Noo 05235-1-F, Space Physics Research Laboratory, University of Michigan, 1965O 30 Smith, Lo Go "Ionization by Lyman-a in the E-Region at Sunrise," Jo Atmoso Terr, Physo 28, 11.9, 19660 4I Balmain, Ko GC "Plasma Probe Studies," Aeronomy Report No, 11, University of Illinois, May 1, 1966o 5o Su, Co Ho and Ain Ao Sonino "Theory of Electrostatic Probe in a Moderately Ionized Gas," Physo Fluids 8, 124, 1967o 60 Medicus, Go "Theory of Electron Collection of Spherical Probes," Jo Applo Phys, 32, 2512, 1961, 7~ Kanal, M, "Theory of Current Collection of Moving Spherical Probes," Scientific Report No, JS-5, ORA Noo 03484, 03599-9-S, Space Physics Research Laboratory, University of Michigan, 1962, 80 Sagalyn, Ro Co, Mo Smiddy, and J. Wisniao "Measurement and Interpretation of Ion Density Distribution in the Daytime F-Region," J, Geophyso Research 68, 199, 19635 9, Nagy, A, Fo, Lo Ho Brace, Go Ro Carignan, and Mo Kanal, "Direct Measurements Bearing on the Extent of Thermal Non-Equilibrium in the Ionosphere," J, Geophys, Research 68, 6401, 19635 10 Laframboise, Jo Go "Theory of Spherical and Cylindrical Langmuir Probes in a Collisionless, Maxwellian Plasma at Rest," UTIAS Report No, 100, University of Toronto, 11o Mott-Smith and I, Langmuir. "The Theory of Collectors in Gaseous Discharges," Physo Rev, 28, 7279 1926o 12, Bettinger, Ro T, and E, H, Walker, "Relations for Plasma Sheaths about Langmuir Probes," Physo Fluids 8, 748, 1965o.39

13. Hoegy, W, R. and L. H. Brace. "The Dumbell Electrostatic Ionosphere Probe: Theoretical Aspects," Scientific Report No. JS-1, ORA No. 03599-5-S, Space Physics Research Laboratory, University of Michigan, 1961. 14o Nagy, A. F. "Measurement of Charged Particle Parameters in the Lower Ionosphere," Status Report No. 3, ORA No, 07084-3-P, Space Physics Research Laboratory, University of Michigan, 19660 15. Narcisi, Ro So and Ao Do Bailey0 "Mass Spectrometric Measurements of Positive Ions at Altitudes from 64 to 112 km," J, Geophys. Research 70, 3687, 1965. 16o Ulwick, Jo CO, Wo Pfister, and Ko Bakero "Results of Rocket Experiment in Auroral Absorption Events," Presented at the Eight COSPAR international Space Science Symposium. Also to be published in Space Research, Volo 80 17. Schulz, Go Jo and So Co Browno "Microwave Study of Positive Ion collection by Probes," Phys. ReVo 98, 1642, 1965, 40

APPENDIX ELECTRONIC SYSTEM TEST AND EVALUATION DATA

ELECTROSTATIC PROBE ELECTRONICS UNIT NO. 17.604 PURPOSE: Charge particle parameter measurement. SENSITIVITIES (F.S.):.008 iA; 1.0 pA; 0.1 pA; 15 pA NUMBER OF: DETECTORS 2, PROBES 1, OUTPUTS 2. POWER REQUIREMENTS: 28 volts; 2o94 watts HI AV: Mago + 2o5 to -2 5 v, dV/dt 10 v/sec Output Impo 500 Q LO AV: Mag. + N/A to - N/A v, dV/dt N/A, Output Impo N/A Q Period: 495 sec. Monitor Output Imp. 33 K 2 ELECTRICAL CHARACTERISTICS OF DETECTORS DETECTOR #1: Range 1: o008 iA (FoSo), dE /d.I 300 v/pA, Input Imp. 30 K Q Range 2: O10 A (F.S.), dEo/dIin 4~O v/pA, Input Imp. 400 Q Voltage Ration of Range I/Range 2 84.25 Output Imp. 2 K 2, Limited at -.5 + 5o5 v. CaLibration Resistance 25 Meg, 2 Megr. DETECTOR #2: Range 1 ol A (F.Ao), dEo/dIin 25 v/pA, Input Imp. 2.5 K 2 Range 2 -15 pA (FoA.), dEo/dlin 33 v/pA, Input Imp. 533 Ratio of Range I/Range 2 7ol Output Imp. 2 K 2, Limited at -o5 + 5o5 vo Calibration Resistance 25 Megro 2 Meg, TIMERS: MASTER: PERIOD 500 M and 25 M SEC IN SYNC. WITH N/A RANGE: PERIOD 500 M and 50 M SEC TRIGGERED BY FF #2 DETECTOR~ PERIOD 100 M and 1 SEC CALIBRATION: ON: 100 M and 1 SEC INTERVALS: 100 M SEC PROBE: PERIOD N/A SEC IN SYNC. WITH N/A 42

Unit No: 17.604 Date: 10/21/65 Sensitivity:.008, 1.0, o100, and 15 t a Checked by D. F. CROSBY Source Voltage and Current: 28 v and 105 MA At Ambient: Full Scale Output: 5.50 volts AVo/AIin: Det #1 3.6 and, 30355, Det #2 0.31 and, 2.2 volts/pA Range Period: 50 Ms and 500 Ms Calibration Period: 100 Ms and 1 sec Ratio of Hi to Lo Current Ranges: Det #I 125, Det II 150 Det #1 Det #2 Temp C Output A/ Bias Output' Bias Volts dO in Level Volts o in Level I II I II I II I II I II I II 25 5.50 5-50 303-5 3 26 2668 0 5-50 5.50 22.75.31 2.68 0 FLAGS: Range 1 (Hi.S) 2, Range 2 (LoS)O Output Imp. 47 K DET #1 2 DET #2 0 Output Imps 47 K HI AV N/A, LO AV N/A Output Impo N/A SIZE: 3" Dia 16-13/16" long WEIGHT: 4767 GRAMS (10.5 lb incl. cable) 45

AV PERFORMANCE DATA Unit No. 17.604 Date 10/21/65 Checked By D. F. Crosby At Ambient: Magnitude: + 2.5 v to -2.5 v Period: 495 M/sec Slope: HI 10 LO N/A slope, v/sec Temp. Period Magnitude ~C Milli Sec. +v -v HI LO 25 1495 2.5 2.5 10.1 v/sec -15 476 2.3 2.5 10.25 v/sec 50 489 2.42 2.4 9.5 v/sec 25 25.5 2.5 2.5 -15 24.5 2.5 2.45 square wave 70 27 2.46 2.5 44