IEEE Ttan actionz on NUcteoa Scentce, Vot. NS-25, No.4, Augwust 1978

DEFINITION OF THE LINEAR REGIONOF X-RAY -INDUCED CABLE RESPONSE*

Charles E. Wuller, L. Carlisle Nielsen, and David M. ClementTRW Defense and Space Systems GroupRedondo Beach, California 90278

Abstract

Cable response to X-rays is linear with incidentfluence, provided the deposited charge in cable dielec-trics is directly proportional to the X-ray flux. Toestimate the level at which the linear region ends, wediscuss three nonlinear processes that modify the de-posited charge profile in a hypothetical cable model:field-limiting in vacuum gaps, ionization effects inair-filled gaps, and radiation-induced dielectric con-ductivity. The exact level at which limiting of theNorton driver in an elemental length of cable beginsdepends on the cable geometry and the X-ray source.Estimates of the onset of nonlinearities caused byfield-limiting and by dielectric conductivity are foundin terms of cable and source parameters. With air-fil-led gaps,the Norton driver is always nonlinear. In ad-dition to limiting of the Norton drivers, the load re-sponse of a long cable may be limited because propa-gating currents are attenuated by the induced conduc-tivity of the bulk of the dielectric.

section of cable depends on the response of the entirecable including its loads, even in the case of losslesstransmission lines.

The exact value of flux at which nonlinearitiesbegin depends on the mechanism and on the constructionof the particular cable,e.g., gap size, dielectric ma-terial and so forth. Our approach in what follows isto define a hypothetical cable with the characteristicsof braid-shielded cables found in satellites or missiles.Then, we predict the short circuit current per unitlength of cable as a function of flux including eachlimiting effect, one at a time. We will identify sen-sitivity parameters that affect the onset of each pro-cess. Following that we will discuss transmission linesthat are simultaneously lossy and driven by nonlinearcurrents. The models we present will be reduced toequivalent-circuit models that can be easily evaluatedwith a circuit analysis computer program.

Definition of Cable and X-Ray Source Parameters

Introduction

The voltage and current responses of a cable toX-rays are linear with incident photon fluence, provid-ed that the cable loads and cable impedance are time-independent, and that the photon-electron transport isnot field-limited. When these conditions do not obtain,the response is sublinear with fluence, and it is ofinterest to determine both the limiting effects respon-sible for this nonlinear behavior as well as the break-point between the linear and nonlinear regions.

The problem of determining the response of a cableto X-ray photons divides naturally into three parts:(1) determining the deposition of charge in cable di-electrics (solving the electron-photon transport prob-lem); (2) determining the induced current (solving forthe Norton-equivalent drivers); and (3) determiningthe response of cable loads (solving the transmissionline equations). The execution of the first two stepsis implicit in the operation of the present generationof cable response codes.1'2 The third step has beeneither simulated with a lumped element equivalent cir-cuit3 or solved directly, for example, by finite dif-ference techniques.4 The Norton drivers, which rep-resent the input to the transmission line equations,are linear as long as the deposited charge is directlyproportional to the X-ray flux. This is true whencharge transport is completely determined by the stop-ping power of cable materials. However, as the X-rayflux increases, other processes begin to modify thedeposited charge profile. In this report we will dis-cuss three of these nonlinear effects. The first two,field-limiting in vacuum gaps and ionization effectsin air-filled gaps, occur because gaps are commonlyfound in braid-shielded cables. The third effect, ra-dation-induced dielectric conductivity, is responsiblefor both limiting of the drivers and propagation lossesin the cable itself. In principle, the calculation ofa nonlinear driver and the solution of the transmission-line problem are coupled. This is so because gap ef-fects are voltage-dependent and the voltage in a given

Manuscript received July 30, 1977.

*Work supported by the Defense Nuclear Agency underContract DNA001-77-C-0084

In this section, we define a hypothetical cable aswell as the X-ray environment normally incident upon it.The cable is assumed to be a 50-Q coax with an innershield radius, an outer conductor radius, and a shieldgap of 0.1, 0.0299, and 0.005 cm, respectively. Theconductors are copper and the dielectric is Teflon.Then, the total capacitance and inductance per unitlength for the cable are 92 pF/m and 0.24 mH/m, and thepropagation velocity is 0.69 times the speed of light.

The X-ray environment is specified to be mono-energetic 50-keV photons whose total fluence is a pa-rameter to be varied. We assume a triangular pulsewaveform whose full-width-half-maximum is 10 ns. Hold-ing the pulse shape constant implies that fluence andflux, and dose and dose rate, are proportional.

In vacuum the replacement current, or image cur-rent, tends to be proportional to the size of the gapsin the cable.1 This is true because the response isproportional to the distance the electrons emitted fromeach conductor travel; and since electron ranges in di-electrics are usually much less than gap sizes, the gapcontrols the response. Therefore, in this sample prob-lem we ignore charge at the center conductor/dielectricinterface (where there is no gap) and take the direct-injected current source to be emission from the shieldwhich is deposited on the dielectric surface. The peakmagnitude of the emission current source Jp is taken as1600(A/m)/(cal/cm2), which is based on average emissionefficiencies for copper from Dellin and MacCallum,5 anda 10-ns pulse risetime. Then, the emission current Jas a function of time is

J = J h(t), (1)

where h(t) is the envelope of the radiation pulse whosevalue at the peak of the pulse is unity. As a check weexamine the linear short circuit current caused by thissource for a braided coax cable in vacuum. The emis-sion current is weighted by the ratio of the total ca-pacitance C to gap capacitance C

C J = 140 A/mC9 p cal/cm (2)

0018-9499/78/0800-1061$00.75 ( 1978 IEEE 1061

Multiplying by the pulse width of 10 ns yields a nor-malized response (charge transfer per unit length perunit fluence) of 1.4 x 10-8 C-cm/cal, which is consis-tent with both analysis and experiment.1

Field-Limiting in Vacuum Gaps

Consider the equivalent circuit for a section ofcable given in Fig. 1. The current driver Jt shownthere represents transmitted charge across the shieldgap which charges up the gap capacitance Cg. But thetransmitted current Jt establishes a retarding elec-tric field which opposes the motion of subsequentlyemitted electrons. To estimate the fluence at whichelectrons will be stopped and returned to the emittingsurface, thus limiting response, we set the gap poten-tial energy at the end of the pulse equal to the meaninitial energy of created electrons E,

e V = E, (3)

where e is the electronic charge and V is the_gapvoltage. For the 50 keV X-rays assumeg here, E forcopper equals 1 42 keV (Ref. 5). In the open-circuitlimit, the total charge Qt crossing the gap is equalto the integral of the emission current

Q F J AtE t C (4)

g g

where F is the fluence level, and At is the full-width-half-maximum of the triangular pulse. Then, the onsetof field-limiting will occur at a fluence

E CF = -s-- (5)e J At

p

When this expression is evaluated, using the param-eters from the last section, it corresponds to -2.5cal/cm2. The expression indicates that - on accountof the field-limiting effect - the upper bound of thelinear regime decreases as the electron spectrum soft-ens, as the gap thickness increases, and as the emis-sion yield increases.

are short compared with typical pulse lengths, we seeka nonrelativistic steady state result dependent on theinstantaneous gap voltage and on the photo-emissionenergy distribution. Since the circumference of a gapis much greater than its width, we approximate the sys-tem by a planar diode. Then, the electron distributionfunction f(x, v) is given by the Vlasov equation

af afv -f + a -f = 0ax 3v (6)

where the deceleration from the field buildup in thegap is

-e Va = m

m d (7)

where m is the electronic mass, and d is the gap width.This expression ignores space charge interactions inthe gap. From the theory of quasilinear partial dif-ferential equations, total energy

mv2 axu = 2 m ' (8)

is a constant of the motion in Eq. (6) and any functionof u is a solution of Eq. (6). We can construct thesolution for the diode region 0 < x < d subject to theboundary conditions that the distribution function atthe emitting surface f(x = 0, v > 0) is known and thatall particles reaching the other side have positivevelocities f(x = d, v < 0) = 0. The first moment ofthe distribution function is the transmitted current.After transforming to the energy variable and defininga normalized energy distribution of emitted electronsn(E), we get

Jt = Jp h(t) | n(E) dE. (9)g

The emission energy distribution could be found indetail from analytic transport theory or Monte Carlocalculation; however, for this illustration, we take aresult from the simple X-ray - induced emission theorygiven by Schaefer.6 The differential energy yielddY/dE at normal incidence is approximately

3-z 10w

U

2-O 10

uJ

LU,

w

x -

0r1-4C,m

0

mmI-m0-4

1o-1 1FLUENCE (cal/cm2)

Figure 1. Response as a function of fluence of a unitsection of cable including field-limitingof electron emission into the gap

An analytic expression for the current transmittedacross the gap Jt can be obtained by starting with theVlasov equation (the collisionless Boltzman transportequation). Because electron transit times in a gap

dY/dE = 4i (dE/dx) (10)

where pi is the linear absorption coefficient at theincident X-ray energy for interaction with the ithelectron shell and dE/dx is the electron stopping power.Now it is known that the electron range varies roughlyas E2 for a number of materials. Thus, the stoppingpower and the differential energy yield should vary as

E and dY/dE is proportional to E. This approximatelylinear energy variation has been observed both inMonte Carlo calculations and in experimental results.The use of a roughly linear energy spectrum appearsjustified as long as photon energies are not too near

absorption edges and the Compton contribution is ignored.Figure 2 shows the distribution used in this calculation.We assume that the lower bound of the distribution is1 keV.

The peak short circuit current will be sublinearwith respect to fluence when the integral in Eq. (9)becomes less than unity. Figure 1 shows the responsesvs fluence of a unit section of cable driven by thefield-limiting source. The breakpoint between thelinear and nonlinear parts of the current plot is closeto the 2.5 cal/cm2 level estimated above. The energy

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delivered to a l-Q load between the shield and centerconductor is also given in the figure. (One ohm isessentially a short circuit compared with the capaci-tive impedance.) Also plotted is the voltage built upacross the dielectric layer, which is equal in magni-tude to the voltage across the gap because of the shortcircuit condition. The potential saturates at 42 kV,the voltage required to reduce the transmitted currentto zero. Note that this implies an electric field of6 x 105 V/cm in the dielectric. This field is morethan twice the rated strength of Teflon (2.4 x 105 V/cm), although less than that of Kapton (2.8 x 106 V/cm), which is the strongest of dielectrics used in ca-bles. This suggests that there may be combinations ofenvironments and cable types for which dielectricbreakdown could occur. Further investigations of sucha possibility are anticipated with the use of our de-tailed cable code.

n (E)

1 EENERGY (keV)

Figure 2. Assumed differential energy spectrum ofelectron emission from the cable shield

In Fig. 1 and similar figures that follow, trans-late the abscissa from fluence to peak flux, dose, andpeak dose rate using the conversion factor 1 cal/cm2corresponds to 108 cal/cm2 * s, 105 rad(Si), 1013 rad(Si)/s. Note that this is incident energy.

The time history of the short circuit current istriangular and identical to the X-ray pulse shape inthe linear regime. With the onset of limiting, thelatter part is clipped off and the pulse gets progres-sively narrower with increasing fluence. Figure 3shows that the current waveform changes abruptly be-tween 1 and 10 cal/cm2. The triangular shape at 1cal/cm2 shows that response was still linear at thislevel.

i-

zw

0 1 cal/cm2

3 cal/cm2cc 0.50X

N

0z210 cal/cm2

0 10 20TIME (ns)

Figure 3. Normalized short-circuit current waveformsat three fluence levels showing the effectof field-limiting in the gap

Ionization Effects in Air Gaps

When an air-filled cable gap is irradiated by X-rays, ionization of the air results in a secondary con-duction current that tends to mitigate the primaryphoto-Compton current emitted from the metal surface.To include the air conductivity effect, we will calcu-late the radiation-induced transient air conductivityof the gap and translate this into a time-dependentshunt resistance

Ra = C /Cg a(t), (11)

which is then inserted into the cable equivalent circuitshown in Fig. 4. The conductivity is calculated bysolving air-ion rate equations for the concentrationsof secondary electrons, and generic positive and gener-ic negative ions. The coefficients such as attachmentrates, recombination rates, etc., which enter the rateequations, and the particle mobilities are functions ofthe electric field in the gap. Thus, the conductivityis coupled to the rest of the circuit through the in-stantaneous gap voltage.7

I-

zw:

0

C.)I-

GW0I

w0L

mzm

0

r-0

FLUENCE (cal/cm2)

Figure 4. Response as a function of fluence of a unitsection of cable including transient con-ductivity in the air-filled gap

The dose rate in air at 1 atm of pressure, whichis required in the conductivity calculations, is 1.8 x1013 (rad(air)/s)/(cal/cm2) and includes energy losscontributions from the primary electrons crossing thegap. The short circuit current is shown in Fig. 4 asa function of fluence, from 10-3 to 102 cal/cm2. Theresponse is always nonlinear in this range. Figure 5shows the characteristic bipolar signal of the air gapcable response. This shape can be explained as follows.The emission current source transfers charge across thegap. Charging continues until the electric field andthe conductivity in the gap have built to the pointwhere the secondary electron current can compete withthe emission current and discharge the potential builtup during the first part of the pulse. The dischargeleads to the sign reversal in the current. As fluenceincreases, the time required for the secondary currentto become comparable to the emission current decreases.This trend can be seen in the current waveforms at 10-3and 10-1 cal/cm2 given in Fig. 5. Above 10-1 cal/cm2the current spikes are very sharp, occuring in the firstfew nanoseconds of the radiation pulse, and the shortcircuit current remains near zero for the rest of theevent. Now, returning to Fig. 4, the magnitudes of

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both peaks in the short circuit current have been plot-ted along with the energy that would be delivered to al-Q load. The dependence is sublinear with fluencethroughout the range examined.

It should be pointed out that a conductivity pic-ture of air ionization is appropriate only as long asthe motion of the secondary electrons and ions is com-pletely specified by their mobilities. At low pres-sures, this is no longer true, and a coupled solutionof Poisson's equation and the equations of motion forparticle dynamics is required. This has been consid-ered by Wuller in one dimension (radial) for coaxialcables.8 For a cable with a 0.01-cm gap the transi-tion from air-like to vacuum-like response was foundto occur near 0.1 atm.

1.0

z

0.5 10 3 cal/cm2

F O0

N

-0.5

0z

TIME (ns)

Figure 5. Normalized short circuit current waveformsat two fluence levels showing the effectof ionization in an air-filled gap

Radiation-Induced Dielectric Conducti

Ionization of the cable dielectric can have a

shunting effect on the direct-injection current result-ing from radiation-induced conductivity. This conduc-tivity, in general, has prompt and delayed parts,

a() =K D(t) + KIt LW) exp[-(t-t')/-]dt'. (12)

Cc: pd0 0

The dose rate is found from the peak dose rate, D(t) =

Dp h(t), and K,, Kd, A, and T are empirical parametersdetermined from short pulsed irradiations.9 For Teflon,K and Kd are 1.1 x 10-5 (mho/F)/(rad/s) and 280 (mho/F) /(rad), A is 1, and T is 216 ns. Weingart, et al.,10and Sullivan and Ewing1l agree on the prompt coefficientfor Teflon; however, Sullivan and Ewing do not reportdelayed conductivity data. In the rest of this section,we assume that the transient dielectric conductivity isentirely prompt. Then, the transient resistance perlength for a uniformly irradiated dielectric region hasthe form

R = l/K Dph(t) C, (13)

where C is the capacitance per length of the region.

into the dielectric. The peak dose rate in the bulkof the Teflon Dpb is 9.8 x 1011 (rad/sec)/(cal/cm2).Assuming that energy is uniformly deposited by elec-trons stopping in the dielectric, the dose rate in thestopping region Dpe will be enhanced by a factor E ofabout 50 times the bulk dose rate. Figure 6 shows thecable equivalent circuit containing shunt resistancesin the dose-enhanced and bulk regions. In the shortcircuit case

e b

and the node equations for this circuit

and

(14)

dV VI = j+ Ce e + eSc = dt R

e

dV VI = C b bsc b dt Rb '

(15)

(16)

can be solved for the short circuit current Isc' sub-ject to the condition that both the current source andthe inverse of the resistances (conductances) have thesame time history, i.e.,

J = JR = constant.R1

The result for the short circuit current is

= J h(t)[ lSC 1 + (D C /D C)pe e pb b

+ J h(t) 1 1

lea, (17)P l + (C /C) l + (D C/D C)

Lee pb b

where

K (D C + D C tp pe e pb bJ h(t') dt'.

e b Jo

This expression will be useful for explaining our re-sults. Note that the first term follows the radiationpulse, while the second damps out as a function of ac-cumulated dose.

We should see evidence of dielectric conductivity,i.e., the onset of limiting, when the discharging timeof the enhanced region capacitance through its shuntresistance is comparable to the full-width-half-maximumof the X-ray pulse

(18)R C At.e e

With the use of Eq. (13) to evaluate R at the peak of

the pulse, then

l/K D = At. (19)p pe

Note our definition of the enhancement factor is suchthat Dpe = i Dpb. Relating Dpb to the total nonenhanc-ed dose Db via Db = Dpb At, we obtain

To illustrate limiting due to dielectric conduc-tivity alone, we revise our model cable, eliminatingthe gap. Assuming that the gap has been filled withTeflon, the shield emission current will penetrate oneelectron range (X7.5 x 10-4 cm for 42 keV electrons)

(20)Db = l/EKP.

1064

For Teflon, this corresponds to 2 x 103 rad in thebulk of the Teflon or -0.2 cal/cm2 incident.

10' 1FLUENCE (cal/cm2)

of the driver in each elenental section.

1.0

zwcccc

D -~~~~~~~~i2

05

(0 .

0wcN

a:

0z

TIME (ns)

Figure 6. Response as a function of fluence of a unitsection of cable including transient di-electric conductivity in the enhanced andbulk regions

Figure 6 shows our data for the response of thecable section obtained by evaluating the equivalentcircuit over a range of fluences. Above 2 cal/cm2 wehave plotted the magnitudes of both current peaks thatare visible in the current waveforms. Figure 7 com-pares the current waveforms at three fluence levels.From the linear (triangular) shape at 10-2 cal/cm2,the current peak narrows and moves away from the peakof the photon pulse. The second term of Eq. (17) dom-inates the waveform except at very high fluence (10cal/cm2), when it appears as an initial spike on topof the term proportional to the X-ray pulse shape. Re-turning to Fig. 6, note that the break between thelinear and nonlinear regimes occurs at a few tenths ofone calorie per square centimeter, agreeing with ourprediction. Also shown on this figure are the energyin a l-Q load and the voltage developed across the en-hanced region. The voltage saturates at a value cor-responding to an electric field of 2.6 x 105 V/cm. Asin the field-limiting case, the field in the dielectricexceeds the strength of Teflon (2.4 x 105 V/cm). Itis, however, not clear that dielectric breakdownstrengths have any meaning when the material is highlyconductive.

Lossy Transmission Lines

Consider a long cable which is uniformly irradi-ated along its length. Now it is clear for the vacuumand air gap cases that the limited driver, i.e., theshort circuit current in an elemental section of cable,is coupled through the gap voltage to the solution ofthe rest of the cable equivalent circuit. In the ab-sence of direct numerical techniques for the solutionof the transmission line equations with nonlineardrivers, one can simulate a long cable by repeatedlumped element sections in a circuit analysis code.When the cable is long compared with the distancetraveled by a signal for the duration of the pulse,we will see a broadening of the load current waveformbecause of the staggered arrival times of current fromdifferent sections of the cable. The gap voltages,and thus the drivers, are dependent on cable lengthbut any nonlinearity is associated with the limiting

Figure 7. Normalized short circuit current waveformsat three fluence levels showing the effectof transient dielectric conductivity

We wish to distinguish this situation from propa-gation losses in the cable itself. Dielectric conduc-tivity provides a shunt path throughout the dielectricvolume which is at least as big as the conductivitydue to X-ray dose rate in the bulk of the dielectric.In this situation, as the driver from one point in thecable propagates down the line, it is further dissipat-ed in the bulk conductivity of the rest of the cable.

To illustrate propagation losses in the load re-sponse of a long cable, consider a 20-m gapless cablemade of repeated sections whose equivalent circuit isanalogous to that in Fig. 6, along with an appropriateseries inductance. The cable is terminated at bothends in a matched 50-a load. The load response as afunction of fluence will include the effects of bothlimiting of the driver in each section and dissipationalong the length of the cable from dielectric conduc-tivity. The qualitative features of the response ofa short 1-m cable vs the response of the 20-m cablecan be seen by comparing Figs. 6 and 8. The break-point between the linear and nonlinear regimes occursaround 0.1 cal/cm2 for either length. Peak currentand load energy in the 20-m case increase very slowlyin the limited regime. Long cable response in Fig. 8has nearly saturated compared with similar curves inFig. 6 which show a steady but sublinear increase inthe response in the limited regime. Data are shown inFig. 8 for two treatments of the conductivity. Thesecorrespond to using the expression for conductivitygiven in Eq. (17) with and without the second term,i.e., delayed conductivity. Accounting for delayedconductivity does not affect the peak load currentbut it does decrease load energy by a factor of about5. This difference in energy is explained by the factthat with prompt conductivity only, the cable returnsto the lossless state at the end of the pulse; butwith delayed conductivity, energy continues to be dis-sipated in the cable as the signal propagates to theloads after the pulse is over. Furthermore, it wasonly in this 20-m cable including delayed conductivitywhere we saw a response-vs-fluence plot that did notincrease monotonically. The slight dip in energy

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centered at 6 cal/cm2 was present in our calculations.We speculate that some other choice of parameters wouldalter the magnitude of the dip, or eliminate it. Fur-ther study is indicated to quantify the situations un-der which response might decrease with increased flu-ence.

02 --102102

20-m CABLE WITHMATCHED LOADS

_ 10 10

z ~~~~~~~~~~0w>mz

1 m

CONDUCTIVITY-O / @ CURRENT: PROMPT OR

PROMPT + DELAYED

Xi 10 1 _ 0// *ENERGY: PROMPTONLY 10-_ ENERGY: PROMPT+ DELAYED

10-2 10-210 3 10i2 1o0- 1 10 1o2

FLUENCE (cal/cm2)

Figure 8. Load response of a 20-m cable as a functionof fluence, comparing the effect of delayedconductivity

In Fig. 9, several load current waveforms areshown. At 0.01 cal/cm2 in the unlimited region, thecurrent has the broadened shape characteristic of apropagated signal. Of course, the shape is the samewith and without delayed conductivity. At 10 cal/cm2in the limited region, delayed conductivity almostcompletely attenuated current from points far awayfrom the end of the cable. The reflection apparent inthis waveform is characteristic of an open circuit atthe other end of the cable. This can be explained be-cause the shunt impedance presented by the delayed con-ductivity lowers the cable impedance below that of theload (50 Q). Thus, the other end looks like an opencircuit.

uiI-

z0-iawN-i

0z

TIME (ns)

Figure 9. Comparison of normalized load current wave-forms for 20-m cable at two fluence levels,showing the effect of limiting by promptand delayed conductivity in the dielectric

Conclusions

We have examined three processes that can causethe X-ray -induced response of a shielded cable to benonlinear with fluence. The level at which the linearregion ends and the nonlinear region begins depends ondetails of the particular cable geometry and materialsand or the X-ray environment. Estimates for the levelat which limiting attributable to each process beginsfor short cables with short circuit loads are as fol-lows.

Field-Limiting in Vacuum Gaps: Limiting dependson the average electron energy, the emission currentper unit length per unit fluence, and the gap geometry

E CF = -eJ -t (cal/cm2).

p

Ionization in Air-Filled Gaps: At one atmosphereof pressure, air conductivity leads to nonlinear re-sponse at all fluences considered (>10-3 cal/cm2).

Radiation-Induced Dielectric Conductivity: Lim-iting depends on the coefficient of prompt conductivityand the dose enhancement factor

D = 1/f K (rad).b P

In addition to the limiting observed in the shortcircuit current, load response is further limited bythe dielectric conductivity of the bulk of the cable.Propagation losses occur through this shunt as signalstravel down the cable to its loads. Moreover, delayedconductivity (when present) greatly reduces load re-sponse.

References

1. D. M. Clement, C. E. Wuller, and E. P. Chivington,IEEE Trans. Nucl. Sci. NS-23, 1946 (1976).

2. W. L. Chadsey, B. L. Beers, V. W. Pine, andC. W. Wilson, IEEE Trans. Nucl. Sci. NS-23,1933 (1976).

3. L. C. Nielsen, et al., "SGEMP Environments Study,"TRW Defense and Space Systems Group, 4733.4.75-72,July 1975.

4. P. R. Trybus and A. M. Chodorow, IEEE Trans. Nucl.Sci. NS-23, 1977 (1976).

5. T. A. Dellin and C. J. MacCallum, "A Handbook ofPhoto-Compton Current Data," Sandia Laboratories,SCL-RR-720086, December 1972.

6. R. R. Schaefer, J. Appl. Phys. 44, 152 (1973).

7. C. E. Wuller, "The Transient Air ConductivityContribution to Missile Cable SGEMP Response,"TRW Defense and Space Systems Group, 99900-7779-RU-00, December 1974.

8. C. E. Wuller, "Secondary Electron SGEMP Currentsin Cable Gaps at Partial Pressures," TRW Defenseand Space Systems Group, 99900-7810-RU-00, Novem-ber 1975.

9. V. A. J. van Lint, J. W. Harrity, and T. M.Flanagan, IEEE Trans. Nucl. Sci. NS-15, 194(1969).

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10. R. C. Weingart, R. H. Barlet, R. S. Lee, and W.Hofer, IEEE Trans. Nucl. Sci. NS-19, 15 (1972).

11. W. H. Sullivan and R. L. Ewing, IEEE Trans. Nucl.Sci. NS-18, 310 (1971).

Charles E. Wuller was born in Belle-ville, Illinois, September 11, 1945.He received the B.S. degree in Physicsfrom St. Louis University in 1967, andthe M.S. and PhD degrees in Physicsfrom the University of Missouri, Colum-bia, in 1969 and 1973.

In 1968 he was in the Space Sci-ences Laboratory, Marshall Space FlightCenter (NASA). From 1973 he has workedfor TRW Defense and Space Systems Group

on nuclear radiation effects. In his current researchhe carries out analyses of the EMP and SGEMP responseof missile and satellite systems.

Dr. Wuller is a member of the IEEE and the Ameri-can Physical Society.

L. Carlisle Nielsen was born in Ogden,Utah, June 16, 1929. He received theB.A. degree from Harvard in 1950, theM.S. from the University of New Mexicoin 1956, and the PhD from the Universityof Utah in 1962, all in Physics.

He has worked mainly on variousaspects of nuclear weapons developmentand weapons effects with the U.S. AirForce, Lawrence Livermore Laboratory,EG&G Corp., and at TRW Defense and Space

Systems, where he has been since 1973. His presentwork at TRW is concerned with EMP and SGEMP hardeningof spacecraft and missile systems.

David M. Clement was born in Pittsburgh,Pennsylvania, July 14, 1940. He receiv-ed the B.S. degree in Physics from Geor-getown University, Washington, D.C., in1962 and the PhD in Theoretical NuclearPhysics from the University of Pitts-burgh in 1967.

After teaching physics for severalyears at the University of California,he joined TRW Defense and Space SystemsGroup in 1973. He is currently working

in the field of SGEMP radiation effects on satelliteand missile systems.

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