3ir^ Research Report

STDP MODELS FOR ELECTROMAGNETIC PULSE PRODUCTION FROM UNDERGROUND NUCLEAR EXPLOSIONS, PART IV: MODELS FOR TWO NEVADA SOILS

Charles N. Vittitoe Weapon Effects Research Department

This r e s e a r c h was supported by the Advanced Resea rch P ro jec t s Agency of the Department of Defense under ARPA O r d e r No. 1424.

Pr in ted May 1972

SANDIA LABORATORIES OPERATED FOR THE UNITED STATES ATOMir ENERGY COMMISSION BV SANDIA CORPORATION j ALBUQUERQUE NEW MEXICO LIVERMORE. CALIFORNIA

liAued by SandLa Conpofiation, a pKunt coruOuLctoA, to the. UrCUtd Statt& Atomic EnojiQij Commiiiion

NOTICE

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, sub­contractors, or their employees, makes any warranty, express or Implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any Information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

SC-RR-72 0173

MODELS FOR ELECTROMAGNETIC PULSE PRODUCTION FROM UNDERGROUND NUCLEAR EXPLOSIONS. PART IV:

MODELS FOR TWO NEVADA SOILS

Charles N. Vittitoe

Weapon Effects Research Department Sandia Laboratories

Albuquerque, New Mexico 87115

May 1972

ABSTRACT

The frequency variation of the electrical parameters of a ssimple of Nevada tuff is modeled by a Debye relaxation model. Less success occurs for similar modeling of a dry granite sanaple. Data from R. L. Ewing are used to estimate the secondary electron mean lifetime in the dry granite sample as 2 x 10"^" sec with a mobility of 111 esu. Difficulties with similar estimates for tuff are mentioned, together with resulting uncertainty in calculated electromagnetic fields close to an underground nuclear explosion. Appendices show that the model obeys the Kramers-Kronig relation and contain discussion of an interpretation of large dielectric constants.

1

ACKNOWLEDGEMENTS

The author is indebted to H. B. Durham and G. A. Kinemond for gathering references which contained the data on the tuff and grani te samples used h e r e . Robert Ewing graciously furnished his p re l iminary data on gamma ray-induced conductivity in g ran i te . Helpful d iscuss ions with S. L. Thompson and A. C. Switendick in addition to those mentioned above are also acknowl­edged. L. G. Lee contributed programming aid. F . Biggs and R. E. Lighthill provided excellent evaluation of coefficients to r ep resen t the frequency variat ion of the sample e l ec t r i ca l p r o p e r t i e s .

2

TABLE OF CONTENTS

Pag

Introduction 5

The Ground Model 5

Model for Nevada Tuff 13

Model for Dry Granite 16

Conductivity Enhancement of Tuff Caused by Gamma Radiation 20

Conductivity Enhancement of Grani te Caused by Gamma Radiation 24

Difficulties with Tuff P a r a m e t e r s 2 6

APPENDIX A - Effect of Gamma Radiation on Dielectr ic Constant 2 7

APPENDIX B - The Dispers ion Relation 31

APPENDIX C - Large Dielectr ic Constants 35

MODELS FOR ELECTROMAGNETIC PULSE PRODUCTION FROM UNDFRGROUND NUCLEAR EXPLOSIONS, PART IV

MODFLS FOR TWO NEVADA SOILS

INTRODUCTION

During typical underground nuclear burs t s in Nevada, numerous instrumentat ion cables

extend very close to the explosion cen te r . Often these cables a re embedded in concre te , soil ,

rock, or other fil ler m a t e r i a l s . Near the burs t a c lo se -m e lec t romagnet ic pulse (EMP) will be

produced in the surrounding m a t e r i a l s . The EMP then s c a t t e r s from the embedded conductors

and induces cu r ren t s which may in ter fere with the m.easurement of such quantities as weapon

diagnostics or sys tem ha rdnes s . In this repor t the two ex t r emes of Nevada-type soil a re t rea ted

in an at tempt to bracket the variat ion of the p a r a m e t e r s considered as the soil type changes .

Samples of tuff and grani te a re modeled with Debye relaxation p a r a m e t e r s to account for frequency-

dependent p r o p e r t i e s . The Compton e lec t ron cu r ren t provides the driving force for the E M P .

P r o p e r t i e s of the m a t e r i a l de termine how well the EMP couples energy into the cables and other

nearby conductors . Radiation-induced conductivity is also discussed, since it must be included

in the e lec t r ic field calculat ion.

THE GROUND MODEL

In this section the soil is physically modeled m an attempt to account for the frequency-

dependent e lec t r ica l permit t iv i ty and conductivity. A model t rea ted by Longmire and Longley

has the advantage of allowing a t ime domain solution for the cur ren t density in the soil after the

applied e lec t r ic field intensity is given. The Debye relaxation model t rea ted next is shown to give

the same frequency var ia t ion with additional freedom in the choice of sign for some of the paramete

Following Longmire and Longley, ^ let us model the ground by the e lec t r i ca l c i rcui t m

F ig . 1. With an applied voltage of the form V e , the cur ren t I is given by

:«,=m.. .c™*2:-j™^. a, o n R n itoC

n

Here , the R a re allowed to vary with t ime to account for changes m the ear th that might be

produced by nuclear radiat ion. Changes m the capaci tances a re not expected to occur . Such

capaci tances a re caused by c racks and holes m the soi l . Under i r radia t ion for short t imes , the

dimensions a re not expected to change. However, the e lec t r ica l p a r a m e t e r s of the lossy d ie lec t r ic

may vary . Radiation dose r a t e s must be ext remely la rge to change the number density for a

pa r t i cu la r type of molecule m the soi l . Hence die lect r ic constant changes a re not expected (see

Appendix A). However, the soil conductivity will vary with radiation dose. In fact, the radiat ion

5

IS likely to produce re s i s t ance m para l le l with each of the capac i tors and, hence, augment the

shunt r e s i s t ance caused by the i r lossy d ie lec t r ics which is accounted for by R . This l a t t e r

short ing should depend upon the die lect r ic ma te r i a l which might be a i r or water .

I

^c

f'l f̂

Fig . 1 Frequency-dependent e lec t r ica l model of the ground (Longmire & Longley).

Let us assume that the voltage V m Fig. 1 is applied to a length L of a cube of the soil by

means of a para l le l plate capaci tor as indicated m Fig . 2. Division of Eq. (1) by L then converts

V(t) to E(t). If the a r ea of the plates is A (or, equivalently, consider the volume of c ros s - sec t i ona l

a r ea A m a para l le l plate capaci tor of infinite a rea) , division by A converts the cur ren t to a current

density. Equation (1) can then be wri t ten as

l(t) R (t)A o

iwC L E(t) + ^" ^ E(t) +J2

L .

n R A + — ^ n lOjC

E(t)

With the definitions

?, = 4„C L

1 R A ' "i 1

1 1 47r?^

1 V,

th is becomes

10.71 f CO + iwS f '~ -—• ^" ' ^n^n 3(t) = ^ ^ E ( t ) + ^ E ( t ) + ; ^ ^

»2 2 E(t) (2)

6

I

I

(i)v

Fig . 2 Extension of the circui t model to a cube of lossy m a t e r i a l inse r ted as a d ie lect r ic in a para l le l plate capaci tor .

Equation (2) may also be wri t ten

IWT) 3(t) = A E(t) + -r^ E(t) + V a J (t) ,

' o 47r ^—^ n n

where , for each frequency component oJ in the applied voltage.

E (t) a J (t) = ^ V -

n nw J _ ^ 477 ^n ^"^n

With a = ^ . Eq. (3) becomes

itoa a J (t) = E (t) n nw 8 + iw w

•̂ n

Since each frequency component yields 3E /gt = iojE , this becomes

a J = —5 TT n nco o2 2

8 + w '̂ n

BE ^ - T ^ + w^E ^n 9t w

M u l t i p l i c a t i o n of (5) by p and a d d i t i o n of t h e t i m e d e r i v a t i v e of (5) y i e l d s

fta a 0 + - i ' n*^n ;̂ t J + a no)

a h^

\ ^ 2 2 ?t +

ria 2a B ?tfl n n n "̂ n 3i

2 ^a. ' 2 a fi CO ?>8 ' CO n n n n

2 St 2 2 ?,t fi^ + co («^ ̂ " 1

E . CO

(6)

Sa 5/3 n n

W h e n —— = —-— = 0, t he e q u a t i o n s i m p l i f i e s t o Bt 3t ' ^ ^

ft J + BJ 3E

nco _ CO n nco at at

(7)

T h u s , o u t s i d e t he r a d i a t i o n r e g i o n w h e r e r e s i s t a n c e s and c a p a c i t a n c e s a r e i n d e p e n d e n t of t i m e ,

t h e e x p l i c i t f r e q u e n c y d e p e n d e n c e d r o p s out and s u m m a t i o n o v e r t he f r e q u e n c i e s in t h e a p p l i e d

e l e c t r i c f ie ld g i v e s t h e t i m e d o m a i n r e s u l t o b t a i n e d by L o n g m i r e and L o n g l e y

Bt ^n n 9t (8)

S i n c e , f o r s h o r t i r r a d i a t i o n t i m e s t h e c a p a c i t o r d i m e n s i o n s , d i e l e c t r i c p e r m i t t i v i t i e s , and h e n c e

c a p a c i t a n c e s do not c h a n g e .

ag 8 ?̂ a "̂ n n n

3t a St •

T h e m o r e g e n e r a l e q u a t i o n t h e n s i m p l i f i e s t o

;^a a 8 + - ^ n n 3t

SJ J + a nco

nco n St

a + n

28^0; Sa„

ii^'^^) 2 St

c St

4 .2 2 ^n '^ ^ \

2 St

(i ^ '̂) (9)

One of Maxwell 's equations yields:

VXH =^ (J + (TE) + ^ | ^ . (10) c c sc

If the cur l of the magnet ic field can be neglected, no driving cur ren t is p resen t , and harmonic

t ime dependence is assumed, then the total cur ren t is given by

[ icof (11)

A ma te r i a l is classif ied as a good conductor if the conduction cur ren t density (CTE) in (11)

is la rge compared to the displacement cur ren t density \-T-^ EJ . A poor conductor is one in which

the displacement cur ren t dominates . Fo r the soils t r ea ted he re , the two t e r m s a re of comparable

s ize over some portion of the frequency range of in t e res t . Consider a sample of Nevada tuff from

nea r the Diamond Mine s i te . With f = lo'^ Hz, ^ = 0. 02 m h o / m (= 1. 8 x 10^ sec"-^) and c = 30,

^ ^ = 1.2 . COf

Q

Thus the tuff becomes a poor conductor for frequencies g r e a t e r than 10 Hz and a good conductor

for frequencies lower than 10" Hz. A be t te r insulating ground ma te r i a l with ^ » 10 and cr w 10 m h o / m is a poor conductor for frequencies g r e a t e r than 2 x 10 and a good conductor for

f < 2 X 10^ Hz. Compari

the frequency var ia t ions

f < 2 X 10 Hz. Comparison of Eq. (11) with the rea l and imaginary pa r t s of Eq. (2) produces

2 N a CO

n=l 8 + CO

TJ N a i3

n=l 13̂ + to

Following the suggestion of Longmire and Longley, let us assume that

/3 = 2,7 X lo""^^ s e c ' ^ , (14) n

with

o ^o

and

f = 77 . (16)

9

2 F o r m s s imi l a r to (12) and (13) with N = 1 were derived by Debye, with a m o r e concise

o

method indicated by Jones . Following Jones , let the e lec t r ic field intensity and e lec t r ic displace­

ment be given by the i r F o u r i e r t r ans fo rms :

Then

00

D(t) = /" ®(co) e^'^'^dco,

E(t) = / _^(to) e"*'* dc^ .

• ' - 0 0

D(t) =y" e(co)^(co) e'^'^dco . (17)

In general , e is a complex function of frequency that is here assumed to approach a r ea l , positive

constant (e ) as |co| —> <». Therefore ,

where

00

J c(co) e"^* dco = 2,7 rf^6(t) + a(t)l , (18)

a(t) = ^ J Uoi) - e j e' '^* dco . (19)

Substitution of the t rans form of E^(t) into (17) and use of (18) gives

D(t) = e ^ E ( t ) + /" E( t ' )a ( t - t ') dt ' . (20)

In the special case when a = 0, no d ispers ion occurs and the m o r e usual d ie lec t r ic constant is

obtained. When it is assumed that at t = 0 a disturbing e lec t r ic field intensity is applied, the

relaxation p roces se s associa ted with a(t) do not occur for t < 0. Hence, a ( t < 0) = 0. This

changes the upper limit of integration in (20) to t. If we general ize the t rea tment by Jones ' ' and

a s sume the relaxation is caused by a s e r i e s of distinct p roces se s (such as damped motion of

var ious types of f ree-charge, damped reor ientat ion of polar molecules , and possible e l ec t ro ­

chemical p rocesses ) , the a(t) can be represen ted by a s e r i e s

N a(t) = ^ a^ exp(- t /T^) (21)

n=l

10

for t > 0. If the m a t e r i a l has a conductivity at z e ro frequency, th is can be r ep resen ted by the

separa t ion of an n » 0 from the summation and the, assumption that UT ' " for all o). Then the o

complex d ie lec t r ic constant includes the DC conduction t e r m as wel l . In that ca se , the t rans form

of (19) gives N ar 4i7i(T_

e(co) - f = / _ ! 1 , 1 00 * - - ' 1 + 1(4) n=l

CO (22)

Separation into r ea l and imaginary pa r t s gives

N a T

2 2 n=l 1 + CO T

(23)

N coa T 4ffa c,(co) = - E - ^

n = l 1 + CO T CO (24)

where f(to) = f (co) + ie.(co). The imaginary par t may also be wri t ten in a form in which the con­

ductivity is be t te r specified:

1 CO

N , a T CO , T ^ J _ n n

^o Z-« 4ff , 2 2 n ^ 1 + CO T

F o r the case N = 1 and cr = 0, E q s . (23) and (24) a r e known as the Debye equations and have been ° 3 4

found applicable to dilute solutions and some ear th m a t e r i a l s . (Appendix B indicates that the usual d ispers ion relat ion is satisfied by this form of the d ie lec t r ic constant . )

The n r ep re sen t the amplitude of physical relaxat ion p r o c e s s e s and mus t be r ea l . Since

damping is expected, the T a r e requi red to be rea l and posi t ive. However, the a may be negat ive.

Because of production of damping by iner t ia l , in te ra tomic , and in te rmolecu la r fo rces , some p r o c e s s e s

may occur which induce an e lec t r ic polarizat ion opposite to the applied e lec t r ic field intensi ty. F o r

example , a polar ized molecule might in teract with i ts neighbors to induce a polar izat ion in the

direct ion opposite to the applied field. Such a react ion might be m o r e probable at low frequencies

where react ion with neighbors could be m o r e impor tant .

5 Wait and Fu l l e r have used a form s imi l a r to E q s . (23) and (24) in modeling the e a r t h ' s

d i spers ive quantit ies by Debye relaxat ion p r o c e s s e s . The i r equations have the forms (MKS units):

e(w)

^o

M

= E m=l

, ^m • Tm

1 + COT m

11

CT(CO) = a^+ YJ

2 M CO c T (6 - y ) "^ o m m m

With the substitutions

2 m=l 1 + (COT )

M 00 ^—^, ' m o

m = l

«m = 1 / V '

a = 8 e (6 - y ) , m ^m o m 'm '

and conversion to a consistent set of units, the Wait-Fuller results are easily shown to be equivalent

to those of Longmire and Longley in Eqs. (12) and (13).

The standard treatment for dispersion theory assumes that each charged particle of mass

m. interacts with a harmonic electromagnetic field. Various degrees of sophistication may include

a restoring force l-mo). (x. - x. )) f a damping force (-m.d.x.) proportional to the particle velocity,

the electric field contribution to the force (q.E J , and perhaps magnetic forces on the particle J. L \J L cLx

in addition to the radiation reaction terms. Where the latter two forces are neglected, the

displacement of the charge is

q E ^i—total

X . " —1 / 2 2 . ^ \

m^ Ico^ - CO + iwd . I

Thus the induced polarization can be positive or negative, depending on the relative sizes of the

various parameters. For an atom the natural frequencies 4o./2ff of the electrons range from

visible to ultraviolet. For molecules there are additional terms because of the vibration of the

nuclei about equilibrium positions and because of molecular rotations. These frequencies are in 3

the infrared part of the spectrum. Small crystals in a material may interact with an electro­magnetic field, giving still smaller natural frequencies that would produce ainomalous dispersion at radio frequencies.

In fitting experimental data to evaluate the parameters in Eqs. (12) and (13), the a might

be restricted to positive values since they represent the inverse of a resistance per unit length.

However, negative allowed values of a in Eqs. (23) and (24) indicate the a can indeed be negative.

This might be treated in the circuit model as an interaction between neighboring capacitors.

12

MODEL FOR NEVADA T U F F

Data on a sample of Nevada tuff have been collected by the USGS, and by Grubb. The

die lect r ic constant variat ion with frequency is i l lus t ra ted in F ig . 3. P a r t of these data is l isted

in Table I.

10"

if

1 1 1 1 1 1

A USGS. Dec 1970 • Grubb, 150 ft depth • J

k o Grubb, 100 ft depth 1

tX>V 10*

lo'

10̂

lo'

,„0

^W - ^W^

^ ^ ^ ^ S ^ ^ ^ j ^ j ^ ^ 1

• ^^^^^szzW Relative dielectric constant "1 at Diamond Mine site

1 . 1 1 . 1

f (Hz) 10' 10' Uf

F ig . 3 Dielec t r ic constant of tuff a s a function of frequency. The c rossha tched a r e a indicates the variat ion with var ious core samples chosen.

TABLE I, Ear ly USGS Elec t r i ca l P a r a m e t e r s for Nevada Tuff Sample*

f(Hz) (mho/m) (10^ s e c ' ^ )

10^

103

10^

10^

10^

lO''

10^

35100

4110

620

166

45

25

22

0.0124

0.0128

0.0131

0.0138

0.0158

0.0214

0,0555

11.2

11.5

11.8

12.4

14.2

19.3

50.0

*See Appendix C for additional comments concerning la rge permit t iv i ty va lues .

Data for these seven frequencies were substituted into (13) to obtain the seven coefficients

f and a for n = 1, . . . , 6. Substitution back into (13) yields reasonable agreement with data in

the range 2,7 x 10 < co < 10^ s e c ' l . Using these same coefficients in (12) with an estimate for

a gives less satisfactory agreement with Fig. 4. In view of the spread in data, the coefficients

are still a reasonable representation of the tuff conductivity. Solving the problem in the reverse

order is not nearly so satisfying. The variation of f over about four orders of magnitude gives a

better determination of the coefficients than the conductivity data which vary only within a factor of

two over the oj range plotted.

100 -

n 1 I I I—I—I I 11—I—I I I I

Diamond Mine resistivity

'j

I I 11 1 1 I 11 1 n A USGS, Decl970 o Grubb, 150 ft depth o Grubb, 100 ft depth

P ^ Samples from B sensor drill

FTS Samples from dipole drill

0.01

- aoi5

iJ I l - l - L

10̂ 10' 10^ f(Hzl

10'

Fig. 4 Measured resistivity of tuff as a function of frequency. The cross-hatched areas indicate the variation with sample chosen.

A somewhat better fit is possible to the frequency variation of f and o- if the (3 are also

allowed to vary. A program has been developed by Biggs and Lighthill which will use Eqs. (12)

and (13) and find coefficients e , a , 8 .and a . This minimizes the square of a normalized oo o n n

difference between a set of (oj, (, a) data points fed in and the calculated values of c, <T. The fit

may not be the absolute minimum to the fitting parameter but is at least a local minimum. The

coefficients from this program are listed in Table II with the resulting curves illustrated in

Figs. 5 and 6. These results are consistent with the data, indicating that Debye relaxation

processes properly account for the frequency variation of the electrical properties of tuff within

the frequency range of the data.

14

TABLE II. Coefficients for a Sample of Tuff

1

2

3

4

5

6

3 . 0 2 X 10

2 . 8 8 X 10^

3 . 9 0 X 10^

1 .28 X lo'^

2 . 6 3 X lo'^

8 , 1 4 X 10^

7 , 7 4 X 10^

8 , 2 5 X 10^

8 , 6 8 X 10"*

1,07 X 10^

1 ,50 X l o ' '

7 , 0 7 X 10^

9,72 1,13 X 10 sec

o r

0,0126 m h o / m

Run No, ' 2 1 I x 10 b i llllllll I llllllll I llllllll I llllllll I llllllll I lllllll

1x10"̂

I lx#^

1x10

1x10 ,01 • """•' • """•' • I ' """'I ' '"""I ' " iJJUj

1X10°^ 1x10°^ 1x10°^ 1x10°^ Omega

Fig. 5 Permittivity variation with angular frequency predicted by fit to data for Nevada tuff sample.

1x10 ,09 Run No. = 21 _ llllllll] I iiiiiiij I llllllll I iiiiiiij I iiijiiij I iiiiin

o o

1x10" j i n i l l i l I l l l l l l l l I l l l l l l l l I l l l l l l l l . i i i ini l I HUM.

1x10 ,02 1x10 ,04 1x10 ,06 1x10 ,08

Omega

Eig, 6 Conductivity (sec ) of a sample of Nevada tuff as predicted by fit to cT, e data.

MODEL FOR DRY GRANITE

As an example of a be t te r insulating ground m a t e r i a l , G, A, Kinemond of Sandia

Labora to r ies has furnished some data on dry grani te . The data a re l isted in Table III.

TABLE III. E lec t r i ca l P a r a m e t e r s for Grani te Sample

f(Hz) cr(mho/m) q(sec )

10

l o '

10^

10^

10^

10^

10^

10,20

9 ,95

9.70

9.46

9,11

8,71

8,30

7.00 X 10

2 .21 X 10 '

7.30 X 10 '

2 .40 X 10"

7.84 X 10 '

2.62 X 10"

8.80 X 10"

-7 6,30 X 10

1,99 X 10"̂

6,57 X 10"̂

2,16 X 10^

7,06 X 10^

2,36 X 10^

7,92 X 10^

Straightforward substitution into Eq. (12) yields values of a which produce oscillations in Q ^

{(co). The UNFOLD program has the unique capability of least square fitting theoretical curves

to data with added requirements such as constraining the function to be s 0, or having bounds on

higher derivatives in order to reduce oscillations. Accuracy of the data is one of the input

variables which limit the variations forced by the added constraints. Substitution of the data into

(13) with ^ = 2ff X 10 , as before, yields the coefficients

c - 8,39

a^ = 1.34 X 10^ ,

a^ = 1.26 X 10^ ,

ag = 1.21 X 10^ , (25)

a^ = 1.32 X lo"^ ,

a^ = 1.84 X 10^ , b

a^ = 2.81x10^ . b

The agreement with ( data is excellent as indicated in Fig. 7. However, the conductivity predicted 4 '_

by Eq, (12) is too low. This might not be too serious a difficulty if the function —^ for the granite C0€

sample were small over the limits of interest. Unfortunately, the data from Table II indicate that

the function is small only at the upper end of the frequency scale, f > 10 MHz. Thus, underestimates

of the conductivity can be tolerated only at high frequencies. In like manner, underestimates of f 2

appear to be tolerable for frequencies below 10 Hz, since the granite is a "good conductor" in that region.

Substitution of the data into the conductivity equation (12) produces coefficients which cause

the f to vary over nearly an order of magnitude, as seen in Fig. 8, and thus is a poorer fit to the

data.

Figure 9 shows the results when the coefficients are estimated from the separate ( and or 7

results and after processing with the Biggs-Lighthill program mentioned earlier, and indicates

that these dry granite data do not fit the model treated here. For further calculations with this

material, the coefficients in Eq. (25) are recommended if the signal propagation speed is to have

the correct frequency variation. The coefficients in Fig. 9 are recommended if conductivity

effects are to be emphasized.

17

, ,.07 Run No. = 23 1 x 10 biiiiniij ri!nii[ iiiiiiii| luiinij i iiiui| i inn

l x l O ° ^ t

I lxl0°5 o

1x10

1x10 I l l l l l l l l I l l i y i l l I l l l l l l l l I I I I I U l l I l l l l l l l l I I I I JJId

lxl0°2 ixlO^

Omega (sec ) (a)

1x10°^ 1x10°^ h

, ,»02 Run No. - 23 i X l u I I iiiiin| I mil l ] I iiiiini i iiiiiii] i iiiiiii| i iiiiti

c: o •:;; 1X 10 ,01

1x10 ,00

(b)

I l l l l l l l l I l l l l l l l l I l l l l l l l l I i i l i y J I l l l l l l l l I i i i i u l

.02 .04 ,06 1 X 10"" 1 X 10"^ 1 X 10"^ 1 X 10

Omega (sec )

(b)

.08

F i g . 7 The conductivity (sec ) and permit t iv i ty resul t ing from a fit to the grani te permit t iv i ty data .

IXIQOV

l x # ^

lx l0°5^

1x10"

IxlO*'

Run No, = 24 I iiiiii| I llllllll I iiiiiij I iiiiiii| I mill

iiniiiil I llllllll I IIIIIMI I llllllll I llllllll I I HIM

1x10 ,02

1x10 ,04

1x10 ,06

1x10 ,08

Omega (sec )

(a)

1x10" Run No, = 24

— 01 •5! IxlO"^

1x10 ,00

11111111] I lllllll] I I I I

fit

TTnq

data

foo=8,39

(b)

I llllllll I HUM! I llllllll II I I iiiniil [ II M 1x10

,02 1x10

,04 1x10

1.

,06 1x10

,08

Omega (sec ) (b)

Fig . 8 The conductivity and permit t ivi ty result ing from a fit to the granite conductivity data .

-2.95 X 10̂

-6.85 X lo '

4.08 X lo''

2.32 x l o '

1.22x10*

6.03x10*

1 — r n 1 1—r-

1.96x10

1.96xl0'

2.34xl0'

6.84xlo'

9.80X 10*

l.SOxlo'

= 1.18 X lO' sec '

I I I !

Fig . 9 The conductivity and d ie lec t r ic constant for a dry grani te s amp le . A indicates coefficients es t imated from separa te fits to f and cr; B indicates coefficients after p rocess ing for be t te r e s t imates of a and S ,

n '̂ n

CONDUCTIVITY ENHANCEMENT OF T U F F CAUSED BY GAMMA RADIATION

Solution of specific p rob lems would be great ly simplified if Eq. (9) could be converted to the

form of Eq, (8), F o r Nevada tuff, the a (~ l / R ) were found to be on the o r d e r of 3 x 10 to 7 - 1 '̂ ' ^ 8 - 1

3 X 10 sec except for n = 6, while ff « 1, 13 x 10 sec , Hence R is the smal les t r e s i s t ance 8

in the circui t and dominates the cur ren t flow except for frequencies > 10 Hz where the n = 6 t e r m

is significant. In a typical nuclear radiat ion environment the Compton cur ren t density and induced -8

voltages initially follow the y pulse, with e folding t imes near 1 shake (10 second). The highest p

frequency contributing significantly to the source is then expected to be l ess than 10 Hz. Recal l

that

at R

, SR 1 n

2 3t

2 ^ n̂ at (26)

With the assumption that the init ial r e s i s t ance R is la rge compared to any changes that occur in -8 ^

~ 10 second, neglect of the t ime variat ion of a is justified and Eq, (9) may be replaced by Eq. (8),

20

As the Compton e lec t rons slow down, secondary e lec t rons a re c rea ted and the ground con­

ductivity is enhanced. The conductivity of the ground is given by

= <7oi ̂ £ ^^i\\ ' (27)

where (j is the ambient value and the summation is for the N species of charge c a r r i e r s formed

by the radiat ion. Because of the re la t ively high ^y expected (~0.01 mho/m) and the l a r g e r

mobility of e lec t rons compared to ions, only e lec t rons a re included h e r e , i . e . , N = 1. The

chemical composition of tuff is assumed to be SiO„, 70 percent ; H O , 10 percent ; A i O ,

12 percent ; and K „ 0 , 8 percen t . F o r crys ta l l ine SiO , Van Lint suggests an inc rease in con­

ductivity given by

ACT = 4 x lO '^^ Q m h o / m , (28)

-3 -1 where Q is the energy deposition r a t e in MeV m sec , In t e r m s of the g a m m a - r a y flux y

-2 -1

(MeV m sec ),

Q = - | | = i , (29)

29

A / u / ^ 4 x i o " . / MeV \ ACT (mho/m) = y - ^ ,

'̂ \m s e c /

A l.^yh 36 x lO"^^ . / MeV \ , „ . .

^ \ cm s e c /

Data indicate that other m a t e r i a l s have changes in conductivity varying as y to some power .

The exponent, however, always appears to be close to one. Such a formula neglects the specific

e lec t ron depletion p r o c e s s e s that would be expected to introduce a t ime delay in the conductivity

decay after the y peak has occur red .

In the soi l the secondary e lec t ron number densi ty might be approximated by

'^''e . , 2 dt = S + a ,n + a ,n " . (31)

e o l e '^ol e

21

where

a . = -10 sec ol

-7 3 )3 . = -10 cm /sec ,

S = f̂ , e ^ e

^ = number of electrons produced by each primary electron R

^ = p(1.23 X 10^ cm^/gm) ,

and 33 eV are assumed to produce each secondary electron. The Compton electron flux in the soil

(f ) can be approximated by

f = kf , (32) e y

where k is in the range 0. 005 through 0. 01. The proportionality constant is the ratio of the mean

forward range of electrons to the Compton interaction mean free path of the gamma rays. This

equation also assumes steady state conditions; i . e . , the gamma flux does not change significantly

in the time difference between a Compton electron and a gamma ray traveling the Comptoh

electron's mean forward range. The mean forward range of the latter in air is approximated by

" - '^•^^^T^ (33) (0.30 -I- T)p

3 where p is the density (gm/cm ), T is the electron kinetic energy in MeV, and R is the electron

11 3 range in centimeters. Extension of this to Nevada tuff with p = 1.91 gm/cm and T = 1 MeV gives

-12 R = 0. 126 cm. An electron speed of 0. 9c indicates that 4 x 1 0 second is required to travel R. Thus the quasi-static approximation is reasonable for the Compton electron flux.

12 The parameter j3 is an order of magnitude estimate obtained from Bates. In sea level

air a would be -10 sec"-^, mainly because of three-body attachment to 0- molecules. In the

tuff the a , niight be assumed to attach more quickly because of the higher density. It might also

be argued that the value should be lower because of the lack of proper molecules for attachment.

Data for parameters a and ^ are necessary to improve the electron number density determination.

If dn /dt « f̂ , the steady-state approximation is reasonable and (31) may be solved for n .

In the solution of the resulting quadratic equation, the ambiguity concerning the two solutions is

resolved by requiring n to be positive.

22

If the (? , t e r m can be neglected (consistent with the data for SiO„) and dn /dt can be ol 2 e

neglected, a form equivalent to van Lin t ' s is obtained:

^kf ACT = uen = -ue "^ • (34)

^ % 1

Thus in this approximation, equating to van Lint ' s express ion gives a resu l t for crys ta l l ine SiO„:

(x(esu)

a . (sec ) o l

1.8 X 10 . (35)

In the next section it can be observed that this relat ion applies reasonably well to grani te ; a

following paragraph indicates that it may apply to tuff a l so . The la rge SiO„ content in these

m a t e r i a l s may account for this behavior .

An es t imate of the e lec t ron mobility is now requi red . Modeling of the tuff as condensed

a i r and neglecting possible e lec t r i c field variat ion give the e lec t ron mobility

^= 10 e s u p ^ . ^ / p ^ ^ j , (36)

where

R 9 1 1

3 X 10 esu of mobility = 1 m v ' s e c " . (37)

Such a formulation overs implif ies the problem and is only justified by the lack of data for a be t te r

e s t ima te .

An additional difficulty occurs because of the p r e s s u r e s which may be p resen t . F o r example ,

2 a gamma flux of 2 x 10 r / s e c incident upon an SiO„ sample will deposit about 4. 8 cal pe r gm of • -8

m a t e r i a l for a pulse width of 10 s e c . Assumption of a density near 2 g m / c c and a Griineisen

coefficient nea r one r e su l t s in a p r e s s u r e inc rease of 0,4 a tmosphere . At l a r g e r flux r a t e s nea r

a weapon cavity in Nevada, proport ional ly l a r g e r p r e s s u r e i nc reases a re expected s imply because 13

of the deposition of gsimma-ray energy. Shock waves typically t r ave l at around 20 cm/ j / sec .

Hence these p r e s s u r e i nc r ea se s a r r i ve much l a t e r in t ime . Such p r e s s u r e effects a re expected

to change the e lec t ron mobili ty and at tachment p a r a m e t e r s .

Equation (36) gives (ja 644 esu for the assumed tuff. Back substitution into (35) gives an

es t ima te for a , : o l

- a , (est) = 3.6 xlO s e c ' . o l

23

This at tachment ra te is somewhat l a r g e r than expected, and may not be reasonable for Nevada tuff.

However, secondary e lec t rons live about l o " second in water^* and the tuff sample is es t imated

to be 10-percent H^O. Thus the above es t imate is conceivable.

CONDUCTIVITY ENHANCEMENT OF GRANITE CAUSED BY GAMMA RADIATION

Pre l im ina ry resu l t s a re available for an exper imenta l measu remen t of the conductivity of

a dry grani te sample subjected to the photon beam from the Hermes II acce l e ra to r . ^^ At a flux 1 1 2 3

of 2 X 10 y MeV/(cm sec) the measu red value was 1.045 x lO" mho/m±20 percen t . The conductivity pulse had a full width at half-maximum of less than 5 nsec wider than the y pulse .

5 Field intensi t ies up to 6 x 10 V/m were applied without producing breakdown as the pulse

t r a v e r s e d the m a t e r i a l . The van Lint express ion for pure SiO„ would predict a peak conductivity -3

of 1.01 X 10 m h o / m in this situation, in excellent ag reement !

An analytical es t imate of the Hermes gamma pulse shape is given in F ig . 10. Use of the 9 - 1 -6 3

p a r a m e t e r s -a^^ = 5 x 10 sec and -^^^ < 3 x 10 cm / s e c r e su l t s in the secondary e lectron density in F ig . 11. Since the n only r i s e s to 1.76 x 10^^ e l e c t r o n s / c m ^ , the a , t e r m dominates

e ol the secondary electron at tachment in the differential equation. F o r compar i son , -« values of

9 -1 10 -1 °^

10 sec and 10 sec have r e su l t s as indicated. Exper iments at l a r g e r dose r a t e s a re requi red

to be t te r define ^^^ for grani te . Thus the shape of the conductivity pulse is an aid to determination

of the e lectron attachment p a r a m e t e r s . The magnitude of the conductivity can also be used to

es t imate the mobili ty of the conduction e lec t rons in the dry gran i te . Where it i s assumed that the

conductivity is at tr ibutable ent i rely to the e lec t rons .

ACT = fien = 1.045 x 10 m h o / m = 9.4 x 10 s e c " . (38)

-I I I l l j I I I I I I I I I ] l I II I I I I I I I I II [•

IxK

8xlC

27

> S 6x10^^

•""4x1026

2xlC

QLLUJULL

35.4 nsec / j ~ Aexp{-(-^^iM\n

l l l l l l l l li 111 r 800 1000 1200

T(nsec) 1400

Fig. 10 Equivalent point source of gamma rays for Hermes pulse ,

24

Equation (31) gives us the es t imate for n i l lus t ra ted in F ig . 11, i . e . , a peak value of 1 4 - 3 ^

1.76 X 10 cm . The es t ima te for e lec t ron mobil i ty in grani te i s , from Eq. (38),

H= 111 esu = 3.7 X l O ' ^ m^ v " ^ sec""^

The ^i and a a r e reasonably consistent with the e a r l i e r predict ion in (35). Equation (36) would ° 3

give a value of 490 esu for grani te (p = 2 .5 g m / c m ), suggesting that the model of granite as condensed a i r leaves something to be des i red .

Since the wate r d isplaces any a i r in the g ran i te , addition of wa te r would be expected to

inc rease the absolute value of a and dec rea se the e lec t ron mobil i ty.

Run No, = 22 3 I I I I ] I I I I ] I I I I ) I I I I ] M I I I I I I L

4 x 1 0 14

S 3 X 10 t/l a o

i 2 X 10 O)

14

14

03

1x10 14 (a) :

h I • 111 iJif, I . I T4NLI 1 1 1 1 1 1 1 1 1 1 1 1 r

800 1000 1200

T(nsec)

(a)

1400

IX # -

8 x 1 0 - 0 1 -

Run No, = 22 I I I I I I I 1 I I I I I I I M I I I I I

X ro E a>

?:

C

6

4

xlO'

xlO"

•01

•01

2x10 • 0 1 -

Fig . 11 (a) The e lec t ron density variat ion with t ime for th ree e lectron at tachment p a r a m e t e r s « (sec~^) and (b) normal ized to unit ampli tude.

25

DIFFICULTIES WITH TUFF PARAMETERS

Experimental conductivity data as a function of dose rate for tuff appear much more

difficult to obtain. Typical grain size indicates that the sample should be l/4-inch or more thick.

The machined surfaces are somewhat rough, making electrical contact more difficult without

trapping air. Presence of about 10 percent of water by weight and possibilities of air pockets in

the tuff make extrapolation of results from other materials less dependable.

Let us consider briefly what limits can be placed upon the tuff parameters. Under the

assumption that tuff is composed of molecules like those in granite, with a little more space for

air or water, and that the electrons disappear by interactions with the molecules, the presence of p _ 1

air suggests a lower bound of 10 sec for -a , . A high concentration of water would increase 9 -1 "

this to values larger than 5 x 1 0 sec . The shape of the conductivity pulse is reasonably 9 -1 9 -1

invariant for -o , ^ 10 sec ; thus 10 sec appears reasonable. The electron mobility would

increase sharply in air and decrease in water pockets. Hence, effective mobility might either

increase or decrease from the granite value. Matching the induced conductivity also depends upon the a , value chosen. ol

In order to predict successfully the electromagnetic fields close to an underground nuclear

explosion and the associated coupling of that electromagnetic energy into instrumentation cables

that may be buried in the Nevada tuff, more information is required concerning the surrounding

material properties. Conductivity measurements as a function of gamma-ray dose rate would

allow the electron attachment parameters and mobility to be determined. With order-of-magnitude

uncertainty in these parameters, a correspondingly high uncertainty must be expected in the

calculated signals.

26

APPENDIX A

Effect of Gamma Radiation on Dielectr ic Constant

27-28

APPENDIX A

Effect ol Gamma Radiation on Dielectr ic Constant

Definitions-

e l + 47rxe

^e - E lec t r i c susceptibi l i ty

N ~ Number of molecules of type i per unit volume

p - Average dipole moment of each molecule of type i

r) = Number of charge c a r r i e r s ol type i per unit volume

)j. - Mobility of charge c a r r i e r s of type i

a - ^ q^M r̂,̂ 1

The dipole moment per unit volume is given by

P = x E = y ] N P * . — -^e— -^-^ 1 1

1

Thus , in the case of a s ca l a r permit t iv i ty ,

y] N r . • ' - - ' 1 1

1

F o r the d ie lec t r ic constant to change significantly, the N must change. Large radiation doses a re

requi red for even one in 10 of the molecules of a cer ta in type to be affected. Hence d ie lec t r ic

constant changes a re not expected. The ionization does c rea te new species such as secondary

e lec t rons with zero dipole moment and many types of ions. Relatively high mobility of the

e lec t rons causes conductivity to be affected easily by the radiation environment .

= 1 + 47r

29-30

•

APPENDIX B

The Dispersion Relation

•

3 1 - 3 2

APPENDIX B

The Dispers ion Relation

The Debye relaxat ion model of the e lec t r ica l p roper t i e s of the ground led to the complex

d ie lec t r ic constant

N e(a)) V^ __n_n_^__ 4ffi

^ , ~. 2 ~ i ' to n=I 1 + to

N I n=l

1 n n 2 2

a t , to 2 2

1 + to T n

(B. 1)

16 given in E q s . (23) and (24). Landau and Lifshitz have shown that , as a r e su l t of causal i ty , the

r ea l and imaginary pa r t s a re requi red to obey the K r a m e r s and Kronig (or dispersion) re la t ion .

Following Landau and Lifshitz (with only the change in t ime dependence from e to e ) , the

d ispers ion re la t ions a r e

c,(to) = - i p / •x + to

dx to

(B.2)

1 r" ^i^''^ dx (B.3)

Here , f is the r ea l l imit of c as to -» <=, ff is the l imit of the m a t e r i a l conductivity as to -» 0, and

P indicates the Cauchy pr incipal value of the in tegra l .

Landau and Lifshitz define f(to) by the equation

00

C(t0) = l + / ' 1(7)6"*^^ d r . (B.4)

Such a definition immedia te ly yields

e(-to) = €*(to) . (B.5)

or that the r ea l (imaginary) par t of ( is an even (odd) function of to. Such an approach omits the

physical bas i s for this l imita t ion. The t e r m f. m.ust be an odd function of to to insure decay of an

e lec t romagnet ic wave when i ts direct ion i s r e v e r s e d by the t ransformat ion to -» -to. The rea l

par t of the displacement vector D should a lso bea r the same relat ion to the r ea l par t of fE when

this t ransformat ion o c c u r s . This is insured by f being an even function of to. The Debye relaxat ion

m^odel i s easi ly seen to satisfy these c r i t e r i a .

33

Direct substitution from (B, 1) into (B.2) , (B. 3) yields

2 1 /•"" e - € N 01 tOT i p f ^ ^ dx = - V " " •n J X + to ^ . 2 2

n=l 1 + to T n

and

IT J X + to ^ 1 , 2 2 n=l 1 + to T

with p roper t r ea tment of the poles at x = -to and x = ±i/T . Helpful identi t ies in the analysis include

"firh'--'-''{ ̂ f~^-'' -00 U X - to

and

" dx 3 j (jx = 2P / J x(x + to) Jr, n 2 2

0 X - to

0

Hence the Debye relaxat ion model of the e l ec t r i ca l p roper t i e s of the ground gives a complex d ie lec t r ic

constant that is consistent with the K r a m e r s - K r o n i g re la t ion .

34

APPENDIX C

Large Dielectric Constants

35-36

#

•

APPENDIX C

Large Dielectric Constants

4 5

Experimental values of dielectric constant sometimes attain values of 10 or 10 . Such

large values may be caused by layering of the material being measured. As an example, consider

a parallel plate condenser composed of two parallel layers of material. One layer is assumed to

have permittivity ( , zero conductivity, and thickness d. The other layer has negligible e(e = 0),

conductivity cr , and thickness qd. Simple analysis indicates that such a condenser behaves as if

the space between the condenser plates were filled with a homogeneous dielectric having the com­

plex dielectric constant

€ (̂1 + q)

^ ~ 1 + it0€j^q/4ffcr2

This effect was reported in 1914 and is referred to as the Maxwell-Wagner mechanism in Kittel's 17 work. The equation suggests that this effect could be interpreted as one of the Debye relaxation

mechanisms in Eq. (22). Kittel indicates that large permittivities may imply a thin dielectric

layer (large q) and are only associated with materials that have large conductivities {CT„). Such an

effect can cause significant difficulty in the attachment of electrodes to a sample of Nevada tuff

for parameter measurements. Such layering may also be present in the material itself.

As an example of the effect of this mechanism, consider the following parameters which

may be appropriate for a measurement of Nevada tuff:

(J = 0. 0126 mho/m = 1. 13 x 10 sec '^ ,

q » 1 .

3 For f.q = 10 , the real part of ( r ises four orders of magnitude as the angular frequency decreases

7 2 -1 from 10 to 10 sec . This variation is shown in the following illustrations for two choices of a , Figs.C-1 and C-2.

37

#

Ul

Ul

OHESA

Fig. C-1 Illustration of the Maxwell-Wagner effect for p _ 1

various choices of f q, n = 1. 13 x 10 sec , and q » 1.

OHEBA

Fig. C-2 Illustration of the Maxwell-Wagner effect for 5 -1 various choices of e q, a = 1. 13 x 10 sec ,

1 ^ and q 55. 1.

•

38

REFERENCES

1. C. L. Longmire and H. J . Longley, T ime Domain Trea tmen t of Media with Frequency-Dependent E l ec t r i ca l P a r a m e t e r s , Report MRC-N-1 , Mission Research Corporat ion, P . O. Box 1356, Santa Barba ra , California, 93101, March 12, 1971,

2. The Collected P a p e r s of P e t e r J . W. Debye, In tersc ience Pub l i she r s , I n c . , New York, 1954.

3 . D, S. Jones , The Theory of E lec t romagne t i sm, The MacMillan C o , , New York, 1964.

4. A. D. Pet ronsky, B. F . Vorisov, M. A. Kleymenov, and Yu. N. Troshkin , "Absorption Coefficients and Effective E lec t r i c Res is t iv i t ies of Rock Blocks in Mining A r e a s , " Akademiia Nauk SSSR, Izvestya, Phys ics of the Solid Ear th , J^ , 639 (1970).

5. J . A. Fu l l e r and J . R. Wait, Elec t romagnet ic Pulse T ransmi s s ion in Homogeneous Dispers ive Rock, Institute for Telecommunicat ion Sciences , Department of C o m m e r c e , Boulder, Colorado, in terna l repor t , d is t r ibuted at the P r i m e Argus EMP meeting, December 8-9, 1971, Sandia Labora to r i e s , Albuquerque, New Mexico.

6. Table I data were obtained from the United States Geological Survey by pr ivate communication with Gary Kinemond, Sandia Labora to r i e s , December 30, 1970. The Grubb data were taken by methods s im i l a r to those repor ted by R. N. Grubb and J . R. Wait, "In Situ Measurements of the Complex Propagation Constant in Rocks for Frequenc ies from IMHz to 10 MHz, " E lec t ron ics Le t t e r s 7, 506 (1971).

7. F rank Biggs, Sandia Labora to r i e s , pr ivate communication, F e b r u a r y 1972.

8. F . Biggs and D. E . Amos , Numer ica l Solutions of Integral Equations and Curve Fit t ing, SC-RR-71 0212, Sandia Labora to r i e s , September 1971.

9. V, A, J . van Lint, pr ivate communication to W. R. Graham of Rand Corporat ion, noted in January 1970.

10. W. H. Sullivan and R. L, Ewing, A Method for the Routine Measurement of Die lec t r ic Photoconductivity, SC-DC-71 3696, Sandia Labora to r i e s , July 1971,

11. H, J , Longley, Compton Curren t in the P r e s e n c e of Fie lds for LEMP 1. LA-4348, Los Alamos Scientific Labora tory , Apri l 1970.

12. D. R. Bates , Atomic and Molecular P r o c e s s e s , Academic P r e s s , New York, 1962.

13. P r e s s u r e effects of g a m m a - r a y energy deposition were suggested by J . Fleck at the P r i m e Argus EMP Meeting, December 8-9, 1971, Sandia Labora to r i e s , Albuquerque, New Mexico.

14. Max S. Matheson, The Format ion and Detection of In termedia tes in Water Radiolysis , Radiation Resea rch , Supplement No. 4; 1964, pp. 1-12; L . M. Dorfman and M. S. Matheson, "Pu l se Rad io lys i s , " P r o g r e s s in Reaction Kinet ics , Vol, 3, Pergamon P r e s s , New York. 1965, pp, 237-301.

15. R. Ewing, Sandia Labora to r i e s , pr ivate communication, December 1971.

16. L, D. Landau and E, M, Lifshitz, E lec t rodynamics of Continuous Media, Addison-Wesley Publishing Company, I n c , Reading, Massachuse t t s , 1960,

17. C. Kittel , Introduction to Solid State Phys i c s , John Wiley & Sons, I n c . , New York, 1959.

39

DISTRIBUTION:

Commanding Officer H a r r y Diamond Labora to r i e s Washington, D. C. 20438

Attn: J . E. Tompkins W. T . Wyatt A. Renner

Maj. Gen. Edward B. Gil ler U. S. Atomic Energy Commission Division of Mil i tary Application Washington, D. C. 20545

U. S. Atomic Energy Commission Washington, D. C. 20545

Attn: Headquar te rs L ib r a ry F o r : C. H. Reichardt

Advanced Research Pro jec t s Agency (5) The Pentagon, Room 3D-148 Washington, D. C. 20301

Attn: Verne Fryklund

Los Alamos Scientific Laboratory (4) P . O. Box 1663 Los Alamos , New Mexico 87544

Attn: John Malik, J-DOT R. E . Pa r t r i dge , J-DOT B. R. Suydam, J -DOT L. W. Mil ler , J -16

Universi ty of California (5) Lawrence Radiation Labora tory P . O. Box 808 L i v e r m o r e , California 94550

Attn: D. E . Nielson, L-531 L. F . Wouters , L-40 M. Knapp. L-531 R. J . Lytel , L-531 J . P . Vajk

Ai r F o r c e Weapons Labora tory (2) Kirt land Ai r Fo rce Base New Mexico 87117

Attn: Car l Baum, WERE J . H. Dar rah , WERE

U. S. Dept. Commerce NOAA Resea rch Labora to r i e s (3) Boulder, Colorado 80302

Attn: J . Wait G. Lerfald A. Glenn Jean

Kaman Nuclear Division (2) Kaman Sciences Corporation 1700 Garden of the Gods Road Colorado Springs , Colorado 80907

Attn: P e t e r Snow John Hoffman

Mission Resea rch Corporat ion (2) P . O. Drawer 719 Santa Barbara , California 93102

Attn: C. L. Longmire H. J . Longley

Mission Research Corporation (2) 933 Bradbury Avenue, S .E . Albuquerque, New Mexico

Attn: D. E , Merewether W. A. Radasky

Stanford Resea rch Institute 333 Ravenswood Avenue Menlo P a rk , California 94025

Attn: A. Whitson

Oak Ridge National Labora tory Oak Ridge, Tennessee 37830

Attn: David Nelson

Commanding Officer Picatinny Arsena l Dover, New J e r s e y 07801

Attn: A. Nordio

Headquar te r s , Defense Nuclear Agency RAEV Washington, D. C. 20305

Attn: Major Frank Vajda

R&D Assoc ia tes (2) 525 Wilshire Boulevard P , O, Box 3580 Santa Monica, California 90403

Attn: W, Graham W, J , Ka rzas R. R, Schaefer

Defense Nuclear Agency AFRRI NNMC Bethesda, Maryland 20014

Attn: Gunter Brunhart

TRW, Inc, Vulnerability and Hardness Labora tory One Space Pa rk Redondo Beach, California 90278

Attn: L, D, Singletary

Science Applications, Inc. (2) P . O, Box 2351 1250 Prospec t Street La JoUa, California 92037

Attn: E . R, Parkinson C. A. Stevens

40

DISTRIBUTION: (continued)

Genera l E lec t r i c Company/TEMPO DASA Information and Analysis Center 816 State Street Santa Barba ra , California 93102

Attn: David Reitz G. W. Rodgers . 1420 R. G. Clem, 1730 A. A. Lieber , 1750 J . W. Kane, 1752 H. B. Durham, 1752 H. M. Poteet , 1752 J . K. Linn, 1752 G. A. Kinemond, 1752 J . E. Cover , 1935 A. M. Clogston, 5000 A. Narath, 50 O. E . Jones , 5100 A. C. Switendick, 5151 L. C. Hebel, 5200 G. W. Gobeli, 5210 J . W. Walker , 5220 C. R. Mehl, 5230 J . H. Renken. 5231 C. N. Vitti toe, 5231 (10) T. A. Green, 5234 E . H. Beckner , 5240 J . E . McDonald, 5300 A. M. Clogston (Actg.) , 5400 L. M. Be r ry , 5500

A. Y. Pope, 5600 T . B . Cook, J r . , 8000 W. F . Gordon, 8177 B. F . Murphey, 8300 J . L . Wirth, 8340 J . A. Mogford, 8341 C. C. Hudson, 9150 R. L. P a r k e r , 9463 R. D. Jones , 9463 G. R. Mil ler , 3152 R. S. Gil lespie , 3151 (3) Cent ra l F i l e s , 3142-1 (20) L. S. Os t rander , 8232 (5)