Sensor

A Study of

and Simulation Notes ‘

Note 245

November 1977

~~aveguideMode Excitation ●

and Propagation in a Par-allel Plate Transmission Line

Terry T. CrowKuang Yuh Wu

Clayborne D. Taylor

Mississippi State UniversityUniversity, MS 39762

-,.

A study of the waveguide mode

a parallel plate waveguide. Since

Abstracr

excitation and propagation is made for

this configuration is used in the simu-

lation of the nuclear electromagnetic pulse, results appropriate for various

simulators are obtained and discussed. The analysis assumes infinitely wide

plates, but the question of finite width plates is addressed.

~---- --

Acknowledgement

The authors wish co express their appreciation to Dr. K. C.”Chen ofthe Air Force Weapons Laboratory for suggesting this work and to Dr. C. E.Bam for reading this paper and offering numerous suggestions for itsimprovement.

L

f‘f;.7,.?...= :: ~

.—- -- .F-- -

.:--- ..

*“: . Av”83D<05Ja ‘ “.--,1 “ - ---~ .. > ., * r.e=–’r–-+---------–.’“., ,,.:..,,...-,..”“.,_.... - .—=.. -.—_——=AFWL-TR-80-401 .

_*%, Af V&T:;-80:401

ELECTROMAGNETIC PULSE SENSOR AND SIMULATIONi

NOTES -EMP 1-27 l.O&hCW’: RiTURN~AWL TEC!{NICA1LIBRARYWHLAND AFB,NM.

May 1980

Final Report

Approved for public release; dis~ril)u~ion unlimit~,d.

..— -—. - -. _.. _ ->—r. ..—

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———

AIR FORCE WEAPONS LABORATORY

Air Force Systems Command

Kirtland Air Force Base, NM 87117

1

i

,

.AFWL-TR-80-401‘* .

This repq~t ~s one in the Note.Se;ies on EMP and related subjects which isan E&Q commun~ty-w%’deseries on EMP technol~gy related matters. The editor is::llrC. E. Baum, Air Force Weapons Laboratory (NT%), Kirtland AFB, New Mexico.The editor should be contacted for any matters related tb this series.

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.:. -. .. -+ .,..-. . .

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BOB L. FRANCISColonel, USAFChief, Electromagnetic Division

BRUCE F. H:?(; ‘Colonel, USHDirector of Nuclear Technology

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EM?

0. AJSTRACT (Con<lnue On reverse stale if necessary and identify ov b{ock number)

This is a series of ten notes on electromagnetic pulse sensors and simulation.Subjects covered in this volume are: A Study of WaveguicieMode Excitation and

Propagation in a Parallel Plate Transmission Line; El@ Simulation and Its

Impact on EM!?Testing’;Electromagnetic Considerations of a Spatial Modal

Filter for Suppression of Non-TEM Modes in the Transmission-Line Type of EMP

Simulators; An Investigation of Portable EXP Simulators/Alternate Simulators;Electromagnetic Surface Wave Propagation Over a Rectangular Bonded Wire Mesh;

over-—-..

DD 1;:;”,, 1473 UNCLASSIFIED

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Electromagnetic Wave Propagation Along a Pair of Rectangular Bonded Wire Xeshes;Surface Wave Propagation on a Rectangular Bonded Wire Mesh Located Over theGround; Equivalent Electroma~ii.c ?ropertiss of a Concentric Wire Cage asCompared to a Circular Cylin~gr; Source Excitation of an Open, E’aEaUeli-E4at’eWaveguide; Source Excitation-af an Open,

.*=-Parallel-PLate ‘Uaveguide,.Ru~EJtlcal. .. .

Results.* . ——-.s

.. .—.=.. ...—:. . .—,.

!

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(W?IWIDaf8 ~ntard)

EMP 1-27

PREFACE

iii

Much of the existing information on 13MPis in the form of notes or semi-formal reports and has not been adequately documented or distributed, Inparticular, there are several series of notes that act as technical journalsfor various areas related to EMP and other related subjects. These noteseries are not exclusively for..oneorganization and are run much as techni-cal journals with an editor, Dr. Carl E, Baum.

The Air Force Weap-onsLaboratory has undertaken to reissue these exist-ing notes in convenient volume units<, The present volume is Volume 27 ofthe Sensor and Simulation Notes, one of the note series in the Electromag-netic Pulse Note Series. The Sensor and Simulation Notes have the reportdesignation EMP 1 in the EMP group of note series.

Contributions to this volume, EMP 1-27, have been made by the followingindividuals at the included organizations:

“Air Force Weapons Laboratory.

Carl E. BaumKorada R. Umashankar

—.—...—Cooperative Institute for Research in Environme”ritalSciences

James R. Wait

University of Illinois

V_.KrichevskyR,’Mittra

Institute for Telecommunication Sciences

David A. Hill

LuTech, Inc.

D. V. Giri

Mississippii State University

Terry T. CrowKuang Yuh WuClayborne D. Taylor

NBC Research and Development Institute of theFederal Armed Forces Federal Republic of Germany

Hagen Schilling

1

iv E3fP1-27

TDR, Inc.

%aurice 1. SancerScott SiegelA.D. Varvatsis

Research for these notes has been funded, in part, by the followlng agencies:

Defense Nuclear AgencyUnited States A5r Force

Contributions to the Note Series are encouraged from all organizationsactively engaged in related research. Active participation throughout the

community will build a collection of information useful to all. Contribu-

tions and questions regarding the Note Series should be directed to:

Dr. Carl E. BaumAir Force Weapons Laboratory, NTMKirtland Air Force Base, New Mexico 87117.

m’

ENP 1-27

TABLE OF CONTENTS

v

NOTE 245 A STUDY OF WAVEGUIDE MODE EXCITATION AND PROPAGATION IN APARALLEL PLATE TRAITSMISS1.ONLINETerry T. Crow, Kuang Yuh Wu, Clayborne D. Taylor,Mississippi State University

NOTE 246 EMP SIMULATION ANE ITS IMPACT ON EMP_TESTINGCarl E. Baum, Air Force Weapons Laboratory

NOTE 247 ELECTRO&U=GNETICCONS.I.DE.LATIONSOF_A SPATIAL MOD& FILTER FORSUPPRESSION OF NON-TEM MODES IN THE TRPJVSMISSION-LINE TYPE OFEMP SIMULATORSD. V. Giri, LuTech, Inc.; Carl E. Baum, Air Force WeaponsLaboratory; Hagen Schilling, NBC Research and DevelopmentInstitute of the Federal Armed Forces, Federal Republic ofGermany

NOTE 248 AN INVESTIGATION OF PORTABLE EMP SIMULATORS/ALTERNATESIMULATORSMaurice I. Sancer, Scott Siegel, A. D. Varvatsis, TDR, Inc.

NOTE 249 ELECTROMAGNETIC SURFACE WAVE PROPAGATION OVER A RECTANGULARBONDED WIRE MESHDavid A. Hill, Institute for Telecommunication Sciences;James R. Wait, Cooperative Institute for Research in Environ-mental Sciences

NOTE 250 ELECTROMAGNETIC WAVE PROPAGATION ALONG A PAIR OF RECTA.NGULAE–BONDED WIRE MESHESDavid A. Hill, Institute for Telecommunication Sciences

NOTE 251 SURFACE WAVE PROPAGATION ON A RECTANGULAR BONDED WIRE MESHLOCATED OVER THE GROUNDDavid A. Hill, Institute for Telecommunication Sciences,James R. Wait, Cooperative Institute for Research in Environ-mental Sciences

NOTE 252 EQUIVALENT ELECTROMAGNETIC PROPERTIES OF A CONCENTRIC WIRECAGE AS COMPARED TO A CIR.CULARCYLINDERKorada R. Umashankar, Carl E. Baum, Air Force WeaponsLaboratory

NOTE 253 SOURCE EXCITATION OF AN OPEN, PARALLEL-PLATE WAVEGUIDEV. Krichevsky, R. Mittra, University of Illinois

3/4

NOTE 254 SOURCE EXCITATION OF AN OPEN, PARALLEL-PLATE WAVEGUIDE,NUMERICAL RESULTSV. Krichevsky, University of–Illinois

245-1ENP 1-27

A STIDY OF WAVEGUIDEMODE EXCI~ATIONAPJD”PROPAGATION IN A PARALLEL PLATE TRANS”MI”SSION-LINE

ABSTFuiCT

@A study of the waveguide mode excitation and propagation is made for a

parallel plate waveguide. Since this configuration is used in the simulationof the nuclear electromagnetic pulse, results appropriate for various simula-

tors are obtained and discussed. The analysis assumes infinitely wide plates,

but the question of finite width plates is addressed.

Acknowledgement

The authors wish to express their appreciation to Dr. K. C. Chen of theAir Force Weapons Laboratory for suggesting this work and to Dr. C. E. Baumfor reading this paper and offering numerous suggestions f-orits improvement.

5/6

1. Introduction

The parallel plate transmission line provides a useful means for

measuring the electromagnetic field interaction. In-this configuration

riearlyuniform electric and magnetic fields are produced, and instru-

mentation can be placed beneath one of the plates. There is, however,

a practical problem associated with the design and excitation of the

parallel plate transmission line; namely, one must provide a transition

section, typically one or two conical transmission line sections, between

the source and the parallel plate configuration (see Figures 1 and 2).

Insofar as the transmission line mode is concerned the transition.

section poses no problems provided the conical line and the parallel

plates have approximately the same cross sectional shape at their inter-

face and provided there is a match between the characteristic impedances.

However, the spherical wavefront propagating along the conical line does

not match the planar wavefront of the TEM mode in the parallel plate

region, hence the

TEM mode occurs.

not sufficient to

excitation of TE and fi waveguide modes as well as the

Finally, in some situations a single input section is

produce the required field strengths. In these cases

(usually wide plate separations), dual input sections are used. Wnen

using dual input sections one must allow provision in the analysis for

the fact that the sources may not fire simultaneously.

In studying the interaction of complex electrical systems with the

electromagnetic pulse generated by a nuclear detonation, the parallel

plate waveguide can be used to simulate the interaction. The electro-

magnetic pulse may be simulated by driving the parallel plates from

7

..

NJ4-m&

cm

pulser

width of top plate = 25m

12.75 Zc = 90 ohms>,/,/,// ,,/,,/

1- ‘O+’I-’J q

/

A’LECS

width of top plate = 40m/

Zc = 125 ohms

t-78-----++-”-ARES

Figure 1. Schematic Diagramdimensions are in

of Twometers

Parallel Plate Simulators. Note that alland the scale is lcm ==25111.

0

t-1

r-d--4

I

w

I

PI II I

1- 4I 210 I 80 ~ 100 I

‘i I 1

I (nominal) 1

~52.5 ,y—-\ ; ;

I I

~i’

\

I I /’ \;apex [

E- 75.7—F - -

\ workingI

\volume

I/

termination \\ /

/52.5 — - ‘

III

a~ex I

II38.9 I

---1i—1

Ien”dof

trestleATTJM I: Design 5

outward earth sloping(nominal)

Tigure 2. Schematic Diagram of o Simulator with Dual Transitions Sections.(All dimensions are in meters)

Iex

NJ

inI

W

245-6 EEIP3-39

conical input sections with appropriate surge generators. ‘Mere

number of these simulation facilities currently in use. Example

geometries for single and dual input parallel plate transmission

simulators are showm in Figures 1 and 2.

are a

line

An additional complicating feature of these simulators is that they

are constructed as finite width parallel plate transmission lines. The

properties of the TEM mode on such a s~ructure have been studied exten-

sively [1,2]. Other studies [3] have shown that the waveguide modes

for open region waveguides differ considerably from the modes of the

more familiar closed region waveguides. The excitation coefficients for

the modes in an open region structure are obtained by matching boundary

conditions at the interface between the conical input section and the

parallel plate region as well as on the waveguide walls [3]. Apparently,

integral equations must be solved numerically to obtain the coefficients

and propagation constants. Due to the complexity of these problems,

the finite-width parallel plate configuration is approximated by using

infinitely wide plates. However expected differences resulting in the

data that are obtained

The analysis that

measured data and with

are noted and discussed.

is presented is validated by comparisons with

data obtained by other investigators.

.

0

.

EMP 1-27 _._.

2.

a. Physical

Electromagnetic Fields in

Waveguide with a Single

Model

One wishes to obtain the electric

plate region of the structure shown in

an Infinite, Parallel Plate

Conical Input Section

24.5-7

and magnetic fields in the parallel

Figure 3 in terms of known quantities

in the input section and the physical dimensions of the parallel plates.

Several simplifying assumptions are made. The plates are assumed to

be perfectly conducting, the analysis is performed in the plane ASB of

Figure 3, the wavefronts are assumed spherical in the conical section and

written as

-jkr .F(X,z) = Vo: e (1)

where r’ = x’ + (z+ ZO)2 (see Figure 4). Also, it is assumed there

are no reflections in the conical section from the parallel plate regionp

and the electric field in the aperture.AMB, Figure 4Y is assumed to be a

planar section of a spherical wavefront.

b. Mathematical Model

If one assumes the apex of the conical input pulser generates spheri-

cal waves, a magnetic current source = - independent of y- is located at

the plane z = O and ~ is given by [4]

where i is the electrica

z = o. From the method of

— —

ii= Eax;

field strength

images,

M= 2Eaxi=-2(~a*

(2)

at the aperture or in the plane

4 )Y” = My ; (3)

11

245-8 EMP 1-27

A

t

A

WE---- .-------A

Figure 3. A Parallel-PlaEe Waveguide with aSingle Conical Tnput Section.

12

m Am

LmJ..w,..-I

m--4

?A

A

Y

B

A

x,

a12 -1 volt I

\“\

\\ ;

J A

r—r

\

\

/ii \1

) II

II

13,p

Figure 4. Two-Parallel-PSate iJaveguidewith a Single Pulser.(Longitudinal section through apex S.)

II 1

11’

245-10EMP 1-27

Substitution of (1) into (3) yields

-jkrc

M = -n e 6“;Y or

o

Since 6 ● ~ = COSO = zo/ro , it follows that

M = -2z0Y

wi~ere r= = xZ+Z:. The constanto

voltage between the plates to unity:

rA –

(4)

-j kro

voe2 (5)ro

V. is defined by normalizing the

i.e.

“B

Choosing the spherical wavefront Ehrough A and B as the path of integration,

i.e., r =f, one finds o0

and

-z -jk(~ - !)NV =

o 0e V/m

80(X2 + z:)

For a charge and current free medium, Maxwell’s equations are

(7)

(8)

(9)

EMP 1-27 245-11

where E and u are the free space values of

and the time dependenceejut

is understood

permittivity and permeability,

btitsuppressed. Since E is

be infinite in extent in theY independent and the

y direction, Maxwell’s

plates are assumed to

equations must be y independent. Thus, for TM waves

(V:z + k2) HY

= jucMY

(lo)

(11)1 “~

E=-—-x ju& az

aHyE“=~—

z jLoS ax(12)

a2 + a2where v2=—— and k =

Xz2Tj).

3X* a~2U/c=

is

c. Frequency Domain

o The standard technique for solving (10) s functionthe Green

G(x,z\x’,o)method; i.e.,

6(X-X’) 6(Z)

H isY

replaced by and M is rep-lacedY

Thus, to find G one must solve>

(13)(V’z + k2) G(x,zix’ O) = jus d(x-x’) 6(z)

Additionally, G must satisfy the same boundary conditions as HY’

(i)“aGZ=o

G is assumed to be a Fourier series of even and odd terms

z45-12 EMP 1-27

.

G= [11 > ‘b:(z)Cos ~n=0,2,4,...

with superscripts e and o representing even and odd integers respectively,

and

E . 1n

if n=O

. 2 if n#O

The solution of (13) for the even terms in G is

where kz = kz - (nn/a)2. To obtain He , one evaluatesn Y

~

a/2

H~(x,z) = My(x’) Ge(x,z\ x’,()) dx’

-aj2

It follows that

-j knze

‘%(15)

the integral

zoimejkk

[1

-jknz

H;(x,z) = ~ a 1‘n nmx e-Z

A: COS ~kn

o n=0,2,4?...

where

a/2 -jk~x~2 + ~2

J

n7rx’ e oA; = Cos — dx‘

a x !2+22

(16)

(17]

(18)

o-a/2

16

EMP 1-27 245-13

Similarly, one can solve for the odd

zom2jk~H“(x,z) =

8oan=l.

terms with the result

,.,

and

niTx2

-jknzekn

(19)

A: for single cone excitation is identically zero; thus

zowejk~ -jknz

Hy(x,z) = ~ a 1 En Aneos+ ‘k (21)o n=0,1,2,3,... n

In (21) it should be observed that the summation is now over all integers,

and

a12

~

~o~ 2n7x’ e-jk4x’2 + z:

An =a

dx‘x12

0+ Zo’

and

k2 = k2 - (2nn/a)2n

Use of (11) and (12) in conjunction with (21)

(23)

leads to

2nVx -jknz—ea

~ ejkl

Ex(x,z) = ~ a ~ & A COS

o n=o n n

27TjzoejkL -jknz

Ez(x,z) = ~ nA sinmek00 a2 n an=() n

(22)

(24)

245-14 EMP 1-27

The first terms in (21), (24).and (25) represent the TEM mode and all

remaining terms are .TMmodes. For finite-width parallel plates TE modes

also are exctted and propagated [3]. Moreover the

rably less attenuated than the TM modes. For both

attenuated above cut-off due to the radiation from

the waveguide. Thus the results that are obtained

wide plates must be interpreted

d. Time Domain, Magnetic Field

carefully.

Having obtained the frequency domainexpressions

TE modes are conside-

secs, the modes are

the open sides of

for the infinitely

in section c, one can

proceed in several ways to evaluate the time domain results. From (21)

[and also (25) though this will not be discussed] one can solve the time

domain problem analytically. From (24}, one can evaluate the field at

various frequencies and by means of numerical inverse Fourier transform

[5] determine the behavior in the time domain.

Showing the u-dependence explicit?, one can rewrite (21) as

Hy(x,z,w) =Zo

—A(u)ej(!&z)w/c

eoarl o

220 En

+;j~~os 2n?l’x

—An(u) M Fn(z,@ (26)an=l o

with

~

a/2 -j ~Jx’2 + z:

An(u) =2nTx’ e

Cos — dx’a X!2+Z2

o 0.

4fJJ2 2nTf2jwl/c -jz ~- (~)

cFn(z,w) = e

e

4

2 2nTr 2j ~-(~)

(27)

(28)

18

●

245-15EMP 1-27

.

and

n.-

a particular u or theThe expression in (26) is the frequency response at

the step function,u(t)response to a d(t) input. The

u(t) =

Fourier transform of

o t<o

(29)

-.

ftictionfrom which it follows that the respon-seto the step excitation is

t) =

=

z1 M 1Td(u) -t”* Hy(x,z,u) e

jut du

5-m

h; (X

(30)

h‘0 + ; h~nY n=1

where o and n refer to the zeroth or nth term. Rewriting the h~” and

collecting terms in a convenient manner, one obtains

and

f(t,!,z,x’) = t + (! - z)/c-[~xft + 22

Ollc

Thus, (31) becomes

[

Ut+‘ot30aV

1

x‘2+2:hso

Y

19—

●

245-16 EMF 1-27

and, since g>dxlz+zzo

, then if— t > z/c—

soh= J-Y aq

t > z/c— (33)

In general one must evaluate (32) subject to the condition that

Ct > lx‘2+22+2— o

Since x’ varies, this means the integral

ways depending on the time, t .

-E

must be done in one of three

1. Ifct<zo+z-R, the integral in (32) is identically

zero.

1[1

2

2. If Zo+z -k < Ct < Z+Z-k,; ’20

the upper limit on

this integral is

x= J(ct+R-z)2-z2’u o

~( 1

2

3. If et > +Z2 -f-z- ! ,— : the upper limit on the integralo

is a{2 .

These statements are basically causality conditions.

Using the identity d(u) d(u) = d(u) $(0) , one finds

c%j-m

(34)

“-l

J

*

d(:)CO

a

20

.

EMP 1-27

The

the

second integral in (34) can be

identity

transformed analytically [6]

..

245-17

using

(35)

where J is the Bessel function of the first kind.o

The final result.of

these manipulations is

Jo&=@x’2+z:)2-z2 p’ (36)

Again, the integral in (36) must

ditions discussed for (32), and

d)2

(e;g., if” Ctj (: + z;,+ z

(36), for hs , must be evaluatedY

be evaluated subject to the same con-

fl depends on the evaluation of (32)

-!2,, then fl = l,). The expression

numerically. First, definea new function

Y(N) which is identical to h; except the summation runs from one to N

rather than from one to infinity. The function Y(N) versus N is shown

in Figure 5. The

●

One other comment

function “calculatedin the pzogram is def.ined

hj(x,z,t)

is appropriate.

4; Y(N)= N=20

21

The integrals

(37)

in (37) are evaiu.aced

using a 15 point Gauss-Legendre quadrature formula. As n increases, the

function to be evaluated oscillates more rapidly. Therefore a change

of variable is performed such that as n increases, the number of Gauss-

Legendre zones from X’ = o to X’ = a./2 increases proportional

The y component of the magnetic field, h~(x,z,t), due to

function excitation is plotted with respect to time (t) and shown

to n.

a step

in

..._ .__.. —_—_—=—_ .

21

.

245-18 EMP 3-39

,52

.66

i I I

[ II

I1I / /I

I 1 I

/I II

I1

I

I I.— ___ --- ____ _

1- -1----–-—--l——— ----- :---------

1 [ I I

t I

1 I

ii

I I

I

I

I [

I 1,{ I

.280 40 80 11 120 160 200

Figure 5. plots of y(~l)versus N, (with a = 40 m, Z. = 20 matx= 0andz=50m for t = 160 ns)

22

245-19

Figures 6 for several field Points in an ALECS*-tvPe facility, while

Figure 7 is appropriate for the ARES** geometrv. Note that time is

measured from t = O , the time at which all the dipoles in the plane

z = O have turned on. Corresponding frequency domain (Fourier Trans-

forms of hy) are shown in Figures 8 and 9. Note that singularities occur

at the cavity resonances of the parallel plates.

e, Time Domain, Electric Field

The electric field calculations in the time domain have been per-

formed using the inverse Fourier

tion. Ex(x,z,w) , (24), has been

varying from the d-c term to 100

follows:

f

o

.5 -lMHz

1- 10 MKz

10 -100’ MHz

transfom rather than an analytic solu-

evaluated for 100 different frequencies

MHz . The frequencies chosen were as

Af

-~

,lMHZ

,2MHZ

2 MHz

ex(x,z,t) has been evaluated using standard Fourier transform techniques:

in this procedure tt is assumed that Ex(x,z,u) is a linear function of

frequency between the individual calculated field values [5]. Since

EX(X,Z,U) as given by (24) is the impulse response then it must be multi-

plied by the Fourier transform of the actual pulse driving the plates--

in the previous section this pulse was assumed to be a unit step.

‘t~irForce Weapons Laboratory/Los Alamos Scientific Laboratories~lectromagnetic Pulse ~alibration ~nd ~imulation Facility.

*i:~dvanced~esearch Electromagnetic Pulse ~imulation Facility.

1.2

0.4

.4

0

.

ALECS SIMULATOR

x =5, Z=3

........ ~=o ,2=3

20 40 60 80 100 120 140nst

Figure 6: The horizontal magnetic field produced by a unit-step

excitation of the ALECS simulator.

.

0.07

0.06

GYi

n 0.04u.N2

bs

0.03

0.02

L

o

I .

I..

I .

I ..

I .

I..

I .I .

.I .

I ..

I .

I..

1 .

t ..●

✚✎

✎

I ...............

I

III

ARES SIMULATOR

x=5, Z=15

.......... x=5, Z=lo

----- . X-5*Z=5

I 1 I I 1 I I I I

o“ 20 40 60 80 100 120 140 160ns 180t

Figure 7: The horizontal magnetic field produced by a unit step excitation of theARES simulator.

I

I

I-J

I

,,

245-22 EMP 1-27

t ALECS SIMULATOR

t-

N 10-’1s

—

~

k“.k.‘ “b.~j“.

x =5, Z=3

.. .. .. . . . . X’O, Z=3 .

1 I , I 1 1 I i i II I i , 1 I I I I III

.1 1 10 1Jo

f in MHz

Figure 8: The Fourier transform offield produced by a unitALECS simulator.

the horizontal magneticstep excitation of the

26

.

EMP 1-27

$

‘3.N

x*

4~o-lo

10-’1 :

10-12.

I

ARES SIMULATOR

. . . . . . . . . x =5, Z=5

—x =5, Z=1O

---- X=5, Z=15

“.

245-23

f in MI-Iz

Figure 9: The Fourier transform of the horizontal magnetic. field produced by a unit step excitation of the

ARES simulator.

27

245-24EMP 1-27

However. for convenience in applying the inverse Fourier transform here

the unit step with exponential damping is considered, i.e.,-at

u(t)e

where a = 4.8 X 105 S-l .

The complex magnitude of the Fourier transform of the vertical

electric field is shown in Figures 10 through 1.5. In contrast with the

results of Figures 8 and 9 the Fourier transform of the vertical electric

field does not exhibit singularities at the cavity resonances. Results

appropriate for the ALECS and ARES simulators are given. Note that it

is only when the frequency is above the lowest cut-off frequency that

there is any z-dependence of the fields.

Time domain results for the vertical electric field are shown in

Figures 16 through 21. These indicate that the TEM mode contribution

is dominant.

f. Comparison of Experimental Data and Theoretical Results

for the ALECS Facility

In 1974 Giles et.al. [7] evaluated the performance of the ALECS

facility in the CW mode. In particular, ~ and b measurements were made

versus frequency at the center of the working volume. Figures 22 and 23

shown the results Of these measurements. On the same figures one can

see the results of the theoretical analysis for CW performance. In

order to compare results, B and Do were chosen such that theo

experimental and theoretical results matched at 5 MHz.

Before interpreting the foregoing results, the question of finite

width versus infinite width plates should be considered. Marin [8]

found that for finite width pIates the TE modes were most important,

i.e., they exhibited less attenuation above cutoff, and the analysis

28

EYP 1-27

G.+

‘3.

IL

1--

.1. I

.01I1

\\

‘\\

.\

\

ALECS SIIHJLATOR

—.—. X=5, Z=3

----- X=0, Z=3

I I I 1 I I I I II I I I I I 1 I I I I I

10f

100 HHz

Figure 10: The Fourier transform of the vertical electricfield produced by a unit step (with exponentialdecay) excitation of the ALECS simulator.

29

245-25 ----”

EMP 1-27

ALECS SIMIJLATOR

‘\‘\

‘\‘\

‘\

,*

—.—. X=5, Z-8-..--- Xmo,z=g

Figure 11: The Fourier transform offield produced by a unitdecay) excitation of the

100 NHZ

the vertical electricstep (with exponentialALECS simulator.

30

lilt’!?1-27

.5

‘3.\Nx’

xr.4

1

.1

.01

245-27,.

1-

I \,\

ALECS SIMULATOR

—-—. x=5, Z=13----- X=o, Z=13

I[ I I I I I I I I I I I I I I 1. I I I I I

1 10 100 MHz

f

Figure 12: The Fourier transform of the vertical electricfield produced by a unit step (with exponentialdecay) excitation of the ALECS simulator.

31

245-29 EMP 1-27

—

3.N

i’x

w—

.1

.01

ARES SIMULATOR

—.—. X=5, Z=5

------- x= Cl,z=’5

1 10f “

Figure 13: The Fourier transform offield produced by a unitdecay) excitation of the

100 MHz

the vertical electricstep (with exponen~ialARES simulator.

32

,

EMP 1-27 245-29

—.

Nz

.

—

.1

.01

—.—.

-----.-~v

SIMLJLA;”OR

x=5, z = 1.0

X=o, Z=lo“\*

\,\

1. ‘\‘\\

\*A

“\.‘+%,

%,‘t’:,

>, ~“i

.’.

x’:>,

‘\‘>

“A*

I

1 I I I I 1 I I I 1 1 I I I I

1

I I I I I

so 100 N!llz

f

.

Vigure 14: The Fourier transfom of the vertical electricfield prodllcedby a unit step (with exponentialdecay) excitation of the ARES simulator.

33

—

245-30 E3fP1-27

I‘\,

\\\

1 ‘\,\,

\-

.11\\

\●

ARES SINULA~OR

—.—. x = 5, z = 15

\*

“\‘\.

\,

\,\,

“\●\

.Olt , I I I I I I III 1 I [ i I I I III ,1 10

f

Figure 15: The Fourier transform offield produced by a unitdecay) excitation of the

100 MHz

the vertical electricstep (with exponentialARES simulator.

34

--J

,, ,,!,

mL_n

h5

30

15

0

1.5

-30

,!,

‘1

1’‘1

I------ ---

;

IIIIIIII

I ALECS sIMULATOR

X=5, Z=3

——. . X=0, Z=3

t 1 1 I I I

o 20 40 60 80 100t

Figure 16: The vertical electric field producedexponential decay) excitation of the

120 140 160ns

by a unit step (withALECS simulator.

,’

,,

E

~

c.ri.*.

N

i’--j

..

45

30

15

0

15

-30

I

III

AJ.ECSSIMULATOR

x= 5,z=8

---- X=0, Z=8

I II 1 1 t I 1

0 20 40 60 80 100 120 lz~() 160ns

t

Figure 17: The vertical electric field produced by R unit step (with

exponential decay) excitation of the A’LECSsimulator.

o

o

~, ,,

w--4

,:,!,’

1.

G.d

.

N

45

30

1.5

0

-15

-30

!11,’

1,

,’ I

II

ALECS SIIJIULATOR

x=5, Z=13

I 1 I 1 1 1 1 L

o 20 40 60 80 100 120 140 160ns

~

Figure 18: The vertical. electric field produced by a unit step (with

exponential decay) excitation of the ALECS sj.mulator.

(J

I

I

>

um

--1o

-20

1’I1I

ARES SXMULATOR

x= 0,Z=5

—--- X=5, Z=5

I 1 I I I I I I

(1 20 40 60 80 100 120 ~L/() “160nst

Figure 19: Tilevertical electric field produced by a unil step

(with exponential decay) excitation of the ARES shmllator.

o 0

3(

20

1.0

0

-10

-20

,,

‘ \ARES SIHIJLATOR

x=5, 2=10

—--- X=o. 2=10

0 20 40 60 80 100 120 140 1.6011s

t

Figure 20: The vertical. electric field produced by a unit step (with

exponential. decay) excitation of the ARES simulator.

.

I ,,

1’

I

,’

F-I$-.mIwm

z.c)

?7

.L8

9

0

.-9

-18

ARES SIMJMTOR

X=5,2=15

---- X=o, Z=15

I I I t I I I I

(1 20 40 60 80 100 120 ]/,Q 160ns

t

Figure 21: The vertical electric field produced by a unit step (with

exponential decay) excitation of the ARES simulator.g

0 @

EMP 1-27 245-37

I20

t

10-Jno 5-[

cmo

0N I — Measured

1

-lo

-20r ----- Calculated

/

1-30~ I , I

10 20 30 40 50 60

Figure 22:

f(in MHz)

Evaluation of the Chlperformance of the ALECSfacility-e-lectric field determination inthe working volume at– x = O, z = 7.5.

41

245-38 EW? 1-27

20 t I I I1 1. 4 I

ml r 1II

-lo

— Measured

-20 ----- Calculated

t

1

I30~ r : t , , , ! t t , 1

10 20 30 40 50 60

f(in Miiz)

Figure 23: Evaluation of the CW performance of the ALECSfacility-magnetic field determination in theworking volume at x = O, z = 7.5.

42

EMP 1-27 245-39

used here did not-include TE modes. 8i;t since the TEM mode contributes

very significantly to the simuLator field there is good agreement between

the measured and calculated data as is shown in FiSures 22 and 23, The

disparity increases significantly at higher frequencies partly because

reflections from the termination (not included in tbe analysis) become

more significant and partly because the waveguide modes supported by the

actual Finite width waveguide have radiation losses. The very sharp var-

iation in the calculated magnetic field may be attributed to--theonset of

mode propagation, e.g. the cutoff frequency for the TM mode is about 12 MHz.

43

245-40 Em 1-27

3. Electromagnetic Fields in an Infinite, Parallel

Plate Waveguide with a Double Conical Input Section

a. Physical Model

In some instances one wishes to obtain field values in the parallel

plate region of a simulator that are higher than those .a~tainablefrom a

single pulser. In these situations, one solution is to use two separate

pulsers and two input sections, Figure 24. One problem that arises is

the nonsimu~taneous firing of the sources, and the analysis must take this

into account if it is to provide meaningful data.

b. Mathematical Model

As in section 2, each source is assumed to generate a spherical

wave, E

~-j krE=vo— 6

r

where r = (xTa/4)2 + (z +2.)2 for the upper (-) and lower (+) cones.

Again, normalizing each source to 1 volt, one obtains a magnetic source

for the upper cone as

[-jk J(x - a/4)2 + Z02 - ~

-zoe 1

%Y =60[(x - a/4)2 + z~l

For the lower cone, the magnetic source becomes

-j k [“’(x+a/4)2+z~ - i

%==-)

Y 60[(x+a/4)2 + z~]

(39)

(40)

o

0

44

EMP 1-27 245-41

—

.—

pulsers ~1I

I

—— ——— ——— ——— —*double conical.transmissionline

input transitionI

two-parallel-plateand/or wave \ transmission linelauncher

17igure’24: A Design for a ?aral.lel-?l.ateTransmission LineSimulators. (VieT~parallel to plates and perPendicu~ar

to direction of propagation, or z direction.)

45

-.

245-42 EMP 1-27

.

●Substitution of (39) into (16) [the upper source analysis is performed

independently of the lower source] leads to

-j~z‘OEM~j?d %‘H~(x,z,L@ = ~ 1 T

‘A~cos~ek , 2> 0 (41)o n=0,2,4,... n

where

Ia/2 nRxf

Cos —ueA=

a-jk#(xl _a/4)2 + ~~

en

dx’(x’- a/4)2+z~

o

and

zowejk% -jknz

‘H~(x,z,~) = ~ ~ 1 ‘A~sin~ek , Z>oo n=l,3,5,... n

.

where

1a/2 sin nmx’

ue a ~jk~(x’-;/4)2+ z:A=n

e dx‘(x’-a/4)2 + 202

0

For the lower cone one obtains expressions for He andY

(42)

(43)

“o

(44)

Ho thatY

are

by

and

ueidentical to (41) and (43) except An and ‘h; must be replaced

f,Aeand ‘A” where

n n

Io nTx’

!2Ae =Cos —

a -jk~(xf+ a/4)2+zo2

ne dx‘

(x’+a/4)2 + 22-a/2 o

Io n?’rx1

.QAe = Cos — _jkd(xr+a/4)2+z2

a

(X’+a/4)2 + 22 e

o dx‘n

o-a/2

(45)

(46)

46

EM? 1-27 245-43

For nonsimultaneous firing of the sources, (41) and (43) should be modi-

fied so that they differ in phase by UT where T is the

between the firings.-.

c. Time Domain, Magnetic Field

The step response for the even terms in the upper

is obtained as follows. Expression (41) is multiplied

spectrum of the step function

time duration

,.

cone excitation

by the frequency

7rti((l))+%

and the Fourier transform is

03

‘- Ia/2 nTfx’

Cos —a -j~d (x-a/4)2 + zo2—.

e dx’ ‘(x’- a/4)2 + Z02

o

(47)

As in the single cone case in section 2, the u integral can be performed

analytically leading to

z‘h~(x,z,t) = *+L I

nnxaeo q

Cos —n=2,4,...

a10

.,

{0Jo ~ ct+2_d(xf-a/4)2+z2o

nnx’Cos —

a .

(x’- a/4)2+z~

2

]2- y 1dx‘

(48)

4_7-.

245-44

with the restriction that ct+!L- ~(x’-a/4)2 + zzo

u sosimilar fashion odd terms for the upper source, h,, ~

EMP 1-27

>2. In a—

and even and oddJ

terms for the lower source, !3hse and !Lhsorespectively, can be derived. o

Y Y

Finally, if one allows the upper source to fire after the lower source by

a time intervai T , one obtains

h;(x,z,t) = ~~(x, z,t) + ‘h~o(x’z’t)

+ ‘h~e(x,z,~l)+x so‘nY(X,Z,TI) (49)

where T1 = t + T . In detail. (49) becomes

2f

1

xz u

h~(x,z,t) = ~+~ ~o~ nmxl—

aaeo rl a

n=2,4,6,... o (x’- a/4)2 + 202

L

{ 4[ 2\+Jo& cT1+!L- / (~~ -a/4)2 + Z2

) f]-z 2

0 dx‘

-1

Ia/2 nTrx’

sin —+ & ~ sin= a

o an=l,3,5 (X! - a/4)2 i-202

0

[{4[

2Jo ~ ct+!?- J(x’ -

II

a/4)2 + 22 - 22u

( 4-J. ~

1]CT1+!-i(x’-a/4)2+z2 2 -Z2 dx~

o )

(50)

48

●

EMP—1. 2.7 245-45

The comments regarding the solution of (36) in section 2 are also

applicable to the solution of (50).

d. Time Domain, Electric Field

Having derived ‘H~(x,z,u)!,s

and Hy(x,z,u) , one can obtain theJ

Fourier transform of the vertical–electric field Ey,(x,z,~) from (24).A

Then, in exactly the same procedure as that described in section 2e,

time domain electric fields may be obtained using the inverse Fourier

transform. Also as before the electric field calculation is made for

exponentially-decaying, unit~step excZtatCon.-

e. Numerical Results for the ATLAS 1“:Simulator

an..

—While the ARES simulator can not propagate TE modes, the Atlas I and

the ALECS simulators can since the waveguide plates are a wire mesh and

hence can support currents transverse to the direction of propagation.

Therefore, the results to be presented subsequently are valid only in a

qualitative sense

the excitation of

should be treated

copious amount–of

since the analysis did not include TE modes. However,

the TEM mode and the asynchronous firing of the pulses

quite accurately by the analysis. Accordingly a

data is pfesented. Since the ATLAS I—simulator is still

under construction there is no measured data to validate the analysis.

For a detailed discussion of the predicted behavior of the ATLAS I

simulator the authors defer.to references [9] through [12].

First the Fourier transform of the vertical.electric field is shown

for various positions within the ATLAS I simulator with an assumed

typical asynchronousfiring of the pulsers. Magnitude plots are given in

Figures 25 through 28 for various points within the working volume.

‘The horizontally polarized, bounded wave simuiator commonly referredto as TRESTLE.

.-

49

245–46 EM? 1-27

2

.

— ~=3,z=75,T=5ns—-— x=13, z=75, T=5ns------ x=26, z=75, T=5ns

I I I 1 f I i i I f 1 I I I I I I 1 I I

Figure 25: The Fourier transform of the vertical electric fieldproduced by a unit step ~~it’nexponential decay)excitation of the ATLAS I simulator.

50

EMP 1-27

0–- r

—

‘3.N

2

1

,2

It-

1. .

0 “--”--” I@ ci

Figure 26: The Fourier transform offield produced by a unit

. __=_decay)excitation of the

245-47

X=o , 2=25, ~ :=5ns

.-....-.x=13, Z=25Y ‘=5nsX=26, 2=25, ‘r=5ns—.—.

1001312

the vertical electricstep (with exponentialATLAS I simulator.

51

.

245-48 EMP 1-27

xw—

2

1

..?

.1.

x=(l, z=,5,T=5ns......... X= 13, z= 5,r= 5ns—.—.x=26, z=5, T=~ns

1 I 1 I I I I { II 1 \ I I i I 1 I I I I I

c1 10f

Figure 27: The Fourier transform offield produced by a unitdecay) excitation of the

100 MHz

the vertical electricstep (with exponentialATLAS 1 simulator.

52

Em 1.27 245-49

.

X=g, Z=50, T=5ns....... X=13, 7,=50,~=5ns

‘-—” X=26, .2=.50,T=5ns

GWI

‘3.

1.

J ‘“k-=1

.~ll--l--u,l,lll ,, 1, i! .,1!1110

f

Figure 28: The l?ouriertransform offield produced by a unitdecay) excitation of the

100 MHz

the vertical electricstep (with exponentialATLAS I simulator.

53

245-30 EMP 1-27

For a unit step excitation (even with exponential decay), the waveguide

modes are much more significant for the ATLAS I simulator than for the

ALECS or ARES due to its dual input sections and due to its lowest cut-

off frequency for the waveguide modes being only 5.7 MHz. It is readily

noted that the higher order modes become increasingly significant with

distance from the input transition section. If only a pure TEM mode were

excited in the simulator then the magnitude plots of the Fourier trans-

form would be straight lines.

A significant contribution to the excitation of the higher order

modes is the asynchronous firing of the pulsers driving the input sections

of theATLASI simulator. This can be seen from figure 29. However, the

deep nulls in the curves at 50 MHz and 100 MHz are due to destructive

interference occurring as a result of the phase difference between the

two sources of the two input sections

As mentioned in the foregoing the ATLAS I simulator can support TE

modes whereas the analysis includes only TM modes. For finite width

plates both the TE and TM modes are evanescent, but for infinite plates

the modes do not radiate. Hence the effect of the TM modes is over

emphasized by the analysis (as shown in Figures 22 and 23) and the effect

of the TE modes under emphasized. One would expect then that the rela-

tive importance of the higher order modes as exhibited in Figures 25

through 28 should be representative. But the asynchronous effecc as

shown in Figure 29 should be quite accurate.

In Figures 30 through 33 the time domain vertical electric field

is presented for an exponentially decaying unit step excitation of the

dual input sections to the ATLAS I simulator. Note that at the center

54

s.

245-51

.

0

EMP 1–27

—

‘3r.

N

L

1-

1..L 1.

x=(), z=50, ~=2ns—

------- X=o, z=50, T=5ns—.—. X.o , z=50, ~=10ns

‘-l-k,

‘%w ~,<,...*‘“i’’-”.?

t

‘i ““p\ ,;,,i!;:,

L,,

i

.01 I1

I I I I I I II { I I I ! L

Figure 29: l%e !Fouriertransform off.iel~.produced by a unitdecay) excitation of the

100 I!XZ

the vertical electric

step (with exponentialATLAS I simulator.

55’

. .

2&5-52

x=0, z=5, T=5ns

--..- X =26, z=5, T=51M

—.— x= 13, z = .5, T = 5ns

E- (Z - !2/ +. Z*)C

Tigure 20: The vertical electric field produced by a unit step

(with exponential decay) excitation of the ATLAS Isimulator.

56

Em 1-27 245-53 --

X=o , z=25,T=5ns

.-.-...x=26, z=25,~=5ns

—.— x1813,~=25, ~=5ns

i I I I I I I I I I I I i ) ! I

o

Figure 31:

29 40 (jQ 80 100 120 140 160 ns

t- (Z - i -1-zo)”/c

The vertical electric field produced by a unit step‘-”(withexponential decay) excitation of the ATLAS 1simulator.

57

245-54 EMT 1-27

1-

c.+

.u 12.0.N;K

al 8.0

0.0

X=o, z = 50, T = ~n~

----- x= 13, z = 50, T= Sfls

I I I I I I I I I I I I I f I Io 20 40 60 80 100 120 140 160 ns

t- (Z - .t -t- zo)/c

Tigure 32: The vertical electric field produced by a unit step(with exponential decay) excitation of the ATLAS I

simulator.

58

24.0

20.0

‘H”L.

?, ~,$’ ‘..

*.

245-55

— X=o, Z=75, ~ =5ns------- X=13, Z=75, ‘T=5ns—.— x=26, z=7.5, T=5ns

1 I J I I I I I I I I I I I I I I20 40 60 80 100 120 1/’+0 160 ns

Figure 33:

t . . (z - P.-1-zo)/c

The vertical electric,field produced by a unit step(w”ithexponential decay) excitation of the ADLAS Isimulator.

59

245-56

of the working volume

26 millivolts/meter.

EMP 1-27

(x=O, 2=50) the peak electric field is about

Baum, et al. [12] predict that the value should be

about 20 millivolts/meter. In arriving at their result Baum, et al. use

ray theory primarily and account for the finite width of the plates. It

is further noted that the overail time domain response follows the pre-

diction presented by Baum, et al., considering that their assumed exci-

tation is a unit step. Also the general behavior at x = 13 , z = 50

follows the roughly sketched waveform that Baum, et al. predict for their

point c. They predict an initial peak of about 11 millivolts/meter

whereas the present analysis yields about 17 millivolts/meter, which is

quite satisfactory agreement in view of the completely different

analyses that are used.

In their predictions of the electric field produced by the ATLAS I

simulator Baum, et al. [12] do not consider asynchronous firing of the

input pulsers.

working volume

input sections

The effect in the electric field at the center of the

due to the nortsimultaneityof the excitations of the dual

is exhibited in Figure 34. First”there is an increase in

the rise time and second if the asynchronous time is sufficiently large,

e.g. T=lOns, a precursor peak occurs. These precursor peaks are

even more pronounced in the horizontal magnetic field computations as

shown in Figure 35 for the same location in the simulator. The magnitude

of the Fourier transform of the horizontal magnetic field is shown in

Figure 36 for a typical location in the ATLAS I simulator.

EMP 1-27..

245-57

32.0 -

24.0 -

6>s 16.0 -

9)

X=o, Z=50, T =2ns

------ X=o , 2=50, T=lOns

—“W X=O, Z=50, T.5ns

-8.0 I I I I 1 I I I I 1 I I20

I I40

I I60 80 100 120 140 160ns

t- (Z - ~ + zo)/c

Figure 34: The vertical field produced by aexponential decay) excitation ofsimulator.

unit step (withthe ATIAS I

61

245-58 EMP 1-27

X=o, z= 50, T = ions

——. X=o,z =50, ~=5ns

--- -. X=o,z = 50, ~ = 2 ns

1 I I 1 I I

130 150 160 170 180 190 200 nst

Figure 35: The horizontal magnetic field produced by a unitstep excitation of the ATLAS I simulator.

62

EMP 1-27 245-59

AU,AS I STMTJT,ATOR

x=(-),~= 50, T = 5ns

..

10-13 I I I I I I I I I 1 I I I 1 I I I I I

.1 1 10

f in MHz

Figure 36: The Fourier transform of the horizontal magneticfield produced by a unit step excitation of theATLAS I simulator.

63

245-60 EMP 1-27

References

1.

2.

3.

4,

5.

6.

7.

8.

9.

10.

11.

12.

Baum, C. E., “Impedances and Field Distributions for Parallel PlateTransmission Line Simulators,” Sensor and Simulation Note 21, AirForce Weapons Laboratory, Kirkland AFB, N.M., Jan., 1966.

Brown, T. L. and K. D. Granzow, “A Parameter Study of Two ParallelPlate Transmission Line Simulators of EMP,” Sensor and SimulationNote 52, Air Force Weapons Laboratory, Kirtland AFB, N.M., Apr. 1968.

Marin, L., “Modes on a Finite-Width, Parallel-Plate Simulator INarrow Plates,” Sensor and Simulation Note 201, Air Force WeaponsLaboratory, Kirtland AFB, N.M., Sept. 1964.

Dudley, D. G. and J. P. Quintenz, “Multi-Modal Transient ExcitationEffects in an InfinLte, Parallel-Plate Wave Guide,” Can. Jour. ofPhysics, 50, 2826 (1972).—

Taylor, C. D. and T. T. Crow, “Induced Electric Currents on SomeConfigurations of Wires, Part 1, Perpendicular Crossed Wires,r’Interaction Note 85, Kirtland AFB, N.M., Nov. 1971.

Campbell. G. A, and R. M. Foster. Fourier Integrals for PracticalApplications. D. Van Nostrand Co.. New York. u. 11. 1948.

Giles, J. C., M. K. Bumgardner, G. Seely, and J. Furaus, “Evaluationand Improvement of the CW Performance of the ALECS Facility,” EG & GReport AL-1085, 29 July 1974.

Marin, L., “Modes on a Finite-Width, Parallel-Plate Simulator IT.Wide Plates, ‘rSensorand Simulation Note 223, ‘Air Force WeaponsLaboratory, Kirtland AFB, N.M., March 1977 (revised September 1977).

Higgins, D., ~The Diffraction of an Electromagnetic Plane Wave bvInterior and Exterior Bends in a Perfectly Conducting Sheet,” Sensorand Simulation Note 128, Air Force Weapons Laboratory. Kirtland AFB,N.M.. January 1971.

Baum, C. E., “General Principles for the Design of ATLAS I and 11,Part I: ATLAS: Electromagnetic Design Considerations for Hori-zontal Version,r’Sensor and Simulation Note 143, Air Force WeaponsLaboratory, Kirtland AFB, N.M., January 1972.

Baum, C. E., et aI..,“Electromagnetic Design Calculations for ATLAS I,Design 1,” Sensor and Simulation Note 153, Air Force Weapons Labora-tory, Kirtland AFB, N.M., June 1972.

Baum, C. E., D. F. Higgins, and D. V, Giri, “Pulser Test Results andPreliminary Estimation of Transient Electric Field Waveforms inATLAS I,” ATLAS Memo 18, Kirtland AFB, N.M., October 1976.

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