———— ..—— ,.

f

.

Sensor and Simulation Notes .

Note 236

11 November 1977

.

The Dipole Nethod (DIES) in SGEMP Simulation “

G. A. SeelyScience Applications, Inc.

2201 San Pedro, NEAlbuquerque, New P!exico87110

Abstract

Some of the practical aspects of this sourcecurrent replacement-simulation technique are examined.A method is described for combining experimental dipoledata with calculated SGEMP volume currents. The resultsfor a limited parameter variation concerning the requi-site antenna grid are reported.

- -.—.. ..—

. *

SectionNo.

11

VIII

INTRODUCTION . . . . . . . . . . . . . . . .

TEST OBJECT DESCRIPTION . . . . . . . . . .

NUMERICAL METHOD FOR OBTAINING DIPOLE DATA

CONVOLUTION OF DIPOLE RESPONSE . . . . . . .

1. DERIVATION OF METHOD . . . . . . . . .

2. ANEXPJIPLE . . . . . . . . . . . . . .

3. CONT~Nuous-\JAvE”DATA . . . . . . . . .

4. EXPERIFIE!IITALCONSIDERATIONS . . . . .

THE SGEhiPCALCLILATIGN . . . . . . . . . . .

.

.

.

.

.

.

.

.

COMBINING TECHNIQUE FOR DIPOLE DATA AND SGEMP\foLu~~~~uRRE~Ts . . . . . . . . . .

1. TIME DERIVATIVE OF SGEMP DIPOLE~L. FAR-FIELD EFFECTS

GRID DETAIL/VOLUME SIZE

i. GENERAL . . . . .

7k. RESULTS . . . . .7 SUWARY . . . . ..).

CN{CLUS1ONS . . . . .

1, GE!iERAL . i . . .

?-. CONCLUSIONS . . “

3. 2ECCi%lEt!DATIONS.

REFERENCES . . . . . .

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PageNo.

5

8

10

25

25

31

34

38

40

42

42

43

45

45

47

54

55

55

56

56

58

‘“

2

b

ILLUSTRATIONS

FigureNo.

1

2

3

4

5

6

7

8

10

11

12

13

15

16

Test ObJect Geometry. . . . . . . . . . . . . . .

Planar View of 2-D.Geometry Showing DipoleRing Positions . . . . . . . . . . . . . . .

Time C)erivativeof_the Ring Dipole Moments . . “ o

Cylinder Response for z-Directeclat (z/a, p/a) = (0.125, 0.0’

Cylinder Response for z-Directedat (z/a, p/a) = (3.125, 0.0

Ring Dipole. . . . . . . .

Ring Dipole. . . . . . . . .

Cylinder Response for z-Directed ~ing Dipoleat (z/a, p/a) = (0.125,0.75) o “ “ . 0 “ o -

Cylinder Response for z-Directed Ring Dipoleat (z/a, p/a) = (-0.875, 3.50). . . 0 . 0 “ “

.Cylinder Response for z-Directed Ring Dipoleak.(.z/a>P/a)_= (3.125, 3.5o) . . . . . . . .

Cylinder Response for D-Directed Ring Dipoleat (z/a, g/a) = (0,25, 0.125) . . . . . . ● .

Cylinder Response for p-Directed Ring Dipoleat (z/a, p/a) = (3,00, 0.125) “ “ “ “ Q “ “ “

Cylinder Response for ;-Directed Ring Dipoleat (z/a, p/a) = (0,25, 0.875) . . . . . . . .

Cylinder Response for p-Directed Ring Dipoleat (z/a, p/a) = (-1,00, 1.625). . . . ● . . .

Cylinder Response for ~-Directed Ring Dipoleat (z/e,= 0/’2)= (-1.00, 3.625) . .: . ● .. .

Cv]inder ResPonse for ~-uirected l?itlg ~ipO~e.

dt_(z/a, ?/a) =.(3,00, 3.625) “ “ “ . 0 s o s

Convo

Convo

ution Methcd Test. . . . . . . . . . . . . .

ution P?ethod?esu?t . . . . . . . . . . . . .

PageNo.

.=

9

12

12

14

15

16

17

18

19

20

21

22

23

24

32

33

3

FigureNO.

17

18

19

20

21

22

23

24

25

Illustrations (continued)

Cylinder Response Obtained from the SGEMP Calculation . .

Cylinder Response Obtained from Convolution withall.25cmGrid . . . . . . . . . . . . , . . , . .

Cylinder Response Obtained from Convolution witha22.5cmGrid. . . . . . . . . . . . . . . . . . .

Cylinder Response Obtained from Convolution withaVaryingGrid. . . . . . . . . .. . . . . . , . . .

Cylinder Response Obtained from Convolution withaVaryingGrid. . . . . . . . . . . . . . . . . . .

Cylinder Response Obtained from Convolution withaVaryingGrid. . . . . . . , . . . . . . . . . . .

Cylinder Response from the SGEMP Calculation witha Slowly Varying Source . . . . . . . . . . . . , .

Cylinder Response Obtained from Convolution withall.25cmGrid . . . . . . . . . . . . . . . . . .

Cylinder Response Obtained from Convolution witha22.5cmGrid. . . . . . . . . . . . . . . . . . .

4

PageNo.

48

48

49

49

50

50

52

52

53

● ✎

0SECTION I

INTRODUCTION

The system-generated electromagnetic pulse (SGEMP) effects on a satel-

lite may prove to be the dominant effects governing satellite survival and

yet these effects are not well understood. There is, at present, no simu-

lation facility which can realistically simulate the satellite environment,

to excite a complete satellite. Consequently, other techniques must be used

in the interim to investigate the complicated phenomenon created by electron

emission from the surface of a satellite.

A novel technique has recently been suggested by Baum (References 1

and 2). The basic simulation scheme involves measuring a transfer function

between an infinitesimal current element outside the system under test and

a critical circuit element buried within the system, Using calculatedSGEMP volume currents, weighted integrals of the transfer functions and the

volume currents yield the total SGEMP response at the circuit level.

o In effect, the technique attempts to take advantage of the better

aspects of the two methods. The electrical response of the interior of a __

large complicated system is at present b-etterdetermined by measurement.

The exterior problem, on the other hand, is presently more amenable to

analysis using existifigSGEMP codes.

Several potential obstacles to implementing this technique immediately

come to mind. Upon closer e;{amination it becomes apparent that most of

these are closely related to a single parameter: the number of dipole posi-

tions required to accurately simulate the external environment.

For example, the most widely used electromagnetic pulse (EMP) simu-

lators (i.e., ALECS, ARES, TEMPS, SIEGE, RES, TORUS, ACHILLES, ATHAMAS,

...) are, this context, single source simulators. That is, the source

doesn’t change during the test (although a few penetrations may be driven

concurrently with the test). With the dipole method, several antenna

positions would be required, with data taken at each antenna position.

The time and cost for the measurement of responses on the satellite

for many dipole volume elements can be circumvented to some extent by using

automated recording instrumentation such as ABACIS* and by constructing an

aut~mated device for moving and positioning the dipole antennas.

This, however, is not the totai answer. The potential for error goes

up rapidly with an increase in the volume of data handled. If many measure-

ments are required, system checks and assurance of data quality suffer by

the sheer time and cos

amount of data. Ifs’

in the instrumentation

caught until the test

home.

limitations imposed by the need for such a large

arge volume of data is required, then potential errors

system and errors in annotating the data may not be

s over, the system dismantled, and everyone has gone

. ●

o

A fine grid detail would necessitate the use of very smal~ dipole

antennas, As size goes down, it is generally true that signal/noise problems

increase which can make it difficult to obtain reliable data. Transmitters,

power supplies and other equipment associated with the dipole antenna would

have to be scaled down accordingly fcr an equivalent quality of data. This

problem is compounded by the rapid variation in both space and time (frequency)

in the near field o-fa dipole antenna. Equipotentials are not available for epositioning of transmitters or for cable routing from the antenna.

An actual satellite would be tested in a finite facility in which,near-

by objects and the earth could behave as reflectors and thereby degrade the

quality O? the simulation. For the close-in antenna positions, these effects

can be made smdll. This is not the case, however, for more dista~t measure-

ments. Not only does the signal/noise go down, the reflections can become

as large as the desired measurement. Thus, a ne~d exists, in some fashion,

to limit the volume size required for the simulation and, if possible, to

take Into account the more distant currents.

t+~Jj-onet1c2 ~po~~~ar]dp,u~om~~jcCalib’ratea ~rlS!VUMe!7~atiCrl sYStsm. Tfijs

continuous-wave system outputs magnetic tape and avoids the necessity ofdigitizing the experiments] data.

6

The requirements on the qual$ty of the experimental data and the calcu-

lated SGEMP currents increase as the number of measurements increase. The

technique for combining the analytical and experimental data would have to

be both accurate and efficient. This is particularly true if continuous-

wave data is recorded, since Fourier transforms and/or inverse transforms

would be required to combine the results.

Further examples could be given, the conclusion would be the same.

The number of measurements required to accurately simulate the external

environment is the single most important parameter impacting the practicality

of the dipole method. In detail, this depends on its implications concerning

volume size required for simulation, grid detail for antenna placement,

antenna size, requirements on the quality of the SGEMP currents, the experi-

mental data and the quality of the combining technique.

In vie~wof these considerations, an effort was undertaken to provide

preliminary data concerning these constraints. For the results to be specific,

a single two-dimensional test object was selected for treatment in the bulk

of the report.

This report is arranged in sections. The test object geometry is

described in Section II. The remainder of the report is devoted to a

description of–the computation techniques, followed by the results and con-

clusions which are presented in Sections VII and VIII, respectively.

7

SECTION II

TEST ~BJ~~T ~EsC~~pTI()~

The test cbject chosen f~r analysis is a right circular copper cylin-

der with a solder ccat sufficiently thick to prevent X-ray transport through

the walls of the cylinder. This two-dimensional object retains some of the

features of an actual satellite yet with the simplicities inherent in two

dimensions. In addition, some experimental and analytical data are available

on this test object (References 3 and 4).

FOP real systems, SGEMP must ultimately couple to interior circuitry

to be of concern. The test object has a circumferential aperture and an

interior axial post electrically connecting the base and the top of the

cylinder. The geometry used for the analysis js shown in Fig. 1.

+

*

8

● ✎

0 (

“/Incident X-ray pulse

“c

[ —45cm A

I— J~3175cm

I—

+43.175cm

1. Test Object Geometry.

i-

9

SECTION 111

NUMERICAL METHOD FOR OBTAINING DIPOLE DATA

1. GENERAL

At this stage of the investigation it was convenient to numerically

simulate the experimental dipole data. This would provide initial data for

use as testing functions for combining techniques, grid detail and volume

size without the expense of first doing the experiment, The numerical data

could also be retained for later comparison to experimental results, as well

as giving some indication of the importance of more distant current elements .

Direct t~me stepping of Maxwell’s equations In two dimensions was

chosen as the simplest available technique for obtaining the dipole-satellite

interaction functions.

The algorithm is a simplified version of the fields algorithm in the

MAD2 SGEIIIPcode (Reference 4). Special use was made of the simplicities

introduced by a single dipole source in any one calculation> and by usin9

a uniform grid size. Additional simplifications were made by factoring out

constants that occur repeatedly in the calculation.

The cylinder response results for representative dipole locations are

described in the following subsection.

2. EXEMPLARY DPsTA

Figure 2 displays the antenna positicns for which data is described

in this section. The numbers beside the ping dipoles ’correspond to the

graph numbers for the specific antenna positions and polarizations. In

Fig, Z, the z-coordinate is vertically upward and the c-coordinate

is ticrizo~ital.The coordin~te origin is located on the center top of t~ie

cylinder; a is the cylirtderradius (0.45 m).

.

0

Table 1 lj~ts the iocati~n of the antenna positions corresponding

to the graph number. Dimensions are given in units of the cylinder radius a.

10

.

TABLE 1

ANTENNA POSITIONS AND POLARIZATIONSFOR DATA PRESENTED IN SECTION 111

Graph Antenna PositionNo. z/a P/a Polarization

2

4

6

15

i8

T6

28

0.125 0.0

3.125 0.0

0.125 0.75

-0.875 3.50

3.125 3.50

0.25 - Q:J253.00 0.125

0.25 0.875

-1.00 1.625

-7.00 3.625

3.00 3.625

z-directed dipole

z-directed dipole

z-directed dipole

z-directed dipole

z-directed dipole

p-djrected dipole

p-directed dipole

p-directed dipole

p-directed dipole

p-directed dipole

p-directed dipole

Figure 3 displays the time derivative of the antenna dipole moment P

used to obtain the results in this section. The peak value of P is 1 Am.

The time scale_ct/a is normalized to the cylinder radius and the speed of

light. Thus, when et/a = 1, the time t is 0.45 m/O.3 ns/m = 1.5 ns.

The time dependence for the antenna dipole moment corresponds to the

time dependence for a critically damped series F(LCcircuit. Although not

crucial at this stage, this choice is a reasonable approximation for a

realizable pulse-driven small dipole antenna. The 10-90 rise time for the

dipole current in F~gure 3 is 1 ns.

The locations given for the tangential magnetic HC, HS (Am-l) and

~orwal electric EC, ES (Yin-l)fjelds ~re indic~~ed jn ~j~, 2+ The coordi-

nates zrz g?ven in Table 2.

11

,

Ring Antenna Positions/

4~

k 18

28 f--42

IIla Symmetry Axis

/I

iI

23(I-266 ~-

.----- --.--— 0~j-el~LGcatio I’ls

-34

Scale: Q/go

Figure 2. Planar View of 2-D Geometry Showing~ip,~?~.:,,:3PiI-qPositions.

-1?DOT (Am)

0.6

0.0 rI ! t

0.0 4.0 8.0 12.G 16.

12

.-- —.

TABLE 2

FIELD LOCATIONS FOR DATAPRESENTED IN sECTIoN III

Field .=Component

__..Locati.onz/a p/a

‘- HC (Am-l) -0.875 0.125

EC (Vm-l) -1.0 0.125

HS (Am-l) -0.875 1.125

ES (Vm-l) -1.O 1.125

Figures 4 through 14 display the tangential magnetic field and the.—

normal electric fields for the ir!dica.teciantenna positions and polarizations,

Data of particular interest is for the antenna position corresponding

to graph No. 2 (Fig. 4). This result would provide the simplest comparison

to experimental data when it is available.

An additional feature worthy of note is the persistence of the static

part of the electric field coupling to the cylinder even for antennas some

distance from the cylinder (ES for graph Nos. 4, 15, 28, 39, and 42).

In Fig. 12 (graph No, 34), it is of interest to notice that the normal

electric field on the cyl~nder surface ES is proportional to the antenna]s

dipole moment (t!letime integral of PDOT in Fig. 3). This would indicate

that at this distance, the normal electric field is dominated by the static

field produced by the dipole antenna.

13

0.00 +-.. —–___-— .....__ L..._~. L____l__—t-

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Ilc

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-121

,./1

02 >

-80.0 -242.-

Flcyrf!4. Cylinder [le~p,on,sefor z-Directed Ring Dipole at (z/a, P/a) = (0-125> 0“0).

e I oi, 11’If18Il,,klllllI 11111)h’,,,kII,!,’1, ,,~ 1,,,, ,,,,,,,, ,,, ,:

.

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0.

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-0.16

wwl

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-3.6

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_.-_-. L-.-.–-_.–. 1___ l-_ .—..

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:

—.—. 1

; II

~.. . .. . 1“--”~–,. 1

——-

11.M k+ M [!1. ,OLI 1.21-1111 I.LE101 2.IK+O1 J.11F41

(,1/(4

“x

P-’’’”

m-.-..2”-=”

–._._—.L-. __.. . . . l:----------- L. ___.–L _________

[C

—.—..-—,1......—-,-.—.‘~v\/.-.,_.—–.7 .–___

F_,—.

!.ul [11 tj ml 1]0 .a+ul 1.f.r111 2.u~l[) .111:+[:T”/?

{,

v ,,

Figure 51.

1’

0.08

0.04

‘o.u

-0!04

-0,.,08

32.0

16.0

0.

-16.0

-32.0

:

.—— —–L–—-- L—.._— L__——--–L__..l.__. —- .I11’3

—

7/‘r L———..————1, —~==—————

~ —__.aTc_—.’—_

u II+Ou H.lx+[1’[1I.’Y’IO1 I [Irtol Z.ll[”4 ill .!.lLl”{i)

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[1/n

Ii

—.l~l- -l——— —.L._-_—

Es

/\

b-+’-–-––------”-----1’l——l —m ..—_.,_, .-

ti.(IFI00 1.m 01 I.(x-+1)1c1 /17

2.. [II- fIIi 2.hri[

Ii

ICylinder Response ’’foi+’’DirectededRing Dipole at (z/a, ~/a) = (3.125,i0.0).

.

,,

!,

1’

2.oil

1.00

0.L

-1.0{1

-2.IM

!-0

1(N3.

50.

I

- 5nt

—. — _.. --.. -l_..—..—.———.——— —- L--–J-.——

IIL

, ~._._” —., –--——.-—

, –—.-...~ ———,

--4.lx+ Ulu

\

[J.w !0[1 I.LFIO1 l.Gr+ol 2.Qr,ol2,~fi’1[LI/[1

\‘\LL‘\ /’”,/‘\.__../-”” [;

.-.. .–.—..l— . . .. ...–.... l.-..—.--l-.—–-~ ———..~———

0.34

0.1

-0.34

-0.6U

300.

150.

0.i

-150.

11:)

I.-

L.–——l._—-..—_ l_——_____ l___ I—__——_

_+-——----———Es ———’-———

—-—”

/

-%/-..J---’_

/

-100.

Figure 6. Cylinder Response for z-Directed Ring Dipole at (z/a, p/a) = 0.125$,

9

.

*

::

0.050

0.025

0.

-0.0?5

-0.050

P.-J

14.4

0.

L

- 7.2

-14.4

..—- .. —-L -_.–..._. 1_.-.~_._-.. l_—––-__—___ .,.

_.... _. l_–—._.l_— —_..__.L.--~-

[: [,

I

--~+\!I%$v’u-

~J-

L

,,,1,

0.14

0.07

-0.07

-0.14

— —-L..—- J-_~_..–. ~.-L——_

1!2.

3.60 ____ I .~. J—-–_-L_L_ —__J,_—._

o.

-1.80

— —-,-—. ---~ ..—1 .Ix!ol Z. UE+U1 ‘?,I,F<,

-’”w’

J i5-3.60

Figure 7. Cylinder Response for z -Directed Ring Dipole at (z/a, p/a) = (-01.875, 3.50).

II

1,,,

1,

0.02

0.01

0.[1

-0,01

-0.02

wm

—.-.L_. —1 .———L_–_—_ ..l. ——l.-l —

t 0.04

I{L

‘i.I!F. [w

-0.04

4-M --t--—---—L””-—-~---J-------..-L””--- _._.-L___ 1-

2.15

0.

-2.15

.4. W

I 14.4

1.2

0.

- 7.2

.14.4

____ .1—. —–— L.–—-.__._.___..—___ .. L-—.-. ————L————-..

I l{.i

~—-- ... . .1_.___.—.._l_——.— L._ . . . .–.. L__ .. ..—

t

E“s

6’,.I

—-—---l--- — “%-=..2 - —-— -

flu fui Fjl. ;[’ l,dr{cli I. f,rl[ll

‘:1

,:.iJ~d\ ,!< W IU

(; I /u

JH

,_

Figure 8, Cylindei-Response for z-Direcwd Ring Dipole at (z/a, p/a) = (3.125, 3.50).

,0,,1,

: m

0.06

0.03

0.r

0.03

0.06

wu

4.00

?.(JO

o,[

-?.(IO

-4.00

._——–..l-—––_-l. – I____ L–.— —-l –-——–

tK

“—-T “i”-------1-~ r—-——’~

1\/i& IF+U[] H.w FOu 1.2E+01 , 1.6E+01 2.tiE+ol2.w+{

-1 f:”l”/Fl\ -\L.-\-“’-%-=’

—.—...

Ec

L—.. –_.. L____ ~._._..L----- ._ J_

26

..—.—

———....

0.02

O.oi

0.I

-0.01

-0.02

_._-— L–__.—___L _____ J_—— 1 ____ _ _..J _______

}{s

—--=-=–-”I””-=’-””W----- ““I.tiE+Ol .2.DE+O1 2.W

2[;

4.00 -

0. -0.

I-4.00 -

-8.00

~

Es

r’\,__,_-+-----_____ .“-----------

/r—L —. .—.~__ _-_T._

~q— ““‘- ‘-”T—-—- ‘“k.m+ou 8.OEMO 1.2E+01 1.6Ew1

CT)Fl2.nlE+ol2.w=lf

26

Figure 9, Cylinder Response for p -Directed Ring Dipole ‘at,(z/a, p/a) = (0.25, 0.125).

,,

‘,’

1’

I

0.(.KJ3

o,I

-0.003

-0.006

N

.—. ..—---.i---- —_--l-_ ~--&-_.__-_J ___

tic

O.ul

(3.40

0’.

-0,40

-0.80

.–.—-”-L .— — L J—-.---~.

v

28

0.010

0.005

u,c

-0.005

-U.010

4,0(3

2.00

0.

(1

-2.05

-4.00

.—L————_A_———J_.. -J—.—.—t------

tls

1..

—-——————J--___L-_--L___,J________

ES A

-/ ‘p \~f’’J——’ ‘--). ..._..--r —.

GEa a. 13c{.00y---—-.r-..—————.—

l..mdi I. GE+O1 Z.ufl+ol 2.w&CTIFI

28

gLlrL?1‘o. Cylinder Response for p-llirectedRing Dipole at (z/a, p/a) = (3.00, 0.?25).

O,,

I

:

U.06

().43

0.

-0..43

-0.86

NF

58.0

29.0

-2).0

..__. ~–— ... ..L—.–-..––-—.LQ.—.———~—~

W

_lr --,_.r.—-—— ~ .–-—..

7——. ——

‘- -4.<E+OLI 8. mm 1. $E+U 1 I .6E+01 Z. OE+O1 2.W+I

<. ,CT/R

30

–.——--.l---- —1..—~ _._—._.L.–._._L______–___

Ec

—// L~-- /

1 $,\\_Kl@———.—.—-—.—.1 I

—— —. \

4.oE+oo EJ.CIE+UO

~-—-. ~.

I . 2E+CI 1. +01

T]

2. OE+O1 2. w+l

CTIFIJ.,

\LJ”

30

‘1

11,1

0.18

0.09

0.[

-0.09

-0.18

115.

5J.5

0.

. 57.5

-115.

[

~–— l~..— L–___-.–.A._..-

Hs

30L

_---_J-J I I I 1

ES——--———————

._—---—————————/ ..-.r-

p7

L—–~_..-..–T – _._-.r---- , ––—

t. O’E+OO

~ -.–— .-

8. oE+OO 1.2E+01 1.EiE+O1 2. OE+O1 2. KE+{

CT/FI

30

~Figure “11. CylInder Response for kilirectea Ring Dipole at (z/d, pid) = (G.2~, 0.87 S). f

,J

I

0.46

0.2

(1.I

-0.2,1

-0.46

t-d 31.0m

15.15,“

o.I

-15,15

-–...~_—-_... ._—__—L—._..— _L~1

t

/.—-. . . ..— —. —...—-. ——. —-1l.&EILN

~.-.

n. kwrl

I

~ ...– -

1.2E+01 I-ff+ol 2.’UE+CI1 2.UE+O

criR

0.14 +————J————— -J L—_-_—-_l_._-.-l--------

0.07

0.

1-0.01

31J-0.14

..——–-l._-__l I ——-—--—.~~—..

EC

P-’1“

‘$y\........ . . P.+ Q=Q+’-----D. dlhon 0.Olzml 1.2E+01 I.5E+OL, 2.tw+nl 2.UEJ

cl-/Fl

,928.-

464.-

0...0.

-464.-

-92H.–

--—_.._––l_______J_ .L.-.-.__—._l___ ._l.__.-i-

ES

,.-—-— —,___ . . —— —.. —...I

\\

T—------r-----” ‘.-l-OIE+00 8,m too 1.2E+OI I .ix*o 1 2.OE+OI2.MEto

cl-/F3

\--. .... ___

—––—”-—3U1-.

Figure 12. Cylinder Respunse for p-Directed Ring Dipole at (z/a, p/a) = (-1 .00, 1.625).I

I

O) ,,, ! ,,,!8 h

::

0. 0,?

0

-IJ.ril

-0.02

NJu 2.UO -

1.40 –

o. -u.

-1.40-

‘ -2.00-

. . . . . .

_. ____L__-.J_— 1-—.—_.L -------J

/-.—-.+__—.T.----—

1 G- “T-7————U. OE+OO R.UE*UO 2.LIE+OI2.W+I

CT/fi

_–—. -l-..———J————

EC

0.014

0.007

0.

-0.0’07

I_ -0.0141

21.0

10.5

0.[

-10.5

1-..

-21.0

39

T——

-1————————— ——-r—--11.OE4-0,0

~.—.8.OE+OO 1.2E+U1 1.6E+OI 2. UE+O1 2-W+

CT/Fl

.- .-

39

= (-1.00, 3.625).

. . . —.

().070“.

0.035-

-0.lm

-0.0?0

P-J

.&2.1.0-

10.5.

-10.5

-21.0

-.–.—.-L-——— “– -.–l.——.-. ——J—————

112

1- — l—.—_—._————

$~%w,y...-s%-...——--—-.-——‘—L/1U.o+0’0 13,[K+UU I.lx+ol 2.!JE+O1;.W

cl /’i

II

_–. .—...L.—.—---–.——L—————————1_____--l. .......-.—J-—. – - -

0.030

0.015

0.

-0.015

-0.030

4.20-

2.10-

0. -n.

-2.10

-4.2U

__-—-._.l.–-—._ ..——J——.—————L____ .-—.-l.—-—. -J —

HC

-_— .. --- ..- -...

TT—. -— ---~.

k-lx+ 8. CE+lm 1.2Ei Ol l.iiE40’CT/R

\\“

__ .__—-. .“— - .— --~- .—-_–

2.UF.+012.W

-. —..-.___l_._——_l._.—..—.——l————~——J— —---.—

\

Figure 14. Cylinder Response for p-Directed Ring Dipole at (z/a, p/a) = (3.00, 3.625).

oI ! ,. ,,.,

,“,

e,1

,,,

CONVOLUTION OF DIPOLE RESPONSE

Use of the experimental dipole measurements-calculated SGEMP volume

currents will require “interfacing the two sets of data and combining them

to result in the predicted SGEMP system response. Be70w is a brief deriva-

tion of the method we can use when processing experimental pulse data. The

procedure would avoid the need for first Fourier transforming, combining,

and then inverse transforming back into the time domain at each antenna

location. The method is now described..

For specified volume currents, it is assumed that the system’s response

is linearly related to the system stimulus. Letting ‘ibe the response and I

be the stimulus, the relation can be expressed

m

V(t) =,( I(~)K(t - ~)d~ (1)

-m

Equation (1) can be thought of as a linear transformation frbm the set I to

the set V with the transformation being specified by K.

Also K is the impulse }“ssponse. Substitution of-I(t) = t(t) into Eq. (1)

results in e response V(t) = K(t).

A useful feature of+q. (1) is that if the response ‘iI(t)is known for

a specific stimulus Ii(t), then it is possible to obtain the response V(t)

for a different I(t). If I~(t) is an impulse (= d[t)), then the procedure

is quite straightforward. For the more general case-,it is useful to apply

a Fourier transform.

In several inst-antes,it–is possible to inverse t;+a.nsformthe inter-

mediate result directly so -thatthe final r~SIJl~ can be st?~~d QXp~jC~~~:/

in the time domain. This turns out to be the case for the stimulus Ii(t)

we are using for the dipole volume current (the volume current on a critically

damped series RLC circuit). The resulting expression is obtained below.

25

Direct Fourier transformation of both sides of Eq. (1) (and application

of the shifting theorem) results in

;(u)=;(Lo)’i(Ld)

where in particular

(2)

(3)

(The tildes refer to the respective transforms.)

For a critically damped series RLC circuit, the transform of the volume

current Ii(t) is given by

-m

(4)

where Ii(t) has been normalized to 1 Am at t = T (the peak amplitude), u(t)

is the unit step, and T is the circuit time constant.

Performing the integration in Eq. (-l),substitution of ~l(w) into Eq. (3)

*_

26*

.- -. -..

(7)

-m

K(T) ‘ +

[

Vi(T) + 2T *(T) (8)

where the inverse transform has been identified in

K into Eq. (1) and using a change of variable T’ =

(7). Substituting

(9)

-co,.. — ——

For pulse application, further sim~lifications occur.

I T<(2, VI(T)— =&(T)=o *

For

It < T, I(t -—

The final result is**

c

of casuality.*The condition on VI is equivalent to the condition**Concerning units, -recall” that the antenna volume current Ii(t) was normalized

to 1 Am at peak amplitude.

27

A useful check is to let I(t) = Ii(t). If Eq. (10) is valid, then

V(t) should be equal to Vi(t). First recognizing that

VI(T) + 2T ~ (T) + T’ ~ (T) = T2e-T~T ~ [eT/TV(~)]

and substituting this aridII(t - T) into Eq. (10)

(12)

Integration of Eq. (12) by parts twice results in

w (0) are zero.since V1(0)I at

The numerical analog of Eq, (10) fisnow discussed. All operations of

the convolution would be Ferformed cn a computer, that is, not a continuous

integration, but a summation on a finite mesh.

28

4D The numerical analog

time spacing is given b.y

of Eq. 10) that appears appropriate

k=2

------ V;l, v;, v;, V;=o

where the

t=

and dt is

subscript

superscripts refer to the time value

!L*dt, v(t) +VL

the time step. (The time has been shifted

on the computer. )

It will be shcwn below that the numerical

= Ii(t) is substituted into Eq. (15). In terms

by 2*dt to

analog is exact

avoid

iform

(15’)

(16)

(17)

a negative

of the finite quantities

(18)

when I(t)

29

Now 1et k = 6 for ‘example. Equation (15) becomes (performing the sum)

-- e[

-3%; 4 -3’2) + 21+‘2<’$-2(2’+‘1+‘-W2-21+“

o

30

.

2. AN EXAMPLE

Before proceeding further, a simple test was performed to gain confi-

dence in the method. In Fig. 15, graph No. 1 displays a critically damped

current density J1 at antenna position 2, the center top of the cylinder.

Graph No. 2 in the same figure is the resulting tangential magnetic field

“--Z-ancl3,-Section lll)-.Graph No. 3 in Fig. 16on the cylinder side, ”HS (Figs.

is the impulse response* at this location (obtained by applying the bracketed

term in Eq. (15) to HS in graph No. 2). The convolution method and an assumed

second current density J2, graph No. 4, results in a second magnetic field

tiS,graph No. 5. The test consisted of using the fields algorithm with J2

and comparing the resulting HS, graph No. 6, with the convolution result,

graph No. 5. Within graphical accuracy, the results are the same. (The t’

shift in graph No. 5 is consistent with the numerical algorithm, Eq. (15).)

-+Graph No. 3 is actually the negative of the impulse response.

me

-—

31

--

G.Uf LJl

[).

w

1-

fl.tlr”ol

----- _...J-.... .J - _l. ._ ... l.-...—.–-L—-----

.J1

.

—---...-. .- ,_ ,----- ...---- “-+-.,q=...-.—-.r--.—-”l ___.,-—. -

!.of+rlo 8.OE.00 l,2E+oi I.W*O1 2.UE+L-112.lE*r/ c-r/fl,../,

//,“,.,’

\//

-,

I

I

a ,,

11 ,,,!,,’“’1,,11 I 1,1!!1‘,1, ,11,,1 1,I!} ,11

I

1

Figure 15.

,, ,!

_l.. . . . . . L. ..-.-. --J

I15?14

I

Convolution Method Test.

I ‘ .:-’.2.0[’+012.I;F$[

I(.

:

2.[IIE-.O2

Il.of .02

mu

1.2F+lln

G. m-cll

a. —

o.

-G. OE -01

‘1-1.JF+IJII

1- 1 .._, -_ -.,.1. _ . .- l-—._._L___—

-——- —,.1 ...- .. . J . ...... 1 ....1 . ., -_ I__ _..... _,

J2 /“” \

/\ *

/ \

... /’..

I

.-, ,., .,, .. .

8.IX-W

1’-4.OIE-02,,

-8.OE-102

B.EME-02

Y.OF-02

0.

0.

4. W-02 _

-1?.OF-W _

_......-_ -L—__-._L ______ .L. ____.__L- _. . .– -1 __ L-

l–————__J____—. ___ _-._ J----- ...L...__ J. . ... .

lj~/J~ ‘-l

–--”--r ‘-”

\

q. OEA(JO

/-\-- ~

~_._.–- . ,. ,-. .8 FAOO 1.2FA’01 1 EFJ.01

[;r/Cl2. GF+O1 .?.kE+.I

‘L.//

\ /\/=- (;

Figure 16. Convolution Method Result.

1’

I

I 1’

3. CONTINUOUS-bL4VEDATA

In some circumstances, jt would be advantageous to obtain the experi-

mental dipole data with continuous-wave (CW) measurements, particularly

whenever signal/noise is a serious problem with pulse techniques. Depending

on the method, interfacing cw data with the transient SGE1’4Pcurrents would

require Fourier transforming, combining, ~nd then inverse transforming back

into the time domain at each antenna location. Below is a brief description

of the method that appears to offer the most advantages.

Continuous-wa\~edata would be obtained in the form of a transfer func-

tion, Texp(ti),with the reference signal, amplitude, and phase, emanating

from the dipole antenna. I

probebly be the voltage at

tally small dipoles, the d

voltage

3PA 3VA

-n- = CAhe at

n most circumstances, the reference signal would

the antenna’s input terminals, VA. For electri-

pole moment PA is linearly related to the antenna

(20)

where CA and he are the antenna’s capacitance and equivalent electrical

length, respectively. (These quantities WOUJ$ have to be calculated or

measured for a specific antenna.) T;ws, if -& is tne desired reference

for combining with the SGEMP

~exp(w) is given by (assumed

most engineering hardware)

currents, the transform of the impulse response

time dependence e+jmt , the circumstance fcr

K(t), the impulse response, is then given by the inverse transform of Kexp.

(k-iceK(t) is obtained, then t!w conv~lution procedure

would be the same a.soutlined in the previous section

34

with the SGE!4Pcurrent-s

for pulse data..

e

.

The major advantage of the above method is that it avoids the need to

Fourier transform the SGEMP currents. Furthermore, the cw data could be

processed (inverse transformed) immediately into the form K(t). Thereafter,

the combining of either cw data or pulse data with SGEMP currents would be

the same, a djstj{c> advantage.

‘--Two additional considerations are worth mentioning at this point. The

first is that a_dvan_tageshould be taken of any special symmetries that would

occur in the final SGEMP scenario, For example, for end-on X-ray incidence

on a cylinder, the exterior problem is independent of azimuthal angle. Thus,

continuous-wave dipole data should be summed in azimuthal angle prior to

inverse transforming to obtain the impulse response, This substantially

reduces the amount of inverse transforming required,

Several transforming techniques are available that can be used. A

major consideration is that continuous-wave data would not in general be

obtained with uniform frequency steps. ABACIS, for example, has frequency

steps that grow linearly with frequency.

@

Subroutine GFOR (on the AF!dLcomputer),which utilizes Guilleman ’s

technique and does not require uniform time or frequency stepping, appears

to offer several advantages. It has been used extensively on other programs

and is well understood. In fact, the original software for ABACIS was designed

to interface with GFOR. Basic usage information follows.

—

——

35

SUBROUTINE GFOR USAGE INFORMATION

CALL GFOR (lND, NT, T, Y, NF, N, Z)

lND - Determines whether forward or reverse transform is done.

If IND = Cl,the reverse transform is done.

If IND = 1, the fcrwara transform is done.

NT - This is the number of time-value pairs. If the forward transform is

is done, this parameter specifies the number of input values. If the

reverse transform is done, this parameter specifies the number of

times at which the transform is to be integrated.

T - Array containing time \ialuesfor transforms.

Y - If the forward transform is done, y is the array of F(t) values. If

the reverse transform is done , y is an array large enough to contain

the new F(t) values.

NF - This is the number of frequencies stored in array U.

w - Array containing frequency values.

z - Array for G(M) values. For the forward transform, z must be as large

as 2.WF. For the inverse transform, .Z(2N-1)contains a real ‘falues o’f

G(bl) for W(N), Z(2N) contains imaginary c~mponents of G(’d)for fre-

quency W(N).

ADDITIONAL REQUIREMENTS

COIl!JiO!l/STUFF/DUM(3), TP

DUN (3) - UriUSEil

TP - Contains the value 2*!T.

COMMON/JF/JF(7), X!!(7),CNK(7), SNK(7)

JF(7) - Array of pointers to array M which tel~s GFOR when AW changes.

KM(7) - Array of AW values corresponding to spacing in array w.

36——

.

Sign convention is as follows.

tmax

Forward1

Z(w) = e-jut ~(t) ~t

tmin

Reverse f(t) =+I

ej’”tZ(LO)do

n

In the forward transform f(t) must be set to zero at Tmin and Tmax. In the

reverse transform, there is no restriction on the values of Z(U) at O and~max”

a 37

4. LXPERIMENTAL CONSIDERATIONS

It will be recalled that in Eq. (10), the convolution method given is

for an antenna dipole moment corresponding to the time dependence for a criti-

cally damped series RLC circuit. Referring to Eq. (10), with what appearsto be relatively simple modifications, the directly recorded experimental pulse

mta could be K(t).

(22)

Not only wculd this substantially reduce the numerical processing, it should

provide a significant improvement in the overal? quality of the final result.-.,

The first bracketed ([ ]) term in K(t) consists of %&and a constant

times its time integral. The AFWL presently has the instrumentation to

perform this sum directly on the experimental data for a real time pulse

(with an active integrator) or for a sample time pulse (with a sample time

integrator).

The second bracketed (~ ]) term is the time derivative of the first

term times a constant. Development of a good electronic differentiator

should not be too difficult, particularly for a sampling scope-repetitive

pulser instrumentation system.

Then, for example, the first bracketed term in K(t) could be input to

channel ,4of a dual channel sampling oscilloscope, the second bracketed term

could be input to channel B. The recorded signal would then be in the A + B

mode.

With this appr~ach, the directly recorded experimental result wcwld tie!,““2Xp

(t), with an appropr~ate multiplying constant for sensor sensit~vity, etc.

Then for a specific, SGEPIPscenario, the appropriate SGEMP S~imUIUS I&)

would be used in Eq. (10) to give the predicted SGEMP response ‘J~~(t).

*38

t

o

‘v@) = I IS+ - T) Kexp(T) d~

,.

(23)

o

The question of which experimental data to record is an extremely

important factor affecting the overall quality of the

recommended that the hardware be developed for direct

impulse response.*

final result. It is

recordirigof the

— . .. .

*’11above should not be confus~d with voltage. F~x,perimental quantity of interest (\’/m-z), then Vi

y determined exper

.

rt

example, if B1 is the= B(t). lf ~ an~/or

m~ntal “quantity for Fulsa

SECTION V

THE SGEMP CALCULATION

The SGEMP predictions in this report were made with M.AD2,a computer

code designed to solve two-dimensional self-consistent problems associated

with systems generated electromagnetic pulse phenomena. The temporal formal-

ism is second-order and time reversible. Cylindrical coordinates were used

for all the computations. Documentation of the cylindrical version is found

in Reference 3.

ln the computations it was assumed that the X rays were incident on

the cylinder top. The electron emission energy and angular distribution

were taken to be that given in Reference 3 (nominally, the

and angular distribution).

A Gaussian time history, full width at half-max of 6

~f 0.42 Jm“ (10-’ cal/cm2) was assumed incident on the illuminated end of

the cylinder.

PIMBS 1A energy

ns, with a fluence

The electron emission data used in the computations is given in

Table 3 below. The nomenclature is ti~at used in the MAD2 code (Reference 4).

40

oELECTRON

-M@L-0.9000E+O0

0.1500E+O0

O,21OOE+O1

0.2700E+OI

0.3300E+01

0.3900E+01

0.4500E+OI

0.5180E+01

0.5700E+01

0.6300E+01

0.6900E+01

0.7500E+01

O.81OOE+O1

0.8700E+01

0.9300E+OI

0.9900E+01

O.1O5OE+O2

O.111OE+O2

—.

EMISSION DATA

&f(E)6E

~

0.2060E+O0 =_

0.2850E+01

0.2030E+O0

0.1190E+O0

0.3850E-01

0.3370E-01

0.2470E-01

0.2190E-01

. .

TABLE 3

USED IN THE SGEMP C44LCULATION

= ns(t)f(E) +g(6)

0.1290E+02

0.2280E+02

0.3000E+02

C.3630E+02

O.421OE+O2

0.4790E+02

0.5370E+02

0.6000E+02

2g(9) sin6~.

O.1OOOE+O1

O.1OOOE+O1

O.1OOOE+O1

O.1OOOE+O1

O.1OOOE+O1

O.1000E+O1

O.1OOOE+O1

O.1OOOE+O1

0.1890E-01 0.6720E+02 O.1OOOE+O’

0.1530E-01 O.771OE+O2 O.1OOOE+O’

0.9760E-02

0.8560E-f12

0.6060E-02

0.4030E-02

0.3380E-02

0.2350E-02

0.1680E-02

0.6640E-03

COMBINING TECHNIQUE FOR DIPOLE DATA

ANLISGEMP VOLUME CURRENTS

1. TIME DERIVATIVE OF SGEMP DIPOLE MOMENTS

In the computations, the space surrounding the satellite was divided

into specific volume elements. At each time step in the SGEMP calculation,

a sum was performed over each elemental dipole moment’s time derivative

occurring in a specific volume and written onto disk. At the end of the

calculation, these quantities apSG~ (A-m) were then sorted and written back

onto disk as a function of time for @ach volume element, These are the

quantities that are used to convolve with the impulse response from a dipole

antenna located at the center of the same volume.

The algorithm for storing the

permits changing the volume size in

example, small volumes in close and

used for storing the SGEMP informat-

ments.

SGEMP dipole moment’s time derivative

dif-ferentregions of space. Thus, for

larger volumes farther away could be

on without increasing the storage requre-

The combining method consisted of the following steps.

(1) The SGEMP ~ Iwerecalculated and stored on disk.

(2) A grid detail was specified for antenna placement.

(3) Dipole data ‘wasobtained for these antenna locations (as

described in Sectflon111”)and converted to the equi\ialentimpulse response.

(4) A convolution was performed cn the dipole impulse response

and the total 2PSG for that volume of space (as described in Section IV).

(5) ~~e procedure was continued until all the SGEMP currents

were taken into account.

Results were obtai~ed for several combinations of volume size and grid

fietaii. The pertinent results and representative data are presented in

Section VIII.

A !cethsd fai-taklng into account the distant SGEP,P currents is

described in the following section.

42 9

o 2. FAR FIELD EFFECTS

The coupling of the more distant currents to the satellite in an SGEMP

environment is not expected to be an important effect, particula]mlyfor the

nigh fluence case. However, it is possible to include these effects with

little additional effort and thereby avoid any uncertainties associated with

this aspect of the simulation.

In essence, from the SGEFIPcalculation, the several stored dipole

moments in a particular angular direc~ion (~:=_>rfar field) are replaced

with a weighted time-shifted sum. Thus, with this method, experimental

dipole far-field data is needed for only a single antenna distance in each

angular interval. Generalization of the method to three dimensions would be

straightforward.

To be specific, suppose that far-field experimental data is obtained

at–each angle eM’ 1’”=1,2, ,..)J_,and that the distance from the antenna

center to the satellite center is rM“

The far-field SGEMP volume elements

K positioned at cylindrical coordinates ZK, 6~ (with respect to the satellite ~

center) are sorted to the appropriate angular interval 6M.

‘K= tan-l(zK/cK) ,

43

.

The r-~ fall off and the time delay fcireach SGEHP volume element are

then taken into account by performing the sum*

--l

equiv

‘MK=t-

‘K - %] ‘c

This quantity

+

~ M(t) Ieq~iv

+

would then be used for the SGEMP ~ for the antenna position rtq>9r,1.

*Irithe far fle’icionly the transverse components contribute.

44

.

GRID DE-TAIL/VOLUMESIZE

1. GENERAL

The volume size and grid detail required for simulation are major

parameters impacting the practicality of the dipole method (DIES). The

distant SGEMP currents can be taken into account by the method described

in Section VI, paragraph 2 (far-field effects). Similarly, for the

intermediate range antennas (--a few satellite radii) the major considera-

tion in grid detail appears to be the frequency content of the SGEMP

~~lrrentsin that region of space (this can be inferred from Section 111,

numerical

a l]alfwa

The

grid deta

The

dipole data). That is, a grid dimension should be smaller than

elength for the shortest wavelength of interest.

remaining question is the more difficult one, the requisite

1 in the immediate vicinity of the satellite, the near field.

techniques described earlier in this report provides the means

to vary the grid detail/\~olume size and obtain parametric information

about this constraint. For the reasons given above, the data presented

jn this section emphasize the conditions in the near field.

Using the calculated SGEP?Pcurrents (described in Section V) and

numerical dipole data (Section III), results were obtained for several

differing grid details. It soon became apparent that grid dimensions in

the 10 to 20 cm range wculd be required in the immediate vincinity of

the cylinder. For larger grid dimensions, the quality of simulation

rapidly declined.

The procedure for comparison was as follows. In the SGEMP calcu-

lation, the surface ta.ngentiaimagnetic afidnGrma.1electrlc f~elds were

calculated and retaineci.* Using a specific grid, numerical dipo;e results

fields were compared to those obtained in the SGEMP calculation,

*The circumferential gap in the cylinder was closed during this serieS of .comparisons.

45

.

No single parameter was found (at least that could be directly calcu-

lated from the data) that provided a measure of the quality of simulation.

Rather, the precedure was to cGmpare the fields at several locations on the

cylinder surface as described above.*

Representative data for some cases of interest are described below.

For ease of comparison, in each case the data g~ven is for the tangential

magnetic field on the cylinder side, %.

*In the future, some thought should be given to defining a single, globalparameter that can be used as a measure of the quality of simulation.

—

46

. .

2. RESULTS

Figures 17 through 22-display representative data obtained for differinq

grid detail of antenna placement. The quantity given is HS (Table 2, Section

III).I

Figure 17 is the result obtained from the SGEMP calculation (described

in Section VI). The time scale is normalized to the speed of light and the

cylinder radius (0.45 m).

Figure 18 is the result obtained from,convolving the SGEMP currents

with antenna responses. Small ring dipoles (both polarizations) were

positioned in each of the cells shown in the inset. That is, the antenna

grid was 11.25 cm byll.25 cm,

Comparing Fig. 17 and 18, it appears that the method works very

well for a sufficiently fine antenna grid. ‘“The p-eakamplitudes agree to

within approximately 5%.

In Fig. 19, the antenna grid dimensions were doubled (22.5 cm by 22.5

cm). As is evident in the figure, the peak amplitude is down approximately

20% from the direct SGEMP result.

In the next figure, Fig.20, a varying grid size was tried, small Cells

in close and large cells farther away. It is evident that this choice is not

an improvement over the 22.5 cm grid.

In Fig. 21 , the number of antennas were doubled immediately on top of

the cylinder. This resulted in some improvement im the peak value.

In Fig. 22, a.n11,25 cm grid immediately adjecent to the cylinder and

a 22.5 cm grid was used for the remainder of the locations. Comparing to

Fig. 17, this choice appears to offer a reasonable compromise between the

number of antennas in the near field and the quality of simulation.

The grid shown in Fig, 22 is not an optimized grid. For one radius

or farther away from The cylinder, the antennas can be positioned slightl:~,.fa-rt-herapart.than shown without serious degradation in quality. H~~wever,

it should be apparent that not much variation is required to substantially

(>10%) change the result.

47

. .

3.J-

2.0

L.o

-HS(PJI-L)

SGM4P

(3.0 4.iJ

cT/3.

Figure 17. Cylinder Response (?bta

a.fl 12.0

ned from the SGEMP Calculation.

3.0

-HS(Am-l)

GridDetail

1.0

Illlitllllll I

tiip~le

I I l[l! 1111111convolution

! 1 2 I t $ 1 ? I

I ! I1 1 I t I t

I I11 II

III

!!!~!I

\

\\

.Tr~A

~’igwQ 780 Cylinder Response obtained from Convolution with a11.25 cm Grid.

—..

48

. ,

3.0

2.0,

1.0.

0.0.

L

3.0

2.0

L.o

0.0

I I I

-HS (Am-l)

Detail

DipoleConvolution

i

}I I

4.0 8.0 12.0

cT/A

Figure 19. Cylinder Response Obtained from Convolutionwith a 22.5 cm Grid.

! 1 i

-HS(h-l)GridDetail

— DipoleConvolution

/-

/

,/’

I /L1.o 4.0

i8.0 12.0

C’I’/.\

Figure 20. Cylinder Response Obtained frcm Convolutionwith a Varying Grid.

49

.

3.0.,

2.0

1.0

I I 1 1

.Hs(~-L)

GridDetail

DipoleConvolution

-

\

\

,

0.0I / t 1

0.0 4.0 8.0 11.0

Figure 21. Cylinder Response Obtained from Convolutionwith a Varying Grid.

3.0 ! ! 1 I

1 Grid-Hsum-l)

\Detail

Ill

.2.0!lipola

Iconvolution

1.0

1~ 1 ‘ ~

1// \\

/’ \I /

0.4 I I i0.0 4.0 9,0 “+0-

CT,G

Figure 22. Cylinder Response Obtained from Convolutionkiitha Varying Grid.

50 a

—

Although not conclusive, it is suggested that the requisite fineness

of antenna grid positions is due to the substantial static-like coupling

(1/r3) of the dipoles to the satellite and to the nature of the SGE!~D~~r~el~ts;

The bulk of the SGEMP currents travel at a speed that is slow comparei

to the speed of light. For example, a 10 keV electron has a velocity appro~-

imately one-fifth the speed of light. Thus, even though the current’s time

history may be slowly varying, the apparent center of a local SGEMP dipole

moment is not well approximated by the center point of a large grid.

In particular, half-dipoles directly connected to the satellite would–-

be desirable for the first layer of measurements.

A simple method was available for assessing the importance of the time

variation of the SGEMP currents concerning grid detail in the near field.

Figure 23 displays the SGEMP result for a much slower time history X-ray

source (the PIMBS-qA time history, Reference 3).

Figure 24 is the convolution result for an antenna placement grid as

indicated. It exhibits excellent agreement with the calculated SGEMP result

(Fig. 23).

Figure 25–is the convolution result for a 22,5 cm by 22.5 cm antenna

Grid. Comparing this result to Fig. 23, it is apparent that the quality

of simulation is substantially reduced by the larger grid.

51

0.4

0.2-

0.0 I0.0 4.0 8.0

CT/A

Figure 23. Cylinder Response from the SGEMP Calculationwith a Slowly Varyjng Source.

0.

0.

9.

0.0 4.0

,C?,f?i

Figure 24, Cylinder Response Obtained from Convo’with a 11.25 cm Grid.

52

“

8.0

ution

—,

*

o.-4“

0.2

/

1 ,, \ - “’*U 1.JCL4J.

J -HS M-l)

DipoleConvolution

//

/

I i0.00.0 4.0 8.0

CT,

Figure 25. Cylinder Responsewith a 22.5 cm Gr

@btained from Convolutiond.

3. SUMMARY

The grid detail for antenna placement in the near field shown in

Fig. 22 appears to offer a reasonable compromise between grid detail and

quality of simulation. The grid shown is not an optimized grid, but is a

reasonable compromise.

Requisite grid detail in the near field appears to be dominated by

strong static coupling and by the fact that the currents move slowly com-

pared to the speed of light. Half-dipoles are needed in the measurements

for the layer adjacent to the satellite.

.

e

54

* .—

1.

sect

With

direct time stepping of Maxwell’s equations in two dimensions was used to

numerically simulate the experimental dipole data.

SECTION VIII

CONCLUSIONS

GENERAL

Results impacting the dipole method (DIES) are summarized in this

on. Conclusions are presented, followed by recommendations.

Measurements were not available for testing the problems associated

combining the experimental and analytical data. As a consequence,

For simplicity, the test object-(described in Section II) and the

analysis method (Section 111) are two dimensional. The numerical method

for obtaining dipole data is described in Section III. Results in that

section may be retained for comparison to experimental data.

The results given for antenna position 2 (Table I.and Fig. 4) would

be the simplest comparison since for this case the excitation is aximuth-

ally symmetric. For the other antenna positions, the tangential magnetic

and normal electric fields on the exterior of the cylinder (HS, ES) must

be interpreted as the azimuthally symmetric part of the cylinder response.

The results given are to be compared to a sum in azimuth of the experi-

mental cylinder response, or equivalently, a sum in azimuth over a specific

antenna location (z,p).

A method for convolution of the dipole response that offers several

,ld\iantages~s described in Section IV. A technique for processing experi-

mental continuous-wave data.is_described in that section. The major fea-

tures of–the combining techniques for dipole data and SGEMP currents are

summarized in Section VI. A method

effect5.

is given for including far field

55

Results obta-ir-e-dconcerning requisite grid detail in the near field of the

satellite are summarized in Section VII.

2. CONCLUSIONS

The method works, Figure 22 (Section VII) displays an antenna grid

detail that offers a reasonable compromise between the number of antennas

in the near field and the quality of simulation (an 11.25 cm by 11.25 cm

grid adjacent to the cylinder, a 22.5 cm by 22.5 cm grid in the remainder

of the near field).

Distant SGEMP currents can be accounted for by the method described

in Section VI, paragraph 2.. The recommended convolution method is presented

in Section IV.

3. RECOMMENDATIONS

The method shows potential for obtaining reliable information concern-

ing SGEMP effects on a satellite. This includes consideration of several

of the major practica] constraints in both obtaining the experimental data

and combining with the calculated SGEMP results.

Consideration should be given to replacement of the bulk of the volume

currents by an equivalent surface current layer (Reference 5). Use of this

method could substantially reduce the number of required antenna positions.

Techniques for doing this and the effects on the quality of simulation are

being examined by the author.

A parallel effort is recommended. Analysis should not be carried too

far until real experimental data is processed by the procedure.

Instrumentation is not presently available for obtaining reliable

experimental data. This is due mainly to the need to electrically isolate

the dipoles for the close in measurements and to maintain a phase or time

reference. Developmental effort would be required, less effort would be

needed to obtain experimental pulse data. Effort should redirected

towards constructing a small self-contained pulse-driven dipole (and a

56

small half-dipole). The critically damped antenna current described in

this report offers several advantages. Construction of the hardware to

obtain the equivalent impulse response is recommended.

A more realistic satellite geometry should be addressed in the analysis.

Results on the simplified model in this report justify going to a three-

dimensional object with electronic circuitry in the interior. Since the

method works, internal data of real interest could be obtained in a first

experiment.

-. --

4) 57

REFERF3iCES

1. %auni,C. E., “Some Types of Small HIP Simulators,” MiscellaneousSimu?ator Memos, Memo 9, 22 December 1976.

2. Baum, C. E., ‘iEMPSimulators for Various Types of Nuclear EMP Environ-ments: An Interim Categorization,i’adapted from AF}ILSSN 151 and alsopublished in the Special Joint Issue on the Nuclear ElectromagneticPulse, IEEE Trans.on Antennas and Propagation, January 1978 and IEEETrans. on Electromagnetic Compatibility, Februiry 1978.

3. Fishbine, B., B. Goplen, R. E. Clark and G. Seely, “Two- and Three-Dimensional Calculations for the PIMBS 1A Cylinder Experiment,Theoretical Note 291, February 1977.

4. Goplen, B:, R. Clark and B. Fishbine, “MAD% - A Computer Code for System-Generated Electromagnetic Pulse (SGEMP) Calculations in Two Dimensions,”Theoretical Note 290, January 1977.

58

c~. Barrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-tiill,1961, pp. 106-1IO.