Computer Codes for EMP Interaction and Coupling - IEEE Xplore

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IEEE TRANSACTIONS ON ANTENNAS ANDPROPAGATION, VOL. AP-26, NO. 1 , JANUARY 1978

Computer Codes for EMP Interaction and Coupling R. M. BEVENSEE, JAMES N. BRITTINGHAM, F. J. DEADRICK, MEMBER,IEEE, THEODORE H.LEHMAN, EDK.MILLER, SENIOR MEMBER, IEEE, AND ANDREW J. PoGGIo, MEMBER, IEEE

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Abstract-The properties ofa number of digital computercodes code to another. In addition, accuracy and field anomaly conappropriate for various classes of external coupling problems are siderations apply generally. described. Limitations and approximations of numerical methods in Because of thecommonality, theseaspects of numerical general are reviewed. Thin-wire codes are tabulated to indicate their techniques are discussed frrst. Thin-wire frequency and timebasic properties, special features, and structures analyzed, including grid models of surfaces and wire stick models of aircraft. Surface codes domain codes applicable to antenna responses, bulk current are tabulated for bodies of revolution, arbitrary surfaces and hybrid predictions,and wire grid responses are next reviewed and the surface-wire or surface-aperture configurations m or below the ‘‘m important properties of many codes are tabulated. nance” regime, and GTD codes for higher frequencies. Various aperture A similar discussion of surface codes follows, including ones codes for studying apertures m planes, m empty bodies, or with a wire for bodies of revolution in the resonance regime, arbitrary pickup behind the aperture are summarized and tabulated. Some codes surface and hybrid codes, andGTDcodesforcomputing for long cables above or belowthe earth are reviewed. Conclusions surface currents in the EMP spectral range. Then aperture code warn against imprudent use of computer codes in gened.

I. INTRODUCTION

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work is summarized andtheimportantproperties of some available codes are tabulated. Finally,a few of the available shielded cable codes are discussed and tabulated.

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HIS paper discusses computercodes applicable to EMP interaction and coupling problems. Not all aspects of the 11. LIMITATIONS AND APPROXIMATIONS interactionand couplingproblems are addressed, andthe OF NUMERICAL METHODS number of codesincluded is necessarily limited. Discussions of codes applicable to the interior coupling problem associated A. Sampling Requirements with large systems is omitted. Codes which address this class of Any numerical treatment requires discretized sampling of problems are either trivial in that they are applicable to small parts of the total system or they are very complex and well physically continuous (for the most part) functions. The sambeyond the scope of this paper. Therefore, discussions in this pling densities of most interest in EMP-type interaction/coupaper are limited to the available and relatively general com- pling computations are spatial (for resolving field and source distributions), and timelfrequency (for resolving transient putercodes usedprimarily forexternalexcitationsonor waveforms andtransfer functions). A detailed discussion of across outer boundary surfaces of bodies. sampling requirements is outside the scope of this paper. Some The choice of a code to be used in solving aparticular problem is nontrivial and many factors such as model require- brief comments can be made, however; for detailed informaeach ments, computer requirements, accuracy, resources, and costs tionthe reader is referred to thedocumentationfor [ l ] , [2], must be considered. The computer code descriptions method or computerprogram. Spatial sampling requirements are related tothe spatial presented in this paper are structured to aid in this selection variation of the dependent variable. Of course, one must be process. using samples or Most of the codes presented are based on integral realiza- able to describeadequatelythisvariation basis functions over subdomains of the overall interval. Immetions of Maxwell’s equationsandmomentmethodsolution l i depend schemes [3]. These methods without exceptionrequire spatial diately,one can see thatthe samplingdensity w discretization, frequency or temporal discretization, and uponthe basis functions. Sinceintegral equationmethods afield description, and since computer-aided solutions of a large number of coupled equa- generally depend on near tions. As a result, samplingrestrictions and computer speed momentmethods involve the use of inner productswith and storage requirements do not vary significantly from one weight functions, there is also a dependency of sampling density on these factors. Finally, sampling densities depend on the complexity of the structure, requiring more samples per waveManuscriptreviewed September 24,1976; revised May 26, 1977. This work was supported by The U.S. EnergyResearch and Developlength or square wavelength for complex structures. ment Administration under Contract W-7405-ENG-48. Frequencyor time samplingrequirements are also related R. M . Bevensee, J . N. Brittingham, F. J. Deadrick, E. K. Miller, and to the resolution required in these domains. Naturally, the two A. J. Poggio are with the LawrenceLivermoreLaboratory,University of California, Livermore, CA 94550. domains are related through the Laplace or Fourier transform. T. H. Lehman,was with the Lawrence Livermore Laboratory, For the purposes of this discussion let us state that the samUniversity of California, Livermore CA. He is now with Science pling requirement also will depend upon the basis and weight Applications, Inc., Albuquerque, N M 87100. 0018-926X/78/0100-0156$00.75 0 1978 IEEE

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BEVENSEE et al. : EMP INTERACTION AND COUPLING

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functions in time. The other stringent requirementsarise from the interrelation of the maximum time window T , , maximum positive frequency range F,, frequencyincrement Af, and time increment At as given by

B. Near-Field Anomalies

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Numerical solutions yieldingacceptable far-field accuracy may exhibit nearE-field anomalies due to certain properties of the numerical treatment. These anomalies may take the form of doublet and singlet or lower-order behavior of the tangential and radial electricfields at a conducting surface due to amplitude and derivative discontinuities in the computed current distribution. Such nonphysical results, in effect, introduce fictitious sources at the discontinuities and So can render uncertain the microscopicnear fields. But theirimpacton macroscopic observables, such as voltage excitedonan antenna or energy collected by an object,is usually not serious when estimating EMP “worst case” effects.

Computer storage comprises two components, one for the codeandoneforthe variables. Thelatter, which includes storage of the matrix elements, dominates thevariable storage in both the time and frequency domains andis proportional to fl. At someexpense ofcomputingtime,for three-dimensional time-domain problems the storage can be made 0:N4I3 for a volume distribution of interacting elements and a P I 2 for a surface distribution of elements. One can solve problems with N 5 500 on the CDC 7600 computer in core. Symmetry can be exploited t o reduce greatly both computingtime and storage requirements,Twoor three mutually perpendicular symmetry planes can occur,androtational symmetry (eitherdiscrete orcontinuous) is also common. Both types decrease computation requirements by 1 ) reducing variable storage and matrix fill time 2 ) reducing factorization time, and 3 ) shortening current computationtime.

D. Accuracy The accuracy of an EMP computation in a practical situation is generally difficult to establish because of two fundamentaltypes of errors. The physicaZ modeling error results from replacing the physical problem by an idealized matheC Speed and Storage matical one. The numerical modeling error results from obtainThecomputer timeassociated with afrequency-domain ing anapproximate numerical solution tothemathematical computationat a single frequency can be approximated as problem. The literature is full of solutions of mathematically idealized problems, each of which relates t o a very small class of practical problems, and often in a manner which makes it difficult to assess the physical modeling error. where A , D are computer- and algorithm-dependentcoeffiConsidering the storage and accuracy of highAspeed digital cients, N is the number of current samples (basis functions) computers and the insensitivity of the current distribution to used to model the problem, Nz is the number of sources, and basis and test function representations and multiple junction NA is the number of points at which the near or far field is treatment,many nontrivialnumericalmodels can be solved subsequently computed.Theterms, in order,correspond to for EMP response with negligible error, 5 3 dB in currents and matrix fill time, matrix inversion or factorization time, current near fields. We mustnow learn how to assess the physical calculation time, and field evaluation time. For near-field com- modeling errorsinorder to applynumerical problem soluputations A = D . In a thin-wire code with fast matrix factor- tionsto a larger class of practicalproblemswithgreater ization,thematrix fill time predominates until N 3 300, confidence. while for surface codes the matrix factorization time will predominate when N ,> 100. Note that for an equivalent wire of length L, N 0:L / h and N 2.rrLlh is usually adequate, while for 111. THIN WIRE COMPUTER CODES a surface of area S, N a S/h2 and N 2 10.rrS/h2is usually adequate. Thus the computation time can vary as f3 or f6 for A. Applications large numbers of current samples on wires and surfaces, resNumerical methods of solving interactionand coupling pectively. Representative computation times in seconds on the problems have been implemented most successfully with thinCDC 7600 computer for N = 100, 200 (and hr, = 1, NA = 0 ) wire computer codes run on large high-speed digital cornare 3 , 2 5 for wires and ~ 212, for surfaces. In time-domain computations, both the fill time and solu- puters. They have been used, for example, to 1) solve for the tion time for the currents each time step are weaker functions energy absorbed, peak current,etc., of inadvertent straight of N . The running time for an efficient code would behave wire and loop antennas in free space or protruding from flat surfaces; 2) obtain the response of complicated wire antennas approximately as such as log-periodic structures; 3) compute the EMP currents induced on aircraft modeled by grids of interconnected wires; and 4) study field penetrationthrough arrays of parallel or where NT is the number of time steps. The first two terms crossed wires simulating gridded shields. These codes are invariably foundedon an electricfield constitute the matrix fill time and the last term is the currentsolution time through NT steps. On the CDC 7600 com- integral equation (EFIE), which states that the net tangential puter, for N = 100, 200 and NT = 100, T 100, 390 s, electric field on a wire surface equals the current density times surfaceimpedance there. Usually, the surfaceimpedance is respectively. e-,

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-26, NO. 1 , JANUARY 1978

zero unless a lumped load is present. The thin-wire assumption is invoked to eliminate angular variation aroundthe wires, whereby the current is assumed to flow along the axis of each wire, and the surface condition is enforced a radius away from the axis. The frequency domain codes are more efficient than time domain codes when the thin-wire model consists of so many interacting segments that time a domain solution would require prohibitive computer storage. The inclusion of ground effects by either Sommerfeld integral evaluation or a reflection coefficient technique [4], useful if the wire structure is 20.11 above a lossy ground, is also simpler in the frequency domain.Frequency domain response may then be Fourier transformed to obtain time domain EMP responses. For wide-band computationsthe time-domain solution is moreefficient and allows more tractible treatment of nonlinearloading, but canrequireconsiderably morecomputer storage.

wire groundscreen, and the latter allows for two displaced ground planes (cliff problem). References to other computer codes for solving radiation and scattering problems are found in the Computer Program Descriptions of this TRANSACTIONS since July 1972. Time Domain In the time domain, the network equations take the form v m ex (t) -

x n

Z m nIn(t) -

x

Zhn I n (t’) = ZL rnIm(t),

n

1< m < N

(5)

which the first sum represents contributions to the electric field at the mth elemen; from current elements which have contributed during the interval ( t - At, t) and the secondsum represents contributions from more distant current elements at earlier times t’ < t - At. The set of (5) is solved for the various In(t) in a time-stepping fashion. The relative sizes of B. Frequency Domain the Zmn-andZmn’-matrices depend on the relation of timeIn the frequency domain, the EFIE is reduced to a set of step cat to thevarious segment lengths AZ. N network equations [3], the mth one being WT-MBA/LLLl B [ 131 exemplifies a general-purpose timedomain code (last entry in Table I). The time step must be VmeX ZmnIn=ZLmIm3 1 < m < N (4) small enough so that At < 1/12F, for several percent accun racyin computed currents, F, being the highest frequency specified in the response. The code is written with an interupon constraint the < where N is the number of current elements, V k e xis the discre- polation scheme dependent tized. realization of the driving field in the kth element, 2, is c a t , (Al),,, being the maximumsegment length. Other codes time the discretized realization of the impedance between the mth 1171 are based ontheoppositeconstraint.Computed and nth elements, ZLm is the discretizedrealization of the responses should be checked for insidious errors by recomput. surface impedance of the mth element and I , is the discre- ing with smaller At and(Lv),,, The time-domain solutionofthe thin-wire electric field tized realization of the current on the mth element. The Z,, and Z L m are functions of frequencyand geometry of the integral equation is moreefficient for analyzingdirectly the system and assume different values fordifferent choices of EMP response of simple deliberate antennas such as loops and straight wires, which have been extensively studiedand testing and expansion functions. Table I includes the properties of frequencydomain thm reported in the open literature (i.e., [18, ch. l o ] , [19], [20]). For example, contours of constant load energy absorbed and wire codes inuse during the last few years. Approximate, general limitations of these computer codes peak current can readily be computed with the time-domain code WT-MBA/LLLlB andplotted in the load resistance are summarized as follows. 1, seg- versus antenna lengthplane. 1) Segment length/radius 2 10; wire radius/Xmi, ment length/hmin S 1/6. The segment length t o radius restricThis code has alsobeen used to compute EMP temporal tion is relaxed in AMP [8] . current response of complex structures consisting of many 2) Most codes treat wires as lossless exceptforlumped multiple junctionsof straight wires. loads; WF-OSU [6], [14] is an exception. It allows lossy wires D. Wire Grids and Stick Models and/or dielectric sleeves. Thin wire codes have beenused to model surfaces using 3) Longestsegment/shortestsegment ratio should not be grids or stick models. For example, stick model computations large. in the frequency domain for the Boeing 747l have been made 4) Segments connected t o a multiple junction shouldbe nearly the same length and have the same or nearly the same by Boeing [ l o ] , a version of AMP [9], and with WF-SYR [5]. Wire grid computations have been made by many researchers radii. 5) Usually all wires have the same radius; WF-SYR [5] is an and, as with stick models, a comprehensive overview is beyond the scope of this paper. exception. Reservations have been voiced regarding the accuracy of 6) Most cases assume a homogeneousambientmedium. this modeling method. The stick model does notallow circumExceptions are WF-OSU2 [7] and WF-OSU/LLL2 foran ferential variation of the current and retains reasonable accuantenna above aperfectly conducting ground plane;and TEMPO [15], WF-MBA/LLLl [ 9 ] , WF-OSUlhTPSl [ 111 and racy for bulk current only. The presence of a magnetostatic WF-LLL2B [I21 which allow either a lossy or lossless ground ’ See t h e paper by Lee et 02. in this issue. plane. In addition, WF-MBA/LLLl and AMP allow for a radial

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BEVENSEE e t al. : EMP INTERACTION AND COUPLING

TABLE I DESCRIPTION O F VARIOUS THIN-WIRECOMPUTER CODES (ALL EXCEPT THELAST ARE WRITTEN IN THE FREQUENCY DOIvlAIN) 1.

Expansion;Organization (contact) €ode

Test Name

Functions (Computer) Structure Type

Special Features References and

1100 cards; 314008 interconnected forantennaspor-thin wires tion with6 0 points and =

(1)

V

with U(t) the Heaviside stepfunction.The SEM [ 5 ] - [9] represents an electromagnetic variable (field, current, charge, etc.) in the s-plane domaindue to an impulsive excitation (the impulse response) as

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Up(?,s) =

x v&,

S)%.(O(S

01

0018-926X/78/0100-0165$00.750 1978 IEEE

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+ &(e, r^,s) ( 2 )