TDFARS: A Procedure to Quantitatively Identify Time-Domain Radiation Sources E. K. Miller 3225 Calle Celestial Santa Fe, NM 87501-9613 505-820-7371,
[email protected] G. J. Burke, LLNL Livermore, CA 94550 925-422-8414
[email protected] T. K. Sarkar, Syracuse University Syracuse, NY 13244 315-443-3715
[email protected]
INTERNATIONAL SCIENTIFIC RADIO UNION 2001 ELECTROMAGNETIC THEORY SYMPOSIUM May 13-17 Victoria, Canada
TDFARS: A Procedure to Quantitatively Identify Time-Domain Radiation Sources E. K. Miller 3225 Calle Celestial, Santa Fe, NM 87501-9613, USA G. J. Burke Lawrence Livermore National Laboratory, Livermore, CA 94550, USA T. K. Sarkar Syracuse University, Syracuse, NY 13244 USA Abstract: A technique called FARS (Far-field Analysis of Radiation Sources) that was developed to identify the amount of farfield radiation originating of a per-unit length or area basis from a perfectly conducting body in the frequency domain i s outlined here for the time domain and some results presented for a Gaussian-pulse excited straight-wire antenna and scatterer.
INTRODUCTION AND BASIC APPROACH A procedure called FARS was described by Miller [1] as a possible means of determining the quantitative contribution on a per-unit length or per-unit area basis to the power radiated from some object in the frequency domain. Extension of FARS to the time domain (TDFARS) is presented here. The frequency domain version of FARS (FDFARS) keeps track of the incremental far field contribution at an observation point due to each wire segment or surface area into which an object under study is divided. The conjugate dot product of the total field with the incremental field is then formed and integrated over all observation angles which produces the FDFARS power contributed by that segment or area to the total radiated power. A spatial integration of the FDFARS power over the object equals the usual total far-field power. Time-domain FARS, or TDFARS, works in essentially the same way as in the frequency domain, but with the addition of tracking the time variation of the power and energy radiated by an object being studied [2]. A dot product of the incremental far E-field from segment i, e i (r,t) and the total far field E(r,t) at observation point r and observation time t yields the incremental power flow p i,TDFARS = e i(r,t).E(r,t)/ηo . The linear power density (LPD), P i,FARS(t), at time t is found by integrating the incremental power flow over 4¹ steradian observation angles. The total FARS power at time t comes from summing over all segments and is identical to the total radiated power, P rad(t), obtained in the usual fashion, with the radiated linear energy density (LED) and total radiated energy found by an additional integration in time.
SOME RESULTS FROM TDFARS Applying TDFARS to a straight, 10.1-m wire dipole excited at its center by a Gaussian voltage pulse yields a late-time spatial distribution of LEDs, shown in Fig. 1, that smoothly varies between a peak at each end of the wire and a double peak in the vicinity of the excitation, showing these places to be the largest sources of radiated energy. The non-zero LEDs found between these peaks indicate that radiation at a lower rate also takes place along the entire length of the wire. These TDFARS results are qualitatively similar to those derived analytically by Smith and Hertel [3] for the energy radiated by a Gaussian-in-time current filament. The fact that a radiation field is produced by accelerated charge seems consistent with these results where the maximum charge acceleration would be expected in the source region and at the wire ends. As shown in Fig. 2, scattering from the same wire by a normally incident Gaussian-pulse plane wave produces LEDs that decrease monotonically in either direction from a peak at the wire’s center. For incidence from 10-deg off axis, however, the center peak disappears to be replaced by two dominant end peaks, with that on the far end being about twice that on the near end relative to the incidence direction. These TDFARS results for the LEDs are compared with FDFARS results for the LPDs on a 10-wavelength wire in Figs. 3 and 4. For both the antenna and scatterer cases, the FD and TD results are qualitatively similar, but with the former exhibiting an oscillatory behavior due to the standing current that is produced. CONCLUDING COMMENTS Results obtained from FARS in both the frequency domain and time domain for simple, straight-wire antennas and scatterers appear physically plausible and consistent with charge acceleration being the cause
of radiation fields. Further work is needed with more complex geometries, especially in the time domain, to confirm the utility of FARS for showing where far-field radiation originates. REFERENCES [1] E. K. Miller, “PCs for AP and Other EM Reflections,” IEEE Antennas and Propagation Society Magazine, Vol. 41, No. 2, pp. 82-86 and Vol. 41, No. 3, pp. 83-88, 1999. [2] E. K. Miller and G. J. Burke, “Time-Domain Far-Field Analysis of Radiation Sources,” IEEE Antennas and Propagation Society International Symposium Digest, Salt Lake City, UT, pp. 2058-2061, 2000. [3] G. S. Smith and T. W. Hertel, “On the Radiation of Energy from Simple Current Distributions”, to be published in the IEEE Antennas and Propagation Society Magazine, 2001. ENERGY PER SEGMENT (J)
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POSITION (m) Figure 2. The Linear Energy Densities per segment for the 10.1-m wire scatterer excited by unitamplitude plane waves incident from broadside and 80 deg from broadside (the right end in this plot).
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POSITION ON WIRE (m) Figure 3. The normalized linear power densities from FDFARS (the x’s) and linear energy densities from TDFARS (the circles) for the 10.1-m center-excited dipole are qualitatively similar, but with the former exhibiting oscillations due to the standing current wave. 0.15
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Figure 4. The normalized FDFARS (the x’s) and TDFARS (the circles) for scattering by a 10.1-m wire of a plane wave incident 80 deg from broadside are again qualitatively similar, but again with oscillations appearing in the former and not the latter.
