An Application of Chaos Theory to the High Frequency RCS Prediction of Engine Ducts
We establish a connection between the Lyapunov exponent and SB ray methods which places a limit on the ability to make numerically deterministic or convergent predictions. When this limit is reached the ray fields are essentially random. One method, valid for ergodic straight ducts, is to represent the random ray field component by a field composed of randomly directed plane waves. We demonstrate that predictions made under this assumption have very similar bistatic RCS characteristics to those of an accurate modal solution.
Estimates of the Lyapunov exponent are directly related to average ray divergence and hence average ray intensity. For ergodic ray tracing this can be determined by the tracing of a single ray in order to place limits on the ability to achieve convergence. The computational cost of estimating the Lyapunov exponent is usually negligible compared to the cost of a full RCS prediction where all the rays on the entry plane must be traced.
KeywordsLyapunov Exponent Radar Cross Section Chaos Theory High Frequency Limit Entry Plane
Unable to display preview. Download preview PDF.
- G.A. Deschamps, September 1972, ‘Ray techniques in electromagnetics’, Invited paper, Proceedings of the IEEE, Vol. 60, No. 9.Google Scholar
- A.J. Mackay, July 1988, ‘Chaos theory and first-order ray tracing in ducts’, IEE Electronics Letters, Vol. 34 No. 14, pp 1388–1389Google Scholar
- A.J. Mackay, April 1998, ‘Chaos theory applied to first order ray tracing in ducts’, DERA Malvern, UK, report DERA/SN/R/TR980002/1.0, (available through DRIC)Google Scholar
- A.J. Mackay, March 1999, ‘New representations of ray tracing, chaos theory and random waves in straight ducts’, DERA Malvern, UK, report DERA/S&P/RAD/CR990108/1.0, (available through DRIC)Google Scholar
- A.J. Mackay, December 1999, ‘Application of chaos theory to ray tracing in ducts’, IEE Proceedings Radar, Sonar and Navigation, Vol 146, No 6, pp298–304Google Scholar
- M.C. Gutzwiller, 1990, ‘Chaos in classical and quantum mechanics’, Springer Verlag, Interdisciplinary Applied Mathematics Series.Google Scholar
- M. Berry, 1989, ‘Some quantum to classical asymptotics’, section 4 pp251, Les Houches 1989 Session LII, Chaos and quantum physics, North Holland publishing 1991.Google Scholar
- E.J. Heller, 1989, ‘Wavepacket dynamics and quantum chaology’, section 9, pp548, Les Houches 1989 Session LII, Chaos and quantum physics, North Holland publishing 1991.Google Scholar
- A.J. Lichtenberg and M.A. Lieberman, 1983, ‘Regular and stochastic motion’, Springer Verlag, Applied Mathematical Sciences 38.Google Scholar
- U. Smilansky, 1989, ‘Theory of chaotic scattering’, section 7 pp371, Les Houches 1989 Session LII, Chaos and quantum physics, North Holland publishing 1991Google Scholar