WAVE EMISSION BY RESONANCE CROSSING

The emission of collective waves by a moving charged particle in a, no nuniform medium is discussed. Emission occurs in a nonuniform medium w hen the local dispersion relation of the collective wave is satisfied. This is a form of resonance crossing. Using the Weyl symbol calculus, a local expansion of the collect wave equation driven by the particle source is derived in the neighborhood of the crossing. The collective wave dispersion manifold and the gyroballistic wave dispersion manifo ld can be used as a pair of local coordinates in the neighborhood of t he resonance crossing, which greatly simplifies the analysis. This cha nge of representation is carried out using a metaplectic transform (a generalization of the fourier transform). The Wigner function of the e mitted wave field is then computed in;the new coordinates. The Wigner function is a phase space scalar, hence the numerical value is invaria nt under linear canonical transformations. This invariance is invoked to finally arrive at the Wigner function in the original (physical) co ordinates. The wave-action and -energy emission rates are then compute d from the Wigner function. (C) 1995 American Institute of Physics.