STRUCTURE OF LASER-INDUCED NORMAL MODES IN FINITE INHOMOGENEOUS-PLASMA

An analytic treatment of the problem of normal modes resulting from the decay of an electromagnetic pump wave propagating in a strongly inhomogeneous finite plasma is presented. Asymptotic solutions of the Weber equation and, alternatively, the WKB method, are applied to formulate dispersion relations which agree. Simple formulae for the complex growth rate ρm = ρm, are obtained as functions of the coherence length κ-1/2 (κ being the wavenumber mismatch gradient), the plasma length L, and the basic gain length L0. Where numerical results are available, they agree with the eigenvalues from the formulae to within 10% or better. The m th mode appears if, and only if, the inequality amL0<κ-1/2<bmL holds, where am, and bm are certain eigenvalues which, respectively, increase and decrease with m. The first part of the inequality determines the threshold pump intensity, whereas the second part defines a starting length. © 1979 American Institute of Physics.