Theory of transfer of waves in dispersive media with applications to Langmuir and radio waves in plasmas

A general theory of wave transfer in dispersive medium is presented which is applicable when the wave lengths are much smaller than the scale lengths of the macroscopic parameters. It is assumed that collective oscillations can be quantized and an equation of transfer is derived for the occupation number N(k vector, x vector,t), of quanta in the state of momentum Dirac constant k vector and energy Dirac constantω(k vector,x vector). Expressions are derived relating N(k vector,x vector,t) to the specific intensity of energy, I/sub ω/, and relating the quantum mechanical annihilation rates to the classical damping coefficients. The linear atmosphere approximations are used to study the effects of l-wave propagation in the time-dependent Type III radio burst problem. It is shown that for frequencies less than 10 MHz, the time in which l-waves are absorbed by Landau damping is shorter than the collisional damping time in the solor corona. A modified form of the one-dimensional quasilinear equations is derived taking into account a finite electron density scale height. It is shown that the effects of refraction on the burst profile may be handled in a general way and that the linear atmosphere approximations may be applied to the radio waves at the fundamental frequency of generation