A study on microwave instability induced radiation

It has been shown in the context of a solvable model that the microwave instability can be described in terms of “coherent states”. Building on this model, we first show that the simplicity of the model arises from the fact that the key integral-differential equation can be reduced to the Karhunen-Loeve equation of the theory of stochastic processes. We present results on the correlation functions of the electric field. In particular, for the second order correlation function, we show that a relation akin to the Hanbury Brown-Twiss correlation holds for the coherent states of the microwave instability induced radiation. We define an entropy-like quantity and we introduce a Wigner distribution function representation