Nonlinear Relaxation Time Model

In the collisional kinetic plasmas theory, the traditional approach lies on the use of an approximative collisional term in order to avoid the issue of the full complicated equation. In this work, we present a new simple nonlinear relaxation model based on two different relaxation times, namely, $\tau_1$ and $\tau_2$. In contrast with many models in kinetic plasmas theory, our model has the striking feature of not being directly linearized when the local thermodynamic equilibrium is assumed. It is also proved that the model satisfies the H-theorem and the conservations laws (particles, momentum and energy conservation during the collisions). The basic theoretical framework is outlined and it is applied for three distinctive relevant applications: 1) The relaxation to equilbrium in the spatially homogeneous case. The expression found for the distribuition function $f$ shows that the nonlinear term can either accelerate or decelerate the relaxation process; 2) Electrons runaways in a cooling plasma. We use the condition of vanish collision term, $C(f)=0$, to find the distribution function $f$ of the electrons in the runaway phenomena; 3) Negative differential resistance in GaAs. In this application, the drift velocity and the density of the electrons are calculated. In addition, the threshold electric field and the density of the electrons at the upper conduction band are calculated and the values found show good agreement with other results present in the literature.