Strong-radiation-field generalization of the elementary kinetic theory of plasma

A new system of simple equations is derived to study the fundamental plasma characteristics in the context of the elementary kinetic theory and of a s trong laser field. Along with usual equations duly revisited, the new syste m contains an equation giving the time evolution of the difference of the e ffective temperatures along and perpendicular to the external field polariz ation. It gives the possibility to get the information an the anisotropy of the electron distribution function and on its evolution. While in the weak field case only one collision frequency is sufficient, for the same physic al situation in the strong held case, it is found wise to introduce three d ifferent collision frequencies, helping to disentangle different aspects of collisional plasma heating, and to get a more detailed insight into the pl asma behavior. As a whole, the new set of equations is much more informativ e than the usual set, allowing one to address, in a simple way, a variety o f processes, including, among others, high-order harmonic generation and wa ve mixing. The results obtained by solving the new equations of the element ary kinetic theory are checked against the results of the exact numerical t wo-dimensional solution of the corresponding kinetic equation. The agreemen t is quite satisfactory, especially for the initial stages of laser-plasma interaction. The reasons for the incipient discrepancy at later times are d iscussed. The new equations are implementable and can be profitably applied to physical situations for which an exact kinetic approach is still prohib itive.