Self-consistent description of Langmuir waves in an inhomogeneous plasma

A set of evolutionary equations is proposed for a self-consistent description of Langmuir wave dynamics in an inhomogeneous plasma. In contrast to the traditionally used set of equations consisting of the kinetic Boltzmann–Vlasov equation for the distribution function and the Poisson equation for the scalar potential of the wave electric field, we describe the latter with the help of a vector potential. This makes the set of equations an evolutionary type of system, which allows solving the initial problem for the distribution function and the wave field. The inclusion of non-resonant particles into consideration with the help of permittivity makes it possible to solve the kinetic equation only for resonant particles. This radically reduces the amount of numerical calculations and allows solving the problem on a personal computer, while the traditional approach in which the kinetic equation is solved for all particles requires much more computational resources. The results obtained include various cases of homogeneous and inhomogeneous plasma as well as the cases of a single wave and a wide spectrum.