How can one solve exactly some problems in plasma theory

A review of a technique for the application of a new Lambert W function for solving transcendental equations arising in classical problems of plasma and electron beam theories is presented, and the basic mathematical properties of the Lambert W function are outlined. The problems discussed include equilibrium electric charge of a solitary body in plasma, nonlinear ion-acoustic waves, the equilibrium configuration of a neutralized electric beam, the dynamics of shaping virtual cathodes in a medium with viscous friction, and the study of the dispersion equation for electron plasma waves in the framework of generalized Boltzmann kinetics.