One-dimensional dispersion of a finite mass of particles of like charge concentrated in a plane

With the aid of kinetic theory, a solution is obtained for the problem of one-dimensional dispersion into vacuum of charged particles that at an initial moment of time are concentrated in the plane x=0. The problem is solved in the approximation of collisionless equations with allowance for a self-consistent electric field.A unique asymptotic expression for one-dimensional dispersion is obtained. The relation between the dispersion problem of a charged gas layer and expansion from a point is demonstrated.