Theory of nonlinear space charge waves in neutralized electron flows: Gas-dynamic approach

The problem of the structure and dynamics of nonlinear longitudinal space charge waves in an electron flow that is treated as a gas and is described by an adiabatic equation of state with an arbitrary adiabatic index is solved exactly, and the solution obtained is examined in detail. The isothermal case is considered separately. It is shown that the waves in question can occur in the form of a fast or a slow space charge wave. The boundary values of the velocity and amplitude of these waves are obtained. The effect of the finite transverse dimensions of the electron flow on the structure of the wave and its dynamics is investigated.