A hydrodynamic approach to modeling the space charge problem
A new model is suggested to investigate the influence of a beam charge on the evolution of the charge-density distribution function. The spherically symmetric charge-density distribution of a beam acting on an external homogeneous constant electric field is considered. A new nonlinear boundary problem that takes the influence of a beam’s electric field on the evolution of the charge-density distribution function into account is formulated. The solutions of such a problem can be used as tests in calculation methods that are applied in practice.