Numerical solution of a model self-consistent electrodynamic problem

The numerical solution is discussed of the model self-consistent problem for dense electron bunch motion under the action of induced wave and intrinsic bunch field reconstructing during its motion. A ring electron bunch is moving in a closed coaxial resonator with perfectly conducting walls. The corresponding group of the Maxwell equations and relativistic Newton equation are solved by the finite-difference method. It is shown that while numerical simulation with underestimated initial data decelerated bunch motion is observed. For some initial position the bunch is being introduced into the center of resonator and is being oscillating. But the bunch with a lesser charge is being moved forward in all cases