On the solution of self-consistent problem for charged particle bundle in the Penning trap

It is shown that under certain conditions for the spatially bounded charged particle gas cloud the Vlasov equation can be solved. The solution describes pulsation of a uniform particle bundle in the Penning trap, and in the case of nonuniform bundle - the initial pulsation stage. It's also shown that under investigated conditions the considered pulsation calculation is reduced to solving of an ordinary differential equation, and for initial stage of nonuniform bundle pulsation - to solving two such equations.