A method to ensure increased radial losses for a selected population of particles from an axially symmetric magnetic trap is described. The method is based on the resonance action of a rotating perturbation magnetic field on the particles. The possible mechanisms and properties of the transverse transfer of particles in this case are discussed. The numerical investigations made with a one-particle approximation allow estimation of the efficiency of the proposed method of pumping. The ion pumping from the thermal barrier of a tandem mirror fusion reactor is considered as an example.