Magnetic field effect on charged Brownian swimmers

We calculate the effective diffusion of a spherical self-propelled charged particle swimming at low Reynolds number, and subject to a time-dependent magnetic field and thermal agitation. We find that the presence of an external magnetic field may reduce or enhance (depending on the type of swimming and magnetic field applied) the swimmer's effective diffusion, hence we get another possible strategy to control its displacement. For swimmers performing reciprocal motion, and under an oscillating time-dependent magnetic field, mechanical resonance appears when the swimmer and magnetic frequencies coincide, thus enhancing the particle's effective diffusion. Our analytical results are compared with Brownian Dynamics simulations and we obtain excellent agreement.