Motion of a Charged Particle in a Randomly Varying Magnetic Field

The motion of a charged particle in a randomly varying uniform magnetic field is investigated. Stability of the mean position and mean square displacement are determined rigorously in the case of random binary variations (telegraph signal). It is found that the mean position can be stable if the fluctuating part of the magnetic field is large enough compared to the uniform background. The stability regions are obtained in the parameter plane. It is also found that the mean square displacement can be unstable even in the region where the mean is stable. After an initial diffusive motion (with a calculable diffusion coefficient), the charged particle either acquires wild oscillations in its trajectory (stable mean, unstable mean square) or quickly leaves the region where it started (unstable mean).