Motion of a Charged Particle in Inhomogeneous Magnetic Field

The motion of a charged particle in the static magnetic field which is applied parallel to z direction and whose magnitude varies in y direction monotonously tending to 0 is discussed. The orbit of the particle is a spiral directing ± B ×∇ B when the speed of the particle does not exceed a certain value determined by its initial position, whereas when the speed is sufficiently high the particle is driven continuously in the direction of diminishing field strength. The criterion is given as to when the particle shows a spiral motion. When the variation of the field strength is exponential type, the orbit is exactly calculated as an example, and the validity of the theory is confirmed.