Quantum effects on the motion of charged particles near the neutral surface of an ultrasonic magnetic field

The problem of quantum motion of charged particles in a magnetic field is extended to the case where the magnetic field has a neutral surface. This situation may occur in ultrahigh magnetic fields generated by multi-terawatt laser pulses interacting with a plasma of similar to 10-100 eV. Far from the neutral surface the drift approximation holds for the classical motion and the Landau description holds for the quantum motion. Near the neutral layer at a classical distance less than the Larmor radius the particle motion is nonadiabatic. Here the quantum motion is described by a Schrodinger equation and new quantum levels for the particle transverse energy are found, with a separation that depends on the particle momentum along the neutral surface.