The Non-relativistic Charged Bose Gas in a Magnetic Field II. Quantum Properties

Abstract

The formalism presented in a paper by V. Kowalenko and N. E. Frankel (1994, Ann. Phys. (N.Y.)234, 316) is used here to evaluate the various response functions of the charged Bose gas in an external magnetic field at T=0K, where quantum effects dominate. By introducing recently developed asymptotic expansions for the particular Kummer function that appears in these response functions, analytic expressions for the dispersion relations of longitudinal and transverse modes are obtained in both the weak and strong field limits, thereby overcoming the problems caused by the system's anisotropy. As expected, taking the B→0 limit of the weak magnetic field results yields the already known field-free results while the results obtained for strong magnetic fields are heavily influenced by the cyclotron motion of the particles. Bernstein modes or resonances for the system are also evaluated in the strong magnetic field limit. In addition, the screening potentials for a test-particle immersed in the system are evaluated in both magnetic field limits. As the field is turned off, the screening potential for a weak magnetic field reduces to the field-free result, which consists of a Debye-like potential multiplied by an oscillatory term. This potential becomes isotropic for large distances away from the test-particle. In the strong field limit the screening potential is composed of a Debye-like potential multiplied by powers of the displacement in the direction of the magnetic field, but does not contain the oscillatory behaviour of its weak field counterpart. To demonstrate the versatility and power of the asymptotic expansions presented here, they are applied to the classical Maxwellian magnetoplasma, whereupon the dispersion relations for the longitudinal oscillations are obtained in both magnetic field limits. New expressions for Bernstein modes differing from those originally found by Bernstein are also derived.