Strong coupling effects on plasma dispersion in a magnetic field.

Abstract

In weakly correlated plasmas the potential energy of the particles is much less than their kinetic energy. In cases, however, where the potential energy of the particles is equal to or greater than their kinetic energy (strongly coupled plasmas), a special approach is called for. In this work we consider a non-relativistic homogeneous one -component plasma in equilibrium in the presence of a uniform external magnetic field. There are three major schemes of approximations which can be used to obtain the dispersion properties of strongly coupled plasmas. Within these approximation schemes, coupling effects on transverse modes only occur through longitudinal-transverse coupling, since all these schemes consider longitudinal internal field only. In this work the STLS method is opted, primarily for reason of simplicity and also, it is probably satisfactory for low-frequency phenomena. It is known that for strong coupling, the longitudinal plasma exhibits negative dispersion. The main interest in studying transverse modes lies in determining whether a similar change takes place and what the critical coupling is. This problem is related to the Malmberg-O'Neil experiment, where a strongly magnetized, strongly coupled electron plasma is being generated; a further feature of the experiment is that because of the strong magnetic field, quantum effects are important. For quantum plasmas we consider the case of spinless particles in the LLL (Lowest Landau Level) at T = 0(DEGREES)K. The approach used to study this problem is through a perturbation analysis of the plasma dispersion relations. This is justified even for strong coupling, since the effect is proportional to k('2) (k is the wave vector) and it is sufficient to consider the k (--->) 0 limit. We also derive new high-frequency sum rules for plasmas in magnetic field which serve as a standard of comparison from which we obtain, apart from the detailed concrete calculations based on the STLS model, some general results for the dispersion of all transverse modes. As a by-product of the calculation, new systematic results for the dispersion of low-frequency waves in weakly coupled classical and quantum plasmas are obtained.