ANOMALOUS RESISTANCE OF RANDOMLY INHOMOGENEOUS HALL MEDIA

The problem of averaging the resistance rho triple-over-dot e of a randomly inhomogeneous medium in a strong magnetic field is considered for the case when the fluctuations of the Hall (antisymmetric) components of the macroscopic resistance tensor exceed greatly its diagonal elements. A possible anisotropy of the inhomogeneity defined by various characteristic space-scales lambda-z, lambda-perpendicular-to (along and across the magnetic field respectively) is taken into account. An anomalous bulk resistance (rho-e perpendicular-to >> rho-o) arises for lambda-z/lambda perpendicular-to >> >> (beta-DELTA-2)-1, where rho-0 is the microscopic specific resistance, beta >> 1 is the Hall parameter and DELTA the relative fluctuation of rho-0-beta (beta-DELTA >> 1). The cause of the anomalous resistance is the strong tortuousness of the current lines, the distribution of which may be of both a quasi-homogeneous and fractal nature (for lambda-z/lambda-perpendicular-to >> (beta/DELTA)1/2; the effective resistance attains its maximum rho-e perpendicular-to almost-equal-to rho-0-beta-DELTA at the transition point between these two regimes. A variational principle is formulated for Hall current flow. Size effects (dependence of rho-e perpendicular-to on the longitudinal size of the sample b(z)) are studied in the various regimes. The application of the results to a description of plasma current opening switches is discussed.