Plasma Conductivity in a Magnetic Field

Abstract

If the plasma is located in a magnetic field then the two-fluid model becomes quite complicated. Current flowing along the magnetic field is subject to Ohm’s law with the usual value of the conductivity. In plasmas located in a magnetic field this ordinary conductivity is called the longitudinal conductivity. The transverse conductivity is smaller than the conductivity in the direction of the magnetic field. If the transverse current is carried only by electrons which move under the influence of an externally applied electric field the plasma possesses an anisotropic conductivity. The rules for anisotropic conductivities are as follows: first, the conductivity at right angles to the field is reduced in inverse proportion to the square of the magnetic field; second, the current does not only flow parallel to the applied electric field, but also at right angles to it (Hall effect). A plasma in which the electrons perform several cyclotron gyrations between collisions is called a magnetoplasma. A plasma magnetized in this way must have a density that is not too high and must be located in a strong magnetic field. If the anisotropy of the conductivity is significant, in a magnetoplasma the transverse conductivity will be much smaller than the longitudinal conductivity and the current perpendicular to the electric field (the Hall current) will be considerably larger than the current parallel to the electric field. However, in a highly ionized plasma the anisotropy of the conductivity is attenuated by the following three effects. First, the current can be carried at right angles to the field by the ions as well as the electrons. Second, the current transverse to the magnetic field can be produced by forces of a nonelectrical nature, e.g., a pressure differential, in addition to the electric field. Finally, charge separation leads to plasma polarization, i.e., the appearance of an internal electric field in the plasma. Thus, the current will not only be determined by the externally applied electric field, but also by polarization fields.