Plasma Conductivity in the Presence of a Static Magnetic Field
The relationship between the plasma current density and the electric field becomes more complicated in the presence of a DC magnetic field. The following equation defines this relationship:
where σ is the plasma conductivity tensor which is a function of the electron density, collision frequency and magnetic flux density. Using the definitions:
where q is the electron charge, me is the electron mass, ne is the collision frequency, and ω is the angular frequency of the electromagnetic field, the inverse of the plasma conductivity can be written as:
where B is the magnetic flux density which has three components Bx, By, and Bz. The inverse of the plasma conductivity is used because it can be written in a compact, convenient form. The plasma conductivity is a highly nonlinear function of the magnetic flux density. The conductivity exhibits resonant behavior at a critical magnetic flux density given by the simple formula:
At this critical magnetic flux density the electrons continually gain energy from the electric field at all phases of the RF cycle. This principle, called electron cyclotron resonance is used in ECR reactors.