In an electrical discharge in crossed electric and magnetic fields, electrons describe cycloidal paths between collisions causing many more collisions with gas molecules. As a result, the crossed magnetic field exerts a considerable influence on the Townsend first ionization coefficients alpha and gamma . These coefficients are a function of E/N, where E is the electric field and N is the gas number density, and determine the sparking potential of a uniform electric field geometry of the electrodes. In a nonuniform electric field geometry such as that which exists in a coaxial cylindrical geometry, the Townsend criterion will yield the corona inception potential. In the present work, the sparking voltages in the presence of electric and magnetic fields are examined with the ratios of the electrode diameters as parameters and varying in the range of 2 to 50. The lower value represents a quasi-uniform electric field and the higher values highly nonuniform fields. To facilitate these calculations the electron energy distribution in electric fields alone is examined first. Using the energy distribution function, the mean energy and drift velocities are calculated and compared with available results. The theory is then extended to a crossed magnetic field to calculate the current multiplication. It is shown that a magnetic field increases the breakdown voltage according to the effective reduced electric field concept.
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