Anisotropic Electron Distribution and the dc and Microwave Avalanche Breakdown in Hydrogen

The Boltzmann transport equation is solved taking into account vibrational, dissociation, excitation, and ionization losses in hydrogen at $\frac{E}{p_0}$ between 40 and 450 V/cm-mm Hg. No approximations are made regarding the angular dependence of the electron distribution function. At the high $\frac{E}{p_0}$ the distribution function is sufficiently anisotropic that it cannot be represented by a two-term expansion in spherical harmonics. It is shown that the concept of "effective" field in microwave breakdown remains valid in the presence of anisotropies provided the circular frequency is much larger than the electron growth rate. The temporal growth rate of the electron density is calculated and compared with the experiments of Rose and of Cottingham and Buchsbaum. The effects of anisotropy on the diffusion coefficient and on the microwave breakdown equation are discussed.