The preionization level and other initial conditions necessary for the formation of spatially homogeneous pulsed avalanche discharges at high gas pressures are examined. Assuming properly shaped electrodes with no strong edge effects, the minimum preionization level required for homogeneous discharge initiation is found to depend on the voltage rise time across the electrodes as well as on the total pressure and various electrochemical properties of the gas mixture which govern the net rate of change of the first Townsend coefficient with respect to the local electric field strength. Our predictive results are found to be consistent with experimental observations.
Taylor's analysis of the intense spherical explosion has been extended to the cylindrical case. It is found that the radius R of a strong cylindrical shock wave produced by a sudden release of energy E per unit length grows with time t according to the equation R=S(γ)(E/ρ0)1/4t1/2, where ρ0 is the atmospheric density and S(γ) is a calculated function of the specific heat ratio γ. For γ=1.4, S(γ) is found to be approximately unity. For this case, the pressure p1 behind the shock wave decays with radius R according to the relation p1=0.216E/R2. Applying the results of this analysis to the case of hypersonic flight, it can be shown that the shock envelope behind a meteor or a high-speed missile is approximately a paraboloid given by R=(D/ρ0)1/4(x/V)1/2 where D and V denote the total drag and the velocity of the missile, respectively, and x is the distance behind the missile.
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