Stagnation Pressure of Imploding Shells and Ignition Energy Scaling of Inertial Confinement Fusion Targets

The stagnation pressure pₛ of imploding cylindrical ( n0ex0ex=0ex0ex2) and spherical ( n0ex0ex=0ex0ex3) shells is found to scale as pₛ/p₀∝M₀^2(n+1)/(γ+1), where M₀ is the Mach number of the imploding shell and p₀ its maximum pressure. The result holds approximately for Mach numbers in the range 2<M₀<25 relevant for inertial confinement fusion capsules and is of key importance for their ignition energy scaling. It is derived analytically on the basis of similarity solutions for an ideal gas with adiabatic exponent γ.