Scaling laws for spherical pinch experiments

Spherical pinch experiments are characterized by a central discharge in a spherical vessel followed by an inductive discharge in the vessel's peripheral shell gas. An analysis is carried out of the evolution of the imploding shock waves produced by the shell explosion in order to find out if the central discharge can be contained and compressed by the converging shocks, so as to maintain its temperature for a time sufficiently long for breakeven. The analytical model adopted is essentially that of the recent paper of Ahlborn and Key (Plasma Phys. 23: 435, 1981). One finds that the converging shocks are indeed capable of containing and compressing the central plasma. In addition, if the central spark reaches the critical temperature T /SUB L/ =2.58 keV by the deposition of an energy density of 1.86x10/sup 8/JXg/sup -1/, the scaling law required in order to contain such a plasma for breakeven is /rho//sub 0/R(E /SUB s/ /M /SUB s/ ) /SUP 1/2/ greater than or equal to1.96 X 10/sup 6/, where /rho//sub 0/ is the initial fill gas density, R is the radius of the spherical vessel, and E /SUB s/ is the energy deposited in the peripheral shell mass M /SUB s/more » . The general applicability of the model to other fusion devices based on the implosion principle is discussed.« less