Transition from I 4 to I 2 scaling of K-shell emission in aluminum array implosions

Abstract

It has been observed experimentally that optimal K-shell emission scales as I 4 over a limited range of currents in Z-pinch imploded plasmas. It is also known that in order to conserve energy at a sufficiently high current level, this scaling must change and become less than or equal to I 2. This result follows because the energy sources, PdV work and ohmic heating scale as I 2. In this work, we study theoretically how the scaling of K-shell emission changes as the current is progressively increased. This study is based on a comparison of the implosion characteristics of a number of 1-D radiation hydrodynamic simulations of imploding aluminum wire arrays in which it is assumed that X-ray emission occurs primarily as a result of thermalization of kinetic energy and that the maximum kinetic-energy-per-ion that is generated before the plasma stagnates on axis is kept constant while the mass and current are increased. Results are presented that show the range of validity of previously developed phenomenological models that examined I 4 scaling. In addition, the roles that opacity, initial conditions, total mass, density, temperature, and the strength of the magnetic field play in influencing the scaling of total, and K-shell emissions as the current is increased are discussed.