Model of enhanced energy deposition in a Z-pinch plasma

Abstract

In numerous experiments, magnetic energy coupled to strongly radiating Z-pinch plasmas exceeds the thermalized kinetic energy, sometimes by a factor of 2–3. An analytical model describing this additional energy deposition based on the concept of macroscopic magnetohydrodynamic (MHD) turbulent pinch heating proposed by Rudakov and Sudan [Phys. Reports 283, 253 (1997)] is presented. The pinch plasma is modeled as a foam-like medium saturated with toroidal “magnetic bubbles” produced by the development of surface $\text{m=0}$ Rayleigh-Taylor and MHD instabilities. As the bubbles converge to the pinch axis, their magnetic energy is converted to thermal energy of the plasma through $\mathrm{pdV}$ work. Explicit formulas for the average dissipation rate of this process and the corresponding contribution to the resistance of the load, which compare favorably to the experimental data and simulation results, are presented. The possibility of using this enhanced (relative to Ohmic heating) dissipation mechanism to power novel plasma radiation sources and produce high K-shell yields using long current rise time machines is discussed.