Theoretical prediction of [tau]E and [beta]⁻ in a large aspect ratio LDX

Abstract

The Levitated Dipole Experiment (LDX) is a novel experiment to study the confinement of a high-temperature plasma in the magnetic field of a superconducting ring of wire. The levitated magnet produces a poloidal closed-line magnetic field characteristic of an ideal point dipole or a hard core Z-pinch magnetic configuration. The point dipole and hard core Z-pinch configurations share similar physics and may be respectively considered to be the zero and large aspect ratio approximations to LDX. The present work focuses on a hard-core Z-pinch magnetic configuration. An analysis is presented that theoretically predicts (1) the maximum pressure p., (2) the energy confinement time TE and (3) the average beta / by solving a proposed self-consistent model of plasma. The model makes the optimistic assumption that transport is purely classical in the region of the profile that is magnetohydrodynamically (MHD) stable against interchange modes. For the interchange unstable region, a quasilinear MHD transport model is developed. The analysis of MHD quasilinear transport starts with an assessment of stability corrections due to axial flows. The axial flows are taken as an approximation to the LDX toroidal flows, expected to appear due to non-ambipolar transport. It is shown that the subsonic axial flows create only negligible correction to the plasma stability and the MHD transport analysis is performed for a static plasma. The evolution of the particle density, energy and magnetic field in the MHD unstable region is investigated using the quasilinear approximation. The exact transport equations are derived for a static plasma in the hard core Z-pinch magnetic configuration. The equations are generalized to an arbitrary axisymmetric closed-filed line magnetic configuration.

(cont.) It is shown that violation of the marginal stability criterion leads to a rapid time-scale transport (i.e. much faster than classical transport), which brings the pressure profile back to marginal stability and forces particle density to be inversely proportional to V = d / B. The applicability of the quasilinear approximation is numerically tested in a hard core Z-pinch magnetic configuration using a non-linear numerical code. The numerical results confirm the theoretical conclusions that the plasma maintains its marginally stable pressure profile through anomalous transport. The requirement of the marginally stable pressure profile plus p - V-'density profile completes the model and provides sufficient information to calculate TE and /3 in the hard core Z-pinch magnetic configuration. The predictions show that the performance of a large-aspect ratio LDX is strongly coupled to the maximum achievable edge temperature with relatively good performance achieved when T, > 10 eV. Performance should be further improved by the finite aspect ratio in the real experiment. Analytic and numerical calculations lead to explicit scaling relations for TE and , that can be tested in future LDX experiments.