Driving rotamak currents with minimal power dissipation

Abstract

The Rotamak is a proposed thermonuclear fusion device which employs rotating magnetic fields (RMF) to generate an azimuthal current to produce a field-reversed configuration. The efficiency of the currents that produce the field reversal by RMFs was debated some 40 years ago. The debate revolved around whether the currents would incur dissipation by the conventional Spitzer perpendicular resistivity, or whether some other relation between current and dissipation would be more appropriate. By employing an electron–ion pitch-angle scattering model, we find that the dissipation is non-Spitzer in nature. However, curiously, there appears to exist a regime where the power dissipated to maintain the current becomes vanishingly small.

Energizing charged particles by an orbit instability in a slowly rotating magnetic field

“…The RMF B 1 induces an electric field E which is determined in part by the boundary conditions, and is therefore not unique. Two different sets of boundary conditions have been employed in past studies, each leading to vastly different stability criteria [1][2][3][4]. Here we show that there is in fact a large family of boundary conditions consistent with the problem, and that a one-parameter subset of these characterizes those configurations most relevant to laboratory plasmas.…”

“…Secondly, one can answer the question of how sensitive the stability diagram is to perturbation in the boundary conditions. It is shown that the stability diagrams in some previous studies [3,4] are in fact highly sensitive to such perturbations. However, this is an exceptional case.…”

“…and therefore the p = 0 case is always unstable for |α| 1 with γ ∼ |α| −3/4 . The p=1 case is special and worth discussing since it has been previously studied [3,4]. In this case, u 1 = 0 is an exact root for all (α, β), as can be seen by the vanishing of the constant term in the characteristic polynomial (32).…”

“…Previous analyses [3,4] have used the p = 1 case to model single-particle confinement in field reversed configurations (FRCs) maintained by RMFs. The idea in these analyses is that RMF parameters α and β should be chosen such that both electrons and ions are confined for all time.…”

“…We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break µ-invariance and energize particles. This model system of low frequency RMF has been studied before, albeit in studies focused on finding conditions for stable solutions [1][2][3][4], and is particularly important to current drive in field-reversed configuration (FRC) plasmas [5,6]. However, previous treatments have not addressed two important aspects of the problem, namely the roles of adiabatic invariance and boundary conditions in the theory.…”