Flux amplification in helicity injected spherical tori

Abstract

An important measure of the effective current drive by helicity injection into spheromaks and spherical tori is provided by the flux amplification factor, defined as the ratio between the closed poloidal flux in the relaxed mean field and the initial injector vacuum poloidal flux. Flux amplification in magnetic helicity injection is governed by a resonant behavior for Taylor-relaxed plasmas satisfying j=kB. Under the finite net toroidal flux constraint in a spherical torus (ST), the constrained linear resonance k1c is upshifted substantially from the primary Jensen–Chu resonance k1 that was known to be responsible for flux amplification in spheromak formation. Standard coaxial helicity injection into a ST operates at large M, with M the characteristic dimensionless parameter defined as the ratio between the toroidal flux in the discharge chamber and the injector poloidal flux. Meaningful flux amplification for ST plasmas is limited by a critical kr at which edge toroidal field reverses its direction. The kr is downshifted from k1 by a small amount inversely proportional to M. The maximum flux amplification factor Ar≡A(k=kr) scales linearly with M. At the other end of k, substantial flux amplification A(k=ko)∼1 becomes available for ko that scales inversely proportional to M, a significant departure from that in spheromak formation. These important parameters follow the inequality ko<kr<k1<k1c. Even though Ar is greater than M in a typical ST, detailed q-profile considerations further constrain the maximum useful flux amplification factor in a ST to be smaller than M. The scaling laws are given analytically in the asymptotic limit of M⪢1, but numerical solutions indicate that they are useful even for M∼1.