Reactor prospect of spheromak concept by electrostatic helicity injection

Abstract

The highest performing spheromaks in the laboratory are formed by electrostatic helicity injection. Discharges with up to 1MA plasma current and core electron temperature as high as 500eV have been recently obtained. For such a scheme to scale-up to a reactor, however, a much higher current multiplication factor (plasma current over injector current) must be achieved. It is shown here that spheromak current multiplication is linearly proportional to flux amplification (ratio of poloidal fluxes inside and outside the separatrix of the mean field). Hence, spheromak optimization is centered around achieving high flux amplification, which is provided by linear or nonlinear resonant coupling between helicity injector and the spheromak force-free eigenmode. The nonlinear resonant field amplification is the most promising route to high flux amplification in a realistic plasma that often significantly deviates from the Taylor state. Accessing such nonlinear resonant field amplification can be facilitated by auxiliary current drive around the magnetic axis and auxiliary heating to break the electron temperature constraint on flux amplification.

Numerical computation of the helical Chandrasekhar–Kendall modes

“…The primary result of the paper is a new formulation that numerically computes the helical CK modes as a standard matrix eigenvalue problem, which is suitable for numerical implementation in a torus of complex poloidal cross section. This capability can be of use for current and future design optimizations for reversed field pinch, spherical tokamak [14], and spheromak [15] experiments, and for astrophysical radio lobe analysis [16].…”

“…These force-free eigensolutions are uniquely determined by the chamber geometry, and play an essential role in determining the relaxed states of a driven plasma [4,7], in which the spatial overlap of the CK modes and a vacuum field generated by external current provides the coupling between the external helicity source and the driven plasma [8]. In fact, resonant coupling [9][10][11][12] is the physical mechanism underlying the self-organization of system-scale magnetic fields by magnetic relaxation in the laboratory formation of spherical tokamak [13,14], spheromak [15], and reversed field pinch by helicity injection. It is also thought to be a competing paradigm for the generation and sustainment of large scale magnetic fields in astrophysical radio lobes [16].…”

“…Although much of the design constraint and optimization for laboratory helicity injection applications involves only the axisymmetric CK modes in an axisymmetric toroidal chamber [17,14,15], as the target magnetic configurations are axisymmetric [18], helical or non-axisymmetric CK modes can play a subtle role in determining the operating boundary and the degrees of intrinsic non-axisymmetry in the experiments. This comes about in two ways.…”

A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions

“…For weak stochasticity, even small perpendicular current associated with the plasma inertia, can produce significant modulation in λ along the magnetic field line due to the Pfirsch-Schlüter effect [8]. As the MHD instabilities die down and the flux surfaces reheal, like those in laboratory confinement experiments with reversed field pinch [9], spheromaks [10], spherical tokamak [11,12,13], and tokamak disruptions [14], or in the solar corona [15] and radio lobes [16], one can end up with a force-free plasma with λ(ψ) a function of the flux surface label ψ, also know as a nonlinear force-free magnetic field [17,18,19,20], which despite the deviation from the constant λ Taylor state, retains the key feature of magnetic self-organization via a resonant coupling between the helicity injection source and global magnetic configuration [21,22,23]. Further evolution of such a nonlinear force-free plasma, for example, a post-thermal-quench tokamak plasma undergoing a cold vertical displacement event (VDE), is governed by the slow transport process, namely the resistive decay of the plasma current.…”