Analytic equilibrium of elongated plasmas bounded by a magnetic separatrix and the problem of resistive axisymmetric X-point modes

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role for the understanding of ELMs in tokamaks and their active control via so-called vertical kicks. The first step in the development of an analytic model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate and relatively simple analytic MHD equilibrium for a plasma column with noncircular cross section bounded by a magnetic separatrix

Analytic equilibrium of "straight tokamak" plasma bounded by a magnetic separatrix

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role in the understanding of Edge Localized Modes in tokamak experiments and their active control via so-called vertical kicks. With this motivation in mind, the first step in the development of an analytical model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate, but at the same time relatively simple analytical magnetohydrodynamic equilibrium for a plasma column with a noncircular cross section bound by a magnetic separatrix. An early example is Gajewski's equilibrium solution [R. Gajewski, Phys. Fluids 15, 70 (1972)], which, however, has the shortcoming that infinite external currents placed at an infinite distance from the X-points produce the elliptical elongation of the plasma column. In this article, Gajewski's solution is extended to the case where external currents are located at a finite distance from the boundary of the plasma current density and the latter is distributed uniformly over a domain bound by a nearly elliptical magnetic flux surface

Resonant Axisymmetric Modes

Axisymmetric modes in shaped tokamak plasmas are normally associated with vertical displacement events. However, not enough attention has been given to the fact that these modes can be resonant in two different ways. Firstly, for a plasma bounded by a divertor separatrix, a generic n=0 ideal-MHD perturbation, ξ, is singular at the divertor X- point(s), where Beq · ∇ξ = 0, with Beq the equilibrium magnetic field. As a consequence, n=0 perturbations can give rise to current sheets localized along the divertor separatrix. Secondly, a feedback-stabilized n=0 mode tends to acquire an Alfv ́enic oscillation frequency. As a result, a resonant interaction with energetic particle orbits can lead to a new type of fast ion instability

Fast-ion-driven vertical modes in magnetically confined toroidal plasmas

A new type of fast particle instability involving axisymmetric modes in magnetic fusion tokamak plasmas is presented. The relevant dispersion relation involves three roots. One corresponds to a vertical plasma displacement that, in the absence of active feedback stabilization, grows on the wall resistivity time scale. The other two, oscillating close to the poloidal Alfv ́en frequency, are normally damped by wall resistivity. The resonant interaction with fast ions can drive the oscillatory roots unstable. Resonance conditions, stability thresholds and experimental evidence are discussed

Vertical displacements close to ideal-MHD marginal stability in tokamak plasmas

Elongated tokamak plasmas are prone to instability, initiated by vertical displacement perturbations, which can be suppressed if a perfectly conductive wall is placed near the plasma boundary, providing passive feedback stabilization. For the more realistic case of a resistive wall, the vertical mode can still grow on the relatively slow resistive wall time scale. Active feedback control is then required for complete stabilization. However, the slow growth is far from ideal-MHD marginal stability on the stable side, i.e., provided that the wall is sufficiently close to the plasma. It is shown that the resistive growth rate can be significantly faster, scaling with fractional powers of wall resistivity, if the wall position satisfies the criterion for ideal-MHD marginal stability, thus posing more stringent conditions for active feedback stabilization

Axisymmetric oscillatory modes in cylindrical magnetized plasma bounded by a conducting wall

A comparison between analytic theory and numerical simulations of axisymmetric modes in magnetically confined, cylindrical plasma with non-circular cross-section bounded by a conducting wall is presented. If the wall is close to the plasma, modes are oscillatory, with frequency scaling with the Alfven frequency. The two frequencies differ when the plasma cross-section is elongated, but they become equal in the circular limit. The mechanism for oscillatory behavior is a consequence of the currents induced on the perfectly conducting wall when the plasma is displaced from its equilibrium positions. The induced currents exert a restoring force on the plasma, and the oscillation frequency is a combination of the strength of this force and the plasma mass density. An additional parameter, depending on the distance between the wall and the plasma boundary, also affects the oscillation frequency so that the frequency becomes large when the wall-plasma boundary distance approaches zero.& COPY; 2023 Elsevier B.V. All rights reserved