Stable anisotropic plasma confinement in magnetic configurations with convex–concave field lines

Abstract

It is shown that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability (Tsventoukh 2011 Nucl. Fusion 51 112002). This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with combination of mirrors and cusps. Connection of the convex and concave field line parts results in a reduction of the space charge that drives the unstable E × B motion, as there is an opposite direction of the particle drift in a non-uniform field at convex and concave field lines. The pressure peaking arises at the minimum of the second adiabatic invariant J that takes place at the ‘middle’ of a tandem mirror–cusp transverse cross-section. The position of the minimum in J varies with the particle pitch angle that results in a shift of the peaking position depending on plasma anisotropy. This allows one to improve a stable peaked pressure profile at a convex–concave field by changing the plasma anisotropy over the trap cross-section. Examples of such anisotropic distribution functions are found that give an additional substantial enhancement in the maximal central pressure. Furthermore, the shape of new calculated stable profiles has a wide central plasma layer instead of a narrow peak.

Plasma confinement by magnetic field with convex-concave field lines

“…The simple ideal MHD description gives a strong variation in the stable pressure profile due to the strong variation in the specific volume ∫dl/B: the critical profile being p MHD ∝ (∫ dl/B) −5/3 . However, we have found that there is a strong variation in the stable pressure profile at regions of almost equal specific volume-near min ∫ dl/B, with curvature of alternating sign-with appropriate combination of the convex and concave field line parts [15].…”

“…It is worth noting that the positions of the min ∫dl, and min λ max = max B min , correspond to the min J and hence to the peaking position for the particles with longitudinal and transverse velocity accordingly [15].…”

“…For the particle distribution function F (ε, λ, ψ) = f (ε) G (λ, ψ) p m (ψ) (where ψ is the flux function, λ is the pitch angle, ε is the energy, and ∂f /∂ε should be <0) the kinetic criterion [13,[33][34][35][36][37] gives the stability condition (see [38,39] and [14,15]):…”

“…Figure 1. Sketch of the stabilization effect [15]. Left: the magnetic field lines in r-z for a tandem system mirror-cusp, the current ring coils and the drift-current directions are depicted as well.…”

“…It has been found that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability [14,15]. This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with a combination of mirrors and cusps.…”