Role of the shear flow profile on the stability of magnetic islands

Abstract

Plasma flow affects the stability of a magnetic island via modification of the ion inertial current. It is shown here that certain profiles of plasma velocity with shear may provide a stabilizing influence on the magnetic island. Such profiles of the plasma flow are characterized by inite plasma circulation inside a magnetic island.

Stabilization of magnetic islands due to the sheared plasma flow and viscosity

“…Note that in this paper we consider a nonrotating (locked) magnetic island in a surrounding plasma that is moving with velocity V 0 . For magnetic islands rotating with frequency ω, equation (18) is modified with the transformation [11,20], where ω E is the Doppler shift frequency due to the equilibrium electric field, and k θ = m/r s . In the next section we consider how (18) is modified taking into account the deformation of the magnetic island in a viscous plasma.…”

Propagation of magnetic islands in the Er=0 frame of co-injected neutral beam driven discharges in the DIII-D tokamak

“…[11][12][13][14] Confirmation of the polarization threshold is a key issue for extrapolation to the beta limit of reactor-grade tokamaks and the theory continues to be developed. 15,16 A ''hidden'' experimental variable is the relative propagation frequency of an island at small amplitude, i.e., upon initiation, in the frame in which the local radial electric field E r ϭ0. Consider the frame of reference in which the island is stationary and the plasma streams past it.…”

Effect of sheared flow on magnetic islands

“…͑19͒ imposes that C + + C − = 0. We thus conclude that the solutions with unbalanced localized jumps in MЈ at the separatrix proposed by Smolyakov et al 19 are not allowed in the relaxed state. These solutions represent states with unbalanced localized viscous torques and they will rapidly relax to the solutions examined in Ref.…”

“…18 We have shown that the steady-state transport equation requires that these discontinuities be symmetric ͑i.e., that they be equal on the two branches of the separatrix͒. States with asymmetrical or unbalanced jumps, which were shown to be stabilizing by Smolyakov,19 lead to the rapid spin-up around the O-point of the plasma inside the separatrix in a manner illustrated in Fig. 2.…”

“…It follows that solutions with unbalanced jumps in the vorticity U ͑i.e., jumps that are not antisymmetric with respect to reflection about the midplane of the is-land͒ such as those considered in Ref. 19 are not allowed in a relaxed state. The relaxation of a velocity profile with unbalanced jumps in the vorticity is illustrated in Fig.…”