Verification of a magnetic island in gyro-kinetics by comparison with analytic theory

Abstract

A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steady state for which the analytic theory is formulated. V C 2015 AIP Publishing LLC.In a tokamak, a magnetic equilibrium consisting of nested non-axisymmetric flux surfaces exhibits a current singularity layer where the safety factor is rational, i.e., where q ¼ m/n, with m and n two integers, respectively, the poloidal and toroidal mode numbers of a radial magnetic perturbation dB r ðh; uÞ, called tearing mode. 1-3 The surfaces given by the relation q ¼ m/n are called resonant surfaces. This singularity in the parallel current is clearly nonphysical and must be regularized by non-ideal, typically collisional, effects leading to magnetic re-connection, 4 which represents the destruction of the resonant surfaces into island chains. The formation of magnetic islands represents a change in the magnetic topology. These resistive instabilities are found in both astrophysical and laboratory plasmas. 5 In the case of laboratory plasmas and in particular, in the case of tokamaks, the presence of magnetic islands can have strong consequences for the core confinement, 6 due to the fact that particles can travel across the island following the perturbed field lines which connect one side of the island with the other. This mechanism is usually referred to as parallel streaming and is the term we use in the following. This increase of the (radial) transport leads to the flattening of the radial profiles and therefore to a loss of energy which eventually represents a loss of core confinement.Because of the impact that magnetic islands have on confinement, it is essential to analyse their stability. The nonlinear evolution of the perturbation leading to the formation of magnetic islands is given by the generalized Rutherford equations 6where r s is the radial position of the resonant surface, s R is the characteristic resistive time, D 0 is the matching parameter from the external solution, f 0 is the position of the island in the binormal direction rf and the functions D and F t represent, respectively, the free energy available for reconnection and the acceleration in the binormal direction of the island. In these equations, we have introduced also the radial halfwidth w and the rotation frequency x of the island in the binormal direction. The functions D and F t can be written in terms of the non inductive parallel current J n:i: k as follows:where X is a flux label...

Gyrokinetic simulations of nonlinear interactions between magnetic islands and microturbulence

“…Finally, we use the conservative model with fluid electrons to study the interactions between a magnetic island and the ITG. In our simulations, we find that the magnetic island rotates at the electron diamagnetic drift velocity, which is consistent with the theory of the drift-tearing mode [19,20]. We also observe that the magnetic island can significantly modify the ITG mode structures.…”

“…The magnetic islands can rotate with electrons due to the frozen-in-line effect. The characteristic rotation frequency is the electron diamagnetic frequency[19,20]. This phenomenon is successfully verified both in our linear and nonlinear simulations.…”

The role of MHD in causing impurity peaking in JET hybrid plasmas

“…b) Linear stability inside the island implies zero turbulent transport, which is probably an oversimplification. However, more complete non-linear gyro-kinetic simulations including a large imposed island have demonstrated substantially decreased (perpendicular) turbulent transport in the island region [40,41], so qualitatively our model should be valid.…”

Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

“…A further discussion is reported in Ref. [35]. The next question to be addressed is whether the same findings should be expected in the presence of turbulent transport.…”

“…The numerical results discussed in this paper are based on the solution of the drift kinetic equation as obtained from the code HAGIS [65], augmented by a pitch-angle scattering operator including a correction to ensure momentum conservation [66] and by an magneticisland structure [30], and on the solution of the gyrokinetic equation with the code GKW [67], where a magnetic island perturbation has been implemented for both periodic [62] and non-periodic radial boundary conditions [35]. A brief account of the numerical scheme is given here.…”