Interaction of turbulence with magnetic islands: effect on bootstrap current

Hornsby, W. A.; Siccinio, M.; Peeters, A. G.; Poli, E.; Snodin, A. P.; Casson, F. J.; Camenen, Y.; Szepesi, G.

doi:10.1088/0741-3335/53/5/054008

Cited by 44 publications

(37 citation statements)

References 29 publications

(57 reference statements)

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“…This implies that one needs to consider the parallel gradient of the electron pressure in Eq. (14), which becomes which, after integration, yields…”

Section: A Frozen Electrons Inside the Islandmentioning

confidence: 98%

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

et al. 2015

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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...

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“…This implies that one needs to consider the parallel gradient of the electron pressure in Eq. (14), which becomes which, after integration, yields…”

Section: A Frozen Electrons Inside the Islandmentioning

confidence: 98%

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

et al. 2015

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“…Here, we briefly review gyrokinetic simulation studies on interactions between the ITG turbulence and magnetic islands and on basic physics of magnetic reconnection. Most gyrokinetic studies on the interaction of turbulence with magnetic islands consist of carrying out electrostatic simulations in the presence of a fixed magnetic island (Poli et al 2009;Hornsby et al 2011Hornsby et al , 2012Waltz and Waelbroeck 2012), and it is reported that the production of long wavelength mode by ITG turbulence can give rise to an oscillating vortex flow inside the island separatrix (Hornsby et al 2011), and the oscillation is related to the geodesic acoustic mode (Hornsby et al 2012). The momentum transport associated with a magnetic island interacting with external magnetic perturbation is also studied (Waltz and Waelbroeck 2012).…”

Section: Magnetic Islands and Magnetic Reconnectionmentioning

confidence: 99%

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

et al. 2015

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Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

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“…However, we have verified the statements made in this section using a reduced model in which both radial diffusion as well as collisions are kept. The results of this model will be published elsewhere [33].…”

Section: Finite Electron Temperature Gradient and Bootstrap Currentmentioning

confidence: 99%

The nonlinear coupling between gyroradius scale turbulence and mesoscale magnetic islands in fusion plasmas

et al. 2010

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The interaction between small scale turbulence (of the order of the ion Larmor radius) and meso-scale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neo-classical drive.

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Interaction of turbulence with magnetic islands: effect on bootstrap current

Cited by 44 publications

References 29 publications

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

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

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

The nonlinear coupling between gyroradius scale turbulence and mesoscale magnetic islands in fusion plasmas

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