Measurements of three-dimensional flows induced by magnetic islands
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The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition.
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This article discusses the use of radio frequency (RF) current drive to stabilize large islands, focusing on nonlinear effects that appear when relatively high powers are used to stabilize large islands. We are interested in developing a capability to stabilize large islands via RF driven currents to avoid the need for mitigation to the extent possible. As tokamaks are designed and built with increasing levels of stored energy in the plasma, disruptions become increasingly dangerous. It has been reported that 95% of the disruptions in the Joint European Torus tokamak with the ITER-like wall are preceded by the growth of large locked islands. These large islands are mostly produced by off-normal events other than neoclassical tearing modes. This paper presents theory and modeling for a nonlinear “RF current condensation” effect that can concentrate the RF driven current near the center of a large island, thereby increasing the efficiency of the stabilization. A nonlinear shadowing effect can hinder the stabilization of islands if the aiming of the ray trajectories does not properly consider the nonlinear effects.
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An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized small-scale reconnection processes, essentially between quasi-2D interacting magnetic islands. Charged particles trapped in merging magnetic islands can be accelerated by the electric field generated by magnetic island merging and the contraction of magnetic islands. We derive a gyrophase-averaged transport equation for particles experiencing pitch-angle scattering and energization in a super-Alfvénic flowing plasma experiencing multiple small-scale reconnection events. A simpler advection-diffusion transport equation for a nearly isotropic particle distribution is derived. The dominant charged particle energization processes are (1) the electric field induced by quasi-2D magnetic island merging and (2) magnetic island contraction. The magnetic island topology ensures that charged particles are trapped in regions where they experience repeated interactions with the induced electric field or contracting magnetic islands. Steady-state solutions of the isotropic transport equation with only the induced electric field and a fixed source yield a power-law spectrum for the accelerated particles with index α = –(3 + M{sub A} )/2, where M{sub A} is the Alfvén Mach number. Considering only magnetic island contraction yields power-law-like solutions with index –3(1 + τ {sub c}/(8τ{sub diff})), where τ {sub c}/τ{sub diff} is the ratio of timescales between magnetic island contraction and charged particle diffusion. The general solution is a power-law-like solution with an index that depends on the Alfvén Mach number and the timescale ratio τ{sub diff}/τ {sub c}. Observed power-law distributions of energetic particles observed in the quiet supersonic solar wind at 1 AU may be a consequence of particle acceleration associated with dissipative small-scale reconnection processes in a turbulent plasma, including the widely reported c {sup –5} (c particle speed) spectra observed by Fisk and Gloeckler and Mewaldt et al.
We demonstrate in theory that tearing mode locking and magnetic island suppression by resonant magnetic perturbations (RMPs) can correspond to different states of a same dynamic system governed by the torque balance and the nonlinear island evolution in the Rutherford regime. In particular, mode locking corresponds to the exact steady state of this system. A new exact analytic solution has been obtained for such a steady state, which quantifies the dependence of the locked mode island width on RMP amplitude in different plasma regimes. Furthermore, two different branches of mode locking have been revealed with the new analytic solution and the branch with suppressed island width turns out to be unstable in general. On the other hand, the system also admits stable states of island suppression achieved through the RMP modulation of tearing mode rotational frequency. When the RMP amplitude is above a certain threshold, the island suppression is transient until the tearing mode eventually gets locked. When the RMP amplitude is below the mode locking threshold, the island can be suppressed in a steady state on time-average, along with transient oscillations in rotational frequency and island width due to the absence of mode locking.
The cross-field diffusion of field lines in stochastic magnetic fields described by the 2D+slab model is studied using a semi-analytic statistical approach, the decorrelation trajectory method. We show that field line trapping and the associated stochastic magnetic islands strongly influence the diffusion coefficients, leading to dependences on the parameters that are different from the quasilinear and Bohm regimes. A strong amplification of the diffusion is produced by a small slab field in the presence of trapping. The diffusion regimes are determined and the corresponding physical processes are identified.
In this work, evolution of an incompressible, thermally homogeneous, infinitely conducting, viscous magnetofluid is numerically explored as the fluid undergoes repeated events of magnetic reconnection. The initial magnetic field is constructed by a superposition of two linear force-free fields and has similar morphology as the magnetic loops observed in the solar corona. The results are presented for computations with three distinct sets of footpoint geometries. To onset reconnection, we rely on numerical model magnetic diffusivity, in the spirit of implicit large eddy simulation. It is generally expected that in a high Lundquist number fluid, repeated magnetic reconnections are ubiquitous and hence can lead to a host of magnetic structures with considerable observational importance. In particular, the simulations presented here illustrate formations of magnetic islands, rotating magnetic helices and rising flux ropes—depending on the initial footpoint geometry but through the common process of repeated magnetic reconnections. Further, we observe the development of extended current sheets in two case studies, where the footpoint reconnections generate favorable dynamics.
Magnetic reconnection is a primary mechanism for particle energization in space and astrophysical plasmas. By carrying out two-dimensional (2D) fully kinetic simulations, we study particle acceleration during magnetic reconnection in plasmas with different plasma β (the ratio between the thermal pressure and the magnetic pressure). For the high-β cases, we do not observe significant particle acceleration. In the low-β regime (β<0.1), we find that reconnection is efficient at energizing both electrons and ions. While the distribution of accelerated particles integrated over the whole simulation box appears highly non-thermal, it is actually the superposition of a series of distributions in different sectors of a 2D magnetic island. Each of those distributions has only a small non-thermal component compared with its thermal core. By tracking a large number of particles, we show that particles get energized in X-line regions, contracting magnetic islands, and magnetic island coalescence regions. We obtain the particle energization rate j⋅E by averaging over particle drift motions and find that it agrees well with the particle kinetic energy change. We quantify the contribution of curvature drift, gradient drift, polarization drift, magnetization, non-gyrotropic effect, and parallel electric field in different acceleration regions. We find that the major energization is due to particle curvature drift along the motional electric field. The other particle motions contribute less but may become important in different acceleration regions. The highly efficient particle energization in low-β plasmas may help us understand the strong particle energization in solar flares and accretion disk coronae.
Abstract The safe operation of most tokamaks, especially the large ones, relies on the feedback control of vertical displacement events (VDEs). However, most of these feedback control systems are based on axisymmetric VDE models. In this study, we use NIMROD simulations to study the role of non-axisymmetric perturbations in free drift vertical displacement events on EAST. The high- n modes in the non-axisymmetric VDE grow first, which drives the formation of high- n magnetic island chains. Subsequently, the magnetic island chains grow and overlap with each other, leading to the destruction of the magnetic flux surface, which induces a minor disruption and accelerates the start of the following major disruption. The magnetic island and the stochastic magnetic field allow the toroidally non-axisymmetric poloidal plasma current to jet towards the hoop force direction, forming finger-like and filamentary structures. Such a plasma current non-axisymmetry strongly depends on the anisotropy in the thermal transport coefficients.
Shock waves, as shown by simulations and observations, can generate high levels of downstream vortical turbulence, including magnetic islands. We consider a combination of diffusive shock acceleration (DSA) and downstream magnetic-island-reconnection-related processes as an energization mechanism for charged particles. Observations of electron and ion distributions downstream of interplanetary shocks and the heliospheric termination shock (HTS) are frequently inconsistent with the predictions of classical DSA. We utilize a recently developed transport theory for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets. Particle energization associated with the anti-reconnection electric field, a consequence of magnetic island merging, and magnetic island contraction, are considered. For the former only, we find that (i) the spectrum is a hard power law in particle speed, and (ii) the downstream solution is constant. For downstream plasmoid contraction only, (i) the accelerated spectrum is a hard power law in particle speed; (ii) the particle intensity for a given energy peaks downstream of the shock, and the distance to the peak location increases with increasing particle energy, and (iii) the particle intensity amplification for a particular particle energy, f(x,c/c{sub 0})/f(0,c/c{sub 0}), is not 1, as predicted by DSA, but increases with increasing particle energy. The general solution combines both the reconnection-induced electric field and plasmoid contraction. The observed energetic particle intensity profile observed by Voyager 2 downstream of the HTS appears to support a particle acceleration mechanism that combines both DSA and magnetic-island-reconnection-related processes.
An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized quasi-2D small-scale magnetic island reconnection processes. An advection-diffusion transport equation for a nearly isotropic particle distribution describes particle transport and energization in a region of interacting magnetic islands [1; 2]. The dominant charged particle energization processes are 1) the electric field induced by quasi-2D magnetic island merging, and 2) magnetic island contraction. The acceleration of charged particles in a “sea of magnetic islands” in a super-Alfvénic flow, and the energization of particles by combined diffusive shock acceleration (DSA) and downstream magnetic island reconnection processes are discussed.
The international ITER tokamak has the objective of demonstrating the scientific feasibility of magnetic confinement fusion as a source of energy. A concern towards the achievement of this goal is represented by major disruptions: complete losses of confinement often initiated by a non-rotating ('locked') magnetic island created by magnetic reconnection. During disruptions, energy and particles accumulated in the plasma volume over many seconds are lost in a few milliseconds and released on the plasma-facing materials. In addition, multi-MA level currents flowing in the tokamak plasma for its sustainment and confinement are lost, also in milliseconds, thus terminating the plasma discharge and causing electromagnetic stresses that, if unmitigated, could lead to excessive device wear. Moreover it is shown that magnetic perturbations can be used to avoid disruptions by "guiding" the magnetic island to lock in a position where it is accessible to millimetre wave beams that fully stabilize it.