Nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas. The foundations of modern nonlinear gyrokinetic the- ory are based on three important pillars: (1) a gyrokinetic Vlasov equation written in terms of a gyrocenter Hamiltonian with quadratic low-frequency ponderomotive-like terms; (2) a set of gyrokinetic Maxwell (Poisson-Ampere) equations written in terms of the gyrocenter Vlasov dis- tribution that contain low-frequency polarization (Poisson) and magnetization (Ampere) terms derived from the quadratic nonlinearities in the gyrocenter Hamiltonian; and (3) an exact energy conservationlaw for the gyrokineticVlasov-Maxwell equations that includes all the relevant linear and nonlinear coupling terms. The foundations of nonlinear gyrokinetic theory are reviewed with an emphasis on the rigorous applications of Lagrangian and Hamiltonian Lie-transform perturba- tion methods used in the variationalderivationof nonlineargyrokineticVlasov-Maxwell equations. The physical motivations and applications of the nonlinear gyrokinetic equations, which describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetized plasmas with arbitrary magnetic geometry, are also discussed.

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Foundations of nonlinear gyrokinetic theory

Magnetic reconnection is a topological rearrangement of magnetic field that converts magnetic energy to plasma energy. Astrophysical flares, from the Earth's magnetosphere to γ-ray bursts and sawtooth crashes in laboratory plasmas, may all be powered by reconnection. Reconnection is essential for dynamos and the large-scale restructuring known as magnetic self-organization. We review reconnection theory and evidence for it. We emphasize recent developments in two-fluid physics, and the experiments, observations, and simulations that verify two-fluid effects. We discuss novel environments such as line-tied, relativistic, and partially ionized plasmas, focusing on mechanisms that make reconnection fast, as observed. Because there is evidence that fast reconnection in astrophysics requires small-scale structure, we briefly introduce how such structure might develop. Several areas merit attention for astrophysical applications: development of a kinetic model of reconnection to enable spectroscopic predictions...

https://www.leif.org/EOS/Plasma-Reconnection.pdf

Magnetic Reconnection in Astrophysical and Laboratory Plasmas

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions

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Chapter 5: Physics of energetic ions

An investigation is made into the electron temperature perturbations associated with tearing modes in tokamak plasmas. It is found that there is a critical magnetic island width below which the conventional picture where the temperature is flattened inside the separatrix is invalid. This effect comes about because of the stagnation of magnetic field lines in the vicinity of the rational surface and the finite parallel thermal conductivity of the plasma. Islands whose widths lie below the critical value are not destabilized by the perturbed bootstrap current, unlike conventional magnetic islands. This effect may provide an explanation for some puzzling experimental results regarding error field‐induced magnetic reconnection. The critical island width is found to be fairly substantial in conventional tokamak plasmas, provided that the long mean‐free path nature of parallel heat transport and the anomalous nature of perpendicular heat transport are taken into account in the calculation.

/pdf/helical-temperature-perturbations-associated-with-tearing-48edu7ufcl.pdf

Helical temperature perturbations associated with tearing modes in tokamak plasmas

In magnetic fusion reactors relying on the burning of deuterium and tritium, sufficient confinement of the alpha particles produced in the nuclear reactions is crucial to sustaining the burning plasma. In this article the interactions of these energetic particles with linear and nonlinear Alfve'n waves generated in the magnetized plasma are reviewed.

https://link.aps.org/accepted/10.1103/RevModPhys.88.015008

Physics of Alfvén waves and energetic particles in burning plasmas

Three dimensional MHD simulations of high-{beta} plasmas show that toroidally localized high-n ballooning modes can be driven unstable by the local pressure steepening which arises from the evolution of low-n modes. Nonlinearly, the high-n mode becomes even more localized and produces a strong local pressure bulge which destroys the flux surfaces resulting in a thermal quench. The flux surfaces then recover temporarily but now contain large magnetic islands. This scenario is supported by experimental data.

High- beta Disruption in Tokamaks.

Gyrokinetic-magnetohydrodynamic hybrid simulations have been carried out to study the nonlinear saturation of the torodicity-induced Alfv\'en eigenmode driven by energetic particles in a tokamak plasma It is shown that wave-particle trapping is the nonlinear saturation mechanism for the parameters considered The corresponding density profile flattening of the hot particles is observed The saturation amplitude is proportional to the square of the linear growth rate In addition, a new $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ global Alfv\'en eigenmode is shown to be excited by the energetic particles

Nonlinear hybrid simulation of the toroidicity-induced Alfvén eigenmode.

Measurements on the TFTR tokamak of the electron-temperature-profile evolution and soft-x-ray emissivity on a fast (10-\ensuremath{\mu}sec) time scale during a sawtooth crash show that significant heat is deposited beyond the mixing (or reconnection) radius within 200 \ensuremath{\mu}sec following a sawtooth crash. This extended region in which electron heat is redistributed during the sawtooth crash substantially complicates the determination of heat transport properties from the subsequent heat pulse propagation. It is shown that the relaxation of this extended perturbation is consistent with the power-balance estimates of the local thermal diffusivity.

Ballistic contributions to heat-pulse propagation in the TFTR tokamak.

High-resolution electron cyclotron emission and x-ray image reconstructions have been made simultaneously during the sawtooth crash in the fast rotating plasma with neutral beam injection heating on TFTR. The measured x-ray emission is identical as metal impurity radiation. The results suggest that the sawtooth crash is a full reconnection process of the TFTR sawteeth. The crescent shaped ``hot spot'' in the x-ray emissivity is found not to present flux surfaces. New features are observed during the sawtooth crash, such as an oval-shaped hot spot and a cooler region between the island and the hot spot.

W. Park

Papers

High- beta Disruption in Tokamaks.

Nonlinear hybrid simulation of the toroidicity-induced Alfvén eigenmode.

Ballistic contributions to heat-pulse propagation in the TFTR tokamak.

Analysis of sawtooth oscillations using simultaneous measurement of electron cyclotron emission imaging and x-ray tomography on TFTR.

Bursts of electron cyclotron emission during disruptions of high β discharges in TFTR