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We demonstrate that in a nonuniform plasma, the parametric decay instabilities of kinetic Alfvén waves could be quantitatively and qualitatively different from that in a uniform plasma. Specifically, the decay rate via ion Compton scattering is found to be enhanced, typically, by an order of magnitude. Furthermore, the parity of the decay kinetic Alfvén wave spectrum is broken, leading to finite net wave momentum transfer and, consequently, significant convective plasma transport with implications for confinement improvement. That localized absolutely unstable eigenmodes may be excited by a mode-converted pump wave is also presented.

Taking the collisionless damping of geodesic acoustic mode (GAM) as an example, the physics processes underlying wave particle resonances in the short wavelength limit are clarified. As illus- trative application, GAM excitation by energetic particles in short wavelength limit is investigated assuming a single pitch angle slowing-down fast ion equilibrium distribution function. Conditions for this energetic particle-induced GAM (EGAM) to be unstable are discussed., 4 pages, 2 figures. submitted to Physics of Plasmas

It is well-known that, within the ideal magnetohydrodynamic (MHD) description, there exist two low-frequency Alfven continuous spectra in toroidal plasma devices, such as tokamaks. The corresponding three accumulation frequencies are the beta-induced Alfven eigenmode (BAE) frequency, the ion-sound wave (ISW) frequency, and the zero frequency accumulation point at vanishing parallel wave number, k∥ = 0. To form localized discrete eigenmodes, the plasma with a normal magnetic shear must be ideal MHD unstable. The zero-frequency branch then corresponds to the ideal MHD unstable discrete mode, while the BAE and ISW discrete eigenmode frequencies could be significantly shifted away from the respective accumulation frequencies. Energetic-particle (EP) effects can be analyzed and understood as an effective potential well via the generalized fishbone linear dispersion relation. In particular, it is demonstrated that, for an ideal MHD stable plasma, EPs could play the roles of both discretization and destabilization, and their effect is generally non-perturbative. The theoretical results further predict that EPs preferentially excite the BAE branch over the ISW branch. The zero-frequency branch, meanwhile, becomes the well-known fishbone dispersion relation, giving rise to energetic-particle modes. Extensions to the case of reversed magnetic shear as well as the kinetic effects will also be discussed.

Motivated by the recent global gyrokinetic simulations of electrostatic drift-wave instabilities in the strong plasma gradient region of toroidal plasmas [Fulton et al., Phys. Plasmas 21, 042110 (2014); Xie et al., Phys. Rev. Lett. 118, 095001 (2017); Xie and Xiao, Phys. Plasmas 22, 090703 (2015)], we have carried out the corresponding analytical and numerical investigations in the case of ion temperature gradient driven modes. It is shown that, for sufficiently strong plasma gradients, the eigenmodes are slab-like and predominantly bounded by the plasma non-uniformities. Our results are qualitatively consistent with the simulation observations.

Starting from the coherent four-wave drift wave–zonal flow modulation interaction model of Chen, Lin, and White [Phys. Plasmas 7, 3129 (2000)], nonlinear equations for drift wave–zonal flow interplay are systematically derived from first principles for nonuniform toroidal plasmas. The paradigm model, presented here, is based on a hierarchy in nonlinear wave–wave couplings, which assumes that different drift wave interactions on the shortest nonlinear time scale are mediated by zonal flows. The resulting coherent model demonstrates turbulence spreading to be the cause of transport scaling with system size. The nonlinear saturated state can be either coherent, with limit cycles, or chaotic, depending on the proximity to marginal stability.

Kinetic shear Alfven modes in tokamak plasmas (with or without temperature gradient) are numerically investigated in the full gyrokinetic limit. It is shown that, in the presence of ion temperature gradient (ITG), the threshold value of plasma pressure gradient is well below that for ideal magnetohydrodynamic ballooning instability. It is also demonstrated in a more general sense that, without ITG, the former is identical with the latter. The electromagnetic instability is also found to exist in the second stable region of the ideal modes when a finite ITG is present. The results are compared with previous similar analyses for kinetic collisionless ballooning modes. Possible correlation of the instability with tokamak experiments is discussed.

A new type of high-n discrete Alfven eigenmodes is shown to exist in the large-α (α≡−q2Rdβ/dr) second ballooning stable toroidal plasmas. Here, n is the toroidal mode number, q is the safety factor, β is the ratio between plasma and magnetic pressures, and R and r are, respectively, the major and minor radii. These magnetohydrodynamic eigenmodes are bounded by the α-induced potential wells along the magnetic field line and, thus, exist even in absence of the toroidal Alfven frequency gap. Due to negligible continuum damping via wave energy tunneling, these large-α toroidal Alfven eigenmodes are quasimarginally stable and, thus, could be readily destabilized by energetic particles.

A thorough analysis of energetic particle modes (EPM) stability and mode structures is presented for tokamaks with hollow q profiles. Focusing on the region near the minimum-q surface, EPM gap modes and resonant EPMs are shown to exist as solutions of the same dispersion relation. By controlling the fast ion distribution function, or, equivalently, their fundamental dynamical properties, a smooth transition between these two classes of modes is obtained within the EPM dispersion relation. When toroidal coupling becomes important, it is demonstrated that EPMs may have either single or double hump radial structures. The local analyses of EPM stability and mode structures near the minimum-q surface are put in the broader framework of EPM stability and EPM induced transport in tokamaks with hollow q profiles and a brief summary is also given of present understanding of such problems based on results of three-dimensional nonlinear hybrid magneto–hydrodynamic–gyrokinetic simulations. Possible implications of pr...

Electron temperature gradient (ETG) driven instability in toroidal plasmas is studied with gyrokinetic theory. The full electron kinetics including finite Larmor radius effects, toroidal (curvature and magnetic gradient) drift motion ωD, and transit k∥v∥, is considered. The upgraded numerical scheme for solving the integral eigenvalue equations allows the study of both growing and damping modes, and thus direct calculation of critical gradient. A systematic parameter study is carried out for low β(=plasma pressure/magnetic pressure) circular flux surface equilibria. The basic characteristics of the modes are discussed. The scaling of the critical gradient with respect to toroidicity and to the ratio of electron temperature over ion temperature is obtained. Estimation for the transport induced by the modes is given.

Resonant heating of a magnetized plasma by low frequency waves of large amplitude is considered. It is shown that the magnetic moment can be changed nonadiabatically by a single large amplitude wave, even at frequencies normally considered nonresonant. Two examples clearly demonstrate the existence of the resonances leading to chaos and the generic nature of heating below the cyclotron frequency. First the classical case of an electrostatic wave of large amplitude propagating across a confining uniform magnetic field, and second a large amplitude Alfven wave, propagating obliquely across the magnetic field. Waves with frequencies a small fraction of the cyclotron frequency are shown to produce significant heating; bringing, in the case of Alfven waves, particles to speeds comparable to the Alfven velocity in a few hundred cyclotron periods. Stochastic threshold for heating occurs at significantly lower amplitude with a perturbation spectrum consisting of a number of modes. This phenomenon may have relevance for the heating of ions in the solar corona as well as for ion heating in some toroidal confinement fusion devices.

A linearized gyrokinetic particle-in-cell code is developed to study the excitations of electromagnetic instabilities due to finite ion temperature gradients in tokamak plasmas. The code employs the δf scheme to solve the gyrokinetic equations for ion dynamics; while electrons are modeled as massless fluid. The instability threshold condition of the Alfvenic ion-temperature-gradient (ITG) mode as well as the finite β stablization of electrostatic ITG mode are studied. Here β=8πp/B2 is the ratio between the plasma and magnetic pressure. In the β→0 limit, our code recovers the electrostatic results. As β increases, the destablization of kinetic ballooning mode due to finite ion temperature gradient is observed. The simulation results also reveal two possible critical values of ηi, where ηi=d ln Ti/d ln n is the ratio between the density scale length to the temperature scale length; one of the critical values is for the predominantly electrostatic ITG mode and one for the Alfvenic ITG mode, where ηi,cAITG

Resonant heating of particles by electrostatic and Alfven waves propagating in a confining uniform magnetic field is examined. It is shown that, with a sufficiently large wave amplitude, significant perpendicular stochastic heating can be obtained with wave frequency at a fraction of the cyclotron frequency. This result may have relevance for the heating of ions in the solar corona, and is a generic phenomenon, independent of the type of wave considered.

A fluid–kinetic hybrid electron model for electromagnetic simulations of finite-β plasmas is developed based on an expansion of the electron response using the electron–ion mass ratio as a small parameter. (Here β is the ratio of plasma pressure to magnetic pressure.) The model accurately recovers low frequency plasma dielectric responses and faithfully preserves nonlinear kinetic effects (e.g., phase space trapping). Maximum numerical efficiency is achieved by overcoming the electron Courant condition and suppressing high frequency modes. This method is most useful for nonlinear kinetic (particle-in-cell or Vlasov) simulations of electromagnetic microturbulence and Alfvenic instabilities in magnetized plasmas.

The generation of shear flow by drift waves is an important area of investigation. In a recent paper [Chen et al., Phys. Plasmas 7, 3129 (2000)] an elegant formalism was developed for the generation of shear/zonal flows by drift waves in a toroidal plasma. The study of shear flow generation in fluids and plasmas is put into perspective. In this paper it is shown how a simple slab geometry analysis can lead to a similar dispersion relation and highlight the subtle differences between the slab and toroidal geometries.

An analytical dispersion relation is derived which shows that, in toroidal plasmas, zonal flows can be spontaneously excited via modulations in the radial envelope of a single-n coherent drift wave, with n the toroidal mode number. Predicted instability features are verified by three-dimensional global gyrokinetic simulations of the ion-temperature-gradient mode. Nonlinear equations for mode amplitudes demonstrate saturation of the linearly unstable pump wave and nonlinear oscillations of the drift-wave intensity and zonal flows, with a parameter-dependent period doubling route to chaos.

Extensive magnetohydrodynamic–gyrokinetic hybrid simulations have been carried out to study the excitations of Alfven instabilities by trapped energetic ions in tokamak plasmas. Depending on the parameters, the most unstable mode can be either the toroidal Alfven eigenmode (TAE) or the energetic-particle mode (EPM). In both cases, the dominant instability driving mechanism is the resonance with the trapped-particle magnetic precessional drifts. The mode frequencies of the most unstable modes, meanwhile, tend to be near the toroidal frequency gap in order to minimize the continuum damping. It is also demonstrated that the instabilities can be quenched by reversing the magnetic precessional drifts via either negative magnetic shear or locating the magnetic turning points in the inner (strong B) side of the torus.

The existence of unstable ion temperature gradient driven Alfven eigenmodes (AITG) is demonstrated in tokamak plasmas, which are ideally stable with respect to magnetohydrodynamics (MHD). Conditions for the destabilization of such modes are quantitatively discussed on the basis of numerical solutions of a set of one-dimensional integral equations along the ballooning coordinate (quasi-neutrality and parallel Ampere’s law). Furthermore, theoretical analyses of the eigenmode dispersion relation, which is given in a compact analytical form in the small ion orbit width limit (compared to the radial wavelength), provide a basis for explaining the general properties of the modes. It is emphasized that instability requires both sufficiently strong thermal ion temperature gradients and that the plasma be not too far away from ideal MHD marginal stability.

Effects of finite toroidal rotation on the stability of radially localized ideal magnetohydrodynamic (MHD) modes are investigated analytically for low-beta, large aspect-ratio circular tokamaks. Specifically, it is found that, for the Mercier interchange mode, a finite rotation shear is generally stabilizing. For the double internal kink mode, however, finite toroidal rotation shear further enhances the ballooning destabilizing effect.

Kinetic toroidal Alfven eigenmodes (KTAEs) in finite-β circular tokamak plasmas are investigated. Here, β is the ratio between plasma and magnetic pressures, and, formally, β∼O(r/Rq2), with q being the safety factor, r and R denoting, respectively, minor and major radii. A new effect associated with finite parallel electric field effect due to the ion magnetic drift (IMD) is discovered, which is of the same order as that due to the well-known effect associated with the finite ion Larmor radii. The IMD-induced parallel electric field effect is shown to contribute to potential wells for the eigenmodes. Therefore, the IMD-induced parallel electric field effect can discretize the lower Alfven continuum along the real eigenfrequency. Subsequently, this new branch of KTAEs could be readily destabilized by the energetic ions.

For circular tokamaks, it is demonstrated, both analytically and numerically, that there exists a new frequency gap within the shear Alfven continuous spectrum around the Alfven frequency, ωA=vA/qR, due to the ion compressibility effect. Here, vA denotes the Alfven speed, q is the safety factor, and R the major radius. The frequency gap width, meanwhile, is proportional to the core ion beta, βi (ratio between core ion and magnetic pressures), and, correspondingly, the new discrete toroidal Alfven eigenmode (TAE) inside the gap is referred to as βTAE. Collective excitations of the βTAE by energetic ions are also analyzed.

Alpha-driven toroidal Alfven eigenmodes (TAEs) are observed as predicted by theory in the post-neutral beam phase in high central q (safety factor) deuterium–tritium (D–T) plasmas in the Tokamak Fusion Test Reactor (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. The mode location, poloidal structure, and the importance of q profile for TAE instability are discussed. So far no alpha particle loss due to these modes was detected due to the small mode amplitude. However, alpha loss induced by kinetic ballooning modes (KBMs) was observed in high-confinement D–T discharges. Particle orbit simulation demonstrates that the wave–particle resonant interaction can explain the observed correlation between the increase in alpha loss and appearance of multiple high-n (n⩾6, n is the toroidal mode number) modes.

A gyrokinetic‐magnetohydrodynamic (MHD) hybrid simulation code has been developed in order to study high‐n (where n is the toroidal mode number) MHD instabilities driven by energetic particles in finite‐β tokamaks. Here β is the ratio between plasma and magnetic pressures. Specifically, it is observed that as the core plasma β value increases, there is a corresponding transition from the toroidal Alfven eigenmode (TAE) to the kinetic ballooning mode (KBM). The energetic particle mode (EPM) branches of both the toroidal Alfven mode (TAM) and KBM are shown to be important in this transition. KBM are preferentially excited when the energetic particle velocity is small compared to the Alfven velocity.

A general analytical theory for the two‐dimensional eigenmode structures and stability of high toroidal‐mode‐number (high‐n) shear Alfven modes in axisymmetric tokamaks is presented. This theory, thus, further generalizes the previous work on the high‐n toroidal Alfven eigenmode (TAE) [Phys. Fluids B 5, 3668 (1993)] by including, nonperturbatively, plasma kinetic effects and resonant excitations by energetic particles. Specifically, in addition to recovering the known theoretical predictions on TAE, we have derived new results on global radial structures, as well as stability properties of kinetic toroidal Alfven eigenmodes (KTAE) and energetic‐particle modes (EPM).

The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where k→·B→=0, consistent with previous analytical and simulation studies. Here, B→ is the equilibrium magnetic field and k→ is the wavevector perpendicular to th...

The resonant excitations of high‐n magnetohydrodynamic (MHD) instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed. Here, n is the toroidal mode number. Since, typically, the MHD modes consist of two‐scale structures; one singular (‘‘inertial’’) region and one regular (ideal) region, the energetic particle contributions in the singular region are suppressed by the finite‐size orbits. Analytical dispersion relations can then be derived via the asymptotic matching analysis. The dispersion relations have the generic form of the ‘‘fishbone’’ dispersion relation and demonstrate, in particular, the existence of two types of modes; that is, the MHD gap mode and the energetic‐particle continuum mode. Specific expressions are given for both the kinetic ballooning modes (KBM) and the toroidal Alfven modes (TAM). It is suggested that the stability property may be qualitatively regarded as the ‘‘hybrid’’ of conventional MHD tokamaks and field reversed ion rings.

The final hardware modifications for tritium operation have been completed for the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. These activities include preparation of the tritium gas handling system, installation of additional neutron shielding, conversion of the toroidal field coil cooling system from water to a FluorinertTM system, modification of the vacuum system to handle tritium, preparation, and testing of the neutral beam system for tritium operation and a final deuterium–deuterium (D–D) run to simulate expected deuterium–tritium (D–T) operation. Testing of the tritium system with low concentration tritium has successfully begun. Simulation of trace and high power D–T experiments using D–D have been performed. The physics objectives of D–T operation are production of ≊10 MW of fusion power, evaluation of confinement, and heating in deuterium–tritium plasmas, evaluation of α‐particle heating of electrons, and collective effects driven by alpha particles and testing of diag...

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with ND2 due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where ND is the particle number in a Debye length. The ND2 scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with ND while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collision model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.

The two-dimensional global stability and mode structures of high-n beta-induced Alfvén eigenmodes excited by energetic ions in tokamaks are examined both analytically and numerically, employing the WKB-ballooning mode representation along with the generalized fishbone like dispersion relation. Here, n 蠑 1 is the toroidal mode number. Our results indicate that (i) the lowest radial bound state corresponds to the most unstable eigenmode, and (ii) the anti-Hermitian contributions due to wave-energetic particle resonance give rise to the twisting radial mode structures. © 2015 AIP Publishing LLC.

© 2015 AIP Publishing LLC. The spatial and temporal evolution of parametrically excited geodesic acoustic mode (GAM) initial pulse is investigated both analytically and numerically. Our results show that the nonlinearly excited GAM propagates at a group velocity which is, typically, much larger than that due to finite ion Larmor radius as predicted by the linear theory. The nonlinear dispersion relation of GAM driven by a finite amplitude drift wave pump is also derived, showing a nonlinear frequency increment of GAM. Further implications of these findings for interpreting experimental observations are also discussed.

A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, "Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation," Phys. Plasmas 21, 072121 (2014)]. © 2014 EURATOM.

The nonstationary oscillation of the gyrotron backward wave oscillator (gyro-BWO) with cylindrical interaction structure was studied utilizing both steady-state analyses and time-dependent simulations. Comparisons of the numerical results reveal that the gyro-BWO becomes nonstationary when the trailing field structure completely forms due to the dephasing energetic electrons. The backward propagation of radiated waves with a lower resonant frequency from the trailing field structure interferes with the main internal feedback loop, thereby inducing the nonstationary oscillation of the gyro-BWO. The nonstationary gyro-BWO exhibits the same spectral pattern of modulated oscillations with a constant frequency separation between the central frequency and sidebands throughout the whole system. The frequency separation is found to be scaled with the square root of the maximum field amplitude, thus further demonstrating that the nonstationary oscillation of the gyro-BWO is associated with the beam-wave resonance detuning.

Global radial eigenmodes of energetic-particle-induced geodesic acoustic mode are systematically studied, and their properties are found to depend on the nonuniformities of both the geodesic acoustic mode continuous spectrum and the energetic particle (EP) radial density profile. For a broad EP drive, the eigenmode equation valid for arbitrary EP drift orbit width is derived, and the excited energetic-particle-induced geodesic acoustic mode is shown to be strongly coupled to the geodesic acoustic mode continuous spectrum; resulting in a finite drive threshold in EP density. The cross-scale couplings between micro-, meso-, and macro-scales, discussed in this work, are mediated by the EP dynamics and have many interesting similarities with complex behaviors, expected in burning plasmas of fusion interest.

Linear and nonlinear behaviors of gyrotron backward wave oscillators (gyro-BWO) were investigated by both analytical theories and direct numerical calculations. Employing two-scale-length expansion, an analytical linear dispersion relation corresponding to absolute instabilities in a finite-length system has been derived. Detuning from the beam-wave resonance condition due to the finite amplitude radiation fields, meanwhile, was found to play the crucial roles in the nonlinear physics. Near the start oscillation of the gyro-BWO, the radiation field amplitude saturates when the resonance broadening is comparable to the linear growth rate. Far beyond the start oscillation threshold, the beam-wave resonance detuning effectively shortens the interaction length toward that corresponding to the critical oscillation length for the given beam current. The theoretically predicted scaling laws for the linear stability properties and nonlinear stationary states of the gyro-BWO are in good agreement with numerical re...

The gyrokinetic (GK) electron and fully kinetic ion (GeFi) simulation model of Lin et al. [Plasmas Phys. Controlled Fusion 53, 054013 (2011)] has been thoroughly benchmarked and validated for a two-dimensional (2D) Harris current sheet with a finite guide field. First, a gyrokinetic eigenmode theory for the collisionless tearing mode in the small Larmor radius limit is presented. The linear eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are benchmarked against those from the GK eigenmode analysis in the limit of L≫ρi>ρe, where L is the current sheet half-width, ρi is ion Larmor radius, and ρe is electron Larmor radius. Second, to valid the GeFi model, both the linear and nonlinear tearing instabilities obtained from the GeFi simulations are compared with the Darwin particle-in-cell (PIC) simulation. The validation of the GeFi model for laboratory and space plasmas is also discussed. Meanwhile, the GeFi simulation is carried out to investigate both the linear and ...

Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an eXtended version of Hybrid Magnetohydrodynamics Gyrokinetic Code (XHMGC) to study thermal ion kinetic effects on Alfv\'enic modes driven by energetic particles, such as kinetic beta induced Alfv\'en eigenmodes in tokamak fusion plasmas.

Transport scaling of energetic particles by ion temperature gradient microturbulence in magnetized plasmas is studied in massively paralleled gyrokinetic particle-in-cell simulations. It is found that the diffusivity decreases drastically at high particles energy (E) to plasma temperature (T) ratio because of the averaging effects of the large gyroradius and drift-orbit width, and the fast wave-particle decorrelation. At high energy, the diffusivity follows a (E/T)−1 scaling for purely passing particles, a (E/T)−2 scaling for deeply trapped particles and a (E/T)−1 scaling for particles with an isotropic velocity distribution since the diffusivity therein is contributed mostly by the passing particles.

The instability of a Harris current sheet under a broad range of finite guide field (BG) is investigated using a linearized (δf) gyrokinetic electron and fully kinetic ion particle simulation code. The simulation is carried out in the two-dimensional plane containing the guide field along y and the current sheet normal along z. In this particle model, the rapid electron cyclotron motion is removed, while the realistic mass ratio mi∕me, finite electron Larmor radii, and wave-particle interactions are kept. It is found that for a finite BG∕Bx0⩽1, where Bx0 is the asymptotic antiparallel component of magnetic field, three unstable modes, i.e., modes A, B, and C, can be excited in the current sheet. Modes A and C, appearing to be quasielectrostatic modified two-stream instability/whistler mode, are located mainly on the edge of the current sheet. Mode B, on the other hand, is confined in the current sheet center and carries a compressional magnetic field (δBy) perturbation along the direction of electron drif...

The heating of charged particles by a linearly polarized and obliquely propagating shear Alfven wave (SAW) at frequencies a fraction of the charged particle cyclotron frequency is demonstrated both analytically and numerically. Applying Lie perturbation theory, with the wave amplitude as the perturbation parameter, the resonance conditions in the laboratory frame are systematically derived. At the lowest order, one recovers the well-known linear cyclotron resonance condition k∥v∥−ω−nΩ=0, where v∥ is the particle velocity parallel to the background magnetic field, k∥ is the parallel wave number, ω is the wave frequency, Ω is the gyrofrequency, and n is any integer. At higher orders, however, one discovers a novel nonlinear cyclotron resonance condition given by k∥v∥−ω−nΩ∕2=0. Analytical predictions on the locations of fixed points, widths of resonances, and resonance overlapping criteria for global stochasticity are also found to agree with those given by computed Poincare surfaces of section.

The finite Larmor radius (FLR) effects play an important role in determining the threshold and the growth rate of the mirror instability. In this study, a general dispersion relation of the mirror mode with FLR effects is derived by using gyrokinetic theory. It shows that both the FLR effects and the coupling to the slow sound wave are stabilizing. A gyrokinetic particle simulation code has been developed for simulation of compressible magnetic turbulence driven by the mirror instability. Results of the linear simulation of mirror mode agree well with the analytic dispersion relation.

Nonlinear equations for the slow space-time evolution of the radial drift wave-ion-temperature gradient (DW-ITG) envelope and zonal flow (ZF) amplitude have been derived within a coherent four-wave drift wave-zonal flow model. In the local limit this model demonstrates spontaneous generation of zonal flow and nonlinear drift wave-zonal flow dynamics in toroidal plasmas. The model allows slow temporal and spatial variations of the DW-ITG radial envelope, incorporating the effects of equilibrium variations, i.e., turbulence spreading and size dependence of the saturated wave intensities and transport coefficients. The competition between linear drive/damping and drift wave spreading due to linear and nonlinear group velocities and nonlinear energy transfer between DW and ZF determines the saturation levels of the fluctuating fields. The turbulence intensity level exhibits a transition from Bohm scaling at small system size (Lp∕ρi) to gyro-Bohm for large system size. This system exhibits chaotic behavior and...