Compressional Magnetic Perturbations Research Articles

Gyrokinetic Particle-in-Cell simulation of the effect of compressional magnetic perturbations on the microscopic instabilities in Tokamak

The compressional magnetic component δB|| has been implemented in the gyrokinetic Particle-in-Cell (PIC) code GEM for the fully electromagnetic simulation of microscopic instabilities in high-β tokamak plasmas. The simulation model is formulated for the split-weight scheme that is based on the canonical momentum formulation of the gyrokinetic equation. A pseudo-spectral method is used to solve the coupled gyrokinetic field equations while preserving all finite-Larmor-radius (FLR) effects. The algorithm is verified by the method of manufactured solutions. Simulations of the ion-temperature-gradient-driven (ITG) mode, the kinetic balloon mode (KBM) and the trapped electron mode (TEM) are presented.

Global gyrokinetic study of shaping effects on electromagnetic modes at NSTX aspect ratio with ad hoc parallel magnetic perturbation effects

Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at National Spherical Torus Experiment (NSTX) aspect ratio and high plasma β using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation, with the gyrokinetic codes GENE and GEM being used for local verification and global cross-verification. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced in a high-elongation and high-triangularity NSTX-like geometry compared to a circular NSTX-like geometry. For example, growth rates of kinetic ballooning modes at high-β are reduced to the level of that of collisionless trapped electron modes.

Gyrokinetic particle simulations of the effects of compressional magnetic perturbations on drift-Alfvenic instabilities in tokamaks

The compressional component of magnetic perturbation δB∥ can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δB∥, and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δB∥ is neglected for βe=0.02, and that δB∥ has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. The KBM growth rate decreases about 15% when equilibrium current is neglected.

Progress in simulating turbulent electron thermal transport in NSTX

Nonlinear simulations based on multiple NSTX discharge scenarios have progressed to help differentiate unique instability mechanisms and to validate with experimental turbulence and transport data. First nonlinear gyrokinetic simulations of microtearing turbulence in a high-beta NSTX H-mode discharge predict experimental levels of electron thermal transport that are dominated by magnetic flutter and increase with collisionality, roughly consistent with energy confinement times in dimensionless collisionality scaling experiments. Electron temperature gradient (ETG) simulations predict significant electron thermal transport in some low- and high-beta discharges when ion scales are suppressed by E × B shear. Although the predicted transport in H-modes is insensitive to variation in collisionality (inconsistent with confinement scaling), it is sensitive to variations in other parameters, particularly density gradient stabilization. In reversed shear L-mode discharges that exhibit electron internal transport barriers, ETG transport has also been shown to be suppressed nonlinearly by strong negative magnetic shear, s ≪ 0. In many high-beta plasmas, instabilities which exhibit a stiff beta dependence characteristic of kinetic ballooning modes (KBMs) are sometimes found in the core region. However, they do not have a distinct finite beta threshold, instead transitioning gradually to a trapped electron mode (TEM) as beta is reduced to zero. Nonlinear simulations of this ‘hybrid’ TEM/KBM predict significant transport in all channels, with substantial contributions from compressional magnetic perturbations. As multiple instabilities are often unstable simultaneously in the same plasma discharge, even on the same flux surface, unique parametric dependencies are discussed which may be useful for distinguishing the different mechanisms experimentally.

Fully electromagnetic gyrokinetic eigenmode analysis of high-beta shaped plasmas

A new, more efficient method to compute unstable linear gyrokinetic eigenvalues and eigenvectors has been developed for drift-wave analysis of plasmas with arbitrary flux-surface shape, including both transverse and compressional magnetic perturbations. In high-beta, strongly shaped plasmas like in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)], numerous branches of closely spaced unstable eigenmodes exist. These modes are difficult and time-consuming to adequately resolve with the existing linear initial-value solvers, which are further limited to the most unstable eigenmode. The new method is based on an eigenvalue approach and is an extension of the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], reusing the existing discretization schemes in both real and velocity-space. Unlike recent methods, which use an iterative solver to compute eigenvalues of the relatively large gyrokinetic response matrix, the present scheme computes the zeros of the much smaller Maxwell dispersion matrix using a direct method. In the present work, the new eigensolver is applied to gyrokinetic stability analysis of a high-beta, NSTX-like plasma. We illustrate the smooth transformation from ion-temperature-gradient (ITG)-like to kinetic-ballooning (KBM)-like modes, and the formation of hybrid ITG/KBM modes, and further demonstrate the existence of high-k Alfvénic drift-wave “cascades” for which the most unstable mode is a higher excited state along the field line. A new compressional electron drift wave, which is driven by a combination of strong beta and pressure gradient, is also identified for the first time. Overall, we find that accurate calculation of stability boundaries and growth rates cannot, in general, ignore the compressional component δB∥ of the perturbation.

Relationship between the Pi2 pulsations and the localized impulsive current associated with the current disruption in the magnetosphere

Behavior of fast-magnetosonic-mode MHD signals in the inner magnetosphere that are driven by the impulsive eastward current is investigated as a model of the Pi2 signal at midnight. The magnetosphere is treated as an axisymmetric cold MHD regime with dipole magnetic fields and has the plasmaspheric structure of the Alfven speed distribution. MHD perturbation is assumed to be axisymmetric. Numerical calculation revealed the following: 1) The impulsive current induces the plasmasphere virtual resonance oscillation; 2) The compressional magnetic field perturbation is confined near the equator; 3) The waveform of the compressional magnetic perturbation in the plasmasphere depends on the spatial extent of the source current, its temporal variation, as well as its location; 4) The typical Pi2 waveform in the plasmasphere is obtained when the source current is located near the plasmapause (L ≤10); 5) When the source current is not located on the equator, the compressional component and the poloidal component have different waveforms.

CRRES satellite observations associated with low‐latitude Pi2 pulsations

We studied the electric and magnetic field variations and their relation to the ambient plasma density observed from the Combined Release and Radiation Effects Satellite (CRRES) during two Pi2 events observed on the ground at the low‐latitude (L = 1.2) station Kakioka. At the time of the Pi2s, CRRES was moving outward at L ∼ 5, magnetic local time (MLT) of ∼2200, and magnetic latitude of ∼4°. The satellite was in an apparently detached dense plasmaspheric plasma for the first Pi2 but in a low‐density region for the second Pi2. The first Pi2 had a period of 120 s at Kakioka (MLT ∼ 2000), and the satellite observed a nearly identical oscillation in the (approximately) azimuthal component of the electric field and in the radial and compressional components of the magnetic field. At CRRES the compressional magnetic field and the azimuthal electric field oscillated nearly in quadrature in the decaying phase of the pulsation, which suggests a radially trapped fast mode wave. However, comparison of this observation with numerical models of the plasmaspheric cavity mode is difficult because the plasma density did not have a simple plasmapause structure. The second Pi2 observed at Kakioka exhibited a period of 180 s and was similar to the azimuthal electric field oscillation seen at CRRES but quite different from the compressional magnetic perturbation at the satellite. For this event it is not clear whether the electric field oscillation represents a fast mode wave that was directly related to the ground Pi2 or a local shear Alfvén wave that was not directly related to the Pi2. If the first interpretation is the case, the midlatitude Pi2 is not necessarily confined within the plasmasphere by fast mode trapping or cavity resonance. These examples indicate that electric field oscillations measured by equatorial satellites are a sensitive and possibly better indicator of the onset of substorms and that if the plasma density measurements are also available, the electric field data can be useful for identifying the wave mode of Pi2 pulsations.

Kinetic theory of geomagnetic pulsations: 1. Internal excitations by energetic particles

Motivated by recent satellite observations, we have carried out a comprehensive theoretical analysis on the generation of hydromagnetic Alfvén waves in a realistic magnetospheric plasma environment consisting of a core (∼100 eV) component and an energetic (∼10 keV) component. Our theoretical formulation employs the gyrokinetic equations and, thus, retains anisotropy, finite Larmor radii, magnetic trapping, and wave‐particle interactions in addition to nonuniform plasma equilibria. A set of coupled equations for transverse and compressional magnetic perturbations is derived and analyzed for its stabilities assuming equilibrium distribution functions which are interchange stable. Our findings are as follows: (1) compressional and transverse shear Alfvén oscillations are generally coupled in realistic plasmas; (2) in the decoupled limit, for the compressional wave branch, one recovers the drift mirror instability due to the Landau resonances and τ ≡ 1 + 4π(∂P⊥/B∂B) < 0; here, P⊥ = P⊥(ψ, B) is the perpendicular pressure and ψ is the magnetic flux function; (3) for the decoupled transverse shear Alfvén branch, one obtains the drift Alfvén ballooning instability due to the Landau resonances and free energy of the pressure gradient for τ > 0; (4) for both branches, the most unstable modes have antisymmetric structures and propagate in the diamagnetic drift direction of the energetic ions; and (5) finite coupling can be shown to further enhance the drift Alfvén ballooning instabilities. Thus we conclude that for τ ≥ 0, the coupled drift Alfvén ballooning mirror instability constitutes an important internal generating mechanism of geomagnetic pulsations. The various predicted features of this instability are consistent with satellite observations.

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.

New Method of Magnetic Pumping for Plasma Heating

We propose a variant of magnetic pumping heating which makes use of a torsional rather than a compressional magnetic perturbation. It is efficient in large-aspect-ratio toroidal configurations such as Tokomaks. Typically, in this case, it is twice as efficient as the compressional magnetic pumping for magnetic perturbations of the same intensity, while using a working frequency three times smaller.