Radial Mode Width Research Articles

Hybrid gyrokinetic ion/fluid electron simulation of toroidal tearing modes

The effects of toroidicity and kinetic ions on the resistive tearing mode are systematically studied with the gyrokinetic particle-in-cell simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] and compared with analytic theory. A new field solver in toroidal geometry has been developed for the simulation of low-n (n = 1, 2) modes in tokamaks. It is found that the toroidal effect significantly reduces the growth rate of the tearing mode. The toroidal effect can also increase the radial width of the tearing mode and change the scaling between the radial mode width and resistivity due to the toroidal pressure term in the electron continuity equation. The kinetic effects of ions can decrease the growth rate of the tearing mode. The plasma flux-surface shaping is found to have significant effect on the tearing mode.

Cross-code gyrokinetic verification and benchmark on the linear collisionless dynamics of the geodesic acoustic mode

The linear properties of the geodesic acoustic modes (GAMs) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, and safety factor), electro-magnetic effects, collisions, and the presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the Lagrangian (particle-in-cell) code ORB5, the Eulerian code GENE, and semi-Lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.

Radial mode widths in red giant stars spectra observed byKepler

The Kepler space mission has observed many solar-like pulsators, and helped to decipher their fundamental parameters (e.g: mass, radius, rotation). Most of the achievements recently obtained in that domain result from the analysis of the mode frequencies. However, unique information on non-adiabatic physics derives from the height and width of the modes. In this study, we aim at measuring the mode widths of the pressure modes in thousands of Kepler red giants and to analyze their variations in function of stellar parameters. To achieve that, we used a peakbagging technique on the star radial modes. The results show a relation between the radial mode linewidth and the effective temperature of the star as theoretically predicted. We also unveil a clear dependence with mass and stellar evolution for the radial mode width. This means that the mode damping depends on the evolutionary status of the stars.

Radial Localization of Toroidicity-Induced Alfvén Eigenmodes

Linear gyrokinetic simulation of fusion plasmas finds a radial localization of the toroidal Alfvén eigenmodes (TAEs) due to the nonperturbative energetic particle (EP) contribution. The EP-driven TAE has a radial mode width much smaller than that predicted by the magnetohydrodynamic theory. The TAE radial position stays around the strongest EP pressure gradients when the EP profile evolves. The nonperturbative EP contribution is also the main cause for the breaking of the radial symmetry of the ballooning mode structure and for the dependence of the TAE frequency on the toroidal mode number. These phenomena are beyond the picture of the conventional magnetohydrodynamic theory.

Electromagnetic effects on geodesic acoustic and beta-induced Alfvén eigenmodes

The local kinetic theory of geodesic acoustic modes and beta-induced Alfvén eigenmodes is developed. The local dispersion relations are derived in two opposite limits: and , where k0 = (m − nq)/qR, m and n are poloidal and toroidal mode numbers, and is the electron thermal velocity. It is shown that the nature of the (m ± 1, n) sideband oscillations depends on the radial modes width. The localized modes are mostly electrostatic, while the meso-scale modes of the radial width larger than c/(ωpiq) have a strong electromagnetic component. It is shown that the dispersion relations are remarkably similar provided the radial mode width of the principal (m, n) harmonic is sufficiently small.

MHD study of the reactor-relevant high-beta regime in the Large Helical Device

In the Large Helical Device, the volume averaged beta value ⟨βdia⟩ of 5%, which is the highest value in all heliotron/stellarators and relevant to the reactor requirement, was achieved by optimizing the magnetic configuration from the viewpoint of magneto-hydrodynamic (MHD) characteristics, transport and heating efficiency of the neutral beam. This beta value was instantaneously obtained by pellet injection and maintained for more than 10τE, whereas the steady-state plasma with a maximum ⟨βdia⟩ of 4.8% was sustained for 85τE by gas-puff fueling. While it is theoretically predicted that stochastization of the peripheral magnetic field structure develops with an increment of ⟨βdia⟩, no serious degradation of the global confinement has been observed in the present ⟨βdia⟩ range. The several low-order MHD activities located in the periphery were enhanced with the beta value and sometimes affect the local profiles. The amplitude of the mode in the periphery strongly depends on the magnetic Reynolds number, which is close to that of the growth rate and/or the radial mode width of the resistive interchange instability.

Energetic-Particle-Induced Geodesic Acoustic Mode

A new energetic particle-induced geodesic acoustic mode (EGAM) is shown to exist. The mode frequency and mode structure are determined nonperturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam-driven n=0 mode in DIII-D.

Simulation of cylindrical ion temperature gradient modes in the Columbia Linear Machine experiment

A comparison of the Columbia Linear Machine experiment [A. K. Sen, J. Chen, and M. Mauel, Phys. Rev. Lett. 66, 429 (1991)] with three-dimensional nonlinear electrostatic gyrokinetic simulation results is given, as well as comparisons with linear theory and simple theoretical predictions of nonlinear saturation. Linear theory is in reasonable agreement with the both experimental and simulation results. An analysis of the radial mode width which is localized by variation in the ion temperature gradient is given and compares well with both experiment and simulation. The theoretical estimate of the nonlinear saturation level is within a factor of 2 of what is observed in experiment and in simulation. In addition, both experiment and simulation show excitation of longer wavelength modes with poloidal mode numbers smaller than the linearly most unstable mode.

Plasma rotation and toroidal drift modes

This paper discusses the structure of drift waves in a rotating toroidal plasma. The rotation destroys an underlying symmetry that is the basis for the conventional ballooning representations of perturbations in a torus and alternative descriptions are needed. One such description exploits the residual symmetry that persists despite rotation. It shows that sheared rotation annuls the toroidal coupling between perturbations associated with different magnetic surfaces, so that cylinder criteria rather than toroidal `ballooning' criteria again become relevant. As expected, sheared rotation reduces the radial mode width, and presumably, therefore, the anomalous transport. It can also alter the scaling of anomalous transport with magnetic field from Bohm to gyro-Bohm. Another description of perturbations leads, as is well known, not to eigenmodes but to perturbations with a Floquet-like time dependence on a magnetic surface. We show that this Floquet solution actually conceals an arbitrary time dependence of the perturbation! At the usual leading order in a high mode number expansion, the Floquet form and the eigenmode form are equivalent and are equally valid descriptions. However, in a more accurate theory only the eigenmode form persists. The Floquet form, and its short-term growth rate, should be regarded as transients associated with particular starting conditions and with the use of an idealized (linear) velocity profile.

Poloidal shear flow effect on toroidal ion temperature gradient mode: A theory and simulation

The effect of poloidal shear flow on the global structure and stability of toroidal ion temperature gradient mode is studied theoretically and also numerically using a toroidal particle simulation code. Reasonable agreements are found between the theoretical and simulation results; both indicating that with increasing shear flow the toroidal ion temperature gradient mode is stabilized in the increase of poloidal asymmetry and in the reduction of radial mode width.

Density edge localized modes in rotating plasmas

A linear analysis is presented for the density edge localized mode with realistic tokamak edge plasma and electric field profiles. The mode is driven unstable by the electron temperature gradient and is localized by the density pedestal, with a radial mode width proportional to the square root of the density scale length (in H mode). The mode persists under the observed levels of sheared plasma rotation because of its narrow radial width. Its mode frequency, growth time, poloidal mode number and direction of rotation are all found to be comparable with those of the precursors for small (type III) edge localized modes (ELMs) observed in DIII-D and ASDEX. It is concluded that the density edge localized mode is a promising candidate for the precursors

Transition from resistive-G to ηi- driven turbulence in stellarator systems

By an electromagnetic incompressible two-fluid model describing both ion temperature gradient drift modes (ηi modes) and resistive interchange modes (g modes), a new type of ηi mode is studied in cylindrical geometry including magnetic shear and an averaged curvature of Heliotron/Torsatron. This ηi mode is destabilized by the coupling to the unstable g mode. Finite plasma pressure beta increases the growth rate of this mode and the radial mode width also increases with plasma pressure beta indicating large anomalous transport in the Heliotron/Torsatron configuration. The transport from ηi mode exceeds that from resistive g when the mean-free-path exceeds the machine circumference. For plasma beta above two to three times the Suydam limit, the m=1/n=1 growth rate increases from the ηi mode value to the magnetohydrodynamic (MHD) value.

Radial electric field effect on resistive interchange modes

Shear flow, driven by the radial electric field, has a stabilizing effect on the resistive interchange (or g) mode destabilized by the unfavorable curvature in a heliotron/torsatron. The following conditions are required: (i) kyv0>γgLE/Δ and (ii) Δ<LE, where the flow velocity profile is assumed to be v0 tanh(x/LE), ky is a wave number in the poloidal direction, γg is a growth rate at v0=0, and Δ is a radial mode width at v0=0. The origin x=0 corresponds to a mode resonant surface. When v0 is sufficiently large, the usual Kelvin–Helmholtz instability appears.

Limiter effects on scrape-off layer fluctuations and transport

Edge turbulence experiments indicate that radial particle flux increases as a function of radius up to the scrape-off layer (SOL), and that the Boltzman relation is violated. Resistivity gradient driven turbulence (RGDT) theory has been shown to track the radial dependence of the particle flux in the plasma edge closer than dissipative density gradient driven turbulence (DDGDT) theory. Also, the Boltzman relation is not invoked for RGDT while it is usually assumed for DDGDT. Consequently, RGDT is a more likely candidate for an edge turbulence model. However, Langmuir probe experiments indicate that the particle flux is reduced by as much as 50% in the SOL. Thus, since basic turbulence theories do not account for limiter effects, the primary focus of this study is to include such effects in a RGDT theory of the SOL. We present an analysis of SOL fluctuations using a rippling mode or RGDT calculation which incorporates the essential limiter boundary condition. The line-tying effects caused by a simple conducting poloidal limiter can lead to an order of magnitude reduction of the growth rate in the SOL region when parallel thermal conductivity is neglected. The basic effect of the limiter boundary condition can be understood by exploiting the conjugate relation between the parallel and radial mode widths, a consequence of magnetic shear. A reduction of the connection length, due to the limiter, implies an increase in the radial mode width. Assuming a conducting poloidal limiter with a large radial extent, the increased radial mode width causes an increase in thermal conduction damping which is sufficiently large enough so that the rippling mode is rendered stable for typical parallel thermal conductivities. We have also included the destabilizing effect of impurity radiative cooling in the RGDT analysis which leads to an increase of the growth rate, the saturation potential, and the diffusion coefficient by approximately 30% for typical parameters. Additionally, DDGDT is reconsidered as a viable model of SOL turbulence since it exhibits shorter toroidal mode widths than RGDT; thus, it is less sensitive to the limiter line-tying effect. Saturation level estimates for DDGDT with limiter effects are presented.