J. W. Van Dam

Excitation of the toroidicity-induced shear Alfven eigenmode by fusion alpha particles in an ignited tokamak

The toroidicity‐induced shear Alfven eigenmode is found to be destabilized by fusion alpha particles in an ignited tokamak plasma.

Continuum damping of low‐n toroidicity‐induced shear Alfvén eigenmodes

The effect of resonant continuum damping is investigated for the low‐mode‐number, toroidicity‐induced, global shear Alfven eigenmodes, which can be self‐excited by energetic circulating alpha particles in an ignited tokamak plasma. Resonant interaction with the shear Alfven continuum is possible for these eigenmodes, especially near the plasma periphery, leading to significant dissipation, which is typically larger than direct bulk plasma dissipation rates. Two perturbation methods are developed for obtaining the Alfven resonance damping rate from the ideal fluid zeroth‐order shear Alfven eigenvalue and eigenfunction. In both methods the real part of the frequency is estimated to zeroth order, and the imaginary part, which includes the damping rate, is then obtained by perturbation theory. One method, which is applicable when the eigenfunction is nearly real, can readily be incorporated into general magnetohydrodynamic (MHD) codes. In the second method, the zeroth‐order eigenfunctions may be complex; howe...

A generalized kinetic energy principle

Using three single‐particle adiabatic invariants, we derive an energy principle which generalizes that for the usual guiding center plasma in order to describe the low‐frequency stability of a plasma containing an energetic nonhydromagnetic component (such as the annular electrons in an Elmo Bumpy Torus device).

More on core‐localized toroidal Alfvén eigenmodes

A novel type of ideal toroidal Alfven eigenmode, localized in the low‐shear core region of a tokamak plasma, is shown to exist, whose frequency is near the upper continuum of the toroidal Alfven gap. This mode converts to a kinetic‐type toroidal Alfven eigenmode above a critical threshold that depends on aspect ratio, pressure gradient, and shear. Opposite to the usual ideal toroidal Alfven eigenmode, this new mode is peaked in amplitude on the small‐major‐radius side of the plasma.

Substorm trigger conditions

Critical conditions for the onset of fast interchange dynamics in the stressed geotail during the growth phase of the substorm are derived. We compare the ideal MHD interchange stability conditions (Hurricane, 1997) with kinetically modifled interchange{ ballooning motions. It is shown that fast interchange growth is possible only in the near{Earth boundary of the plasma sheet where the local plasma pressure is near unity since compressibility stabilizes the high beta geotail. The growth rate is proportional to the local current density and exceeds the ion bounce frequency in the local region of fl < 1. Only after su‐cient thinning of the current sheet will the kinetic theory growth rate exceed the bounce frequency of the ions which is the efiective condition for the substorm MHD{space{time scale unloading of the plasma energy stored in geotail.

Mode structure and continuum damping of high-n toroidal Alfven eigenmodes

An asymptotic theory is described for calculating the mode structure and continuum damping of short‐wavelength toroidal Alfven eigenmodes (TAE). The formalism somewhat resembles the treatment used for describing low‐frequency toroidal modes with singular structure at a rational surface, where an inner solution, which for the TAE mode has toroidal coupling, is matched to an outer toroidally uncoupled solution. A three‐term recursion relation among coupled poloidal harmonic amplitudes is obtained, whose solution gives the structure of the global wave function and the complex eigenfrequency, including continuum damping. Both analytic and numerical solutions are presented. The magnitude of the damping is essential for determining the thresholds for instability driven by the spatial gradients of energetic particles (e.g., neutral‐beam‐injected ions or fusion‐product alpha particles) contained in a tokamak plasma.

Curvature‐driven instabilities in a hot electron plasma: Radial analysis

The theory of curvature‐driven instabilities is developed for a plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic theory. A z‐pinch model is used to emphasize the radial structure of the problem. Stability criteria are obtained for the five possible modes of instability: the conventional hot electron interchange, a high‐frequency hot electron interchange (at frequencies larger than the ion cyclotron frequency), a compressional instability, a background pressure‐driven interchange, and an interacting pressure‐driven interchange. Numerical plots of the marginal stability boundaries are presented for parameter values corresponding to the EBT‐S and EBT‐P bumpy torus experiments.

Stability of the global Alfvén eigenmode in the presence of fusion alpha particles in an ignited tokamak plasma

The stability of global Alfven eigenmodes is investigated in the presence of super‐Alfvenic energetic particles, such as fusion‐product alpha particles in an ignited deuterium–tritium tokamak plasma. Alpha particles tend to destabilize these modes when ω*α>ωA, where ωA is the shear‐Alfven modal frequency and ω*α is the alpha particle diamagnetic drift frequency. This destabilization due to alpha particles is found to be significantly enhanced when the alpha particles are modeled with a slowing‐down distribution function rather than with a Maxwellian distribution. However, previously neglected electron damping due to the magnetic curvature drift is found to be comparable in magnitude to the destabilizing alpha particle term. Furthermore, the effects of toroidicity are also found to be stabilizing, since the intrinsic toroidicity induces poloidal mode coupling, which enhances the parallel electron damping from the sideband shear‐Alfven Landau resonance. In particular, for typical ignition tokamak parameters...

Stability properties of high-pressure geotail flux tubes

Kinetic theory is used to investigate the stability of ballooning interchange modes in the high-pressure geotail plasma. A variational form of the stability problem is used to compare new kinetic stability results with MHD, fast MHD, and Kruskal and Oberman [1958] stability results. Two types of drift modes are analyzed: A kinetic ion pressure gradient drift wave with a frequency given by the ion diamagnetic drift frequency ω *pi and a very low frequency mode |ω| ω *pi , ω Di that is often called a convective cell or the trapped particle mode. In the high-pressure geotail plasma a general procedure for solving the stability problem in a 1/β expansion for the minimizing δB∥ is carried out to derive an integral differential equation for the kinetically valid displacement field ξ ψ for a flux tube. The plasma energy released by these modes is estimated in the nonlinear state. The role of these instabilities in substorm dynamics is assessed in the substorm scenarios described by Maynard et al. [1996].

Low frequency stability of geotail plasma

The local flux surface stability of magnetic dipole configurations is investigated in the magnetohydrodynamic (MHD) and drift frequency regimes. Solutions of the plasma equations in the very high beta limit are discussed. A novel procedure is developed for discussing stability in terms of the frequency ratio: the orbit averaged ion drift frequency divided by the ion diamagnetic frequency. This procedure is used to examine the stability of magnetospheric flux surfaces in the neighborhood of the equatorial plane at 6–10 Earth radii (where the plasma beta is ∼5 and where the onset of plasma instabilities may be responsible for triggering magnetic storms) with the following results: (1) MHD ballooning modes are predicted to be stable unless κvxp⩽2/5 where xp is the plasma pressure gradient scale length and κv the vacuum field line curvature at the equatorial plane; (2) drift modes may also be unstable unless η∼2/3, where η is the density gradient scale length divided by the temperature gradient scale length.