Collisionless Trapped Electron Mode Research Articles

On the collisionless trapped electron mode in fluid and kinetic descriptions

The effects of gyro-Landau drift resonances on the collisionless trapped electron mode have been studied. The drift resonances are added to a two pole fluid model of the density response. The gyro-Landau drift resonances in general give good agreement with kinetic theory. Comparison is also made with the fluid model without drift resonances. The toroidal eta i mode is also included in the system

Isotopic effect in transport and the ubiquitous mode

The linear stability of the collisionless trapped electron mode (“ubiquitous mode”) is investigated for the case of multispecies plasmas in low-β toroidal magnetic confinement experiments (JET and TFTR). A moderate reduction in the growth rate of fluctuations with given poloidal wavelength is observed when a heavier ion than the fuelling species, e.g. deuterium, is introduced. The quasilinear energy and particle fluxes are computed for the saturated state, and a model for the observed “isotopic scaling” of transport with the mass of the fuelling ion is presented.

Effects of nonlinear electron dynamics in a fluid model of collisionless trapped-electron mode turbulence

The role of the electron nonlinearity on saturation levels and particle transport in collisionless trapped electron mode turbulence is examined numerically using a two-dimensional fluid model. It is found that the removal of the electron nonlinearity results in an order of magnitude increase in fluctuation and particle transport levels. In addition, the qualitative behavior of the saturated state changes distinctly, including a decrease in RMS wave number in both cross-field directions, deviations from isotropy, changes in transport scalings, and changes in the spectral flow of energy. These results indicate that the electron nonlinearity is responsible for an efficient transfer of internal energy to small dissipation scales, thus resulting in lower fluctuation levels than predicted by ion mode coupling alone. The electron nonlinearity also decreases the phase angle between the density and potential leading to a decrease in the driving source. These results underscore the importance of the cross-correlation on saturation and demonstrate that numerical or theoretical use of ‘‘iδ’’ models to describe weakly collisional or collisionless trapped-electron mode turbulence is not appropriate.

A nonlinear bounce-kinetic equation for trapped electrons

A nonlinear bounce-kinetic equation that is suitable for studies of nonlinear trapped-electron dynamics in the presence of short wavelength electrostatic fluctuations is systematically derived. The equation is used to analyze the nonlinear response of trapped electrons to the short wavelength collisionless trapped-electron mode in a sheared magnetic field. It is shown that nonlinear trapped-electron–wave interaction (trapped-electron Compton scattering) transfers wave energy from long to short wavelengths. However, the transfer rate is significantly restricted by magnetic shear, which limits the interaction to a narrow region near the rational surface that is typically smaller than the linear mode width. Therefore, it is expected that, in a sheared magnetic field, ion Compton scattering rather than nonlinear trapped-electron–wave interaction will be the dominant nonlinear process in short wavelength trapped-electron mode turbulence.

Candidate mode for electron thermal energy transport in multi-keV plasmas

The linear and quasilinear theory of the collisionless trapped electron mode (also called the ‘‘ubiquitous’’ mode) is analyzed, in order to illustrate its possible role in the electron thermal energy transport observed in magnetically confined plasmas. This instability is driven by the combined effects of the plasma pressure gradient (which includes the contributions from the temperature gradients of ions and electrons) and of the local magnetic curvature drift of trapped electrons and of circulating and trapped ions. Depending on the value of its wavelength across the magnetic field, this mode can connect with a branch of the ion temperature gradient instability, provided the ion temperature gradient is sufficiently strong. Also, under certain conditions, it can be driven unstable solely by a combination of electron temperature gradient and Landau damping by trapped electrons. The relevant modes are found to be robust against variation of parameters such as the electron collisionality, and to be consistent candidates in order to explain the experimentally observed rate of electron thermal energy transport from the center of the plasma column.

Simulation of toroidal drift mode turbulence driven by temperature gradients and electron trapping

Turbulence and transport due to fully toroidal ion temperature gradient driven drift waves and a collisionless trapped electron mode have been studied by mode coupling simulations and with the quasi-linear theory. Diffusion coefficients in good agreement with the simulations have been obtained. The observed tendency for equilibration of the temperature and density scale lengths leads to particle or heat pinch effects that are in agreement with experimental trends.