Twodimensional spatial structure of the dissipative trappedelectron mode
Abstract
The complete twodimensional structure of the dissipative trappedelectron mode over its full width, which may extend over several moderational surfaces, is discussed. The complete integrodifferential equation is studied in the limit k_{r}ρ_{i}<1, where ρ_{i} is the ion gyroradius, and k_{r}, the radial wavenumber, is regarded as a differential operator. This is converted into a matrix equation which is then solved by standard numerical methods. Solutions obtained are in reasonably good agreement with onedimensional analytic solutions, in the limits where such results are expected to be valid. More significantly, the present approach can readily treat many physically important cases for which purely analytic solutions are difficult to obtain. The results indicate that the differential equation formulation of the eigenmode equation is valid only for long wavelength modes (k_{ϑ}ρ_{i}≲0.3, with k_{ϑ} being the poloidal wavenumber). For such cases it is found that shear stabilization estimates obtained from the onedimensional radial solution are quite inaccurate for modes overlapping only a small number of moderational surfaces, but become more accurate for modes overlapping many moderational surfaces.
 Publication:

Physics of Fluids
 Pub Date:
 March 1977
 DOI:
 10.1063/1.861876
 Bibcode:
 1977PhFl...20..402R
 Keywords:

 Collisional Plasmas;
 Electron Scattering;
 Magnetically Trapped Particles;
 Plasma Control;
 Plasma Potentials;
 Tokamak Devices;
 Toroidal Plasmas;
 Differential Equations;
 Low Frequencies;
 Operators (Mathematics);
 Temperature Effects;
 Temperature Gradients;
 Plasma Physics