Longitudinal permittivity of a tokamak plasma with elliptic and circular magnetic surfaces

Abstract

The contributions of untrapped and three groups of trapped particles to the longitudinal permittivity of a tokamak plasma with elliptic magnetic surfaces are derived for radio frequency waves in a wide range of frequencies, mode number, and plasma parameters. The analytical expressions of the longitudinal permittivity elements are obtained by using the kinetic theory of dielectric tensor elements, where the drift kinetic equation is solved as a boundary-value problem. Considered is a collisionless plasma model of an axisymmetric tokamak with small ellipticity and a large aspect ratio. The limit to the known results for toroidal plasmas with the circular cross-section of the magnetic surfaces is shown.

CASTOR-K: Stability Analysis of Alfvén Eigenmodes in the Presence of Energetic Ions in Tokamaks

“…It is assumed that the toroidal field is monotonically decreasing with the major radius and that B(s, θ) has only one maximum in θ for a given value of s. This allows the analysis of most plasma shapes including elliptic plasmas with high triangularity, but eliminates "bean-shaped" plasmas or strong elliptic plasmas with d-trapped particles [51]. No orbits -For a given particle energy the different classes of orbits can be traced in the (P φ , µ)-plane.…”

Longitudinal permittivity of magnetospheric plasmas with dipole and circular magnetic field lines

“…However, analyzing the dielectric properties of a magnetospheric plasma with strongly deformed magnetic field lines, we should take into account the possible appearance of the new groups of the trapped particles, similarly to the tokamak plasmas with elliptic magnetic surfaces. 17 These new groups of the trapped particles need an additional description.…”

“…It should be noted that also we have the same dependence for a magnetospheric plasma with circular magnetic field lines ͑evaluated in Sec. IV͒ and for other axisymmetric magnetized plasmas with the minimum of an equilibrium magnetic field, such as the tokamak 17 ͑with both the elliptic and circular magnetic sur-faces͒ and the straight open trap. 9…”

MHD-induced Energetic Ion Loss during H-mode Discharges in the National Spherical Torus Experiment (NSTX)

“…In spherical tokamaks, however, the poloidal magnetic field strength can exceed that of the toroidal field and the radial extent of the drift orbit can be comparable to the Larmor orbit. In conjunction with a relatively small major radius relative to the minor radius, this leads to modification of orbit topologies [2,8,9], particle drifts [10], behavior of Alfvén-type instabilities [11,12], and neoclassical transport [13,14]. For example, the gyroradius of 80 keV D co-injected NB heating ions in NSTX can be ~ 0.3 m at the outboard midplane of the plasma.…”