Quasilinear theory of interchange modes in a closed field line configuration

Abstract

Two important issues for any magnetic fusion configuration are the maximum achievable values of beta and energy confinement time when ideal magnetohydrodynamic (MHD) modes are excited. It is well known that the excitation of the MHD unstable modes typically can lead to violent restructuring of the plasma profiles. The particle and energy transport associated with these modes normally dominates all other transport mechanisms and can lead to plasma disruptions and a rapid loss of energy. This paper analytically investigates the transport of particle density, energy and magnetic field due to the ideal MHD interchange mode in a closed line system using the quasilinear approximation. The transport equations are derived for a static plasma in a hard core Z-pinch configuration and generalized to an arbitrary axisymmetric toroidal closed poloidal filed line configuration. It is shown that violation of the marginal stability criterion leads to rapid quasilinear transport that drives the pressure profile back to its marginal profile and forces the particle density to be inversely proportional to / dl B ∫ . The applicability of the quasilinear approximation is numerically tested for the hard core Z-pinch magnetic configuration using a full nonlinear code.

Fluctuation driven transport and stationary profiles

“…The resulting transport equations determine stationary density and pressure profiles and the direction of the associated turbulence-driven fluxes. When the wave-particle interaction is independent of pitch angle, the kinetic transport equations become identical to the MHD quasi-linear transport equations 6 . The experimental observation of stationary profiles thus can serve as an indicator that turbulence-driven cross-field transport is broadband and of sufficient level to dominate transport processes.…”

“…It has been shown from a quasi-linear development of MHD 6,14 that low frequency fluctuations that satisfy a "random phase approximation" lead to transport that can be described as a diffusion in flux space 6,13,14 identical to Eqs. (6). In the absense of particle and heating sources, the particle number within a flux tube, N = ndl /B ≡ nU , and the entropy density parameter, S ≡ pU γ , are stationary when they are uniform.…”

“…(6) can be combined to show the relationship between the direction of the particle flux and the plasma profiles:…”

Transport Induced by Large Scale Convective Structures in a Dipole-Confined Plasma

“…A density profile with hni / 1=VðLÞ $ L À4 [ Fig. 3] corresponds to a uniform number of particles in a flux tube, which is the marginal stability profile for rotationally driven interchange modes in a dipole plasma [11], and the stationary profile resulting from turbulent interchange mixing [2,12].…”

Confinement improvement with magnetic levitation of a superconducting dipole

“…The marginally stable case to both drift waves and MHD modes, is thus where: This case corresponds to an equal number of particles and entropy per flux tube. These profiles are the expected result of sufficient interchange mixing [8], and they form the design basis for attractive dipole fusion reactor concepts [9].…”