The Neoclassical Polarization Current Modelling Momentum Transfer from a Neutral Beam to a Tokamak Plasma.
Diffusion in an axisymmetric, magnetically confined, toroidal plasma is "intrinsically ambipolar"--that is, there is no net transport of electric charge across the confining magnetic flux surfaces. This property is a consequence of conservation of canonical angular momentum in the toroidal (symmetry) direction, and does not hold when a source of toroidal angular momentum is present. Here, toroidal angular momentum injection by a beam of high energy neutral atoms is modelled as an external contribution to the total electric current. In order to maintain overall ambipolarity of the radial particle transport, the plasma must develop a balancing polarization current that serves to transfer angular momentum to the plasma. This current can only be maintained by 'viscous' damping of a driven equilibrium flow in the poloidal direction--orthogonal to the symmetry direction and tangent to the magnetic flux surfaces. Starting from the ion Fokker-Planck equation with a self-consistent subset of Maxwell's equations and electron fluid equations, a rigorous derivation of a drift-kinetic equation is undertaken by asymptotic analysis in the small parameter that represents the ratio of the Larmor radius to the macroscopic system size. Assuming that the toroidal angular momentum source is small, the drift-kinetic equation is then linearized about a Maxwellian since in the absence of a momentum source the lowest order system has an H-theorem. Deriving boundary conditions and a uniqueness theorem for the resulting linear equation (and constraints) shows that it is plausibly well -posed. The linear equation is then solved in the plateau and banana (long mean free-path) regimes for the transport coefficient that relates the external toroidal momentum input rate to the equilibrium poloidal flow. Boundary layer analysis in both cases is carried out to lowest order but in sufficient detail to show how higher order corrections should be computed. The result is also interpreted as the orthogonal conductivity of the plasma in the reference frame rotating at the toroidal fluid velocity.
- Pub Date:
- Physics: Fluid and Plasma