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Axisymmetric Neoclassical Theory for Low-Collisionality Ions to their Second Larmor-Radius Order

Author: Jesus J. Ramos
Requested Type: Consider for Invited
Submitted: 2015-01-16 10:45:07

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Contact Info:
Massachusetts Institute of Technology
77 Massachusetts Av.
Cambridge, Massachuse   02139
U.S.A.

Abstract Text:
The neoclassical solution for an axisymmetric equilibrium ion distribution
function is extended to the low-collisionality regime characterized by
$nu_i L/ v_{thi} sim rho_i /L equiv delta ll 1$. No geometrical
approximations are made, the poloidal and toroidal components of the magnetic
field being assumed comparable, so the dimensionless collisionality parameter is
$nu_* sim nu_i L/ v_{thi}$. The conventional banana regime solution is based
on a first Larmor-radius order drift-kinetic equation and applies to
$delta ll nu_* ll 1$. The ordering $delta sim nu_* ll 1$ is more
appropriate for fusion-grade plasmas, but requires a drift-kinetic solution
to the second Larmor-radius order. In this case, besides the conventional
$O(delta)$ contributions to the non-Maxwellian perturbation of the distribution
function relative to the Maxwellian and to the poloidal flow velocity relative to
the thermal velocity, new and comparable $O(delta^2 nu_*^{-1})$ contributions
arise. In addition, and for the ordering of the flow velocity
$u_i sim delta v_{thi}$, comparable contributions related to flow effects might
be expected as $O(delta u_i v_{thi}^{-1} nu_*^{-1})$. The solution of this
second Larmor-radius order, low-collisionality neoclassical equilibrium problem
is obtained, with the new effects represented by a new source in the generalized
Spitzer problem for the odd part of the distribution function. This new source
does not contain any net $O(delta u_i v_{thi}^{-1} nu_*^{-1})$ term and its
only $O(delta^2 nu_*^{-1})$ term vanishes if the equilibrium is up-down
symmetric. An explicit geometrical factor quantifies such novel second
Larmor-radius order, low-collisionality effect in equilibria that lack up-down
symmetry. For this $delta sim nu_* ll 1$ neoclassical solution, the
pressure anisotropy part of the Chew-Goldberger-Low stress tensor is comparable
to the gyroviscosity and their contributions to the flux-surface-averaged parallel
momentum equation balance exactly.
$^*$Work supported by the U.S. Department of Energy.

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