# Abstract Details

status: | file name: | submitted: | by: |
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approved | sher15_abst.pdf | 2015-01-16 10:35:06 | Jesus Ramos |

## 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

Co-authors:

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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