Sherwood 2015

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approvedsherwood_slides4.pdf2015-04-07 09:06:02Timothy Collart

Representation of Poloidal Asymmetries in Neoclassical Fluid Rotation Calculations in Axisymmetric Tokamaks

Author: Timothy G. Collart
Requested Type: Poster Only
Submitted: 2015-01-15 17:26:16

Co-authors: W.M. Stacey

Contact Info:
Georgia Institute of Technology
770 State Street
Atlanta, Georgia   33032
United States

Abstract Text:
In axisymmetric tokamaks the leading order “parallel” viscosity terms in the toroidal angular momentum damping term vanish identically on flux surface averaging, leaving the gyroviscous terms as the largest surviving viscous drag. Since the gyroviscous terms depend on poloidal asymmetries, it is important to represent these accurately. The original Braginskii fluid flow-stress-tensor viscosity representation was first extended to low collisionality plasmas in a circular toroidal flux surface geometry [1-3], then further extended to elongated plasmas using an analytic “Miller model” representation [4]. This coordinate system has been updated to describe variations in flux-surface shape between the upper and lower hemispheres, and fitted to flux surface locations determined by the magnetic flux calculated from the Grad-Shafranov equation in RZ geometry. These fitted coordinates are mapped into a modified system, defined to be orthogonal on flux-surfaces, and the resulting updates to the flux-surface averaging and vector operations are applied to the derivation of the plasma continuity and momentum balance equations. By calculating flux-surface averages of the first three Fourier moments of these equations, the fourteen equations required to calculate the poloidal asymmetries in densities, flows, velocities and electrostatic potential are formed. After neglecting radial gradients of asymmetries and fixing higher-orders of asymmetries, a direct substitution method is used to solve this linearized system of equations for the poloidal asymmetries. This routine is iterated until the resulting asymmetries satisfy the original, non-linear equation set. Application to a DIII-D discharge with Deuterium and Carbon rotation measurements found reasonable agreement for the carbon velocities but a factor of three disagreement for the deuterium velocities.
1). Phys. Fluids 28,2800(1985)
2) Nucl. Fusion 25,463(1985)
3) Phys. Plasmas 13,062508(2006)
4) Nucl. Fusion 53,043011(2013)

Please place this poster (Collart, Stacey) adjacent to the (Stacey, Bae) poster

March 16-18, 2015
The Courant Institute, New York University