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Title: On nonexistence of tokamak equilibria with purely poloidal flow

Abstract

It is proved that irrespective of compressibility, tokamak steady states with purely poloidal mass flow cannot exist in the framework of either magnetohydrodynamics (MHD) or Hall MHD models. Nonexistence persists within single-fluid plasma models with pressure anisotropy and incompressible flows.

Authors:
; ;  [1];  [2];  [3]
  1. Association Euratom-Hellenic Republic, Section of Theoretical Physics, University of Ioannina, GR 451 10 Ioannina (Greece)
  2. (United States)
  3. (Germany)
Publication Date:
OSTI Identifier:
20860435
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 12; Other Information: DOI: 10.1063/1.2397042; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; COMPRESSIBILITY; FLUIDS; INCOMPRESSIBLE FLOW; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA CONFINEMENT; STEADY-STATE CONDITIONS; TOKAMAK DEVICES

Citation Formats

Throumoulopoulos, G. N., Weitzner, H., Tasso, H., Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, and Euratom Association, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching. On nonexistence of tokamak equilibria with purely poloidal flow. United States: N. p., 2006. Web. doi:10.1063/1.2397042.
Throumoulopoulos, G. N., Weitzner, H., Tasso, H., Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, & Euratom Association, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching. On nonexistence of tokamak equilibria with purely poloidal flow. United States. doi:10.1063/1.2397042.
Throumoulopoulos, G. N., Weitzner, H., Tasso, H., Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, and Euratom Association, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching. Fri . "On nonexistence of tokamak equilibria with purely poloidal flow". United States. doi:10.1063/1.2397042.
@article{osti_20860435,
title = {On nonexistence of tokamak equilibria with purely poloidal flow},
author = {Throumoulopoulos, G. N. and Weitzner, H. and Tasso, H. and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 and Euratom Association, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching},
abstractNote = {It is proved that irrespective of compressibility, tokamak steady states with purely poloidal mass flow cannot exist in the framework of either magnetohydrodynamics (MHD) or Hall MHD models. Nonexistence persists within single-fluid plasma models with pressure anisotropy and incompressible flows.},
doi = {10.1063/1.2397042},
journal = {Physics of Plasmas},
number = 12,
volume = 13,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • It is shown that transonic poloidal flow leads to ideal magnetohydrodynamic tokamak equilibria with radial discontinuities in the density, pressure, and flow velocity profiles. Transonic profiles are defined as having flow velocities ranging from subsonic to supersonic with respect to the poloidal sound speed (c{sub s}B{sub p}/B). The jump of the equilibrium quantities occurs approximately at the sonic surface and its magnitude is of order {epsilon}{sup 1/2} ({epsilon} is the inverse aspect ratio). Because of the large velocity shear at the sonic surface, transonic profiles may improve energy confinement as suggested by current understanding of tokamak plasma turbulence suppression. (c)more » 2000 American Institute of Physics.« less
  • Recent operation of the Tokamak Fusion Test Reactor (TFTR) (Plasma Phys. Controlled Nucl. Fusion Research 1, 51 (1986)) has produced plasma equilibria with values of Λ≡β p eq+ l i/2 as large as 7, εβ p dia≡ 2μ 0ε {l angle} p {r angle}/{l angle}{l angle} B p{r angle}{r angle} 2 as large as 1.6, and Troyon normalized diamagnetic beta (Plasma Phys. Controlled Fusion 26, 209 (1984); Phys. Lett. 110A, 29 (1985)), β Ndia≡10⁸{l angle}β t⊥{r angle} aB 0/ I p as large as 4.7. When εβ p dia≳ 1.25, a separatrix entered the vacuum chamber, producing a naturallymore » diverted discharge that was sustained for many energy confinement times, τ E. The largest values of εβ p and plasma stored energy were obtained when the plasma current was ramped down prior to neutral beam injection. The measured peak ion and electron temperatures were as large as 24 and 8.5 keV, respectively. Plasma stored energy in excess of 2.5 MJ and τ E greater than 130 msec were obtained. Confinement times of greater than 3 times that expected from L-mode predictions have been achieved. The fusion power gain Q DD reached a value of 1.3 x 10 ₋3 in a discharge with I p=1 MA and εβ p dia = 0.85. A large, sustained negative loop voltage during the steady-state portion of the discharge indicates that a substantial noninductive component of I p exists in these plasmas. Transport code analysis indicates that the bootstrap current constitutes up to 65% of I p.« less
  • The axisymmetric, incompressible, viscoresistive magnetohydrodynamic equations for purely poloidal currents [ital I]([ital r],[ital z]) are transformed into three coupled [ital scalar] partial differential equations. These show that finite [partial derivative][ital I]/[partial derivative][ital z] acts as a [ital volumetric] [ital source] [ital of] [ital fluid] [ital vorticity]'' which drives strong poloidal flows (jets).
  • In tokamak plasma with substantial impurity (n/sub z/Z/sup 2/>>n/sub i/), convective inertia effects lead to strong nonuniformity of both n/sub z/ and the electrostatic potential on a magnetic surface. These effects make the response of the total ion population to poloidal rotation (V-bar/sub q/) highly nonlinear, introducing the possibility of multiple equilibria. The equations are applied to the central sawtooth region of the plasma where the gradients n/sub j/', T/sub j/' are small. Above a critical electron temperature (T/sub c/1) the equilibrium with low V-bar/sub q/ is lost, leading to an m = 0, n = 0 poloidal rotation instability.more » The properties of this mode match the sawtooth disruptions and T/sub c/1 accurately predicts the central electron temperature. The cause of sawtooth disruptions in low impurity plasmas is discussed.« less