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Title: Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null

Abstract

Analytical high poloidal beta equilibria for toroidally axisymmetric plasmas with arbitrary aspect ratio and elongation are described. These equilibria that can describe a transition from nondivertor to divertor configuration are exact solutions of the Grad-Shafranov equation when the toroidal current density is quasiuniform. Generally, these are high poloidal beta equilibria, limited by the appearance of a natural inboard poloidal field null. Some of their properties, including the nonuniformity of the poloidal magnetic field in the poloidal direction, the safety factor profile and the magnetic shear profile near the separatrix, the parameter dependence of the poloidal beta {beta}{sub p} and {epsilon}{beta}{sub p}, as well as the toroidal beta {beta}{sub T} on the aspect ratio and the elongation of the magnetic surface, are discussed. Applications to experiments of the Tokamak Fusion Test Reactor (TFTR) [Sabbagh et al., Phys. Fluids B3, 2277 (1991)] are particularly analyzed.

Authors:
 [1]
  1. Southwestern Institute of Physics, Chengdu, Sichuan, 610041 (China)
Publication Date:
OSTI Identifier:
20782389
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 12; Other Information: DOI: 10.1063/1.2140227; (c) 2005 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; ASPECT RATIO; AXIAL SYMMETRY; CHARGED-PARTICLE TRANSPORT; CURRENT DENSITY; DIVERTORS; EQUILIBRIUM; EXACT SOLUTIONS; GRAD-SHAFRANOV EQUATION; MAGNETIC FIELDS; MAGNETIC SURFACES; MAGNETOHYDRODYNAMICS; PLASMA CONFINEMENT; SHEAR; TFTR TOKAMAK

Citation Formats

Shi Bingren. Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null. United States: N. p., 2005. Web. doi:10.1063/1.2140227.
Shi Bingren. Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null. United States. doi:10.1063/1.2140227.
Shi Bingren. Thu . "Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null". United States. doi:10.1063/1.2140227.
@article{osti_20782389,
title = {Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null},
author = {Shi Bingren},
abstractNote = {Analytical high poloidal beta equilibria for toroidally axisymmetric plasmas with arbitrary aspect ratio and elongation are described. These equilibria that can describe a transition from nondivertor to divertor configuration are exact solutions of the Grad-Shafranov equation when the toroidal current density is quasiuniform. Generally, these are high poloidal beta equilibria, limited by the appearance of a natural inboard poloidal field null. Some of their properties, including the nonuniformity of the poloidal magnetic field in the poloidal direction, the safety factor profile and the magnetic shear profile near the separatrix, the parameter dependence of the poloidal beta {beta}{sub p} and {epsilon}{beta}{sub p}, as well as the toroidal beta {beta}{sub T} on the aspect ratio and the elongation of the magnetic surface, are discussed. Applications to experiments of the Tokamak Fusion Test Reactor (TFTR) [Sabbagh et al., Phys. Fluids B3, 2277 (1991)] are particularly analyzed.},
doi = {10.1063/1.2140227},
journal = {Physics of Plasmas},
number = 12,
volume = 12,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • 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
  • Recent operation of the Tokamak Fusion Test Reactor TFTR, has produced plasma equilibria with values of {Lambda} {triple bond} {beta}{sub p eq} + l{sub i}/2 as large as 7, {epsilon}{beta}{sub p dia} {triple bond} 2{mu}{sub 0}{epsilon}/{much lt}B{sub p}{much gt}{sup 2} as large as 1.6, and Troyon normalized diamagnetic beta, {beta}{sub N dia} {triple bond} 10{sup 8}<{beta}{sub t}{perpendicular}>aB{sub 0}/I{sub p} as large as 4.7. When {epsilon}{beta}{sub p dia} {approx gt} 1.25, a separatrix entered the vacuum chamber, producing a naturally diverted discharge which was sustained for many energy confinement times, {tau}{sub E}. The largest values of {epsilon}{beta}{sub p} and plasma storedmore » 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 keV and 8.5 keV, respectively. Plasma stored energy in excess of 2.5 MJ and {tau}{sub 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{sub DD}, reached a values of 1.3 {times} 10{sup {minus}3} in a discharge with I{sub p} = 1 MA and {epsilon}{beta}{sub p dia} = 0.85. A large, sustained negative loop voltage during the steady state portion of the discharge indicates that a substantial non-inductive component of I{sub p} exists in these plasmas. Transport code analysis indicates that the bootstrap current constitutes up to 65% of I{sup p}. Magnetohydrodynamic (MHD) ballooning stability analysis shows that while these plasmas are near, or at the {beta}{sub p} limit, the pressure gradient in the plasma core is in the first region of stability to high-n modes. 24 refs., 10 figs.« less
  • Heat flux and plasma flow in the scrape-off layer (SOL) are examined for the inboard poloidal field null (IPN) configuration of the spherical tokamak QUEST. In the plasma current (I{sub p}) ramp-up phase, high heat flux (>1 MW/m{sup 2}) and supersonic flow (Mach number M > 1) are found to be present simultaneously in the far-SOL. The heat flux is generated by energetic electrons excursed from the last closed flux surface. Supersonic flows in the poloidal and toroidal directions are correlated with each other. In the quasi-steady state, sawtooth-like oscillation of I{sub p} at 20 Hz is observed. Heat flux and subsonic plasma flowmore » in the far-SOL are modified corresponding to the I{sub p}-oscillation. The heat flow caused by motion of energetic electrons and the bulk-particle transport to the far-SOL is enhanced during the low-I{sub p} phase. Modification of plasma flow in the far SOL occurs earlier than the I{sub p} crash. The M–I{sub p} curve has a limit-cycle characteristic with sawtooth-like oscillation. Such a core–SOL relationship indicates that the far-SOL flow plays an important role in sustaining the oscillation of I{sub p} in the IPN configuration.« less
  • The validity of the analytic large aspect ratio, high-{Beta} equilibria developed by Cowley {ital et al}. [Phys. Fluids B {bold 3}, 2066 (1991)] is extended to include finite aspect ratio equilibria with {ital q}{sup 2}{much_lt}1, where {ital q} is the safety factor. These high-{Beta} equilibria have two regions. Most of the volume lies in the {open_quote}{open_quote}core region,{close_quote}{close_quote} where {psi}={psi}({ital R}). The flux surfaces close in the {open_quote}{open_quote}boundary layer region,{close_quote}{close_quote} which has thickness {delta}. The solutions are valid when {delta}/{ital a}{approximately}O({radical}{epsilon}/{Beta}{ital q}{sup 2}) is small, where {ital a} is the minor radius. Thus, finite {epsilon} is allowed when {ital q}{sup 2}more » is large. The equilibria are completely specified by the midplane profiles of pressure {ital p}({ital R}) and poloidal magnetic field {ital B}{sub {ital P}}({ital R}) and the shape of the plasma boundary, all of which can be measured experimentally. Note the departure from customary specification of {ital p}({psi}), {ital q}({psi}), or {ital F}({psi}). A fast numerical code, requiring a few seconds to execute, has been written to compute and illustrate the analytic high-{Beta} equilibria. The qualitative features of high-{Beta}{sub {ital P}} tokamaks are discussed in detail. {copyright} {ital 1996 American Institute of Physics.}« less