Abstract
Within the single fluid theory for a toroidal,resistive plasma, the favorable average curvature effect [Glasser et al., Phys. Fluids 18, 875 (1975)], which is responsible for the strong stabilization of the classical tearing mode at finite pressure, can also introduce a strong screening effect to the externally applied resonantmagnetic field. Contrary to conventional understanding, this screening, occurring at slow plasma rotation, is enhanced when decreasing the plasma flow speed. The plasma rotation frequency, below which this screening effect is observed, depends on the plasma pressure and resistivity. For the simple toroidal case considered here, the toroidal rotation frequency has to be below , with being the Alfvén frequency. In addition, the same curvature effect leads to enhanced toroidal coupling of poloidal Fourier harmonics inside the resistive layer, as well as reversing the sign of the electromagnetic torque at slow plasma flow.
This work was funded by the RCUK Energy Programme under Grant EP/I501045 and the European Communities under the contract of Association between EURATOM and CCFE. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
I. INTRODUCTION
II. EQUILIBRIUM
III. NUMERICAL COMPUTATION OF THE PLASMA RESPONSE
IV. ANALYTIC INTERPRETATION
V. COMPUTING THE TEARING INDEX USING THE PLASMA RESPONSE
VI. OTHER EFFECTS ASSOCIATED WITH FINITE PLASMA PRESSURE
VII. CONCLUSION AND DISCUSSION
Key Topics
 Toroidal plasma confinement
 39.0
 Plasma pressure
 32.0
 External field
 21.0
 Plasma flows
 18.0
 Torque
 14.0
H05H1/02
Figures
Radial profiles of (a) safety factor q, and (b) equilibrium pressure, for a large aspect ratio toroidal plasma with circular cross section. The pressure is normalized by . The radial coordinate is defined via the normalized poloidal flux . The vertical dashed line in (b) indicates the radial location of the q = 2 rational surface.
Radial profiles of (a) safety factor q, and (b) equilibrium pressure, for a large aspect ratio toroidal plasma with circular cross section. The pressure is normalized by . The radial coordinate is defined via the normalized poloidal flux . The vertical dashed line in (b) indicates the radial location of the q = 2 rational surface.
Computed resistive plasma response for the m = 2 resonant harmonic at slow plasma rotation. At finite pressure (), two regimes of rotational screening of the plasma response are identified, with opposite trends. The two dashed straight lines indicate analytic scaling laws.
Computed resistive plasma response for the m = 2 resonant harmonic at slow plasma rotation. At finite pressure (), two regimes of rotational screening of the plasma response are identified, with opposite trends. The two dashed straight lines indicate analytic scaling laws.
Comparison of the poloidal components of the m = 2 plasma response currents near the q = 2 rational surface, at (a) a finite plasma pressure and (b) vanishing plasma pressure. The same plasma resistivity and rotation frequency are assumed, with and . Note that the range of the xaxis covers only 0.08% of the whole plasma minor radius in each case.
Comparison of the poloidal components of the m = 2 plasma response currents near the q = 2 rational surface, at (a) a finite plasma pressure and (b) vanishing plasma pressure. The same plasma resistivity and rotation frequency are assumed, with and . Note that the range of the xaxis covers only 0.08% of the whole plasma minor radius in each case.
The real and imaginary parts of the numerically computed plasma response (dots) and the leastsquare fits (lines) using the analytic relation (3), for a large aspect ratio equilibrium with vanishing plasma pressure. The plasma response is scanned versus the toroidal rotation frequency . The magnetic Lundquist number for the plasma is assumed to be .
The real and imaginary parts of the numerically computed plasma response (dots) and the leastsquare fits (lines) using the analytic relation (3), for a large aspect ratio equilibrium with vanishing plasma pressure. The plasma response is scanned versus the toroidal rotation frequency . The magnetic Lundquist number for the plasma is assumed to be .
The real and imaginary parts of the numerically computed plasma response (dots) and the leastsquare fits (lines) using the analytic relation (3), for a large aspect ratio equilibrium with finite plasma pressure (). The plasma response is scanned versus the toroidal rotation frequency . The magnetic Lundquist number is assumed to be . The horizontal axis along the top of the figure is subject to an additional normalization factor of .
The real and imaginary parts of the numerically computed plasma response (dots) and the leastsquare fits (lines) using the analytic relation (3), for a large aspect ratio equilibrium with finite plasma pressure (). The plasma response is scanned versus the toroidal rotation frequency . The magnetic Lundquist number is assumed to be . The horizontal axis along the top of the figure is subject to an additional normalization factor of .
The computed TM eigenvalues plotted in the complex plane, as the magnetic Lundquist number S varies, for a finite pressure, nonrotating resistive plasma. The point, where the real growth rate bifurcates into two (complex conjugate) branches, corresponds to . The critical S value, for marginal stability of the TM, is .
The computed TM eigenvalues plotted in the complex plane, as the magnetic Lundquist number S varies, for a finite pressure, nonrotating resistive plasma. The point, where the real growth rate bifurcates into two (complex conjugate) branches, corresponds to . The critical S value, for marginal stability of the TM, is .
Radial profiles of the poloidal Fourier harmonics for the plasma radial displacement (a, b) and perturbed parallel current density (c, d). Compared are the eigenfunctions of unstable tearing modes for the case with vanishing plasma pressure (a, c) and the case with a finite plasma pressure (b, d). The vertical dashed lines indicate the radial location of the q = 2 rational surface. The Lundquist number is for both cases.
Radial profiles of the poloidal Fourier harmonics for the plasma radial displacement (a, b) and perturbed parallel current density (c, d). Compared are the eigenfunctions of unstable tearing modes for the case with vanishing plasma pressure (a, c) and the case with a finite plasma pressure (b, d). The vertical dashed lines indicate the radial location of the q = 2 rational surface. The Lundquist number is for both cases.
Comparison of the computed total toroidal electromagnetic torque across the plasma column, induced by the response of a rotating resistive plasma to a static external field, produced by a coil current located at the minor radius r = 1.2a. Two plasmas, with the same Lundquist number but with different equilibrium pressures ( and 1.6, respectively), are compared. The marsf computed torques (dots) are also compared with the analytic estimates (lines).
Comparison of the computed total toroidal electromagnetic torque across the plasma column, induced by the response of a rotating resistive plasma to a static external field, produced by a coil current located at the minor radius r = 1.2a. Two plasmas, with the same Lundquist number but with different equilibrium pressures ( and 1.6, respectively), are compared. The marsf computed torques (dots) are also compared with the analytic estimates (lines).
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