skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration

Abstract

A Solovev-like solution describing equilibria with field aligned incompressible flows [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 19, 014504 (2012)] is extended to non parallel flows. The solution expressed as a superposition of Bessel functions contains an arbitrary number of free parameters which are exploited to construct a variety of configurations including ITER shaped ones. For parallel flows, application of a sufficient condition for linear stability shows that this condition is satisfied in an appreciable part of the plasma region on the high-field side mostly due to the variation of the magnetic field perpendicular to the magnetic surfaces. Also, the results indicate that depending on the shape of the Mach-function profile and the values of the free parameters the flow and flow shear may have either stabilizing or destabilizing effects.

Authors:
;  [1]
  1. Department of Physics, University of Ioannina, GR 451 10 Ioannina (Greece)
Publication Date:
OSTI Identifier:
22303814
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 8; Other Information: (c) 2014 EURATOM; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BESSEL FUNCTIONS; CONFIGURATION; EQUILIBRIUM; INCOMPRESSIBLE FLOW; ITER TOKAMAK; MAGNETIC FIELDS; MAGNETIC SURFACES; MATHEMATICAL SOLUTIONS; PLASMA; SHEAR; STABILITY

Citation Formats

Kaltsas, D. A., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr, and Throumoulopoulos, G. N., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr. Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration. United States: N. p., 2014. Web. doi:10.1063/1.4892380.
Kaltsas, D. A., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr, & Throumoulopoulos, G. N., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr. Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration. United States. doi:10.1063/1.4892380.
Kaltsas, D. A., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr, and Throumoulopoulos, G. N., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr. Fri . "Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration". United States. doi:10.1063/1.4892380.
@article{osti_22303814,
title = {Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration},
author = {Kaltsas, D. A., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr and Throumoulopoulos, G. N., E-mail: dkaltsas@cc.uoi.gr, E-mail: gthroum@cc.uoi.gr},
abstractNote = {A Solovev-like solution describing equilibria with field aligned incompressible flows [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 19, 014504 (2012)] is extended to non parallel flows. The solution expressed as a superposition of Bessel functions contains an arbitrary number of free parameters which are exploited to construct a variety of configurations including ITER shaped ones. For parallel flows, application of a sufficient condition for linear stability shows that this condition is satisfied in an appreciable part of the plasma region on the high-field side mostly due to the variation of the magnetic field perpendicular to the magnetic surfaces. Also, the results indicate that depending on the shape of the Mach-function profile and the values of the free parameters the flow and flow shear may have either stabilizing or destabilizing effects.},
doi = {10.1063/1.4892380},
journal = {Physics of Plasmas},
number = 8,
volume = 21,
place = {United States},
year = {Fri Aug 15 00:00:00 EDT 2014},
month = {Fri Aug 15 00:00:00 EDT 2014}
}
  • The ideal magnetohydrodynamic stability of solar coronal arcades where all the field lines are tied to the photosphere is examined. Two sets of photospheric boundary conditions are examined, and the first detailed quantitative comparison is presented. It is found that conditions where all components of the perturbation vanish at the photosphere are significantly more stable to interchange modes than those for which a displacement along the field lines is allowed there. Much stronger radial pressure gradients are needed to destabilize the former case. It is also found that three sample force-free fields are stable to all perturbations which were imposed.more » These results outline a pressing need for a more precise treatment of the transition region/corona boundary in stability problems. 25 references.« less
  • A WKB theory is formulated for large-{ital n} ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning representation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/{ital n}), where {ital n} is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.
  • The linear and nonlinear stability of a nonmonotonic {ital q} profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, {ital S}, and taking on a double/triple tearing structure at high {ital S}. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure. In addition, this velocity shear decreases the stabilizing effect ofmore » finite pressure seen previously for tearing modes at high {ital S}. Nonlinear calculations show the generation of a large, m=1, n=0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfv{acute e}nic, sheared toroidal flows have a minimal effect on weakly coupled, localized instabilities. {copyright} {ital 1999 American Institute of Physics.}« less
  • The effect of sheared axial flow on the Z-pinch sausage instability has been examined with two-dimensional magnetohydrodynamic simulations. Diffuse Bennett equilibria in the presence of axial flows with parabolic and linear radial profiles have been considered, and a detailed study of the linear and nonlinear development of small perturbations from these equilibria has been performed. The consequences of both single-wavelength and random-seed perturbations were calculated. It was found that sheared flows changed the internal m=0 mode development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to smallmore » amplitudes and only long wavelengths continued to grow. Full stability was obtained for supersonic plasma flows.« less
  • A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the Z-pinch is presented in which plasma flows are included in the equilibrium. With sheared axial flows it is found that substantial stabilization of internal modes is possible for some equilibrium profiles. For this to occur equilibria with a change in fluid velocity across the pinch radius of about Mach 2 are required. However, this ignores the surrounding vacuum and for the more realistic free boundary modes flows of about Mach 4 are required to stabilize all global MHD modes. This stabilization of MHD modes is not observed for allmore » equilibria however. This fact, combined with the supersonic flow speeds required for stability, make it unlikely that a Z-pinch could in practice be stabilized by the introduction of sheared flow. {copyright} {ital 1996 American Institute of Physics.}« less