100 research outputs found
Tokamak MHD equilibria with reversed magnetic shear and sheared flow
Analytic solutions of the magnetohydrodynamic equilibrium equations for a
cylindrically symmetric magnetically confined plasma with reversed magnetic
shear, s < 0, and sheared flow are constructed by prescribing the safety
factor-, poloidal velocity- and axial velocity- profiles consistently with
experimental ones
Multitoroidal configurations as equilibrium flow eigenstates
Equilibrium eigenstates of an axisymmetric magnetically confined plasma with
toroidal flow are investigated by means of exact solutions of the ideal
magnetohydrodynamic equations. The study includes "compressible" flows with
constant temperature, but varying density on magnetic surfaces and
incompressible ones with constant density, but varying temperature thereon. In
both cases eigenfunctions of the form Psi_{nl} = Z_l(z)R_n(R) (l, n=1,2,...)
describe configurations with lxn magnetic axes. By varying the flow parameters
a change in magnetic topology is possible. In addition, the effects of the flow
and the aspect ratio on the Shafranov shift are evaluated along with the
variations of density and temperature on magnetic surfaces.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004,
Nice (France
Two-fluid tokamak equilibria with reversed magnetic shear and sheared flow
The aim of the present work is to investigate tokamak equilibria with
reversed magnetic shear and sheared flow, which may play a role in the
formation of internal transport barriers (ITBs), within the framework of
two-fluid model. The study is based on exact self-consistent solutions in
cylindrical geometry by means of which the impact of the magnetic shear, s, and
the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components on
the radial electric field, its shear and the shear of the ExB velocity is
examined. For a wide parametric regime of experimental concern it turns out
that the contributions of the toroidal and poloidal velocity and pressure
gradient terms to the electric field, its shear and ExB velocity shear are of
the same order of magnitude. The impact of s on ExB velocity shear through the
pressure gradient term is stronger than that through the velocity terms. The
results indicate that, alike MHD, the magnetic shear and the sheared toroidal
and poloidal velocities act synergetically in producing electric fields and
therefore ExB velocity shear profiles compatible with ones observed in
discharges with ITBs; owing to the pressure gadient term, however, the impact
of s on the electic field, its shear and the shear of ExB velocity is stronger
than that in MHD.Comment: 25 pages, 21 figure
Magnetohydrodynamic "cat eyes" and stabilizing effects of plasma flow
The cat-eyes steady state solution in the framework of hydrodynamics
describing an infinite row of identical vortices is extended to the
magnetohydrodynamic equilibrium equation with incompressible flow of arbitrary
direction. The extended solution covers a variety of equilibria including one-
and two-dimensional generalized force-free and Harris-sheet configurations
which are preferable from those usually employed as initial states in
reconnection studies. Although the vortex shape is not affected by the magnetic
field, the flow in conjunction with the equilibrium nonlinearity has a strong
impact on isobaric surfaces by forming pressure islands located within the
cat-eyes vortices. More importantly, a magnetic-field-aligned flow of
experimental fusion relevance and the flow shear have significant stabilizing
effects in the region of pressure islands. The stable region is enhanced by an
external axial ("toroidal") magnetic field.Comment: 17 pages, 8 figure
Exact magnetohydrodynamic equilibria with flow and effects on the Shafranov shift
Exact solutions of the equation governing the equilibrium magetohydrodynamic
states of an axisymmetric plasma with incompressible flows of arbitrary
direction [H. Tasso and G.N.Throumoulopoulos, Phys. Pasmas {\bf 5}, 2378
(1998)] are constructed for toroidal current density profiles peaked on the
magnetic axis in connection with the ansatz , where ( is a parameter, labels the magnetic surfaces;
and are the density and the electrostatic potential,
respectively). They pertain to either unbounded plasmas of astrophysical
concern or bounded plasmas of arbitrary aspect ratio. For , a case which
includes flows parallel to the magnetic field, the solutions are expressed in
terms of Kummer functions while for in terms of Airy functions. On
the basis of a tokamak solution with describing a plasma surrounded
by a perfectly conducted boundary of rectangular cross-section it turns out
that the Shafranov shift is a decreasing function which can vanish for a
positive value of . This value is larger the smaller the aspect ratio of the
configuration.Comment: 13 pages, 2 figures. v2:Eq (3) has been corrected. A new figure (Fig.
2) has been added in order to illustrate u-contours in connection with
solution (24) and the Shafranov shift. Also, a sentence referring to Fig. 2
has been added after Eq. (25
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