629 research outputs found
A comparison of Vlasov with drift kinetic and gyrokinetic theories
A kinetic consideration of an axisymmetric equilibrium with vanishing
electric field near the magnetic axis shows that del f should not vanish on
axis within the framework of Vlasov theory while it can either vanish or not in
the framework of both a drift kinetic and a gyrokinetic theories (f is either
the pertinent particle or the guiding center distribution function). This
different behavior, relating to the reduction of phase space which leads to the
loss of a Vlasov constant of motion, may result in the construction of
different currents in the reduced phase space than the Vlasov ones. This
conclusion is indicative of some limitation on the implications of reduced
kinetic theories in particular as concerns the physics of energetic particles
in the central region of magnetically confined plasmas.Comment: 9 page
Lyapunov stability of flowing MHD plasmas surrounded by resistive walls
A general stability condition for plasma-vacuum systems with resistive walls
is derived by using the Frieman Rotenberg lagrangian stability formulation
[Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit
for external modes does not depend upon the gyroscopic term but upon the sign
of the perturbed potential energy only. In the absence of dissipation in the
plasma such as viscosity, it is expected that the flow cannot stabilize the
system.Comment: 9 page
Tokamak-like Vlasov equilibria
Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field
can be reduced, up to a selection of ions and electrons distributions
functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice
of the distributions functions. In contrast to two-dimensional translationally
symmetric equilibria whose electron distribution function consists of a
displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In
order to be able to carry through the calculations, this deformation is
produced by means of either a Heaviside step function or an exponential
function. The resulting Grad-Shafranov-like equations are established
explicitly.Comment: 11 page
Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
A recent study on axisymmetric ideal magnetohydrodynamic equilibria with
incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf
5}, 2378 (1998)] is extended to the generic case of helically symmetric
equilibria with incompressible flows. It is shown that the equilibrium states
of the system under consideration are governed by an elliptic partial
differential equation for the helical magnetic flux function containing
five surface quantities along with a relation for the pressure. The above
mentioned equation can be transformed to one possessing differential part
identical in form to the corresponding static equilibrium equation, which is
amenable to several classes of analytic solutions. In particular, equilibria
with electric fields perpendicular to the magnetic surfaces and
non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric
equilibria with isothermal magnetic surfaces, helically symmetric
equilibria are over-determined, i.e., in this case the equilibrium equations
reduce to a set of eight ordinary differential equations with seven surface
quantities. In addition, it is proved the non-existence of incompressible
helically symmetric equilibria with (a) purely helical flows (b) non-parallel
flows with isothermal magnetic surfaces and the magnetic field modulus being a
surface quantity (omnigenous equilibria).Comment: Latex file, 13 pages, accepted in J. Plasma Phy
Cylindrical ideal magnetohydrodynamic equilibria with incompressible flows
It is proved that (a) the solutions of the ideal magnetohydrodynamic
equation, which describe the equlibrium states of a cylindrical plasma with
purely poloidal flow and arbitrary cross sectional shape [G. N.
Throumoulopoulos and G. Pantis, Plasma Phys. and Contr. Fusion 38, 1817 (1996)]
are also valid for incompressible equlibrium flows with the axial velocity
component being a free surface quantity and (b) for the case of isothermal
incompressible equilibria the magnetic surfaces have necessarily circular cross
section.Comment: 7 pages, latex, no figure
Vlasov versus reduced kinetic theories for helically symmetric equilibria
A new constant of motion for helically symmetric equilibria in the vicinity
of the magnetic axis is obtained in the framework of Vlasov theory. In view of
this constant of motion the Vlasov theory is compared with drift kinetic and
gyrokinetic theories near axis. It turns out that as in the case of
axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18,
064507 (2011)] the Vlasov current density thereon can differ appreciably from
the drift kinetic and gyrokinetic current densities. This indicates some
limitation on the implications of reduced kinetic theories, in particular as
concerns the physics of energetic particles in the central region of
magnetically confined plasmas.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1104.042
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