hide
Free keywords:
-
Abstract:
Exact solutions of the equation governing the equilibrium magnetohydrodynamic states of an axisymmetric plasma with incompressible flows of arbitrary direction [Phys. Pasmas 5 (1998) 2378] are constructed for toroidal current density profiles peaked on the magnetic axis in connection with the ansatz S=-ku, where S=d/du[ρ(dΦ/du)²] (k is a parameter, u labels the magnetic surfaces; ρ(u) and Φ(u) 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 k=0, a case which includes flows parallel to the magnetic field, the solutions are expressed in terms of Kummer functions while for k≠0 in terms of Airy functions. On the basis of a tokamak solution with k≠0 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 k. This value is larger the smaller the aspect ratio of the configuration.
