Hydromagnetic asymptotic equilibria with vacuum, closedline dominant B and parallel dominant J
Abstract
The paper considers the construction of an asymptotic solution to the magnetohydrostatic (MHS) equations in the case where the spatial domain in which the solution is sought belongs to the torus homology class, and a vacuum magnetic field dominates along with a parallel current. Solenoidfield theory is reviewed, the realcharacteristic part of the MHS problem is analyzed, and singlevalued asymptotic solutions are obtained for a general magneticfieldline differential equation as well as for the parameter L. It is proven that the problem of constructing an asymptotic solution to the MHS equations in the case considered can be reduced to solving a weakly singular Hammerstein integral equation to the lowest significant order and a weakly singular inhomogeneous Fredholm integral equation of the second kind for each of the higher orders.
 Publication:

Nuovo Cimento B Serie
 Pub Date:
 March 1976
 DOI:
 10.1007/BF02726742
 Bibcode:
 1976NCimB..32....1L
 Keywords:

 Field Theory (Physics);
 Magnetic Fields;
 Magnetohydrostatics;
 Solenoids;
 Vector Currents;
 Fredholm Equations;
 Singular Integral Equations;
 Toroidal Plasmas;
 Vacuum Effects;
 Plasma Physics