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MHD Equilibria with Cusped Plasma‐Vacuum Interfaces
Author(s) -
Kaiser R.
Publication year - 1994
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19940740708
Subject(s) - cusp (singularity) , gravitational singularity , magnetohydrodynamics , plasma , boundary (topology) , physics , mathematics , plane (geometry) , mathematical analysis , class (philosophy) , symmetry (geometry) , geometry , quantum mechanics , artificial intelligence , computer science
The free‐boundary MHD equilibrium is considered in the case of plane symmetry and constant current profile. We prove the existence of solutions in a neighbourhood of cusp singularities of the plasma‐vacuum interface. In both cases — the “plasma” and “vacuum cusps” — we derive a power law describing the asymptotic shape of the cusps; the allowed exponents are half‐integers. This leads to a natural classification of cusps. The solutions are classified accordingly and their asymptotic behaviour close to the cusp is found to depend only on the class to which the solution belongs.