A class of three-dimensional isothermal laminated equilibria and their stability

Three-dimensional ideal magnetostatic equilibria with laminated magnetic field in which one component of the magnetic field vanishes, are constructed for isothermal coronal plasmas in the presence of uniform gravity. Three subsets of the general solution are found to be absolutely stable, when subject to rigid anchoring of the magnetic field lines at the base of the atmosphere. The magnetic fields in these cases carry currents. For equilibria with general magnetic strength variations, the criteria for stability are obtained by minimizing the energy integral. Numerical solutions for the Euler-Lagrange equations that result from the minimization procedure are given, and are used to determine critical equilibrium parameters that give a bound for the marginal stability. For low values of plasma β (≡ 8πp/B²), the scale length of the plasma density variation can be small and the magnetic shear can be large, suggestive of the observed fine plasma loops and the rapid fluctuation of the inclination angle of the field lines in the sunspot penumbra.