Nova: a nonvariational code for solving the MHD stability of axisymmetric toroidal plasmas

CASTOR: Normal-Mode Analysis of Resistive MHD Plasmas☆

The heating of coronal loops by resonant absorption of Alfven waves is studied in compressible, resistive magnetohydrodynamics. The loops are approximated by straight cylindrical, axisymmetric plasma columns and the incident waves which excite the coronal loops are modelled by a periodic external driver. The stationary state of this system is determined with a numerical code based on the finite element method. Since the power spectrum of the incident waves is not well known, the intrinsic dissipation is computed. The intrinsic dissipation spectrum is independent of the external driver and reflects the intrinsic ability of the coronal loops to extract energy from incident waves by the mechanism of resonant absorption. The numerical results show that resonant absorption is very efficient for typical parameter values occurring in the loops of the solar corona. A considerable part of the energy supplied by the external driver, is actually dissipated Ohmically and converted into heat. The heating of the plasma is localized in a narrow resonant layer with a width proportional to η
1/3. The energy dissipation rate is almost independent of the resistivity for the relevant values of this parameter. The efficiency of the heating mechanism and the localization of the heating strongly depend on the frequency of the external driver. Resonant absorption is extremely efficient when the plasma is excited with a frequency near the frequency of a so-called ‘collective mode’.

Numerical simulation of coronal heating by resonant absorption of Alfvén waves

Large-scale complex eigenvalue problems

There exist a number of observations of magnetohydrodynamic (MHD) activity that can be related to resistive MHD modes localized near the plasma boundary. To study the stability of these modes, a free boundary description of the plasma is essential. The resistive plasma–vacuum boundary conditions have been implemented in the fully toroidal resistive spectral code castor (Complex Alfven Spectrum in Toroidal Geometry) [Proceedings of the 18th Conference on Controlled Fusion and Plasma Physics, Berlin, edited by P. Bachmann and D. C. Robinson (European Physical Society, Petit‐Lancy, Switzerland, 1991), p. 89]. The influence of a free boundary, as compared to a fixed boundary on the stability of low‐m tearing modes, is studied. It is found that the stabilizing (toroidal) effect of a finite pressure due the plasma compression is lost in the free boundary case for modes localized near the boundary. Since the stabilization due to the favorable average curvature in combination with a pressure gradient near the bou...

K. Lerbinger

Papers

Normal Mode Analysis for Resistive Cylindrical Plasmas

Computing complex eigenvalues of large non-Hermitian matrices