A new finite element approach to the normal mode analysis in magnetohydrodynamics

Ideal MHD stability calculations in axisymmetric toroidal coordinate systems

“…The original representation also contributes to pollution [14] of the MHD spectrum because the finite element expansion chosen forces incompressibility only to second order in the inverse aspect ratio. Moreover, the stbrage requirements of these codes are very large, so that large toroidal mode numbers (n > 1C) cannot be accurately treated.…”

“…s showing that the PEST 8 = 9 [as defined by Bq, (14)] is the proper choice P producing straight field lines if $ is used as the toroidal angle. These simple PEST coordinates, however, do not necessarily result in the construction of a numerical mesh which gives optimal weighting to the regions of bad magnetic field line curvature where, for example, ballooning modes have their maximum amplitude.…”

Spectrum of Electrostatic Modes in a Cylindrical Non-neutral Plasma of Arbitrary Density

“…By contrast, in magnetohydrodynamics (MHD) codes have been developed which compute the entire spectrum of normal modes [18][19][20][21][22]. These codes use the finite element method to convert the differential equations governing linear stability to a generalized matrix eigenvalue problem.…”

“…It was demonstrated that the problem could be resolved by an appropriate choice of basis functions in the finite element method [19]. Later it was shown that an alternative method for avoiding spectral pollution was by using what were termed "finite hybrid elements" [20].…”

Field line resonances in discretized magnetospheric models: an artifact study

“…The consequences of using a discretized representation of the Alfve n continuum because of ®nite grid sizes in numerical models have been studied in much detail (Appert et al, 1975;Pritchett and Dawson, 1978;Appert et al, 1984;Lee and Roberts, 1986). The discretized systems are found to behave like a ®nite number of independent oscillators instead of a real continuum, and this modi®es the physics.…”