Abstract
In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.
Highlights
Reduced magnetohydrodynamics (MHD), a system of approximations introduced in its original form in the 1960s (Greene & Johnson 1961), continues to be used by modern MHD codes, such as JOREK (Franck et al 2015) and M3D-C1 (Breslau, Ferraro & Jardin 2009)
Even in the simple case of a tearing mode in a circular high-aspect-ratio tokamak, energy conservation can only be approximately satisfied, due to the possibility of non-physical gain or loss of kinetic energy
Even without exact energy conservation, meaningful linear results, such as growth rates, could be obtained without any further modifications; the lack of energy conservation required artificial dissipation to be introduced to prevent a crash after nonlinear saturation was reached due to non-physical kinetic energy buildup
Summary
Reduced magnetohydrodynamics (MHD), a system of approximations introduced in its original form in the 1960s (Greene & Johnson 1961), continues to be used by modern MHD codes, such as JOREK (Franck et al 2015) and M3D-C1 (Breslau, Ferraro & Jardin 2009). While many versions of reduced MHD consisting of different equations and using different methods to derive them have been published, the main idea is the same: the removal of fast magnetosonic waves while retaining relevant physics (Strauss 1997; Jardin et al 2012). The removal of these waves eliminates the shortest time scale and allows one to use larger time steps due to the Courant condition. In Appendix A, a technicality in the implementation of the original model is discussed
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