English

A similarity reduction of the generalized Grad-Shafranov equation

Plasma Physics 2024-04-10 v2

Abstract

We extend previous work [Y. E. Litvinenko, Phys. Plasmas 17, 074502 (2010)] on a direct method for finding similarity reductions of partial differential equations such as the Grad-Shafranov equation, to the case of the generalized Grad-Shafranov equation (GGSE) with arbitrary incompressible flow. Several families of analytic solutions are constructed, the generalized Solov\'ev solution being a particular case, which contain both the classical and non-classical group-invariant solutions to the GGSE. Those solutions can describe a variety of equilibrium configurations pertinent to toroidal magnetically confined plasmas and planetary magnetospheres.

Keywords

Cite

@article{arxiv.2401.09061,
  title  = {A similarity reduction of the generalized Grad-Shafranov equation},
  author = {A. I. Kuiroukidis and D. A. Kaltsas and G. N. Throumoulopoulos},
  journal= {arXiv preprint arXiv:2401.09061},
  year   = {2024}
}