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arXiv · 2401.09061

A similarity reduction of the generalized Grad-Shafranov equation

A. I. Kuiroukidis·D. A. Kaltsas·G. N. Throumoulopoulos
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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.

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A. I. Kuiroukidis, D. A. Kaltsas, G. N. Throumoulopoulos. 2024-01-17. A similarity reduction of the generalized Grad-Shafranov equation. https://doi.org/10.1063/5.0198558

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