A similarity reduction of the generalized Grad-Shafranov equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911832100306944 |
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| author | Kuiroukidis, A. I. Kaltsas, D. A. Throumoulopoulos, G. N. |
| author_facet | Kuiroukidis, A. I. Kaltsas, D. A. Throumoulopoulos, G. N. |
| contents | 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 Solovév 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_09061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A similarity reduction of the generalized Grad-Shafranov equation Kuiroukidis, A. I. Kaltsas, D. A. Throumoulopoulos, G. N. Plasma Physics 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 Solovév 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. |
| title | A similarity reduction of the generalized Grad-Shafranov equation |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2401.09061 |