{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:48Z","timestamp":1760150628988,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study the generalized \u03c7 and \u03b7 cross-helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). \u03c7 and \u03b7, the additional label translation symmetry group, are used to generalize cross-helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behavior in non-ideal MHD, we calculate the time derivative of both helicities using non-ideal MHD equations in which viscosity, finite resistivity, and heat conduction are taken into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that \u03c7 and \u03b7 cross-helicities are not strict constants of motion in non-ideal MHD and show a rate of dissipation that is comparable to the dissipation of other topological constants of motion.<\/jats:p>","DOI":"10.3390\/sym15122203","type":"journal-article","created":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T06:53:16Z","timestamp":1702623196000},"page":"2203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized \u03c7 and \u03b7 Cross-Helicities in Non-Ideal Magnetohydrodynamics"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4116-0468","authenticated-orcid":false,"given":"Prachi","family":"Sharma","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Department of Electrical & Electronic Engineering, Ariel University, Ariel 40700, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6679-3320","authenticated-orcid":false,"given":"Asher","family":"Yahalom","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Department of Electrical & Electronic Engineering, Ariel University, Ariel 40700, Israel"},{"name":"Center for Astrophysics, Geophysics, and Space Sciences (AGASS), Ariel University, Ariel 40700, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1103\/PhysRevLett.48.1256","article-title":"Evaluation of Magnetic Helicity in Homogeneous Turbulence","volume":"48","author":"Matthaeus","year":"1982","journal-title":"Phys. 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