Remark on a magnetically confined plasma with infinite charge
We consider a one-species plasma moving in an infinite cylinder in R3, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. In a recent paper [4] we have supposed that the plasma satisfies the Vlasov equation with a Yukawa mutual interaction (i.e. Coulomb at s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2014-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2014(1-2)/69-98.pdf |
| _version_ | 1818456050569838592 |
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| author | Silvia Caprino Guido Cavallaro Carlo Marchioro |
| author_facet | Silvia Caprino Guido Cavallaro Carlo Marchioro |
| author_sort | Silvia Caprino |
| collection | DOAJ |
| description | We consider a one-species plasma moving in an infinite cylinder in R3, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. In a recent paper [4] we have supposed that the plasma satisfies the Vlasov equation with a Yukawa mutual interaction (i.e. Coulomb at short distance and exponentially decreasing at infinity). Assuming that initially the particles have bounded velocities and are distributed according to a bounded density without any hypothesis on its decreasing at infinity, we have proved the global in time existence and uniqueness of the time evolution of the plasma and its confinement. In the present paper we extend this result to a Coulomb interaction, making on the initial density some assumption of slight decreasing on average at infinity, which however does not imply that the density belongs to any Lp space. The proof is similar, but slightly simpler. |
| first_indexed | 2024-12-14T22:20:30Z |
| format | Article |
| id | doaj.art-fd8cb76f99114a749dd322c434d93508 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-12-14T22:20:30Z |
| publishDate | 2014-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-fd8cb76f99114a749dd322c434d935082022-12-21T22:45:31ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502014-01-01351-26998Remark on a magnetically confined plasma with infinite chargeSilvia Caprino0Guido Cavallaro1Carlo Marchioro2Università Tor VergataUniversità La SapienzaUniversità La SapienzaWe consider a one-species plasma moving in an infinite cylinder in R3, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. In a recent paper [4] we have supposed that the plasma satisfies the Vlasov equation with a Yukawa mutual interaction (i.e. Coulomb at short distance and exponentially decreasing at infinity). Assuming that initially the particles have bounded velocities and are distributed according to a bounded density without any hypothesis on its decreasing at infinity, we have proved the global in time existence and uniqueness of the time evolution of the plasma and its confinement. In the present paper we extend this result to a Coulomb interaction, making on the initial density some assumption of slight decreasing on average at infinity, which however does not imply that the density belongs to any Lp space. The proof is similar, but slightly simpler.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2014(1-2)/69-98.pdfvlasov equationmagnetic confinementinfinitely extended plasma |
| spellingShingle | Silvia Caprino Guido Cavallaro Carlo Marchioro Remark on a magnetically confined plasma with infinite charge Rendiconti di Matematica e delle Sue Applicazioni vlasov equation magnetic confinement infinitely extended plasma |
| title | Remark on a magnetically confined plasma with infinite charge |
| title_full | Remark on a magnetically confined plasma with infinite charge |
| title_fullStr | Remark on a magnetically confined plasma with infinite charge |
| title_full_unstemmed | Remark on a magnetically confined plasma with infinite charge |
| title_short | Remark on a magnetically confined plasma with infinite charge |
| title_sort | remark on a magnetically confined plasma with infinite charge |
| topic | vlasov equation magnetic confinement infinitely extended plasma |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2014(1-2)/69-98.pdf |
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