Gyrokinetic Landau collision operator in conservative form
A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator...
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| Format: | Article |
| Language: | English |
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American Physical Society
2019
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| Online Access: | http://hdl.handle.net/1721.1/120704 https://orcid.org/0000-0003-3739-1562 |
| _version_ | 1826206060586729472 |
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| author | Pan, Qingjiang Ernst, Darin R |
| author2 | Massachusetts Institute of Technology. Plasma Science and Fusion Center |
| author_facet | Massachusetts Institute of Technology. Plasma Science and Fusion Center Pan, Qingjiang Ernst, Darin R |
| author_sort | Pan, Qingjiang |
| collection | MIT |
| description | A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)10.1103/PhysRevLett.106.195002], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods. |
| first_indexed | 2024-09-23T13:23:28Z |
| format | Article |
| id | mit-1721.1/120704 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:23:28Z |
| publishDate | 2019 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1207042022-10-01T14:58:32Z Gyrokinetic Landau collision operator in conservative form Pan, Qingjiang Ernst, Darin R Massachusetts Institute of Technology. Plasma Science and Fusion Center Pan, Qingjiang Ernst, Darin R A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)10.1103/PhysRevLett.106.195002], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods. United States. Department of Energy (Contract DE-FC02-08ER54966) 2019-03-04T15:11:21Z 2019-03-04T15:11:21Z 2019-02 2018-11 2019-02-08T18:00:28Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/120704 Pan, Qingjiang and Darin R. Ernst. "Gyrokinetic Landau collision operator in conservative form." Physical Review E 99, 2 (February 2019): 023201 © 2019 American Physical Society https://orcid.org/0000-0003-3739-1562 en http://dx.doi.org/10.1103/PhysRevE.99.023201 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Pan, Qingjiang Ernst, Darin R Gyrokinetic Landau collision operator in conservative form |
| title | Gyrokinetic Landau collision operator in conservative form |
| title_full | Gyrokinetic Landau collision operator in conservative form |
| title_fullStr | Gyrokinetic Landau collision operator in conservative form |
| title_full_unstemmed | Gyrokinetic Landau collision operator in conservative form |
| title_short | Gyrokinetic Landau collision operator in conservative form |
| title_sort | gyrokinetic landau collision operator in conservative form |
| url | http://hdl.handle.net/1721.1/120704 https://orcid.org/0000-0003-3739-1562 |
| work_keys_str_mv | AT panqingjiang gyrokineticlandaucollisionoperatorinconservativeform AT ernstdarinr gyrokineticlandaucollisionoperatorinconservativeform |