Advanced numerical techniques for time integration of relativistic equations of motion for charged particles
Abstract Advanced numerical techniques for solving the relativistic equations of motion for charged particles are provided. A new fourth-order integrator is developed by combining the Taylor series expansion of the numerical angle of relativistic gyration and the fourth-order Runge–Kutta method for...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Earth, Planets and Space |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40623-023-01902-8 |
| _version_ | 1827724099300884480 |
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| author | Takayuki Umeda Riku Ozaki |
| author_facet | Takayuki Umeda Riku Ozaki |
| author_sort | Takayuki Umeda |
| collection | DOAJ |
| description | Abstract Advanced numerical techniques for solving the relativistic equations of motion for charged particles are provided. A new fourth-order integrator is developed by combining the Taylor series expansion of the numerical angle of relativistic gyration and the fourth-order Runge–Kutta method for integrating the Lorentz factor. The new integrator gives the exact relativistic E-cross-B drift velocity, but has a numerical accuracy much higher than the classic fourth-order Runge–Kutta integrator. Graphical Abstract |
| first_indexed | 2024-03-10T22:09:05Z |
| format | Article |
| id | doaj.art-1e98423e62914efbb25ce234dd3c4904 |
| institution | Directory Open Access Journal |
| issn | 1880-5981 |
| language | English |
| last_indexed | 2024-03-10T22:09:05Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Earth, Planets and Space |
| spelling | doaj.art-1e98423e62914efbb25ce234dd3c49042023-11-19T12:39:00ZengSpringerOpenEarth, Planets and Space1880-59812023-10-0175111210.1186/s40623-023-01902-8Advanced numerical techniques for time integration of relativistic equations of motion for charged particlesTakayuki Umeda0Riku Ozaki1Institute for Space-Earth Environmental Research, Nagoya UniversityInstitute for Space-Earth Environmental Research, Nagoya UniversityAbstract Advanced numerical techniques for solving the relativistic equations of motion for charged particles are provided. A new fourth-order integrator is developed by combining the Taylor series expansion of the numerical angle of relativistic gyration and the fourth-order Runge–Kutta method for integrating the Lorentz factor. The new integrator gives the exact relativistic E-cross-B drift velocity, but has a numerical accuracy much higher than the classic fourth-order Runge–Kutta integrator. Graphical Abstracthttps://doi.org/10.1186/s40623-023-01902-8Equations of motionCharged particleRelativityHigher-order integrationTaylor expansionRunge–Kutta method |
| spellingShingle | Takayuki Umeda Riku Ozaki Advanced numerical techniques for time integration of relativistic equations of motion for charged particles Earth, Planets and Space Equations of motion Charged particle Relativity Higher-order integration Taylor expansion Runge–Kutta method |
| title | Advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| title_full | Advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| title_fullStr | Advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| title_full_unstemmed | Advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| title_short | Advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| title_sort | advanced numerical techniques for time integration of relativistic equations of motion for charged particles |
| topic | Equations of motion Charged particle Relativity Higher-order integration Taylor expansion Runge–Kutta method |
| url | https://doi.org/10.1186/s40623-023-01902-8 |
| work_keys_str_mv | AT takayukiumeda advancednumericaltechniquesfortimeintegrationofrelativisticequationsofmotionforchargedparticles AT rikuozaki advancednumericaltechniquesfortimeintegrationofrelativisticequationsofmotionforchargedparticles |