Comparative study of forward and backward test-kinetic simulation approaches |
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| Authors: | Gabriel Voitcu Marius Echim Richard Marchand |
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| Affiliation: | 1. Institute of Space Science, Atomistilor 409, Magurele 077125, Romania;2. University of Bucharest, Faculty of Physics, Atomistilor 405, Magurele 077125, Romania;3. Belgian Institute for Space Aeronomy, Avenue Circulaire 3, Brussels B-1180, Belgium;4. University of Alberta, Department of Physics, T6G 2G7 Edmonton, Alberta, Canada;1. Institut de Recherche en Astrophysique et Planétologie, CNRS, Université Paul Sabatier, Toulouse, France;2. Department of Physics, Aberystwyth University, Wales, UK;3. Department of Physics and Astronomy, University College London, London, UK;4. Institut de Planétologie et d′Astrophysique de Grenoble, UGA/CNRS-INSU, Grenoble, France;5. GFI Informatique, Toulouse, France;6. LESIA, Observatoire de Paris, CNRS, UPMC, University Paris Diderot, Meudon, France;7. Institute of Atmospheric Physics, Czech Academy of Science, Prague, Czech Republic;8. Física Aplicada I, Escuela de Ingeniería de Bilbao, Universidad del País Vasco, Bilbao, Spain;9. Mullard Space Science Laboratory, University College London (UCL), Holmbury Saint Mary, UK;10. The Centre for Planetary Sciences at UCL/Birkbeck, London, UK;11. German Aerospace Center, Institute of Aerospace Medicine, Linder Höhe, 51147 Cologne, Germany;12. Wigner Research Centre for Physics, Budapest, Hungary;13. Space Research Centre, Polish Academy of Sciences, Warsaw, Poland;14. National Institute of Information and Communications Technology, 4-2-1, Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan;1. Department of Child Neurology, Maastricht University Medical Center, PO Box 5800, 6202 AZ Maastricht, The Netherlands;2. Department of Neurology, Diaconessenhuis, Leiden, The Netherlands;3. Department of Child Neurology, VU University Medical Center, Neuroscience Campus Amsterdam, Amsterdam, The Netherlands;4. Department of Rehabilitation Medicine, VU University Medical Center, Amsterdam, The Netherlands;5. School for Mental Health and Neuroscience, Maastricht University, Maastricht, The Netherlands;6. Department of Neurology, Maastricht University Medical Center, Maastricht, The Netherlands;7. Center of Neurological Learning Disabilities, Epilepsy Center Kempenhaeghe, Heeze, The Netherlands;1. Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking RH5 6NT, UK;2. Centre for Planetary Sciences at UCL/Birkbeck, Gower Street, London WC1E 6BT, UK;3. Southwest Research Institute, San Antonio, TX 78228, USA;4. Institut de Recherche en Astrophysique et Planétologie, 9, avenue du Colonel Roche, B.P. 4346, 31028 Toulouse Cedex 4, France;5. Swedish Institute of Space Physics, Box 812, S98 128 Kiruna, Sweden;1. National Observatory of Athens, Greece;2. Center for Atmospheric Research, University of Massachusetts Lowell, Lowell, MA, USA;3. University of Oulou, Finland |
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| Abstract: | In this paper we perform a comparative study of the forward and backward Liouville mapping applied to the modeling of ring-shaped and non-gyrotropic velocity distribution functions of particles injected in a sheared electromagnetic field. The test-kinetic method is used to compute the velocity distribution function in various areas of a proton cloud moving in the vicinity of a region with a sharp transition of the magnetic field and a non-uniform electric field. In the forward approach the velocity distribution function is computed for a two-dimensional spatial bin, while in the backward approach the distribution function is averaged over a spatial bin with the same size as for the forward method and using a two-dimensional trapezoidal integration scheme. It is shown that the two approaches lead to similar results for spatial bins where the velocity distribution function varies smoothly. On the other hand, with bins covering regions of configuration space characterized by sharp spatial gradients of the velocity distribution function, the forward and backward approaches will generally provide different results. |
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