Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?
Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport ca...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/12/2368 |
| _version_ | 1797500325502910464 |
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| author | Gaetano Zimbardo Francesco Malara Silvia Perri |
| author_facet | Gaetano Zimbardo Francesco Malara Silvia Perri |
| author_sort | Gaetano Zimbardo |
| collection | DOAJ |
| description | Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates. |
| first_indexed | 2024-03-10T03:00:17Z |
| format | Article |
| id | doaj.art-b64e936bd9164bbb9b9bcd8b79240797 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:00:17Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b64e936bd9164bbb9b9bcd8b792407972023-11-23T10:46:11ZengMDPI AGSymmetry2073-89942021-12-011312236810.3390/sym13122368Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?Gaetano Zimbardo0Francesco Malara1Silvia Perri2Physics Department, University of Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, ItalyPhysics Department, University of Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, ItalyPhysics Department, University of Calabria, Ponte P. Bucci, Cubo 31C, 87036 Rende, ItalySuperdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.https://www.mdpi.com/2073-8994/13/12/2368anomalous transportfractional derivativessolar energetic particlesLévy walks |
| spellingShingle | Gaetano Zimbardo Francesco Malara Silvia Perri Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? Symmetry anomalous transport fractional derivatives solar energetic particles Lévy walks |
| title | Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? |
| title_full | Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? |
| title_fullStr | Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? |
| title_full_unstemmed | Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? |
| title_short | Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation? |
| title_sort | energetic particle superdiffusion in solar system plasmas which fractional transport equation |
| topic | anomalous transport fractional derivatives solar energetic particles Lévy walks |
| url | https://www.mdpi.com/2073-8994/13/12/2368 |
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