On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields
In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2382 |
| _version_ | 1797516030913806336 |
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| author | Andrey Saveliev |
| author_facet | Andrey Saveliev |
| author_sort | Andrey Saveliev |
| collection | DOAJ |
| description | In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields. |
| first_indexed | 2024-03-10T06:56:33Z |
| format | Article |
| id | doaj.art-fe3e27bce34441b589a6a452a476667f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:56:33Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fe3e27bce34441b589a6a452a476667f2023-11-22T16:29:29ZengMDPI AGMathematics2227-73902021-09-01919238210.3390/math9192382On the Complex-Valued Distribution Function of Charged Particles in Magnetic FieldsAndrey Saveliev0Institute of Physics, Mathematics and Information Technology, Immanuel Kant Baltic Federal University, 236016 Kaliningrad, RussiaIn this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields.https://www.mdpi.com/2227-7390/9/19/2382Boltzmann equationdistribution functionfluid dynamicskinetic consistent schemesmagnetic fieldsmagnetohydrodynamics |
| spellingShingle | Andrey Saveliev On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields Mathematics Boltzmann equation distribution function fluid dynamics kinetic consistent schemes magnetic fields magnetohydrodynamics |
| title | On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields |
| title_full | On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields |
| title_fullStr | On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields |
| title_full_unstemmed | On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields |
| title_short | On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields |
| title_sort | on the complex valued distribution function of charged particles in magnetic fields |
| topic | Boltzmann equation distribution function fluid dynamics kinetic consistent schemes magnetic fields magnetohydrodynamics |
| url | https://www.mdpi.com/2227-7390/9/19/2382 |
| work_keys_str_mv | AT andreysaveliev onthecomplexvalueddistributionfunctionofchargedparticlesinmagneticfields |