A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
A class of simple kinetic systems is considered, described by the 1D Vlasov--Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The m...
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| Format: | Journal article |
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Cambridge University Press
2018
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| _version_ | 1797057568345948160 |
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| author | Adkins, T Schekochihin, A |
| author_facet | Adkins, T Schekochihin, A |
| author_sort | Adkins, T |
| collection | OXFORD |
| description | A class of simple kinetic systems is considered, described by the 1D Vlasov--Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analog of the Kraichnan--Batchelor model of chaotic advection. The solution of the model is found in Fourier--Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective dissipation channel at wave numbers below a certain cut off (analog of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The full Fourier--Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wave numbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wave numbers ($k$). The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution. |
| first_indexed | 2024-03-06T19:38:18Z |
| format | Journal article |
| id | oxford-uuid:1fc7cb71-85d6-4e6a-9283-3bd515931311 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:38:18Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:1fc7cb71-85d6-4e6a-9283-3bd5159313112022-03-26T11:23:56ZA solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase spaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1fc7cb71-85d6-4e6a-9283-3bd515931311Symplectic Elements at OxfordCambridge University Press2018Adkins, TSchekochihin, AA class of simple kinetic systems is considered, described by the 1D Vlasov--Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analog of the Kraichnan--Batchelor model of chaotic advection. The solution of the model is found in Fourier--Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective dissipation channel at wave numbers below a certain cut off (analog of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The full Fourier--Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wave numbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wave numbers ($k$). The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution. |
| spellingShingle | Adkins, T Schekochihin, A A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title | A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title_full | A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title_fullStr | A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title_full_unstemmed | A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title_short | A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space |
| title_sort | solvable model of vlasov kinetic plasma turbulence in fourier hermite phase space |
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