Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas
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2024
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| _version_ | 1866916477881286656 |
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| author | Banik, Uddipan Bhattacharjee, Amitava Sengupta, Wrick |
| author_facet | Banik, Uddipan Bhattacharjee, Amitava Sengupta, Wrick |
| contents | Distribution functions of collisionless systems are known to show non-thermal power law tails. Interestingly, collisionless plasmas in various physical scenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail in the velocity ($v$) distribution, whose origin has been a long-standing mystery. We show this power law tail to be a natural outcome of the self-consistent collisionless relaxation of driven electrostatic plasmas. We perform a quasilinear analysis of the perturbed Vlasov-Poisson equations to show that the coarse-grained mean distribution function (DF), $f_0$, follows a quasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends on $v$ through the plasma dielectric constant. If the plasma is isotropically forced on scales much larger than the Debye length with a white noise-like electric field, then $D(v)\sim v^4$ for $σ<v<ω_{\mathrm{P}}/k$, with $σ$ the thermal velocity, $ω_{\mathrm{P}}$ the plasma frequency and $k$ the maximum wavenumber of the perturbation; the corresponding $f_0$, in the quasi-steady state, develops a $v^{-\left(d+2\right)}$ tail in $d$ dimensions ($v^{-5}$ tail in 3D), while the energy ($E$) distribution develops an $E^{-2}$ tail irrespective of the dimensionality of space. Any redness of the noise only alters the scaling in the high $v$ end. Non-resonant particles moving slower than the phase-velocity of the plasma waves ($ω_{\mathrm{P}}/k$) experience a Debye-screened electric field, and significantly less (power law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power law tail. The Maxwellian core ($v<σ$) eventually also heats up, but over a much longer timescale than that over which the tail forms. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the development of the universal $v^{-5}$ tail. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_07127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas Banik, Uddipan Bhattacharjee, Amitava Sengupta, Wrick Solar and Stellar Astrophysics Astrophysics of Galaxies High Energy Astrophysical Phenomena Statistical Mechanics Plasma Physics Space Physics Distribution functions of collisionless systems are known to show non-thermal power law tails. Interestingly, collisionless plasmas in various physical scenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail in the velocity ($v$) distribution, whose origin has been a long-standing mystery. We show this power law tail to be a natural outcome of the self-consistent collisionless relaxation of driven electrostatic plasmas. We perform a quasilinear analysis of the perturbed Vlasov-Poisson equations to show that the coarse-grained mean distribution function (DF), $f_0$, follows a quasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends on $v$ through the plasma dielectric constant. If the plasma is isotropically forced on scales much larger than the Debye length with a white noise-like electric field, then $D(v)\sim v^4$ for $σ<v<ω_{\mathrm{P}}/k$, with $σ$ the thermal velocity, $ω_{\mathrm{P}}$ the plasma frequency and $k$ the maximum wavenumber of the perturbation; the corresponding $f_0$, in the quasi-steady state, develops a $v^{-\left(d+2\right)}$ tail in $d$ dimensions ($v^{-5}$ tail in 3D), while the energy ($E$) distribution develops an $E^{-2}$ tail irrespective of the dimensionality of space. Any redness of the noise only alters the scaling in the high $v$ end. Non-resonant particles moving slower than the phase-velocity of the plasma waves ($ω_{\mathrm{P}}/k$) experience a Debye-screened electric field, and significantly less (power law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power law tail. The Maxwellian core ($v<σ$) eventually also heats up, but over a much longer timescale than that over which the tail forms. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the development of the universal $v^{-5}$ tail. |
| title | Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas |
| topic | Solar and Stellar Astrophysics Astrophysics of Galaxies High Energy Astrophysical Phenomena Statistical Mechanics Plasma Physics Space Physics |
| url | https://arxiv.org/abs/2408.07127 |