{"title":"Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas","authors":"Uddipan Banik, Amitava Bhattacharjee, Wrick Sengupta","doi":"arxiv-2408.07127","DOIUrl":null,"url":null,"abstract":"Distribution functions of collisionless systems are known to show non-thermal\npower law tails. Interestingly, collisionless plasmas in various physical\nscenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail\nin the velocity ($v$) distribution, whose origin has been a long-standing\nmystery. We show this power law tail to be a natural outcome of the\nself-consistent collisionless relaxation of driven electrostatic plasmas. We\nperform a quasilinear analysis of the perturbed Vlasov-Poisson equations to\nshow that the coarse-grained mean distribution function (DF), $f_0$, follows a\nquasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends\non $v$ through the plasma dielectric constant. If the plasma is isotropically\nforced on scales much larger than the Debye length with a white noise-like\nelectric field, then $D(v)\\sim v^4$ for $\\sigma<v<\\omega_{\\mathrm{P}}/k$, with\n$\\sigma$ the thermal velocity, $\\omega_{\\mathrm{P}}$ the plasma frequency and\n$k$ the maximum wavenumber of the perturbation; the corresponding $f_0$, in the\nquasi-steady state, develops a $v^{-\\left(d+2\\right)}$ tail in $d$ dimensions\n($v^{-5}$ tail in 3D), while the energy ($E$) distribution develops an $E^{-2}$\ntail irrespective of the dimensionality of space. Any redness of the noise only\nalters the scaling in the high $v$ end. Non-resonant particles moving slower\nthan the phase-velocity of the plasma waves ($\\omega_{\\mathrm{P}}/k$)\nexperience a Debye-screened electric field, and significantly less (power law\nsuppressed) acceleration than the near-resonant particles. Thus, a Maxwellian\nDF develops a power law tail. The Maxwellian core ($v<\\sigma$) eventually also\nheats up, but over a much longer timescale than that over which the tail forms.\nWe definitively show that self-consistency (ignored in test-particle\ntreatments) is crucial for the development of the universal $v^{-5}$ tail.","PeriodicalId":501423,"journal":{"name":"arXiv - PHYS - Space Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Space Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.07127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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 $\sigma
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