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Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameterσ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponentαin the power-law particle-energy distribution function,f(γ)dγ∝γ−αdγ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponentαis in good agreement with the numerical results.
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Universal Nonthermal Power-law Distribution Functions from the Self-consistent Evolution of Collisionless Electrostatic Plasmas
Abstract Collisionless systems often exhibit nonthermal power-law tails in their distribution functions. Interestingly, collisionless plasmas in various physical scenarios (e.g., the ion population of the solar wind) feature av−5tail in their velocity (v) distribution, whose origin has been a long-standing puzzle. We show this power-law tail to be a natural outcome of the collisionless relaxation of driven electrostatic plasmas. Using a quasi-linear analysis of the perturbed Vlasov–Poisson equations, we show that the coarse-grained mean distribution function (DF),f0, follows a quasi-linear diffusion equation with a diffusion coefficientD(v) that depends onvthrough the plasma dielectric constant. If the plasma is isotropically forced on scales larger than the Debye length with a white-noise-like electric field,D(v) ∼v4forσ<v<ωP/k, withσthe thermal velocity,ωPthe plasma frequency, andkthe characteristic wavenumber of the perturbation; the corresponding quasi-steady-statef0develops av−(d+ 2)tail inddimensions (v−5tail in 3D), while the energy (E) distribution develops anE−2tail independent of dimensionality. Any redness of the noise only alters the scaling in the highvend. Nonresonant particles moving slower than the phase velocity of the plasma waves (ωP/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, while its core (v<σ) eventually also heats up but over a much longer timescale. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the emergence of the universalv−5tail.
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- PAR ID:
- 10558761
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 977
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 91
- Size(s):
- Article No. 91
- Sponsoring Org:
- National Science Foundation
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