Search for: All records

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<ω_P/k, withσthe thermal velocity,ω_Pthe 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 (ω_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, 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.