How Alfvén waves energize the solar wind: heat vs work

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base (P _AWb) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance r, which we denote χ _H(r), and the fraction that is transferred via work, which we denote χ _W(r). We find that χ _W(r _A) ranges from 0.15 to 0.3, where r _A is the Alfvén critical point. This value is small compared to one because the Alfvén speed v _A exceeds the outflow velocity U at r < r _A, so the AWs race through the plasma without doing much work. At r > r _A, where v _A < U, the AWs are in an approximate sense "stuck to the plasma," which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach r = r _A, so the total rate at which AWs do work on the plasma at r > r _A is a modest fraction of P _AWb. We find that heating is more effective than work at r < r _A, with χ _H(r _A) ranging from 0.5 to 0.7. The reason that χ _H ⩾ 0.5 in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and r _A. A given amount of heating produces more magnetic moment in regions of weaker magnetic field. Thus, paradoxically, the average proton magnetic moment increases robustly with increasing r at r > r _A, even though the total rate at which AW energy is transferred to particles at r > r _A is a small fraction of P _AWb.

New Closures for More Precise Modeling of Landau Damping in the Fluid Framework

Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the fourth-order gyrotropic fluid moment are expressed through lower-order fluid moments. To obtain a closure of a fluid model expanded around a bi-Maxwellian distribution function, the usual plasma dispersion function Z(ζ) that appears in kinetic theory or the associated plasma response function R(ζ)=1+ζZ(ζ) has to be approximated with a suitable Padé approximant in such a way that the closure is valid for all ζ values. Such closures are rare, and the original closures of Hammett and Perkins are often employed. Here we present a complete mapping of all plausible Landau fluid closures that can be constructed at the level of fourth-order moments in the gyrotropic limit and we identify the most precise closures. Furthermore, by considering 1D closures at higher-order moments, we show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing convergence of the fluid and collisionless kinetic descriptions.

Parametric Instability Driven by Weakly Trapped Particles in Nonlinear Plasma Waves

This Letter describes a new parametric instability mechanism caused by a distribution f_{T} of particles trapped in the potential wells of a wave train. The mechanism explains a nonlinear instability in Trivelpiece-Gould (TG) waves, and it could also be a destabilizing factor in a range of nearly collisionless nonlinear plasma waves. The theory is compared to particle in cell simulations of TG waves.

Parametric Instability, Inverse Cascade, and the 1/f Range of Solar-Wind Turbulence

In this paper, weak turbulence theory is used to investigate the nonlinear evolution of the parametric instability in 3D low-β plasmas at wavelengths much greater than the ion inertial length under the assumption that slow magnetosonic waves are strongly damped. It is shown analytically that the parametric instability leads to an inverse cascade of Alfvén wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfvén waves that initially satisfy e+ ≫ e-, where e+ and e- are the frequency (f) spectra of Alfvén waves propagating in opposite directions along the magnetic field lines. If e+ initially has a peak frequency f0 (at which fe+ is maximized) and an "infrared" scaling fp at smaller f with -1 < p < 1, then e+ acquires an f-1 scaling throughout a range of frequencies that spreads out in both directions from f0. At the same time, e- acquires an f-2 scaling within this same frequency range. If the plasma parameters and infrared e+ spectrum are chosen to match conditions in the fast solar wind at a heliocentric distance of 0.3 astronomical units (AU), then the nonlinear evolution of the parametric instability leads to an e+ spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed f-1 scaling at f ≳ 3 × 10-4 Hz. The results of this paper suggest that the f-1 spectrum seen by Helios in the fast solar wind at f ≳ 3 × 10-4 Hz is produced in situ by parametric decay and that the f-1 range of e+ extends over an increasingly narrow range of frequencies as r decreases below 0.3 AU. This prediction will be tested by measurements from the Parker Solar Probe.