Mediation of collisionless turbulent dissipation through cyclotron resonance.

The dissipation of turbulence in astrophysical systems is fundamental to energy transfer and heating in environments ranging from the solar wind and corona to accretion disks and the intracluster medium. Although turbulent dissipation is relatively well understood in fluid dynamics, astrophysical plasmas often exhibit exotic behaviour, arising from the lack of interparticle collisions, which complicates turbulent dissipation and heating in these systems. Recent observations by NASA's Parker Solar Probe mission in the inner heliosphere have shed new light on the role of ion cyclotron resonance as a potential candidate for turbulent dissipation and plasma heating. Here, using in situ observations of turbulence and wave populations, we show that ion cyclotron waves provide a major pathway for dissipation and plasma heating in the solar wind. Our results support recent theoretical predictions of turbulence in the inner heliosphere, known as the helicity barrier, that suggest a role of cyclotron resonance in ion-scale dissipation. Taken together, these results provide important constraints for turbulent dissipation and acceleration efficiency in astrophysical plasmas.

Erratum: In situ Signature of Cyclotron Resonant Heating in the Solar Wind [Phys. Rev. Lett. 129, 165101 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.129.165101.

In Situ Signature of Cyclotron Resonant Heating in the Solar Wind.

The dissipation of magnetized turbulence is an important paradigm for describing heating and energy transfer in astrophysical environments such as the solar corona and wind; however, the specific collisionless processes behind dissipation and heating remain relatively unconstrained by measurements. Remote sensing observations have suggested the presence of strong temperature anisotropy in the solar corona consistent with cyclotron resonant heating. In the solar wind, in situ magnetic field measurements reveal the presence of cyclotron waves, while measured ion velocity distribution functions have hinted at the active presence of cyclotron resonance. Here, we present Parker Solar Probe observations that connect the presence of ion-cyclotron waves directly to signatures of resonant damping in observed proton-velocity distributions using the framework of quasilinear theory. We show that the quasilinear evolution of the observed distribution functions should absorb the observed cyclotron wave population with a heating rate of 10^{-14} W/m^{3}, indicating significant heating of the solar wind.

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.

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence.

We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 A.U., with a power-law index of around -4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén 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-ß 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.

Stochastic proton heating by kinetic-Alfvén-wave turbulence in moderately high-ß plasmas.

Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are much smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the heating of the solar wind. Using phenomenological arguments, we derive the stochastic-proton-heating rate in plasmas in which ß p ∼ 1 - 30, where ß p is the ratio of the proton pressure to the magnetic pressure. (We do not consider the ß p ≳ 30 regime, in which KAWs at the proton gyroscale become non-propagating.) We test our formula for the stochastic-heating rate by numerically tracking test-particle protons interacting with a spectrum of randomly phased AWs and KAWs. Previous studies have demonstrated that at ß p ≲1, particles are energized primarily by time variations in the electrostatic potential and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the electrostatic potential. In contrast, at ß p ≳ 1, particles are energized primarily by the solenoidal component of the electric field and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the magnetic field.

Weakly turbulent magnetohydrodynamic waves in compressible low-beta plasmas.

In this Letter, weak-turbulence theory is used to investigate interactions among Alfvén waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of magnetohydrodynamics, and extra terms are then added to model collisionless damping. These equations are used to provide a quantitative description of a variety of nonlinear processes, including parallel and perpendicular energy cascade, energy transfer between wave types, "phase mixing," and the generation of backscattered Alfvén waves.

Weak compressible magnetohydrodynamic turbulence in the solar corona.

This Letter presents a calculation of the power spectra of weakly turbulent Alfvén waves and fast magnetosonic waves ("fast waves") in low- plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfvén waves. High-frequency waves produced by MHD turbulence are a promising explanation for the anisotropic heating of minor ions in the solar corona.

Divergence of neighboring magnetic-field lines and fast-particle diffusion in strong magnetohydrodynamic turbulence, with application to thermal conduction in galaxy clusters.

Using direct numerical simulations, we calculate the rate of divergence of neighboring magnetic-field lines in different types of strong magnetohydrodynamic turbulence. In the static-magnetic-field approximation, our results imply that tangled magnetic fields in galaxy clusters reduce the electron diffusion coefficient and thermal conductivity by a factor of approximately 5-10, relative to their values in a nonmagnetized plasma.