In this paper, weak-turbulence theory is used to investigate the nonlinear evolution of the parametric instability in three-dimensional low-
$\unicodeSTIX{x1D6FD}$
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
$e^{+}\gg e^{-}$
, 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
$f_{0}$
(at which
$fe^{+}$
is maximized) and an ‘infrared’ scaling
$f^{p}$
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
$f_{0}$
. 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
$f\gtrsim 3\times 10^{-4}~\text{Hz}$
. The results of this paper suggest that the
$f^{-1}$
spectrum seen by Helios in the fast solar wind at
$f\gtrsim 3\times 10^{-4}~\text{Hz}$
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.
Spacecraft measurements show that protons undergo substantial perpendicular heating during their transit from the Sun to the outer heliosphere. In this paper, we use Helios 2 measurements to ...investigate whether stochastic heating by low-frequency turbulence is capable of explaining this perpendicular heating. We analyze Helios 2 magnetic field measurements in low- beta fast-solar-wind streams between heliocentric distances r = 0.29 AU and r = 0.64 AU to determine the rms amplitude of the fluctuating magnetic field, delta B sub(p), near the proton gyroradius scale rho sub(p). We then evaluate the stochastic heating rate Q sub(perpendicularstoch) using the measured value of delta B sub(p) and a previously published analytical formula for Q sub(perpendicularstoch). Using Helios measurements we estimate the "empirical" perpendicular heating rate (ProQuest: Formulae and/or non-USASCII text omitted) that is needed to explain the T sub(perpendicularp) profile. We find that Q sub(perpendicularstoch) ~ Q sub(perpendicularemp), but only if a key dimensionless constant appearing in the formula for Q sub(perpendicularstoch) lies within a certain range of values. This range is approximately the same throughout the radial interval that we analyze and is consistent with the results of numerical simulations of the stochastic heating of test particles in reduced magnetohydrodynamic turbulence. These results support the hypothesis that stochastic heating accounts for much of the perpendicular proton heating occurring in low- beta fast-wind streams.
Abstract In this work we analyze plasma and magnetic field data provided by the Parker Solar Probe and Solar Orbiter missions to investigate the radial evolution of the heating of Alfvénic slow wind ...by imbalanced Alfvén-wave (AW) turbulent fluctuations from 0.06 to 1 au. in our analysis we focus on slow solar-wind intervals with highly imbalanced and incompressible turbulence (i.e., magnetic compressibility C B = δ B / B ≤ 0.25, plasma compressibility C n = δ n / n ≤ 0.25, and normalized cross helicity σ c ≥ 0.65). First, we estimate the AW turbulent dissipation rate from the wave energy equation and find that the radial profile trend is similar to the proton heating rate. Second, we find that the scaling of the empirical AW turbulent dissipation rate Q W obtained from the wave energy equation matches the scaling from the phenomenological AW turbulent dissipation rate Q CH09 (with Q CH09 ≃ 1.55 Q W ) derived by Chandran & Hollweg based on the model of reflection-driven turbulence. Our results suggest that, as in the fast solar wind, AW turbulence plays a major role in the ion heating that occurs in incompressible slow-wind streams.
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.
Abstract
The Parker Solar Probe (PSP) routinely observes magnetic field deflections in the solar wind at distances less than 0.3 au from the Sun. These deflections are related to structures commonly ...called “switchbacks” (SBs), whose origins and characteristic properties are currently debated. Here, we use a database of visually selected SB intervals—and regions of solar wind plasma measured just before and after each SB—to examine plasma parameters, turbulent spectra from inertial to dissipation scales, and intermittency effects in these intervals. We find that many features, such as perpendicular stochastic heating rates and turbulence spectral slopes are fairly similar inside and outside of SBs. However, important kinetic properties, such as the characteristic break scale between the inertial to dissipation ranges differ inside and outside these intervals, as does the level of intermittency, which is notably enhanced inside SBs and in their close proximity, most likely due to magnetic field and velocity shears observed at the edges. We conclude that the plasma inside and outside of an SB, in most of the observed cases, belongs to the same stream, and that the evolution of these structures is most likely regulated by kinetic processes, which dominate small-scale structures at the SB edges.
Stochastic heating (SH) is a nonlinear heating mechanism driven by the violation of magnetic moment invariance due to large-amplitude turbulent fluctuations producing diffusion of ions toward higher ...kinetic energies in the direction perpendicular to the magnetic field. It is frequently invoked as a mechanism responsible for the heating of ions in the solar wind. Here, we quantify for the first time the proton SH rate Q at radial distances from the Sun as close as 0.16 au, using measurements from the first two Parker Solar Probe encounters. Our results for both the amplitude and radial trend of the heating rate, Q ∝ r−2.5, agree with previous results based on the Helios data set at heliocentric distances from 0.3 to 0.9 au. Also in agreement with previous results, Q is significantly larger in the fast solar wind than in the slow solar wind. We identify the tendency in fast solar wind for cuts of the core proton velocity distribution transverse to the magnetic field to exhibit a flattop shape. The observed distribution agrees with previous theoretical predictions for fast solar wind where SH is the dominant heating mechanism.
We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi ...acceleration of relativistic particles. This acceleration is not well described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In particular, we show that particle acceleration by subsonic turbulence in radiatively inefficient accretion flows can produce a non-thermal tail in the electron distribution function that is likely important for modeling and interpreting the emission from low-luminosity systems such as Sgr A* and M87.
Between the base of the solar corona at $r=r_\textrm {b}$ and the Alfvén critical point at $r=r_\textrm {A}$, where $r$ is heliocentric distance, the solar-wind density decreases by a factor $ ...\mathop > \limits_\sim 10^5$, but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to $r=r_\textrm {A}$ is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses, $\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$, $U_{\infty } \simeq v_\textrm {esc}$, and $T\simeq m_\textrm {p} v_\textrm {esc}^2/8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})$, where $\dot {M}$ is the mass outflow rate, $U_{\infty }$ is the asymptotic wind speed, $T$ is the coronal temperature, $v_\textrm {esc}$ is the escape velocity of the Sun, $\delta v_\textrm {b}$ is the fluctuating velocity at $r_\textrm {b}$, $P_\textrm {AW}$ is the power carried by outward-propagating AWs, $k_\textrm {B}$ is the Boltzmann constant, and $m_\textrm {p}$ is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux $q_\textrm {b}$ from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for $q_\textrm {b}$ by balancing conductive heating against internal-energy losses from radiation, $p\,\textrm {d} V$ work, and advection within the transition region. The density at $r_\textrm {b}$ is determined by balancing turbulent heating and radiative cooling at $r_\textrm {b}$. I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of $\dot {M}$, $U_\infty$, and $T$. Analytic and numerical solutions to the model equations match a number of observations.
We investigate the effect of ambient turbulence on the mirror and proton-cyclotron instabilities in a proton-alpha particle plasma. We perform three-dimensional hybrid simulations with ...particle-in-cell ions and a quasi-neutralizing electron fluid. The instabilities are driven by the protons with temperature perpendicular to the mean magnetic field larger than the parallel temperature. The description of these instabilities is usually based on the assumption of a uniform and stationary background. However, this assumption is violated by the ambient turbulence. In particular, the turbulent fluctuations modify the particle distribution function by making it spatially inhomogeneous and time-dependent. We compare the properties of the instabilities to the case of a uniform and stationary background and the same average temperature anisotropy and plasma beta. We find that the initial growth rates of the mirror mode are close, but the saturation level is significantly reduced when the turbulence is present. The saturation level of the proton-cyclotron mode is not affected as strongly.
Using a linear stability analysis and two- and three-dimensional nonlinear simulations, we study the physics of buoyancy instabilities in a combined thermal and relativistic (cosmic ray) plasma, ...motivated by the application to clusters of galaxies. We argue that the cosmic-ray diffusion time is likely to be long compared to the buoyancy time on large length scales, so that cosmic rays are effectively adiabatic. If the cosmic-ray pressure p cr is 25% of the thermal pressure, and the cosmic-ray 'entropy' p cr/ rho 4/3 (where rho is the thermal-plasma density) decreases outward, cosmic rays drive an adiabatic convective instability analogous to Schwarzschild convection in stars. Global simulations of galaxy cluster cores show that this instability saturates by reducing the cosmic-ray entropy gradient and driving efficient convection and turbulent mixing. At larger radii in cluster cores where cosmic-ray pressure is negligible, the thermal plasma is unstable to the heat-flux-driven buoyancy instability (HBI), a convective instability generated by anisotropic thermal conduction and a background conductive heat flux. The HBI saturates by rearranging the magnetic field lines to become largely perpendicular to the local gravitational field; the resulting turbulence also primarily mixes plasma in the perpendicular plane. Cosmic-ray-driven convection and the HBI may contribute to redistributing metals produced by Type Ia supernovae in clusters. Our calculations demonstrate that adiabatic simulations of galaxy clusters can artificially suppress the mixing of thermal plasma. When anisotropic thermal conduction is included, the buoyant response of the thermal plasma is not governed by the stable entropy gradient, and mixing (driven by mergers, cosmic ray buoyancy, etc.) is more effective. Such mixing may contribute to cosmic rays being distributed throughout the cluster volume.
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