Showing papers by "Gregory G. Howes published in 2009"

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas

Abstract: This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the inertial range above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvenic fluctuations and a passive cascade of density and magnetic-field-strength fluctuations. The former are governed by the reduced magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvenic component (in the collisional limit, these compressive fluctuations become the slow and entropy modes of the conventional MHD). In the dissipation range below ion gyroscale, there are again two cascades: the kinetic-Alfven-wave (KAW) cascade governed by two fluid-like electron reduced magnetohydrodynamic (ERMHD) equations and a passive cascade of ion entropy fluctuations both in space and velocity. The latter cascade brings the energy of the inertial-range fluctuations that was Landau-damped at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.

Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind.

Abstract: The proton temperature anisotropy in the solar wind is known to be constrained by the theoretical thresholds for pressure-anisotropy-driven instabilities. Here, we use approximately 1x10;{6} independent measurements of gyroscale magnetic fluctuations in the solar wind to show for the first time that these fluctuations are enhanced along the temperature anisotropy thresholds of the mirror, proton oblique firehose, and ion cyclotron instabilities. In addition, the measured magnetic compressibility is enhanced at high plasma beta (beta_{ parallel} greater, similar1) along the mirror instability threshold but small elsewhere, consistent with expectations of the mirror mode. We also show that the short wavelength magnetic fluctuation power is a strong function of collisionality, which relaxes the temperature anisotropy away from the instability conditions and reduces correspondingly the fluctuation power.

Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence

Abstract: Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

Constraining low-frequency alfvénic turbulence in the solar wind using density-fluctuation measurements

Abstract: One proposed mechanism for heating the solar wind, from close to the Sun to beyond approx10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because small-scale oblique Alfven waves (kinetic Alfven waves, KAWs) are compressive, the measured density fluctuations in the solar wind place an upper limit on the amplitude of KAWs and hence an upper limit on the rate at which the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate this upper limit for both coronal holes at 5 R{sub sun} and the near-Earth solar wind. At both locations, the upper limit we find is consistent with models in which the solar wind is heated by low-frequency Alfvenic turbulence. At 1 AU, the upper limit on the turbulent heating rate derived from the measured density fluctuations is within a factor of 2 of the measured solar-wind heating rate. Thus, if low-frequency Alfvenic turbulence is the primary mechanism for heating the near-Earth solar wind, KAWs must be one of the dominant sources of solar-wind density fluctuations at frequencies approx1 Hz. We also present a simple argument for why density-fluctuation measurements do appear to rule out models in which coronal holes are heated by non-turbulent high-frequency waves ('sweeping'), but aremore » compatible with heating by low-frequency Alfvenic turbulence.« less

Constraining Low-Frequency Alfvenic Turbulence in the Solar Wind Using Density Fluctuation Measurements

Abstract: One proposed mechanism for heating the solar wind, from close to the sun to beyond 10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because small-scale oblique Alfven waves (kinetic Alfven waves) are compressive, the measured density fluctuations in the solar wind place an upper limit on the amplitude of kinetic Alfven waves and hence an upper limit on the rate at which the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate this upper limit for both coronal holes at 5 solar radii and in the near-Earth solar wind. At both radii, the upper limit we find is consistent with models in which the solar wind is heated by low-frequency Alfvenic turbulence. At 1 AU, the upper limit on the turbulent heating rate derived from the measured density fluctuations is within a factor of 2 of the measured solar wind heating rate. Thus if low-frequency Alfvenic turbulence contributes to heating the near-Earth solar wind, kinetic Alfven waves must be one of the dominant sources of solar wind density fluctuations at frequencies of order 1 Hz. We also present a simple argument for why density fluctuation measurements do appear to rule out models in which the solar wind is heated by non-turbulent high-frequency waves ``sweeping'' through the ion-cyclotron resonance, but are compatible with heating by low-frequency Alfvenic turbulence.

Steep, transient density gradients in the Martian ionosphere similar to the ionopause at Venus

Abstract: [1] With the Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on the Mars Express (MEX) spacecraft, the electron density can be measured by two methods: from the excitation of local plasma oscillations and from remote sounding. A study of the local electron density versus time for 1664 orbits revealed that in 132 orbits very sharp gradients in the electron density occurred that are similar to the ionopause boundary commonly observed at Venus. In 40 of these cases, remote sounding data have also confirmed identical locations of steep ionopause-like density gradients. Measurements from the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) electron spectrometer and ion mass analyzer instruments (also on Mars Express) verify that these sharp decreases in the electron density occur somewhere between the end of the region where ionospheric photoelectrons are dominant and the magnetosheath. Combined studies of the two experiments reveal that the steep density gradients define a boundary where the magnetic fields change from open to closed. This study shows that, although the individual cases are from a wide range of altitudes, the average altitude of the boundary as a function of solar zenith angle is almost constant. The average altitude is approximately 500 km up to solar zenith angles of 60°, after which it shows a slight increase. The average thickness of the boundary is about 22 km according to remote sounding measurements. The altitude of the steep gradients shows an increase at locations with strong crustal magnetic fields.

The turbulent heating rate in strong magnetohydrodynamic turbulence with nonzero cross helicity

Abstract: Different results for the cascade powerin strong, incompressible magnetohydrodynamic turbulence with nonzero cross helicity appear in the literature. In this paper, we discuss the conditions under which these different results are valid. Our conclusions can be expressed in terms of the density ρ, the rms amplitudes z + and z − of Alfv´ fluctuations propagating parallel and antiparallel to the background magnetic field B0, and the correlation length (outer scale) measured perpendicular to B0, denoted L⊥. We argue that if z + � z − and if the z − fluctuations are sustained by the reflection of z + fluctuations in a strong background magnetic field, then � ∼ ρ(z + ) 2 z − /L⊥ as in previous studies by Hossain, Matthaeus, Dmitruk, Lithwick, Goldreich, Sridhar, and others. On the other hand, if the minority wave type (z − ) is sustained by some form of forcing that is uncorrelated with or only weakly correlated with the z + fluctuations, thencan be much less than ρ(z + ) 2 z − /L⊥, as in previous studies by Dobrowolny, Lazarian, Chandran, and others. The mechanism for generating the minority wave type strongly affects the cascade power because it controls the coherence time for interactions between oppositely directed wave packets at the outer scale.

Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas

Abstract: . The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range of the solar wind must be one, or a mixture, of three electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic Alfven waves. These modes are generally well described by Hall MHD. Determining the applicability of linear kinetic damping rates in turbulent plasmas requires a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid and kinetic simulations will also shed light on whether the presence of spurious wave modes alters the nonlinear couplings inherent in turbulence and will illuminate the turbulent dynamics and energy transfer in the regime of the characteristic ion kinetic scales.

Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas

Abstract: The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range of the solar wind must be one, or a mixture, of three electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic Alfven waves. These modes are generally well described by Hall MHD. Determining the applicability of linear kinetic damping rates in turbulent plasmas requires a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid and kinetic simulations will also shed light on whether the presence of spurious wave modes alters the nonlinear couplings inherent in turbulence and will illuminate the turbulent dynamics and energy transfer in the regime of the characteristic ion kinetic scales.

The Turbulent Heating Rate in Strong MHD Turbulence with Nonzero Cross Helicity

Abstract: Different results for the cascade power in strong, incompressible MHD turbulence with nonzero cross helicity appear in the literature. In this paper, we discuss the conditions under which these different results are valid. We define z+ to be the rms amplitude of Alfven waves propagating parallel to the background magnetic field, and z- to be the rms amplitude of Alfven waves propagating anti-parallel to the background magnetic field. Nonzero cross helicity implies that z+ and z- differ, and we take z- to be less than z+. We find that the mechanism that generates the z- fluctuations strongly affects the cascade power, because it controls the coherence time for interactions between oppositely directed wave packets at the outer scale. In particular, for fixed values of z+ and z-, the cascade power is in many cases larger when the z- fluctuations are generated by the reflection of z+ fluctuations than when the z- fluctuations are generated by forcing that is only weakly correlated with the z+ fluctuations.

Helicity signatures in the dissipation range of solar wind turbulence

Abstract: Measurements of small-scale turbulent fluctuations in the solar wind find a non-zero right-handed magnetic helicity. This has been interpreted as evidence for the importance of ion cyclotron damping. However, theoretical and empirical evidence suggests that the majority of the energy in solar wind turbulence resides in low frequency anisotropic kinetic Alfven wave fluctuations that are not subject to ion cyclotron damping. We demonstrate that a dissipation range comprised of kinetic Alfven waves also produces a net right-handed fluctuating magnetic helicity signature consistent with observations. Thus, the observed magnetic helicity signature does not imply that ion cyclotron damping is energetically important in the solar wind.