Cross-scale nonlinear coupling and plasma energization by Alfvén waves

We present a new channel for the nonlocal transport of wave energy from the large (MHD) scales to the small (kinetic) scales generated by the resonant decay of MHD Alfvén waves into kinetic Alfvén waves. This process does not impose any restriction on the wave numbers or frequencies of initial MHD waves, which makes it superior compared to the mechanisms of spectral transport studied before. Because of dissipative properties of the nonlinearly driven kinetic Alfvén waves, the decay leads to plasma heating and particle acceleration, which is observed in a variety of space and astrophysical plasmas. Two examples in the solar corona and the terrestrial magnetosphere are briefly discussed.     

Compressible sub-Alfvénic MHD turbulence in low-beta plasmas

We present a model for compressible sub-Alfvénic isothermal magnetohydrodynamic (MHD) turbulence in low- beta plasmas and numerically test it. We separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that production of slow and fast modes by Alfvénic turbulence is suppressed. As a result, Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.     

Three dimensional anisotropic κ spectra of turbulence at subproton scales in the solar wind

We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales. We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs. We show that the cascade is carried by highly oblique kinetic Alfvén waves with ω(plas) ≤ 0.1ω(ci) down to k(⊥) ρ(i)～2. Each k spectrum in the direction perpendicular to B0 shows two scaling ranges separated by a breakpoint (in the interval [0.4,1]k(⊥)ρ(i): a Kolmogorov scaling k(⊥)?1?? followed by a steeper scaling ～k(⊥)????. We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate.     

Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.     

Spectral energy dynamics in magnetohydrodynamic turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024(3) collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E(R)k=|E(M)k - E(K)k|, and total energy, Ek=E(K)k+E(M)k, are observed to scale self-similarly in the inertial range as E(R)k approximately k(-7/3), E(k)approximately k(-5/3) (isotropic case) and E(R)(k(perpendicular) approximately k(-2)(perpendicular), E(k(perpendicular))approximately k(-3/2)(perpendicular) (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields E(R)k approximately kE2(k), which is confirmed by the simulations.     

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.     

Spectral slope and Kolmogorov constant of MHD turbulence

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While the Goldreich-Sridhar model predicts a -5/3 slope, shallower slopes have been observed in numerics. We argue that earlier numerics were affected by driving due to a diffuse locality of energy transfer. Our highest-resolution simulation (3072(2)×1024) exhibited the asymptotic -5/3 scaling. We also discover that the dynamic alignment, proposed in models with -3/2 slope, saturates and cannot modify the asymptotic, high Reynolds number slope. From the observed -5/3 scaling we measure the Kolmogorov constant C(KA)=3.27±0.07 for Alfvénic turbulence and C(K)=4.2±0.2 for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger C(K) indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.     

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.     

低频Alfvén波对等离子体非共振加热与随机加热的粒子模拟

采用粒子模拟方法,研究沿背景磁场方向传播的低频Alfvén波对磁化等离子体加热的物理过程.模拟结果表明:离子在垂直和平行于背景磁场的方向都得到明显的加热,在非共振加热阶段,垂直方向比平行方向的加热效果更加显著,形成温度各向异性;在随机加热阶段,垂直和平行方向的温度最终达到饱和且趋于一致.加热过程中,离子所获得动力学温度的最大值由外加磁场能量密度与等离子体密度的比值决定,与Alfvén波的频率及振幅无关;离子在平行于背景磁场方向上被加速,并最终获得相当于Alfvén波相速度大小的流速.     

Evidence of diffusion regions at a subsolar magnetopause crossing

On 1 April 2001, the Polar satellite crossed a subsolar magnetopause associated with antiparallel magnetic fields. Over a width approximately 6 magnetosheath ion skin depths (approximately 3 magnetospheric ion skin depths), perpendicular ion flows different from E x B/B(2) as well as Hall magnetic and electric field signatures were observed. At a smaller scale, the electron flow decoupled from the magnetic field near a deep minimum in the magnetic field strength. Separatrices were identified as boundaries of low frequency electric field turbulence associated with density minima and parallel electric fields. The reconnection rate was less than 2% of the asymptotic Alfvén speed.     

Anisotropy of imbalanced Alfvénic turbulence in fast solar wind

We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The subdominant mode is anisotropic throughout. There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfvén ratio and the different scaling of the Elsasser modes suggests an interpretation of the observed discrepancy between the velocity and magnetic field scalings, the total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.     

Spectrum of magnetohydrodynamic turbulence

We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached; it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of shear-Alfvén fluid and magnetic-field fluctuations at each scale lambda become effectively aligned within the angle phi(lambda) proportional to lambda (1/4), which leads to scale-dependent depletion of the nonlinear interaction and to the field-perpendicular energy spectrum E(k(perpendicular)) proportional to k(perpendicular)(-3/2). Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.     

Mode conversion and anomalous transport in Kelvin-Helmholtz vortices and kinetic Alfvén waves at the Earth's magnetopause

Observations at the Earth's magnetopause identify mode conversion from surface to kinetic Alfvén waves at the Alfvén resonance. Kinetic Alfvén waves radiate into the magnetosphere from the resonance with parallel scales up to the order of the geomagnetic field-line length and spectral energy densities obeying a k(perpendicular)(-2.4) power law. Amplitudes at the Alfvén resonance are sufficient to both demagnetize ions across the magnetopause and provide field-aligned electron bursts. These waves provide diffusive transport across the magnetopause sufficient for boundary layer formation.     

The turbulent Alfvénic aurora

It is demonstrated from observations that the Alfvénic aurora may be powered by a turbulent cascade transverse to the geomagnetic field from large MHD scales to small Alfvén wave scales of several electron skin depths and less. We show that the energy transport through the cascade is sufficient to drive the observed acceleration of electrons from near-Earth space to form the aurora. We find that regions of Alfvén wave dissipation, and particle acceleration, are localized or intermittent and embedded within a near-homogeneous background of large-scale MHD structures.     

柱等离子体中磁流体力学波之间的耦合

采用柱螺旋坐标系 ,把广义磁流体力学方程组简化为四元一阶微分方程组。在ω/ωci→ 0时 ,该方程组化为Hain L櫣ｓｔ方程 ;而当p→ 0 时 ,即是KAppert理论。在这两种情况下 ,Alfv啨ｎ波共振层都是奇异的。Alfv啨ｎ波共振层的奇异性来源于极限的选取谠独爰薜那?,离子的惯性会使理想磁流体中Alfv啨ｎ波共振层的奇异性消失 ,且使磁流体力学波之间相互耦合     

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Energy spectra stemming from interactions of Alfvén waves and turbulent eddies

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 1536{3} points. The Taylor Reynolds number at the maximum of dissipation is approximately 1100, and the initial condition is a superposition of large-scale Arn'old-Beltrami-Childress flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k{perpendicular}{-2} spectrum, the perpendicular direction referring to the local quasiuniform magnetic field.     

Critically balanced ion temperature gradient turbulence in fusion plasmas

Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three?dimensional.     

Measurement of the B0-->phiK*0 decay amplitudes

With a sample of about 227x10(6) BB pairs recorded with the BABAR detector we perform a full angular analysis of the decay B0-->phiK(*0)(892). We make novel measurements of five parameters sensitive to CP violation. We also measure the branching fraction to be (9.2+/-0.9+/-0.5)x10(-6) and determine the fractions of longitudinal and parity-odd transverse contributions as f(L)=0.52+/-0.05+/-0.02 and f( perpendicular)=0.22+/-0.05+/-0.02. The phases of the parity-even and parity-odd transverse amplitudes relative to the longitudinal amplitude are found to be phi( parallel)=2.34(+0.23)(-0.20)+/-0.05 rad and phi( perpendicular)=2.47+/-0.25+/-0.05 rad. We also observe the decay B0-->phiK(*0)(1430).