Jean Carlos Perez

Nature of Subproton Scale Turbulence in the Solar Wind

The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. These results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

SPECTRUM OF KINETIC-ALFVEN TURBULENCE

A numerical study of strong kinetic-Alfven turbulence at scales smaller than the ion gyroscale is presented, and a phenomenological model is proposed that argues that magnetic and density fluctuations are concentrated mostly in two-dimensional structures, which leads to their Fourier energy spectra E(k ){proportional_to}k {sup -8/3} , where k is the wavevector component normal to the strong background magnetic field. The results may provide an explanation for recent observations of magnetic and density fluctuations in the solar wind at sub-proton scales.

Statistical Analysis of Current Sheets in Three-dimensional Magnetohydrodynamic Turbulence

We develop a framework for studying the statistical properties of current sheets in numerical simulations of magnetohydrodynamic (MHD) turbulence with a strong guide field, as modeled by reduced MHD. We describe an algorithm that identifies current sheets in a simulation snapshot and then determines their geometrical properties (including length, width, and thickness) and intensities (peak current density and total energy dissipation rate). We then apply this procedure to simulations of reduced MHD and perform a statistical analysis on the obtained population of current sheets. We evaluate the role of reconnection by separately studying the populations of current sheets which contain magnetic X-points and those which do not. We find that the statistical properties of the two populations are different in general. We compare the scaling of these properties to phenomenological predictions obtained for the inertial range of MHD turbulence. Finally, we test whether the reconnecting current sheets are consistent with the Sweet-Parker model.

SPECTRAL SCALING LAWS IN MAGNETOHYDRODYNAMIC TURBULENCE SIMULATIONS AND IN THE SOLAR WIND

The question is addressed as to what extent incompressible magnetohydrodynamics can describe random magnetic and velocity fluctuations measured in the solar wind. It is demonstrated that distributions of spectral indices for the velocity, magnetic field, and total energy obtained from high-resolution numerical simulations of magnetohydrodynamic turbulence are qualitatively and quantitatively similar to solar wind observations at 1?AU. Both simulations and observations show that in the inertial range the magnetic field spectrum Eb is steeper than the velocity spectrum Ev with Eb Ev and that the magnitude of the residual energy ER = Ev ? Eb decreases nearly following a k ?2 ? scaling.

TOWARD A THEORY OF ASTROPHYSICAL PLASMA TURBULENCE AT SUBPROTON SCALES

We present an analytical study of subproton electromagnetic fluctuations in a collisionless plasma with a plasma beta of the order of unity. In the linear limit, a rigorous derivation from the kinetic equation is conducted focusing on the role and physical properties of kinetic-Alfvand whistler waves. Then, nonlinear fluid-like equations for kinetic-Alfvwaves and whistler modes are derived, with special emphasis on the similarities and differences in the corresponding plasma dynamics. The kinetic-Alfvmodes exist in the lower-frequency region of phase space, ω � k⊥v Ti , where they are described by the kinetic-Alfvsystem. These modes exist both below and above the ion-cyclotron frequency. The whistler modes, which are qualitatively different from the kinetic-Alfv´ modes, occupy a different region of phase space, k⊥v Ti � ω � kzv Te , and they are described by the electron magnetohydrodynamics (MHD) system or the reduced electron MHD system if the propagation is oblique. Here, kz and k⊥ are the wavenumbers along and transverse to the background magnetic field, respectively, and v Ti and v Te are the ion and electron thermal velocities, respectively. The models of subproton plasma turbulence are discussed and the results of numerical simulations are presented. We also point out possible implications for solar-wind observations.

On Weak and Strong Magnetohydrodynamic Turbulence

Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field -->B0. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote -->k||, -->k? characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and -->b? the fluctuating field at the scale -->? ~ 1/k?. We find that when the critical balance condition, -->k||B0 ~ k?b?, is satisfied, the turbulence is strong, and the energy spectrum is -->E(k?) k?3/2?. As the -->k|| width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit -->k||B0 k?b?, the spectrum approaches -->E(k?) k?2?. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.

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.

DIRECT NUMERICAL SIMULATIONS OF REFLECTION-DRIVEN, REDUCED MAGNETOHYDRODYNAMIC TURBULENCE FROM THE SUN TO THE ALFVÉN CRITICAL POINT

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfven critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfven waves (z + fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfven waves (z – fluctuations). We present 10 simulations with different values of the correlation time and perpendicular correlation length L ⊥☉ of outward-propagating Alfven waves at the coronal base. We find that between 15% and 33% of the z + energy launched into the corona dissipates between the coronal base and Alfven critical point. Between 33% and 40% of this input energy goes into work on the solar-wind outflow, and between 22% and 36% escapes as z + fluctuations through the simulation boundary at r = r A. The z ± power spectra scale like , where k ⊥ is the wavenumber in the plane perpendicular to B 0. In our simulation with the smallest value of (~2 minutes) and largest value of L ⊥☉ (2 × 104 km), we find that α+ decreases approximately linearly with increasing ln (r), reaching a value of 1.3 at r = 11.1 R ☉. Our simulations with larger values of exhibit alignment between the contours of constant +, –, , and , where ± are the Elsasser potentials and are the outer-scale parallel Elsasser vorticities.

Drift wave instability in the Helimak experiment

Electrostatic drift wave linear stability analysis is carried out for the Helimak configuration and compared against experimental data. Density fluctuation and cross-spectrum measurements show evidence of a coherent mode propagating perpendicular to the magnetic field which becomes unstable at k⊥ρs∼0.15. By comparing the experimental results with the wave characteristic of linear two-fluid theory, this mode is identified as an unstable resistive drift wave driven by the density gradient and magnetic grad-B/curvature present in an otherwise magnetohydrodynamic stable steady-state equilibrium.

Spectrum of Weak Magnetohydrodynamic Turbulence

Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or nonbalanced, in that the energies of Alfvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy E(v) - E(b) at small field-parallel wave numbers. As a result, the energy spectra of Alfvén waves are generally not scale invariant in an inertial interval of limited extent. In the limit of an infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling E(k) proportional to k(perpendicular)(-2). The generation of a condensate is apparently related to the breakdown of mirror symmetry in nonbalanced turbulence.