Alfvenic Turbulence Research Articles

WALÉN TEST AND DE HOFFMANN-TELLER FRAME OF INTERPLANETARY LARGE-AMPLITUDE ALFVÉN WAVES

In this study, three methods of analysis are compared to test the Walen relation. Method 1 requires a good de Hoffmann-Teller ( HT) frame. Method 2 uses three components separately to find the frame that is slightly modified from Method 1. This method is intended to improve the accuracy of the HT frame and able to demonstrate the anisotropic property of the fluctuations. The better the relation is, the closer the slope of a regression fitting the data of plasma versus Alfven velocities is to 1. However, this criterion is based on an average HT frame, and the fitted slope does not always work for the Walen test because the HT frame can change so fast in the high-speed streams. We propose Method 3 to check the Walen relation using a sequence of data generated by taking the difference of two consecutive values of plasma and Alfven velocities, respectively. The difference data are independent of the HT frame. We suggest that the ratio of the variances between plasma and Alfven velocities is a better parameter to qualify the Walen relation. Four cases in two solar wind streams are studied using these three methods. Our results show that when the solar wind HT frame remains stable, all three methods can predict Alfvenic fluctuations well, but Method 3 can better predict the Walen relation when solar wind contains structures with several small streams. A simulated case also demonstrates that Method 3 is better and more robust than Methods 1 and 2. These results are important for a better understanding of Alfvenic fluctuations and turbulence in the solar wind.

POTENTIAL EVIDENCE FOR THE ONSET OF ALFVÉNIC TURBULENCE IN TRANS-EQUATORIAL CORONAL LOOPS

This study investigates Coronal Multi-channel Polarimeter Doppler-shift observations of a large, off-limb, trans-equatorial loop system observed on 2012 April 10-11. Doppler-shift oscillations with a broad range of frequencies are found to propagate along the loop with a speed of about 500 km s–1. The power spectrum of perturbations travelling up from both loop footpoints is remarkably symmetric, probably due to the almost perfect north-south alignment of the loop system. Compared to the power spectrum at the footpoints of the loop, the Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. We suggest this excess high-frequency power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvenic) turbulence.

ALFVÉN WAVE SOLAR MODEL (AWSoM): CORONAL HEATING

We present a new version of the Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics includes: (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagating waves are responsible for the nonlinear turbulent cascade. The balanced turbulence due to uncorrelated waves near the apex of the closed field lines and the resulting elevated temperatures are addressed. (3) To apportion the wave dissipation to the three temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating. (4) We have incorporated the collisional and collisionless electron heat conduction. We compare the simulated multi-wavelength EUV images of CR2107 with the observations from STEREO/EUVI and SDO/AIA instruments. We demonstrate that the reflection due to strong magnetic fields in proximity of active regions intensifies the dissipation and observable emission sufficiently.

ON QUIET-TIME SOLAR WIND ELECTRON DISTRIBUTIONS IN DYNAMICAL EQUILIBRIUM WITH LANGMUIR TURBULENCE

A recent series of papers put forth a self-consistent theory of an asymptotically steady-state electron distribution function and Langmuir turbulence intensity. The theory was developed in terms of the κ distribution which features Maxwellian low-energy electrons and a non-Maxwellian energetic power-law tail component. The present paper discusses a generalized κ distribution that features a Davydov-Druyvesteyn type of core component and an energetic power-law tail component. The physical motivation for such a generalization is so that the model may reflect the influence of low-energy electrons interacting with low-frequency kinetic Alfvenic turbulence as well as with high-frequency Langmuir turbulence. It is shown that such a solution and the accompanying Langmuir wave spectrum rigorously satisfy the balance requirement between the spontaneous and induced emission processes in both the particle and wave kinetic equations, and approximately satisfy the similar balance requirement between the spontaneous and induced scattering processes, which are nonlinear. In spite of the low velocity modification of the electron distribution function, it is shown that the resulting asymptotic velocity power-law index α, where fe ~ v –α is close to the average index observed during the quiet-time solar wind condition, i.e., whereas αaverage ~ 6.69, according to observation.

Shock acceleration of solar cosmic rays

We investigated the acceleration of solar cosmic rays (SCRs) by the shock waves produced by coronal mass ejections. We performed detailed numerical calculations of the SCR spectra produced during the shock propagation in the solar corona in terms of a model based on the diffusive transport equation using a realistic set of physical parameters for the corona. The resulting SCR energy spectrum N(e) ∝ e−γ exp [− (e/emax)α] is shown to include a power-law portion with an index γ≃2 that ends with an exponential tail with α ≃ 2.5 − β, where β is the spectral index of the background Alfven turbulence. The maximum SCR energy lies within the range emax = 1–300 MeV, depending on the shock velocity. Because of the steep spectrum of the SCRs, their backreaction on the shock structure is negligible. The decrease in the Alfven Mach number of the shock due to the increase in the Alfven velocity with heliocentric distance r causes the efficient SCR acceleration to terminate when the shock reaches a distance of r = 2–3R⊙. Since the diffusive SCR propagation in this case is faster than the shock expansion, SCR particles intensively escape from the shock vicinity. A comparison of the calculated SCR fluxes expected near the Earth’s orbit with available experimental data indicates that the theory satisfactorily explains all of the main observed features.

Combined mechanisms of solar cosmic ray acceleration

Spectra of solar cosmic rays on the Sun’s surface at a flare site and near Earth are modeled using the Monte Carlo method. Two of the most important mechanisms of energy accumulation by the particles are considered simultaneously: the regular acceleration of ions by the impulsive electric field of the current sheet and stochastic acceleration by the Alfvenic turbulence. This leads to substantial variations in the particle spectra in the low-energy region.

Intermittent dissipation and lack of universality in one-dimensional Alfvénic turbulence

Abstract The randomly driven Cohen–Kulsrud–Burgers equation is used to study the influence of viscous intermediate shocks (IS) on Alfvenic turbulence. Some of these structures are unstable and undergo gradient collapse leading, as the viscosity is reduced, to increasingly intermittent dissipation bursts. The slow decay at intermediate scales of stable IS prevents the existence of a usual inertial range. Furthermore, the dissipation is unable to adiabatically compensate for the energy injection, making the total energy sensitive to the viscosity parameter. Turbulence thus looses its universal character. Preliminary simulations extend these conclusions to magnetohydrodynamic equations with anisotropic viscosity, typical of strongly magnetized plasmas.

Modification of Proton Velocity Distributions by Alfvénic Turbulence in the Solar Wind

In the present paper, the proton velocity distribution function (VDF)in the solar wind is determined by solving numerically the kinetic evolution equation. We compare the results obtained when considering the effects of ex- ternal forces and Coulomb collisions with those obtained by adding effects of Alfven wave turbulence. We use Fokker-Planck diffusion terms due to Alfvenic turbulence, which take into account observed turbulence spectra and kinetic effects of finite proton gyroradius. Assuming a displaced Maxwellian for the proton VDF at the simulation boundary at 14 solar radii, we show that the turbulence leads to a fast (within several solar radii) development of the anti-sunward tail in the proton VDF. Our results provide a natural explanation for the nonthermal tails in the proton VDFs, which are often observed in-situ in the solar wind beyond 0.3 AU.

PARALLEL ELECTRIC FIELD SPECTRUM OF SOLAR WIND TURBULENCE

By searching through more than 10 satellite-years of THEMIS and Cluster data, three reliable examples of parallel electric field turbulence in the undisturbed solar wind have been found. The perpendicular and parallel electric field spectra in these examples have similar shapes and amplitudes, even at large scales (frequencies below the ion gyroscale) where Alfvenic turbulence with no parallel electric field component is thought to dominate. The spectra of the parallel electric field fluctuations are power laws with exponents near -5/3 below the ion scales (~ 0.1 Hz), and with a flattening of the spectrum in the vicinity of this frequency. At small scales (above a few Hz), the spectra are steeper than -5/3 with values in the range of -2.1 to -2.8. These steeper slopes are consistent with expectations for kinetic Alfven turbulence, although their amplitude relative to the perpendicular fluctuations is larger than expected.

KINETIC ALFVÉN TURBULENCE AND PARALLEL ELECTRIC FIELDS IN FLARE LOOPS

This study investigates the spectral structure of the kinetic Alfven turbulence in the low-beta plasmas. We consider a strong turbulence resulting from collisions between counterpropagating wavepackets with equal energy. Our results show that (1) the spectra of the magnetic and electric field fluctuations display a transition at the electron inertial length scale, (2) the turbulence cascades mainly toward the magnetic field direction as the cascade scale is smaller than the electron inertial length, and (3) the parallel electric field increases as the turbulent scale decreases. We also show that the parallel electric field in the solar flare loops can be 10(2)-10(4) times the Dreicer field as the turbulence reaches the electron inertial length scale.

Evidence of Kinetic Alfvén Waves in the Solar Wind at 1 AU

Several independent lines of observational evidence of the existence of kinetic Alfven waves (KAWs) in the solar wind are briefly reviewed. Each piece of evidence is inconclusive when considered separately, but when taken together, it is reasonable to conclude from these observations that KAWs in the form of kinetic Alfven turbulence are almost always present in the free-flowing solar wind near 1 AU and, by inference, perhaps throughout much of the heliosphere.

Joint acceleration mechanisms for solar cosmic rays

Using Monte Carlo method we have simulated solar cosmic ray spectra (3He, 4He, O and Fe) at the flare site and at the Earth. It is shown that besides stochastic acceleration by Alfvenic turbulence an impulsive electric field of the current sheet significantly affects the ion energy spectra at low energies. Both mechanisms could explain some peculiarities in the energy spectra of heavy ions observed in experiments onboard ACE.

Magnetic turbulence suppression by a helical mode in a cylindrical geometry

To study processes involved in a helical structure formation in reversed field pinch devices, the scaling of a turbulent boundary layer width associated with a vortex structure having large shears of magnetic field and flow is obtained for reduced magnetohydrodynamics. The coherent vortex, with its flow and magnetic shears, interacts with Alfvén turbulence, forming a turbulent boundary layer at the edge of the vortex. The layer arises from the balance between turbulence diffusion rates and shearing rates and suppresses the turbulence in the structure. The suppression of turbulence impedes relaxation of the coherent vortex profiles, leading to long coherence times. The scaling of the boundary layer width reveals that both magnetic shear and flow shear can effectively suppress magnetic turbulence.

Co-existence of whistler waves with kinetic Alfven wave turbulence for the high-beta solar wind plasma

It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore, in the high-beta solar wind plasma, whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently, the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave (KAW) turbulence creates a plateau by quasilinear (QL) diffusion in the solar wind electron distribution at small velocities. It is found that for whistler energy density of only ∼10−3 that of the kinetic Alfven waves, the quasilinear diffusion rate due to whistlers is comparable to KAW. Thus, very small amplitude whistler turbulence can have a significant consequence on the evolution of the solar wind electron distribution function.

SELF-CONSISTENT MODEL OF THE INTERSTELLAR PICKUP PROTONS, ALFVÉNIC TURBULENCE, AND CORE SOLAR WIND IN THE OUTER HELIOSPHERE

A self-consistent model of the interstellar pickup protons, the slab component of the Alfvenic turbulence, and core solar wind (SW) protons is presented for r ≥ 1 along with the initial results of and comparison with the Voyager 2 (V2) observations. Two kinetic equations are used for the pickup proton distribution and Alfvenic power spectral density, and a third equation governs SW temperature including source due to the Alfven wave energy dissipation. A fraction of the pickup proton free energy, fD , which is actually released in the waveform during isotropization, is taken from the quasi-linear consideration without preexisting turbulence, whereas we use observations to specify the strength of the large-scale driving, C sh, for turbulence. The main conclusions of our study can be summarized as follows. (1) For C sh 1-1.5 and fD 0.7-1, the model slab component agrees well with the V2 observations of the total transverse magnetic fluctuations starting from ~8 AU. This indicates that the slab component at low-latitudes makes up a majority of the transverse magnetic fluctuations beyond 8-10 AU. (2) The model core SW temperature agrees well with the V2 observations for r 20 AU if fD 0.7-1. (3) A combined effect of the Wentzel-Kramers-Brillouin attenuation, large-scale driving, and pickup proton generated waves results in the energy sink in the region r 10 AU, while wave energy is pumped in the turbulence beyond 10 AU. Without energy pumping, the nonlinear energy cascade is suppressed for r 10 AU, supplying only a small energy fraction into the k-region of dissipation by the core SW protons. A similar situation takes place for the two-dimensional turbulence. (4) The energy source due to the resonant Alfven wave damping by the core SW protons is small at heliocentric distances r 10 AU for both the slab and the two-dimensional turbulent components. As a result, adiabatic cooling mostly controls the model SW temperature in this region, and the model temperature disagrees with the V2 observations in the region r 20 AU.

Density Fluctuation Spectrum of Solar Wind Turbulence between Ion and Electron Scales

We present a measurement of the spectral index of density fluctuations between ion and electron scales in solar wind turbulence using the EFI instrument on the ARTEMIS spacecraft. The mean spectral index at 1AU was found to be -2.75±0.06, steeper than predictions for pure whistler or kinetic Alfvén wave turbulence but consistent with previous magnetic field measurements. The steep spectra are also consistent with expectations of increased intermittency or damping of some of the turbulent energy over this range of scales. Neither the spectral index nor the flattening of the density spectra before ion scales were found to depend on the proximity to the pressure anisotropy instability thresholds, suggesting that they are features inherent to the turbulent cascade.

Basic properties of magnetohydrodynamic turbulence in the inertial range

We revisit the issue of spectral slope of MHD turbulence in the inertial range and argue that numerics favor Goldreich-Sridhar -5/3 slope rather than -3/2 slope. We also did precision measurements of anisotropy of MHD turbulence and determined the anisotropy constant C_A=0.34 of Alfvenic turbulence. Together with previously measured Kolmogorov constant C_K=4.2, or 3.3 for purely Alfvenic case, it constitutes a full description of MHD cascade in terms of spectral quantities, which is of high practical value for astrophysics.

ON THE OCCURRENCE OF THE THIRD-ORDER SCALING IN HIGH LATITUDE SOLAR WIND

The occurrence and nature of a nonlinear energy cascade within the intermediate scales of solar wind Alfvenic turbulence represents an important open issue. Using in situ measurements of fast, high latitude solar wind taken by the Ulysses spacecraft at solar minima, it is possible to show that a nonlinear energy cascade of imbalanced turbulence is only observed when the solar wind owns peculiar properties. These are the reduction of the local correlation between velocity and magnetic field (weak cross-helicity); the presence of large-scale velocity shears; and the steepening and extension down to low frequencies of the turbulent spectra. Our observations suggest the important role of both large-scale velocity and Alfvenicity of the field fluctuations for the validation of the Yaglom law in solar wind turbulence.

TESTING A PREDICTIVE THEORETICAL MODEL FOR THE MASS LOSS RATES OF COOL STARS

The basic mechanisms responsible for producing winds from cool, late-type stars are still largely unknown. We take inspiration from recent progress in understanding solar wind acceleration to develop a physically motivated model of the time-steady mass loss rates of cool main-sequence stars and evolved giants. This model follows the energy flux of magnetohydrodynamic turbulence from a subsurface convection zone to its eventual dissipation and escape through open magnetic flux tubes. We show how Alfven waves and turbulence can produce winds in either a hot corona or a cool extended chromosphere, and we specify the conditions that determine whether or not coronal heating occurs. These models do not utilize arbitrary normalization factors, but instead predict the mass loss rate directly from a star's fundamental properties. We take account of stellar magnetic activity by extending standard age-activity-rotation indicators to include the evolution of the filling factor of strong photospheric magnetic fields. We compared the predicted mass loss rates with observed values for 47 stars and found significantly better agreement than was obtained from the popular scaling laws of Reimers, Schroeder, and Cuntz. The algorithm used to compute cool-star mass loss rates is provided as a self-contained and efficient computer code. We anticipate that the results from this kind of model can be incorporated straightforwardly into stellar evolution calculations and population synthesis techniques.

RESIDUAL ENERGY IN MAGNETOHYDRODYNAMIC TURBULENCE

There is mounting evidence in solar wind observations and in numerical simulations that kinetic and magnetic energies are not in equipartition in magnetohydrodynamic turbulence. The origin of their mismatch, the residual energy E_r=E_v-E_b, is not well understood. In the present work this effect is studied analytically in the regime of weak magnetohydrodynamic turbulence. We find that residual energy is spontaneously generated by turbulent dynamics, and it has a negative sign, in good agreement with the observations. We obtain that the residual energy condenses around k_||=0 with its k_||-spectrum broadening linearly with k_perp, where k_|| and k_perp are the wavenumbers parallel and perpendicular to the background magnetic field, and the field-perpendicular spectrum of the residual energy has the scaling E_r(k_perp)\propto k_perp^{-1} in the inertial interval. These results are found to be in agreement with numerical simulations. We propose that residual energy plays a fundamental role in Alfvenic turbulence and it should be taken into account for correct interpretation of observational and numerical data.