Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfvén waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfvén waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.     

Decay instability of kinetic Alfvén waves in preflare plasmas of the loops in active solar regions

We examine the physical conditions for the origin of the decay instability of kinetic Alfvén waves in loop plasmas at the early flare stages. The synchronism conditions are used to derive a modified expression for the nonlinear growth rate of the process of the decay of the primary kinetic Alfvén wave (KAW) into an ion-acoustic wave and a secondary KAW. The threshold amplitude of the primary KAW is calculated in units of the background magnetic field strength in the chromospheric section of loop current circuit.     

太阳大气中动力学阿尔文波的产生与加热研究进展

动力学阿尔文波是垂直波长接近离子回旋半径或者电子惯性长度的色散阿尔文波.由于波的尺度接近粒子的动力学尺度,动力学阿尔文波在太阳和空间等离子体加热、加速等能化现象中起重要作用.因此,动力学阿尔文波通常被认为是日冕加热的候选者.本研究工作深入、系统地调研了太阳大气中动力学阿尔文波的激发和耗散机制.基于日冕等离子体环境,介绍了几种常见的动力学阿尔文波激发机制:温度各向异性不稳定性、场向电流不稳定性、电子束流不稳定性、密度非均匀不稳定性以及共振模式转换.还介绍了太阳大气中动力学阿尔文波的耗散机制,并讨论了这些耗散机制对黑子加热、冕环加热以及冕羽加热的影响.不仅为认识太阳大气中动力学阿尔文波的驱动机制、动力学演化特征以及波粒相互作用提供合理的理论依据,而且有助于揭示日冕等离子体中能量储存和释放、粒子加热等能化现象的微观物理机制.     

On the storage of high-energy protons in the solar corona: The cyclotron instability

We consider the problem of long-time storage of high-energy protons, accelerated in the process of a flare, in coronal magnetic traps. From the viewpoint of the storage, one of the most important plasma instabilities is the kinetic cyclotron instability of the Alfvén waves. We carry out a detailed theoretical analysis of the instability for typical conditions of the solar corona. It is the refraction of the Alfvén waves in combination with a drastic decrease of the instability growth rate with an increase of the angle between the directions of the wave vector and the stationary magnetic field that leads to the possibility of the long-term storage of the flare protons. Sufficient conditions of the storage are determined.     

Kinetic Alfvén waves on auroral field lines

Several observations near moving arcs require particle acceleration in nonstationary electric fields. We suggest that kinetic Alfvén waves play a significant role in the acceleration process. The characteristic properties of kinetic Alfvén waves are summarized and the Hasegawa and Mima (1976) solitary kinetic Alfvén waves are described. The resonant coupling of large-scale surface waves to the kinetic Alfvén wave is discussed. Finally, we show that kinetic Alfvén waves can reasonably well explain the observations of what has hence been called “electrostatic” shocks.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transfer of Energy, Potential, and Current by Alfvén Waves in Solar Flares

Alfvén waves play three related roles in the impulsive phase of a solar flare: they transport energy from a generator region to an acceleration region; they map the cross-field potential (associated with the driven energy release) from the generator region onto the acceleration region; and within the acceleration region they damp by setting up a parallel electric field that accelerates electrons and transfers the wave energy to them. The Alfvén waves may also be regarded as setting up new closed-current loops, with field-aligned currents that close across field lines at boundaries. A model is developed for large-amplitude Alfvén waves that shows how Alfvén waves play these roles in solar flares. A picket-fence structure for the current flow is incorporated into the model to account for the “number problem” and the energy of the accelerated electrons.     

Parametric generation of acoustic-gravity waves by Alfvén waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere permeated by a uniform magnetic field directed against the action of gravity, we investigate the parametric generation of acoustic-gravity disturbances by Alfvén waves propagating along the corresponding field lines. We established that for a weak linear coupling of Alfvén waves, the nonlinear interaction of Alfvén waves propagating in opposite directions (rather than in the same direction) is the predominant generation mechanism of acoustic-gravity disturbances at the difference frequency. In this case, no acoustic flow (wind) was found to emerge at a zero difference frequency in the acoustic-gravity field.     

Generation of low-frequency magnetic field disturbances in coronal loops by proton and electron beams

We consider the generation of low-frequency magnetic field disturbances in coronal loops when low density proton and electron beams propagate in them. Two mechanisms of low-frequency magnetic field perturbation generation are analyzed. The first mechanism is concerned with the longitudinal current generated by charged particles’ beams moving in the loop. It is shown that this mechanism of the Alfvén waves’ generation can lead to development of low-frequency perturbations even if the currents are very weak. It can facilitate the reconnection of magnetic fields and flare development. The second mechanism is not concerned with currents propagating in the coronal loop. It is shown that, in this case, the proton beams can cause an instability with significantly lower values of beam density. We found increments and criteria of the development of instabilities. Not only Alfvén-type perturbations can be generated as a result of development of those instabilities but also kinetic Alfvén-type perturbations can be generated.     

The problem of phase mixed shear Alfvén waves in the solar corona revisited

The problem of phase mixing of shear Alfvén waves is revisited taking into account dissipative phenomena specific for the solar corona. In regions of space plasmas where the dynamics is controlled by the magnetic field, transport coefficients become anisotropic with transport mechanism having different behavior and magnitude depending on the orientation with respect to the ambient magnetic field. Taking into account realistic values for dissipative coefficients we obtain that the previous results derived in context of torsional Alfvén wave phase mixing are actually heavily underestimated so phase mixing cannot be used to explain the damping of torsional Alfvén waves and heating of open coronal structures. The presented results indicate that in order for phase mixing to still be a viable mechanism to explain heating or wave damping unrealistic assumptions have to be made. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Excess heating of corona and chromosphere above magnetic regions by non-linear Alfvén waves

Excess heating of the active region solar atmosphere is interpreted by the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction of this large flux is propagated out to the corona, and a large velocity amplitude exceeding the local Alfvén velocity is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves gets involved in such a case with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formulation for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alvén waves will eventually be thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of thus produced slow-mode waves may provide means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, with higher density as a consequence of increased scale height, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature of the general corona) may be explained in a natural fashion.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.     

One type of three-wave interaction of low-frequency waves in magnetoactive plasma of the solar atmosphere

We study the process of occurrence of “quasi-mode” decay instability of kinetic Alfven waves (KAW) in the chromosphere of a solar active region before a flare, namely, in plasma of magnetic loops near their footpoints. The decay of a primary KAW into a kinetic ion-acoustic wave and a secondary KAW was considered as a specific type of three-wave interaction. Necessary conditions for the KAW decay instability occurrence were found for two semiempirical models of the solar atmosphere with the use of a modified expression for the growth rate of instability in the case of nonlinear interaction of low-frequency waves with an abnormally low excitation threshold. It was shown that the main criteria for the development of this instability significantly depend on the amplitude of external magnetic field in the region under study as well as on a model of the solar atmosphere.     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Model for Propagating Parts of EIT Waves: A Current Shell in a CME

EIT waves are observed in EUV as bright fronts. Some of these bright fronts propagate across the solar disk. EIT waves are all associated with a flare and a CME and are commonly interpreted as fast-mode magnetosonic waves. Propagating EIT waves could also be the direct signature of the gradual opening of magnetic field lines during a CME. We quantitatively addressed this alternative interpretation. Using two independent 3D MHD codes, we performed nondimensional numerical simulations of a slowly rotating magnetic bipole, which progressively result in the formation of a twisted magnetic flux tube and its fast expansion, as during a CME. We analyse the origins, the development, and the observability in EUV of the narrow electric currents sheets that appear in the simulations. Both codes give similar results, which we confront with two well-known SOHO/EIT observations of propagating EIT waves (7 April and 12 May 1997), by scaling the vertical magnetic field components of the simulated bipole to the line of sight magnetic field observed by SOHO/MDI and the sign of helicity to the orientation of the soft X-ray sigmoids observed by Yohkoh/SXT. A large-scale and narrow current shell appears around the twisted flux tube in the dynamic phase of its expansion. This current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields. It intensifies as the flux tube accelerates and it is co-spatial with weak plasma compression. The current density integrated over the altitude has the shape of an ellipse, which expands and rotates when viewed from above, reproducing the generic properties of propagating EIT waves. The timing, orientation, and location of bright and faint patches observed in the two EIT waves are remarkably well reproduced. We conjecture that propagating EIT waves are the observational signature of Joule heating in electric current shells, which separate expanding flux tubes from their surrounding fields during CMEs or plasma compression inside this current shell. We also conjecture that the bright edges of halo CMEs show the plasma compression in these current shells.     

On the theory of the generation of auroral radiation

The stability of the hot plasma located at the curvilinear geomagnetic field in relation to the generation of Alfvén oscillations is investigated. A general expression for the increment is obtained. The increments for the short wavelength disturbances and special energy distribution function in a parabolic magnetic field are presented. The obtained theoretical results are used in interpreting the oscillations of the “auroral radiation” type. The polarization relations in Alfvén waves are investigated.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oblique propagation and dissipation of Alfvén waves in coronal holes

We investigate the effect of viscosity and magnetic diffusivity on the oblique propagation and dissipation of Alfvén waves with respect to the normal outward direction, making use of MHD equations, density, temperature and magnetic field structure in coronal holes and underlying magnetic funnels. We find reduction in the damping length scale, group velocity and energy flux density as the propagation angle of Alfvén waves increases inside the coronal holes. For any propagation angle, the energy flux density and damping length scale also show a decrement in the source region of the solar wind (< 1.05 R_⊙) where these may be one of the primary energy sources, which can convert the inflow of the solar wind into the outflow. In the outer region (> 1.21 R_⊙), for any propagation angle, the energy flux density peaks match with the peaks of MgX 609.78 Å and 624.78 Å linewidths observed from the Coronal Diagnostic Spectrometer (CDS) on SOHO and the non-thermal velocity derived from these observations, justify the observed spectroscopic signature of the Alfvén wave dissipation.     

Effect of small-scale bernstein turbulence on low-frequency plasma waves in the preflare solar chromosphere

The studied region is a part of the current circuit of a magnetic loop in a solar active region in the altitude range of 1400–2500 km above the photosphere. At the earliest stage of development of a flare process, the magnetic field of the loop was assumed to be stationary and uniform in the interval corresponding to weak fields (the so-called deca-hectogauss fields). The conditions for emergence and development of instability of the second harmonic of Bernstein modes in this previously unexamined region were determined. This instability (and low-frequency instabilities emerging later) was assumed to be caused by the sub-Dreicer electric field of the loop, while pair Coulomb collisions were considered to be the major factor hindering its development. The obtained extremely low instability thresholds point to the possibility of subsequent emergence of low-frequency instabilities (and plasma waves corresponding to them) with much higher threshold values against the background of saturated Bernstein turbulence. The frequency of electron scattering by turbulence pulsations in this scenario normally exceeds the frequency of pair Coulomb (primarily ion–electron) collisions. Both the quasistatic sub-Dreicer field in the loop and the weak spatial inhomogeneity of plasma temperature and density were taken into account in the process of derivation and analysis of the dispersion relation for low-frequency waves. It was demonstrated that the solutions of the obtained dispersion relation in the cases of prevalent pair Coulomb collisions and dominant electron momentum losses at pulsations of saturated Bernstein turbulence are morphologically similar and differ only in the boundary values of perturbation parameters. In both cases, these solutions correspond to the two wave families, namely, kinetic Alfven waves and kinetic ion acoustic waves. These waves have their own electric fields and may play the important role in the process of preflare acceleration of energetic electrons.     

Solar wind interaction with the tail of Comet Kohoutek

Helical waves of large amplitude observed recently in the tail of Comet Kohoutek are interpreted as stable waves arising due to non-linear evolution of Kelvin-Helmholtz instability. The dispersion equation for waves of a finite amplitude shows that the phase velocity of these waves should approximately coincide with the velocity of the plasma outflow in the tail rather than with the Alfvén velocity. This fact is shown to be in agreement with observations. One may estimate the magnetic field in the Comet Kohoutek tail from both the amplitude of observed helical waves and the pressure balance at the tail boundary. The field turns out to be of the order of the interplanetary magnetic field or less, i.e. ?25 γ near ～0.5 AU.