Alfvén turbulence in collisionless plasmas

The evolution of Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. In particular, we consider decay of Alfvén waves through three-wave coupling with an ion sound mode in the random-phase approximation. Two decay processes are of particular interest: an Alfvén wave decays into a backward propagating Alfvén wave and a forward propagating ion sound wave, and an Alfvén wave decays into a backward propagating fast magnetoacoustic wave and a forward ion sound wave. The former was widely discussed in the literature, particularly under the coherent wave assumption. The latter was not well explored and is discussed here.     

Surface waves on the plasma sheet boundary

A dispersion equation for the surface waves on the inner boundary of the magnetospheric plasma sheet is obtained. The wave group velocity has both components along and across the magnetic field. For the waves with the period 1 min the transverse component is about 100 km s⁻¹, the parallel component is approximately equal to the Alfvén velocity. Pi2 pulsations, as well as east-westward motions of auroral riometer absorption bays, may be possible displays of surface waves.     

The characteristics of motion of thin magnetic tubes

Starting from the equations of motion of a thin magnetic tube, the characteristic curves and velocities and compatibility relations are derived as basis for investigating its motion and for correctly formulating the problem of stationary solution. It is shown that the characteristic velocity of transverse waves is related to the Alfvén Mach number of the flow in the tube. When the flow velocity exceeds the critical value for the Kelvin-Helmholtz instability, transverse waves cease to exist.     

Field-aligned currents and auroral acceleration by non-linear MHD waves

This paper examines the consequences of the assumption that substorm-associated growth of magnetosphere-ionosphere current systems is triggered by the incidence, on the ionosphere, of a large amplitude Alfvén wave generated in the distant magnetotail. It is pointed out that there is a large body of evidence suggesting that, in the acceleration region near 1 R_E, one is likely to find a major discontinuity in mass density. Following the approach of Cohen and Kulsrud (1974) who studied the steepening of large amplitude hydromagnetic waves into shocks, we demonstrate that the character of the background plasma and magnetic field in the auroral acceleration region near 1 R_E can be ideal for the generation of MHD shocks and that these shocks can lead to the acceleration of ions and electrons as reported by investigators using S3-3 satellite data.     

Coupling modes of hydromagnetic oscillations in non-uniform, finite pressure plasmas: Two-fluids model

Within a framework of the two-fluids approximation, basic modes constituting hydromagnetic coupling oscillations in non-uniform, finite-β plasmas are examined. It is shown that the oscillations consist of a coupling between a localized mode and a propagating one, and a strong peak appears at a resonance point. In the case of isothermal plasma (T_e = T_i), there are two localized modes, the Alfvén (or drift Alfvén) and the ion drift modes, and a propagating mode being known as the fast magnetosonic wave. Coupling oscillations associated with the Alfvén mode exhibit a nearly incompressible character, whereas those with the ion drift mode are compressional and diamagnetic. Furthermore, the slow magnetosonic wave also couples with the localized mode in the case of T_e > T_i. Based on characteristics of these oscillations, the origin of geomagnetic pulsations is discussed in connection with the distribution of plasma parameters in the outer magnetosphere.     

Sweeping-magnetic-twist mechanism for the acceleration of jets in the solar atmosphere

A magnetodynamic mechanism for the acceleration of jets in the solar atmosphere (surges, Brueckner's EUV jets, and so on) is proposed, and a 2.5-dimensional MHD simulation is performed to show how this mechanism operates in the situation of the chromosphere-corona region of the solar atmosphere. It is seen from the result of simulation that together with the release of the magnetic twist, e.g., into a reconnected open flux tube, the mass in the high density twisted loop is driven out into the open flux tube due both to the pinch effect progressing with the packet of the magnetic twist into the open flux tube, and to the j × B force at the front of the packet of the unwinding twist in the off-axis part of the tube. The former, the progressing pinch, is accompanied by an accelerated hot blob, while the latter, the unwinding front of the magnetic twist, drives a cool cylindrical flow, both with velocities of the order of the local Alfvén velocity. One of the characteristic properties of the jet in our model is that the jet, consisting of hot core and cool sheath, has a helical velocity field in it, explaining the thus-far unexplained observed feature.The sudden release of the magnetic twist into an open flux tube is most likely to be due to the reconnection between a twisted loop and the open flux tube. The mass is driven out in the relaxation process of the magnetic twist from the twisted loop to the open flux tube.     

Soft X-ray emission from a hot turbulent current sheet and the precursor phase of solar flares

The properties and development of a high-temperature current sheet characterized by increasing merging velocity are studied and related to the early phases of solar flares. It is shown that the system can be described by the Petschek-type geometry for a wide range of merging velocities. In the diffusion region and the standing MHD shocks a certain low-frequency plasma microturbulence is generated from the very beginning of the reconnection process. We present qualitative solutions for the case of ion-acoustic turbulence in marginally stable state, which provide a comparison with observations. The increasing merging velocity leads to the appearance of the soft X-ray precursor. The precursor temperature maximum should appear during the current sheet formation, before the Petschek regime is established. In the Petschek regime the temperature of the hot plasma decreases due to the decrease of the magnetic field strength at the diffusion region boundary, while the soft X-ray radiation still increases, reaching precursor maximum for merging velocities about 1% of the external Alfvén velocity. The precursor phase ends when the value of the merging velocity surpasses the upper limit for the Petschek regime and the system enters into the pile-up regime, causing a new increase of plasma temperature and soft X-ray radiation.It is shown that Alfvén velocities in the range 800–1200 km s ^–1 are sufficient to explain typical soft X-ray precursors. Cases of low merging velocities and low Alfvén velocities are discussed and can be applied to describe the properties of spotless flares.     

Inductive magnetic footpoint tracking by combining the minimum energy fit with the local correlation tracking and doppler velocity

Time-dependent magneto-hydrodynamic simulations of active region coronal magnetic field require the underlying photospheric magnetic footpoint velocities. The minimum energy fit (MEF) is a new velocity inversion technique to infer the photospheric magnetic footpoint velocities using a pair of vector magnetograms, introduced by Longcope (2004). The MEF selects the smallest overall flow from several consistent flows by minimizing an energy functional. The inferred horizontal and vertical flow fields by the MEF can be further constrained by incorporating the partial or imperfect velocity information obtained through independent means. This hybrid method is expected to give a velocity close to the true magnetic footpoint velocity. Here, we demonstrate that a combination of the MEF, the local correlation tracking (LCT) and Doppler velocity is capable of inferring the velocity close to the photospheric flow.     

Guided waves in magnetospheric tubes of enhanced density

Properties of a guided MHD-wave propagating in a magnetic field tube with the plasma density differing from the ambient density are studied. Like the Alvén wave this wave propagates along the magnetic field and is connected with the field-aligned currents flowing at the periphery of the oscillating tube. The guided wave is accompanied by the magnetic field compression, nevertheless the wave moves without attenuation. The guided wave velocity is between the Alvén velocities inside and outside the oscillating tube. In a tube of elliptical cross-section the propagation velocity depends on the polarization of the wave.     

On the asymmetric nature of micropulsations—I. the spectrum

This paper is based on the postulate that the natural electromagnetic radiation observed in the micropulsation band is accounted for by the eigenmodes of a resonant cavity in the Earth's outer atmosphere, just as the adjacent ELF part of the spectrum is explained by resonances in the Earth-ionosphere cavity. The inner edge of the plasma sheet (the Alfvén layer) forms an effective resonant cavity which we call the Alfvénsphere. Its complex medium is characterized by two parameters, effective conductivity, and effective Alfvén speed: its quasi-stationary states are specified by two state parameters, effective cavity size, and effective time scale for magnetospheric processes, and in principle, they can be evaluated from the power spectra of observed micropulsations. Because of the complex geometry of the cavity and the fact that the vector hydromagnetic wave equation for an asymmetric electric field is not simply separable in spherical and orthogonal dipole coordinates (and the spatial boundary value problem is virtually insoluble), a model is developed which contains the essential physics and admits of tractable equations. A coupling scheme is defined and discussed which permits one to study the eigenvalue equation under conditions of weak and strong coupling as well as the uncoupled case. Emphasis is placed on the most difficult weakly-coupled case because the results can be readily compared with the uncoupled case. The complex dispersion relation-ship is presented and complex eigenvalues are calculated. It is shown that for any mode (v, i, m), the fundamental (i = 1) appears at the highest latitude and the highest harmonic (i = i_max) appears at the lowest latitude. Further it is shown that the fundamental and harmonics are split into multiplet frequency states, clustered at different latitudes, and ordered at a particular latitude by the asymmetric label m. This property is used to explain beating and atitudinal and longitudinal variations in pearl pulsations. It is demonstrated that the east-west magnetic component of the perturbed magnetic field (for any mode) has two spatial resonances (logarithmic and asymmetric) and this feature can be used to derive and interpret the T cos²Θ = const law. This in turn suggests a method for ordering the east-west component power spectra for a station at any latitude below 70° N mag. in terms of v, and evaluating the corresponding phenomenological state parameters. The inescapable conclusion appears to be that there is no intrinsic difference between the ‘different’ classes of pulsations; they are simply the excited eigenmodes of the Alfvénsphere for different quasi-stationary states.     

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.     

Torsional Alfvén modes in dipole and toroidal magnetospheres

Propagation of torsional Alfvén waves in the magnetosphere is examined for two models of the Earth's magnetic field, one where the field is toroidal, the other being a dipole field. Both models yield magnetically guided torsional wave modes which are strongly localized in all directions transverse to the steady magnetic field. The transverse structure is determined by a self-consistent solution of the ideal MHD equations. It is shown that the torsional wave is guided even when b is finite, where b is the component of the wave magnetic field in a direction parallel to the steady magnetic field.     

Physical properties of the quiet solar chromosphere–corona transition region

The physical properties of the quiet solar chromosphere–corona transition region are studied. Here the structure of the solar atmosphere is governed by the interaction of magnetic fields above the photosphere. Magnetic fields are concentrated into thin tubes inside which the field strength is great. We have studied how the plasma temperature, density, and velocity distributions change along a magnetic tube with one end in the chromosphere and the other one in the corona, depend on the plasma velocity at the chromospheric boundary of the transition region. Two limiting cases are considered: horizontally and vertically oriented magnetic tubes. For various plasma densities we have determined the ranges of plasma velocities at the chromospheric boundary of the transition region for which no shock waves arise in the transition region. The downward plasma flows at the base of the transition region are shown to be most favorable for the excitation of shock waves in it. For all the considered variants of the transition region we show that the thermal energy transfer along magnetic tubes can be well described in the approximation of classical collisional electron heat conduction up to very high velocities at its base. The calculated extreme ultraviolet (EUV) emission agrees well with the present-day space observations of the Sun.     

The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun

The dynamics of horizontal plasma flows during the first hours of the emergence of active region magnetic flux in the solar photosphere have been analyzed using SOHO/MDI data. Four active regions emerging near the solar limb have been considered. It has been found that extended regions of Doppler velocities with different signs are formed in the first hours of the magnetic flux emergence in the horizontal velocity field. The flows observed are directly connected with the emerging magnetic flux; they form at the beginning of the emergence of active regions and are present for a few hours. The Doppler velocities of flows observed increase gradually and reach their peak values 4?–?12 hours after the start of the magnetic flux emergence. The peak values of the mean (inside the ±?500 m?s^?1 isolines) and maximum Doppler velocities are 800?–?970 m?s^?1 and 1410?–?1700 m?s^?1, respectively. The Doppler velocities observed substantially exceed the separation velocities of the photospheric magnetic flux outer boundaries. The asymmetry was detected between velocity structures of leading and following polarities. Doppler velocity structures located in a region of leading magnetic polarity are more powerful and exist longer than those in regions of following polarity. The Doppler velocity asymmetry between the velocity structures of opposite sign reaches its peak values soon after the emergence begins and then gradually drops within 7?–?12 hours. The peak values of asymmetry for the mean and maximal Doppler velocities reach 240?–?460 m?s^?1 and 710?–?940 m?s^?1, respectively. An interpretation of the observable flow of photospheric plasma is given.     

Propagation of Alfvén waves in multi-layer solar atmosphere model

In this paper, we idealize the actual solar atmosphere as a multi-isothermal-layer system so as to obtain the energy transmittance of the linear Alfvén wave that propagates through such a system in presence of a uniform oblique magnetic filed. The results indicate that the two-layer model is essentially different to the three-layer one. In the two-layer model, the temperature jump acts as a high pass filter. In the three-layer model, resonant transfer will take place and the transmittance undergoes oscillation as the trigonometric function terms dominate its behavior. For actual solar atmosphere, the result reveals that the lower parts of solar atmosphere are more suitable for those Alfvén waves with period of seconds to transfer their energy.     

The rotation of sunspots in the solar active region NOAA 10930

The rotation of sunspots in the solar active region NOAA 10930 was investigated on the basis of the data on the longitudinal magnetic field and the Doppler velocities using magnetograms and dopplergrams taken with the Solar Optical Telescope installed aboard the HINODE mission. Under the assumption of axial symmetry, areally-mean vertical, radial, and azimuthal components of the magnetic field and velocity vectors were calculated in both sunspots. The plasma in the sunspots rotated in opposite directions: in the leading sunspot, clockwise, and in the following sunspot, counterclockwise. The magnetic flux tubes that formed sunspots of the active region on the solar surface were twisted in one direction, clockwise. Electric currents generated as a result of the rotation and twisting of magnetic flux tubes were also flowing in one direction. Azimuthal components of magnetic and velocity fields of both sunspot umbrae reached their maximum on December 11, 2006. By the start of the X3.4 flare (December 13, 2006), their values became practically equal to zero.     

The structure of the turbulent shock wave propagating in the solar atmosphere across the magnetic field

A consistent account of plasma turbulence in magnetohydrodynamics equations describing transport processes across the magnetic field is presented. The structure of the perpendicular shock wave generated in the solar atmosphere, as a result of either local disturbance of the magnetic field or dense plasma cloud motion with a frozen-in magnetic field, has been investigated. The region of parameters in the solar atmosphere at which the electron-ion relative drift velocity u exceeds the electron thermal velocity V _eand generation of radio emission becomes possible, has been determined. The plasma turbulence inside the front has been shown, under conditions of solar corona, not to cause the oscillation structure of shock front to break down. Under chromospheric conditions, the shock profile is aperiodical. Then, the condition u > V_ecan be satisfied and shock waves having an Alfvén Mach number M which exceeds the critical value M _c 3.3 for aperiodical shock waves can exist (Eselevich et al., 1971a). Arguments are given in favour of the fact that perpendicular shock waves are generated in the Sun's atmosphere when dense plasma clouds, with a frozen-in magnetic field, are expanded.     

Waves in a one-dimensional magnetized relativistic pair plasma

Normal modes of a one-dimensional relativistically streaming electron–positron plasma in a superstrong magnetic field are considered, taking into account possible different bulk velocities and thermal effects. This physical picture corresponds to the plasma present on the open field lines of rotating neutron stars where the observed radio emission is generated. Various cases are considered: relativistic and non-relativistic relative streaming of cold components, and relativistically hot distributions. A distinction between superluminous and subluminous waves (which can be excited by the Cherenkov effect) is clearly stated. In the low-frequency regime the Cherenkov and cyclotron two-stream instabilities occur. Polarization of the quasi-transverse modes changes from circular for the propagation along magnetic field lines to linear for angles of propagation larger than some critical angle that depends on the relative velocity of the plasma components.     

The interaction of an obliquely incidents-polarized plane electromagnetic wave at a warm moving magnetized plasma half-space

The interaction of ans-polarized plane electromagnetic wave incident from a dielectric (or vacuum) region on awarm moving magnetized plasma half-space is considered. The external magnetic field is assumed to be normal to the direction of the wave normal and the velocity of the moving medium. Using the first three moment equations, together with Maxwell's electromagnetic equations, we construct the constitutive relations in the rest frame of the moving medium. The constitutive relations are then transformed to the laboratory frame by invokingMinkowski's equations for the moving plasma medium, and the dispersion relation for the propagating ordinary mode in the moving medium is derived. Expressions are obtained for the phase and group velocities and the index of refraction for the ordinary mode, as also for power reflection and transmission coefficients. It is found that in contrast to the case of a cold magnetized plasma, the ordinary electromagnetic mode excited in the warm magnetoplasma medium getsmodified due to the presence of an external magnetic field. In addition, the various reflection and transmission characteristics for a warm magnetoplasma depend on the velocity of the moving plasma as well as on the strength of the applied magnetic field, as against the case for a cold moving magnetized plasma. Numerical results on the reflection coefficient are presented for several values of the parameters characterizing the electron-plasma temperature, the velocity of the moving medium and the strength of the applied magnetic field.     

Local instabilities of Alfvén waves in high speed streams

A two fluid stability analysis of an inhomogeneous solar wind plasma leads to prediction of possible instabilities of both Alfvénic and magnetoacoustic waves driven by local velocity gradients. The waves predicted to be possibly unstable have short wavelengths in comparison with the length scale of the gradients and, with different thresholds for the value of velocity shear, may have different directions of propagation with respect to the background magnetic field.We have performed a detailed study, based on Pioneer 6 magnetic and plasma data relative to several high speed streams in the solar wind, on the direction of propagation of the transverse waves which are found within the streams and on their association with velocity gradients within the stream structure. The analysis leads to the conclusion that the observed Alfvén waves may be consistent with the hypothesis of local generation through one of the above mentioned instabilities where velocity shear leads in fact to excitation of incompressible waves in directions almost parallel to the magnetic field.