A model of impulsive loop flares caused by anomalous heat conduction

Numerical simulation is made of the impulsive loop flare caused by transient heat conduction along the loop with an applied axial electric current.It is assumed that a segment near the top of the coronal loop is heated to above 10⁷ K by a heat input that is small compared with the total flare energy, which is given by the magnetic energy of the initial current. Due to the heat conduction, a hump appears in the velocity distribution of electrons, which may excite electron plasma waves with a sufficiently high intensity to cause an anomalous resistivity, as shown theoretically in a previous paper. In that paper, an effect of the plasma waves on the dynamics of electrons was taken into account consistently, but an anomalous heating due to an ohmic dissipation of the initial current under the anomalous resistivity was not taken into account.The aim of the present study is to study the subsequent dynamics of the heated gas caused by the anomalous heating, but in order to avoid an unpractically long computation time, the energy density of the plasma waves is estimated by the energy density of electrons in the velocity hump, without taking into account the effect of the plasma waves consistently in the dynamics of the electrons.The initial current starts to decay gradually by an ohmic dissipation under the anomalous resistivity occurring near the top of the loop to heat this region more. The enhanced heat conduction causes the velocity humps in a wider location. Consequently, the anomalous heating continues and spreads in a self-generating way even after the end of the initial minor heating. Thus the temperature near the loop top becomes above 10⁸ K and the high-temperature region spreads in both directions along the loop with such a high speed as (2–3) × 10⁴ km s^–1, which is nearly equal to the speed of flux-limited heat conduction. On the other hand, induced electric field estimated from the anomalous resistivity is 3.3 × 10⁷ V at the termination of the present simulation, under the modest initial current of 1.5 A m^–2.X-ray emissions expected from the present model loop, show three sources, two footpoints with unequal brightness and a coronal source expanding along the loop in both directions.     

Nonlinear kinetic Alfvén wave with Poisson equation correction in the low aurora

Nonlinear kinetic Alfvén waves where m _e /m _i , have been solved both with and without the Poisson equation correction. It is found that the ratio of the perpendicular electric field and magnetic field, and the ratio of parallel and perpendicular electric field increase with deepening of the depressive density soliton. The former ratio may be larger than the Alfvén velocity in the case of a large amplitude solitary kinetic Alfvén wave. The Poisson equation correction is important for the nonlinear kinetic Alfvén wave propagating along the magnetic field, which solves a puzzle of Sagdeev potential to approach infinity in the limit ofK _x 0. This correction causes the solitary KAW possessing an electrostatic character along the direction of wave moving frame. These results have been compared with the observations from the Freja satellite in the low aurora.     

Plasma flow in a curved magnetic field

A beam of collisionless plasma is injected along a longitudinal magnetic field into a region of curved magnetic field. Two unpredicted phenomena are observed: The beam becomes deflected in the directionopposite to that in which the field is curved, and itcontracts to a flat slab in the plane of curvature of the magnetic field.The plasma is produced by a conical theta-pinch gun and studied by means of high speed photography, electric and magnetic probes, ion analyser, and spectroscopy.The plasma beam is collisionless and its behaviour is, in principle, understood on the basis of gyro-centre drift theory. A fraction of the transverse electric fieldE=–v×B, which is induced when the beam enters the curved magnetic field, is propagated upstream and causes the reverse deflection byE×B drift. The upstream propagation of the transverse electric field is due to electron currents.The circuit aspect on the plasma is important. The transverse polarization current in the region with the curved field connects to a loop of depolarization currents upstream. The loop has limited ability to carry current because of the collisionless character of the plasma; curlE is almost zero and electric field components arise parallel to the magnetic field. These play an essential role, producing runaway electrons, which have been detected. An increased electron temperature is observed when the plasma is shot into the curved field. Runaway electrons alone might propagate the electric field upstream in case the electron thermal velocity is insufficient.The phenomenon is of a general character and can be expected to occur in a very wide range of ensities. The lower density limit is set by the condition for self-polarization,nm _i / ₀ B ² 1 or, which is equivalent,c ²/v _A ² ;1, wherec is the velocity of light, andv _A the Alfvén velocity. The upper limit is presumably set by the requirement _{e e} 1.The phenomenon is likely to be of importance, for example, for the injection of plasma into magnetic bottles and in space and solar physics. The paper illustrates the complexity of plasma flow phenomena and the importance of close contact between experimental and theoretical work.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978     

Observations of propagating double layers in a high current discharge

Observations of current disruptions and strong electric fields along the magnetic field in a high-density (2×10¹⁹ m^–3), highly-ionized, moving, and expanding plasma column are reported. The electric field is interpreted in terms of propagating, strong electric double layers (3–5 kV).An initial plasma column is formed in an axial magnetic field (0.1 T) by means of a conical theta-pinch plasma gun. When an axial current (max 5 kA, 3–5 kV) is drawn through the column spontaneous disruptions and double-layer formation occur within a few microseconds.Floating, secondary emitting Langmuir probes are used. They often indicate very high positive potential peaks (1–2 kV above the anode potential during a few s) in the plasma on the positive side of the double layer. Short, intense bursts of HF radiation are detected at the disruptions.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Models of force-free magnetic fields in resistive media

A review is given of some of the basic properties of force-free fields under circumstances when the conductivity of the medium is finite. Then the electric current density is related not only to the magnetic field, but also by Ohm's law to the electric field and plasma velocity, which must be considered in the solutions. It is pointed out that the natural constraint that the electric field and plasma velocity should be finite everywhere is not fulfilled in some previously used models. Models with a constant ratio of the electric current density and magnetic field intensity have been used extensively in the past. They are of some importance since solutions with the plasma at rest are possible only if is constant. However, it is shown that solutions of constant cannot be matched to an external current-free region of finite conductivity since can have no discontinuity in a medium where the conductivity varies continuously. Hence, for most applications models with a varying and a moving plasma must be used. Some new, simple and consistent models, especially of cylindrical symmetry, are derived by prescribing the form of the magnetic field lines, or one electic field component, or one time-dependent electric current component.     

Electron surfing acceleration by electrostatic waves in current sheet

The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v _p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.      

Steady heat conduction in coronal loop unstable against plasma instability

The Fokker-Planck equation is numerically solved to study the electron velocity distribution under steady heat conduction with an applied axial electric current in a model coronal loop.If the loop temperature is so high that the electron mean-free path is longer than the local temperature scale height along the loop, a velocity hump appears at about the local thermal electron velocity. The hump is attributed to cooler electrons moving up the temperature gradient to compensate for the runaway electrons moving down the gradient. If the ratio between the mean free path and temperature scale height is greater than about 2, negative absorption for the plasma waves can appear (waves grow). This effect is enhanced by the presence of axial electric current in the half of the coronal loop in which the electrons carrying the current are drifting up the temperature gradient. Thus, the plasma instability may occur in the coronal elementary magnetic flux tubes. Although the present paper is limited to show the critical condition and linear growth rate of the instability, the following scenarios may be inferred.If the flux tubes change from marginally stable to unstable against the plasma instability, due to an increase in the loop temperature, anomalous resistivity may suddenly appear because of the growth of plasma waves. Then a high axial electric field is induced that may accelerate particles. This could be the onset of impulsive loop flares.For a low electric current, if the loop temperature is sufficiently high to give the negative absorption for the plasma waves in a large part of the coronal loop, steady plasma turbulence may originate. This could be a source for the type I radio noise storm.     

Periodic and non-periodic phenomena in a sunspot region

We have studied running penumbral waves, the homogeneous Evershed effect, and the spatial relation between intensity and Doppler velocity penumbral features of a chromospheric sunspot. The observations were obtained with the multichannel subtractive double-pass spectrograph (MSDP) operating in H at the Vacuum Tower Telescope (VTT) installed at Tenerife (Canary Islands). We derived intensity and Doppler velocity maps at H ± 0.3 Å over a two-dimensional field of view. We have computed the components of the velocity vector (radial, azimuthal, vertical) as a function of distance from the center of the spot under the assumption of axial symmetry. The results show the well-known, from previous observations, general large-scale characteristics of the chromospheric Evershed flow. Our measurements show that the axes along the discrete structures, where the Evershed flow is confined, are not spatially related to the axes along H ± 0.3 Å intensity features, and we suggest that either the flow is confined in flow channels or that it takes place along sheared magnetic field lines. We also detected, for the first time in velocity images, running penumbral waves, which started in the outer 0.3 of the umbral radius and propagated through the penumbra with propagation velocities 13–24 km s^–1. The propagation velocity, as well as the velocity amplitude, is greater for the waves closer to the center of the spot and diminishes as one moves outward.     

Plasma jet and shock formation during current loop coalescence in solar flares

We report on the results of plasma jet and shock formation during the current loop coalescence in solar flares. It is shown by a theoretical model based on the ideal MHD equation that the spiral, two-sided plasma jet can be explosively driven by the plasma rotational motion induced during the two current loop coalescence process. The maximum velocity of the jet can exceed the Alfvén velocity, depending on the plasma (= c _s ² v _A ² ) ratio. The acceleration time getting to the maximum jet velocity is quite short and le than 1 s. The rebound following the plasma collapse driven by magnetic pinch effect can strongly induce super-Alfvénic flow. We present the condition of the shock formation. We briefly discuss the high-energy particle acceleration during the plasma collapse as well as by the shocks.     

Plasma motions in the solar loop of emerging magnetic flux

The results of analyzing variations in the line-of-sight (LOS) velocities in the solar loop at photospheric and chromospheric levels in the region of emerging magnetic flux for the evolving active region NOAA 11024 are reported. The analysis combines the data of multiwave spectropolarimetric observations that were carried out on July 4, 2009, (Tenerife, Spain) using THEMIS solar telescope and the data obtained with GOES, SOHO, and STEREO cosmic satellites. A complex sequence of active events has been studied: formation of the Ellerman bomb, B1 X-ray microflare, and four chromospheric surges that were formed as a result of magnetic reconnection caused by new emerging magnetic flux. The Ellerman bomb was formed in the vicinity of a growing pore. Variations in the velocity V _LOS of the EB had an oscillation character for chromosphere and photosphere. Before the microflare, the average velocities of the upward and downward plasma fluxes in one leg of the magnetic loop were nearly the same—26 km/s. During the microflare, the velocity V _LOS of the ascending and descending flows increased up to ?33 and 50 km/s, respectively. Variations in line-of-sight velocity of a plasma in the second leg of the magnetic loop correlated well with variations of V _LOS in the region of microflare, but they occurred 1.5 minutes later. During the time of observations, four chromospheric ejections of matter were formed and three of them occurred in the region of Ellerman’s bomb formation. Sharp variations in the soft X-ray intensity occurred during these ejections. At photospheric level, variations in the line-of-sight velocity of plasma in the legs of the loop occurred in the opposite direction. In the region of the first leg, velocity V _LOS diminished from ?1.8 to ?0.4 km/s, while the velocity increased from ?0.6 to ?2.6 km/s in the region of the second leg.     

On build-up of magnetic energy in the solar atmosphere

The dynamic response of the solar atmosphere is examined with the use of self-consistent numerical solutions of the complete set of nonlinear, two-dimensional, hydromagnetic equations. Of particular interest are the magnetic energy build-up and the velocity field established by emerging flux at the base of an existing magnetic loop structure in a stationary atmosphere. For a plasma with a relatively low beta ( = 0.03) the magnetic energy build-up is approximately twice that of the kinetic energy, while the build-up in magnetic energy first exceeds but is eventually overtaken by the kinetic energy for a plasma with an intermediate beta ( = 3). The increased magnetic flux causes the plasma to flow upward near the loop center and downward near the loop edges for the low beta plasma. The plasma eventually flows downward throughout the lower portion of the loop carrying the magnetic field with it for the intermediate beta plasma. It is hypothesized that this latter case, and possibly the other case as well, may provide a reasonable simulation of the disappearance of prominences by flowing down into the chromosphere (a form of disparition brusque).The National Center for Atmospheric Research is sponsored by the National Science Foundation.Now at the School of Science and Engineering, The University of Alabama in Huntsville, Huntsville, Alabama 35807.     

High-Resolution Hα Observations of Proper Motion in NOAA 8668: Evidence for Filament Mass Injection by Chromospheric Reconnection

There have been two different kinds of explanations for the source of cool material in prominences or filaments: coronal condensations from above and cool plasma injections from below. In this paper, we present observational results which support filament mass injection by chromospheric reconnection. The observations of an active filament in the active region NOAA 8668 were performed on 17 August 1999 at a wavelength of H–0.6 Å using the 65 cm vacuum reflector, a Zeiss H birefringent filter, and a 12-bit SMD digital camera of Big Bear Solar Observatory. The best image was selected every 12 s for an hour based on a frame selection algorithm. All the images were then co-aligned and corrected for local distortion due to the seeing. The time-lapse movie of the data shows that the filament was undergoing ceaseless motion. The H flow field has been determined as a function of time using local correlation tracking. Time-averaged flow patterns usually trace local magnetic field lines, as inferred from H fibrils and line-of-sight magnetograms. An interesting finding is a transient flow field in a system of small H loops, some of which merge into the filament. The flow is associated with a cancelling magnetic feature which is located at one end of the loop system. Initially a diverging flow with speeds below 10 km s^–1 is visible at the flux cancellation site. The flow is soon directed along the loops and accelerated up to 40 km s^–1 in a few minutes. Some part of the plasma flow then merges into and moves along the filament. This kind of transient flow takes place several times during the observations. Our results clearly demonstrate that reconnection in the photosphere and chromosphere is a likely way to supply cool material to a filament, as well as re-organizing the magnetic field configuration, and, hence, is important in the formation of filaments.     

Two dynamical models for solar spicules

Solar spicules are luminous jets that erupt up to 10 000 km from the surface of the Sun and have diameters, all along their length, of only about 150–200 km. We first review some recent observations made at the H wavelength. According to our models, a solar spicule is a self-channelled proton beam emitted by a magnetic element and surrounded by a cold sheath. The beam originates in a self-excited dynamo that exploits a v × B field and that could be situated either below or above the element, where v is the local plasma velocity and B is the local magnetic flux density. In falling back, the sheath provides a return current of protons that cancels the outgoing current. We discuss the channelling of charged-particle beams of very large cross-section and propose velocity channelling, which is apparently a new concept. We assume a steady state and a hydrogen plasma.     

Siphon flows in the solar corona

The flows in a coronal magnetic arch associated with a pressure difference between the footpoints are investigated. Steady flows are of different types: always subsonic; subsonic in one branch of the arch, supersonic in the second; subsonic-supersonic with stationary shocks which adjust the flow to the boundary conditions in the second footpoint. The large velocity increase along the loop in subsonic-supersonic flows is associated with a large density decrease. A velocity drop and a density jump occur across the shock. The emission of such arches in coronal lines (625 of Mg x and 499 of Si xii) is calculated. It is suggested that the intensity drop along the axis observed in some UV loops is due to the density drop associated with subsonic-supersonic flows.     

Pulsations of microwave emission as a consequence of oscillatory transients in the solar atmosphere

We offer a new interpretation of the origin of oscillations in active regions. Quasi-periodic oscillation trains with periods of 3 min, 5 min, and min arise due to slow oscillatory transients which accompany the appearance of plasma flow along the sunspot's magnetic field. In oscillatory transients of the fast type, occurring in current loop systems, the typical period of oscillations shifts towards values of the order of a second.     

A model for thinning of the plasma sheet

A one-dimensional model for thinning of the plasma sheet is developed on the basis of launching a fast mode MHD rarefaction wave propagating in the tailward direction along the plasma sheet. Behind the rarefaction wave the pressure is reduced, leading to thinning of the plasma sheet and also to an Earthward plasma flow with a speed on the order of the sound speed a₀. The plasma sheet thickness is reduced by a factor of 2 if an Earthward plasma flow speed of 0.8a₀ is induced. The predictions of the model are in reasonable agreement with observations.     

Electric currents and Hα emission in two active regions on the sun

We investigated the structure of magnetic field and vertical electric currents in two active regions through a comparison of the observed transverse field with the potential field, which was computed according to Neumann boundary-value problem for the Laplace equation using the observed H _z -value. Electric currents were calculated from the observations of the transverse magnetic field.There exist two systems of vertical electric currents in active regions: a system of local currents and a global one. The global current is about 2 × 10¹² A. In the leading part of the active regions it is directed upward, and in the tail downward.Flare activity is closely connected with the value and direction of both local and global currents: the flares tend to apear in places with upward currents. The luminosity of H flocculi is also connected with vertical electric currents; the brighter the flocculi, the more frequently they appear in places of upward electric currents.The sensitivity of H emission to the sign of the current suggests that charged particles accelerated in the upper parts of magnetic loops may be responsible for these formations. Joule heating might be important for flocculi, if plasma conductivity is about 5 × 10⁸ c.g.s.e.A model of a flare is suggested based on current redistribution in a system of emerging loops due to changes of loop inductance.     

Diamagnetic boundary layers: A kinetic theory

We present a kinetic theory for boundary layers associated with MHD tangential discontinuities in a collisionless magnetized plasma such as those observed in the solar wind. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary, one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfvén speed, and accordingly such layers are not stable. Several types of layers, in which the current is carried by protons are discussed; in particular, we considered cases in which the magnetic field intensity and/or direction changed across the layer. In every case, the thickness was of the order of a few proton gyroradii and the field changed smoothly, although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfvén speed, consistent with stability of such structures. Our results are consistent with the observations of boundary layers in the solar wind near 1 AU.