Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Viscous-resistive ADAF with a general large-scale magnetic field

We have studied the structure of hot accretion flow bathed in a general large-scale magnetic field. We have considered magnetic parameters , where are the Alfvén sound speeds in three direction of cylindrical coordinate (r,φ,z). The dominant mechanism of energy dissipation is assumed to be the magnetic diffusivity due to turbulence and viscosity in the accretion flow. Also, we adopt a more realistic model for kinematic viscosity (ν=αc _s H), with both c _s and H as a function of magnetic field. As a result in our model, the kinematic viscosity and magnetic diffusivity (η=η ₀ c _s H) are not constant. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. It is found that the existence of magnetic resistivity will increase the radial infall velocity as well as sound speed and vertical thickness of the disk. However the rotational velocity of the disk decreases by the increase of magnetic resistivity. Moreover, we study the effect of three components of global magnetic field on the structure of the disk. We found out that the radial velocity and sound speed are Sub-Keplerian for all values of magnetic field parameters, but the rotational velocity can be Super-Keplerian by the increase of toroidal magnetic field. Also, Our numerical results show that all components of magnetic field can be important and have a considerable effect on velocities and vertical thickness of the disk.     

Hβ Doppler-velocity fields within sites of flares in a solar active region

In this paper, we analyze the relationship between photospheric magnetic fields and chromospheric velocity fields in a solar active region, especially evolving features of the chromospheric velocity field at preflare sites. It seems that flares are related to unusually distributed velocity field structures, and initial bright kernels and ribbons of the flares appear in the red-shifted areas (i.e., downward flow areas) close to the inversion line of H Dopplergrams with steep gradients of the velocity fields, no matter whether the areas have simple magnetic structure or a weak magnetic field, or strong magnetic shear and complex structure of the magnetic fields. The data show that during several hours prior to the flares, while the velocity field evolves, the sites of the flare kernels (or ribbons) with red-shifted features come close to the inversion line of the velocity field. This result holds regardless of whether or not the flare sites are wholly located in blue-shifted areas (i.e., upward flow areas), or are far from the inversion line of the Doppler velocity field (V = 0 line), or are partly within red-shifted areas. There are two cases favourable for the occurrence of flares, one is that the gulf-like neutral lines of the magnetic field (B = 0 line) occur in the H red-shifted areas, the other is that the gulf-like inversion lines of the H Doppler velocity field (V = 0 line) occur in the unipolar magnetic areas. These observational facts indicate that the velocity field and magnetic field have the same effect on the process of flare energy accumulation and release.     

Laminar hydromagnetic thermal boundary layer in fluctuating flow past a limiting surface with variable suction

An analysis of the temperature field in the case of the two-dimensional hydromagnetic flow of a viscous incompressible and electrically conducting fluid, (e.g., of a stellar atmosphere), past a porous, infinite, limiting surface in the presence of a transverse magnetic field, is considered when (i) the free stream velocity oscillates in time about a constant mean; (ii) the suction velocity normal to the limiting surface oscillates in magnitude but not in direction about a non-zero mean; and (iii) there is no heat transfer between the fluid and the wall. Approximate solution is obtained of the energy equation and are given expressions for the temperature field and for the temperature at the limiting surface, when the magnetic Prandtl numberP _m =1 and the magnetic parameterM<1. They are shown graphically followed by a discussion.Research supported by the Alexander S. Onassis Foundation.     

Comparative Analyses of the CSSS Calculation in the UCSD Tomographic Solar Observations

We describe a new method to derive the interplanetary magnetic field (IMF) out to 1 AU from photospheric magnetic field measurements. The method uses photospheric magnetograms to calculate a source surface magnetic field at 15R_⊙. Specifically, we use Wilcox Solar Observatory (WSO) magnetograms as input for the Stanford Current-Sheet Source-Surface (CSSS) model. Beyond the source surface the magnetic field is convected along velocity flow lines derived by a tomographic technique developed at UCSD and applied to interplanetary scintillation (IPS) observations. We compare the results with in situ data smoothed by an 18-h running mean. Radial and tangential magnetic field amplitudes fit well for the 20 Carrington rotations studied, which are largely from the active phase of the solar cycle. We show exemplary results for Carrington rotation 1965, which includes the Bastille Day event.     

Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances

We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B ₀(r),B _0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW _max-W _min, whereW _max andW _min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.     

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.     

High-resolution spectroscopy of active regions

Scatter plots of various pairs of spectral-line parameters that describe the magnetic field and the line-of-sight velocity are discussed in order to relate magnetic structures and the line-of-sight velocity field with characteristic areas of an emerging flux region (EFR).Strong magnetic fields, occurring over about 20% of the resolution elements in the EFR, are either slightly to moderately inclined or transverse. Slightly to moderately inclined strong fields occur in patches near the border of the EFR; the filling factors per resolution element are large, and field strengths are between 800 and 2000 G, and up to 2500 G in pores. There are only a few faculae in the EFR; most of these are located near rapidly growing pores of following polarity.The strongly inclined strong magnetic fields, with field strengths exceeding 1000 G, are located in slightly darkened resolution elements near the line B = 0 separating the magnetic polarities, near large-scale and small-scale upflows. In the central region of the EFR there are some small elements with strongly inclined field of low average field strength of about 500 G, and a tendency for a small-scale upward velocity. These elements may correspond to tops of flux loops during emergence.In 80% of the resolution elements within the EFR the magnetic flux density (averaged over the resolution element) is low, less than 120 G.There is a persistent large-scale velocity field, with upflows near the line B = 0 separating the magnetic polarities and with downflows near rapidly growing pores of following polarity. Some examples of strong small-scale upflows are found in the central region of the EFR, and strong small-scale downflows near rapidly growing following pores. Within the pores and faculae there are no significant small-scale line-of-sight velocities.Based on observations obtained at the Sacramento Peak Observatory (operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation).     

Structure of a simple sunspot from the inversion of IR spectral data

Analysis of spectral data of two neighboring infrared lines, Fe I 15648.5 Å (g = 3) and FeI 15652.9 Å (g_eff = 1.53) are carried out for a simple sunspot when it was near the solar disk center (μ = 0.92), to understand the basic structure of sunspot magnetic field. Inversions of Stokes profiles are carried out to derive different atmospheric parameters both as a function of location within the sunspot and height in the atmosphere. As a result of the inversion we have obtained maps of magnetic field strength, temperature, line‐of‐sight velocity, field inclination and azimuth for different optical depth layers between log(τ₅) = 0 and log(τ₅) = –2.0. In this paper we present few results from our inversion for a layer averaged between log(τ5) from 0.0 to –0.5.     

Effects of the hydromagnetic free convection on the oscillatory flow of a viscous incompressible fluid past a porous limiting surface

The unsteady two-dimensional free convection flow of a viscous incompressible and electrically conducting fluid past an infinite non-conducting and non-magnetic porous limiting surface (e.g. of a star) through which suction with uniform velocity occurs is considered when the free-stream velocity, the temperature of the limiting surface and the induced magnetic field are oscillating in the time about a constant mean value. Expressions, in closed form for the velocity, the skin-friction, the displacement thickness, the induced magnetic field and the electrical current density are obtained by the help of the two-sided Laplace transform technique, when the magnetic Prandtl numberP _m, and the Prandtl numberP are equal to one, and the magnetic parameterM is smaller to one. During the course of analysis the effects of magnetic parameterM, Grashof numberG and non-dimensional frequency are discussed.     

The Influence of a Uniform Magnetic Field of Arbitrary Strength on Turbulence

The spectral tensor of turbulent motion in an infinite conductive incompressible medium is given in the case of a uniform magnetic field of any strenght affecting a homogeneous turbulence. With the help of BOCHNER 's theorem we make sure that the trace u_i(x, t) u_i(x, t) is non-negative. The presence of a weak magnetic field causes a damping of the turbulence, in some cases a strengthening. For strong magnetic fields the norms of the velocity vectors parallel and perpendicular to B approach one and the same value. Compared with the correlation length measured perpendicular to the magnetic field the correlation length measured along the magnetic field increases. Furthermore, our formulas have allowed to calculate the dependence of the α-effect on the magnetic field.     

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     

A model of the magnetized solar wind

A steady state, inviscid, single fluid model of the solar win d in the equatorial plane is developed using magneto-hydrodynamics and including the heat equation wit h thermal conduction but no non-thermal heating (i.e. a conduction model). The effects of solar rotation and magnetic field are included enabling both radial and azimuthal components of the velocity and magnetic fields to be found in a conduction model for the first time.The magnetic field cuts off the thermal conduction far from the sun and leads to an increased temperature at 1 AU and relatively small changes to the radial velocity and density. Models have been found which fit the experimental electron densities in 2 R < r < 16 R . These models predict at 1 AU a radial velocity of 300–380 km·sec^-1 and a density of 8 protons·cm^-3. The latter velocity corresponds to a density profile obtained by Blackwell and Petford (1966) during the last sunspot minimum, and is about 100 km·sec^-1 above that found in previous conduction models which fit the coronal electron densities. The radial velocities are now consistent with the mean quiet solar wind, as are the densities when the experimental values are averaged over a magnetic sector. However, the azimuthal velocity at 1 AU is only 1–2 km·sec^-1 which is low compared to the experimental values, as found by previous authors.     

Generation of waves by the solar magnetic field polarity reversal

In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV ₀ flow with divV ₀ = 0 and with (V ₀ rot₀) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, _A. When _A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV ₀), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When _A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when _A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.     

Evidence for a coronal magnetic bottle at 10 solar radii

The Faraday rotation of a radio source (Pioneer 6) occulted by the solar corona has been measured by Levy et al. (1969). During the course of these measurements, three large-scale transient phenomena were observed. These events were preceded by subflares and class 1 flares. These transient events are interpreted as evidence for a coronal magnetic bottle at 10 R _⊙. The velocity of propagation for the disturbance is set at 200 km/sec; the dimension of the region, 10 R _⊙; field strength at 10 R _⊙, 0.02 G; particle density, 2.0 × 10⁴/cm³; Alfvén speed, 320 km/sec. From the nature of the observations and the lack of related effects from similar flares on the interplanetary sector pattern observed at 1 AU, it is suggested that such coronal magnetic bottles expand to perhaps 10–30 R _⊙ and then contract to a few solar radii. Such a phenomena is evidence for an expansion of the corona with a sub-Alfvénic velocity. It is further suggested that such magnetic bottles may be important in the storage and diffusion of solar generated cosmic ray particles. NAS-NRC Postdoctoral Resident Research Associate.     

Gamma-ray lines and neutrons from solar flares

An analysis, with a representative (canonical) example of solar-flare-generated equatorial disturbances, is presented for the temporal and spatial changes in the solar wind plasma and magnetic field environment between the Sun and one astronomical unit (AU). Our objective is to search for first order global consequences rather than to make a parametric study. The analysis - an extension of earlier planar studies - considers all three plasma velocity and magnetic field components (V _r, V_φ, V₀, and B _r, B₀, B_φ) in any convenient heliospheric plane of symmetry such as the ecliptic plane, the solar equatorial plane, or the heliospheric equatorial plane chosen for its ability (in a tilted coordinate system) to order northern and southern hemispheric magnetic topology and latitudinal solar wind flows. Latitudinal velocity and magnetic field gradients in and near the plane of symmetry are considered to provide higher-order corrections of a specialized nature and, accordingly, are neglected, as is dissipation, except at shock waves. The representative disturbance is examined for the canonical case in which one describes the temporal and spatial changes in a homogeneous solar wind caused by a solar-flare-generated shock wave. The ‘canonical’ solar flare is assumed to produce a shock wave that has a velocity of 1000 km s^#X2212;1 at 0.08 AU. We have examined all plasma and field parameters at three radial locations: central meridian and 33° W and 90° W of the flare's central meridian. A higher shock velocity (3000 km s^#X2212;1) was also used to demonstrate the model's ability to simulate a strongly-kinked interplanetary field. Among the global (first-order) results are the following: (i) incorporation of a small meridional magnetic field in the ambient magnetic spiral field has negligible effect on the results; (ii) the magnetic field demonstrates strong kinking within the interplanetary shocked flow, even reversed polarity that - coupled with low temperature and low density - suggests a viable explanation for observed ‘magnetic clouds’ with accompanying double-streaming of electrons at directions ～ 90° to the heliocentric radius.     

Hydromagnetic free-convection effects on the oscillatory flow in the Stokes' problem past a vertical limiting surface,I

This paper presents an approximate solution to a two-dimensional free-convection flow of a viscous, incompressible fluid past an infinite vertical, porous, limiting surface under the following conditions: (i) the fluid is electrically conducting; (ii) the limiting surface is electrically non-conducting; (iii) the free-stream velocity oscillates in time about a constant mean; (iv) suction velocity normal to the limiting surface is constant; (v) the limiting surface temperature is constant; (vi) the limiting surface is moved impulsively in its own plane with velocityU ₀; (vii) there exist free-convection currents due to the difference between the limiting surface temperature and the free-stream temperature; (viii) a uniform transverse magnetic field is applied. The mean velocity, mean temperature, mean induced magnetic field and related quantities are shown graphically, followed by a discussion.     

Evaluating Mean Magnetic Field in Flare Loops

We analyze multiple-wavelength observations of a two-ribbon flare exhibiting apparent expansion motion of the flare ribbons in the lower atmosphere and rising motion of X-ray emission at the top of newly-formed flare loops. We evaluate magnetic reconnection rate in terms of V _r B _r by measuring the ribbon-expansion velocity (V _r) and the chromospheric magnetic field (B _r) swept by the ribbons. We also measure the velocity (V _t) of the apparent rising motion of the loop-top X-ray source, and estimate the mean magnetic field (B _t) at the top of newly-formed flare loops using the relation 〈V _t B _t〉≈〈V _r B _r〉, namely, conservation of reconnection flux along flare loops. For this flare, B _t is found to be 120 and 60 G, respectively, during two emission peaks five minutes apart in the impulsive phase. An estimate of the magnetic field in flare loops is also achieved by analyzing the microwave and hard X-ray spectral observations, yielding B=250 and 120 G at the two emission peaks, respectively. The measured B from the microwave spectrum is an appropriately-weighted value of magnetic field from the loop top to the loop leg. Therefore, the two methods to evaluate coronal magnetic field in flaring loops produce fully-consistent results in this event.     

A global 3-D simulation of interplanetary dynamics in June 1991

The global dynamics of the solar wind and interplanetary magnetic field in June 1991 is simulated based on a fully three-dimensional, time-dependent numerical MHD model. The numerical simulation includes eight transient disturbances associated with the major solar flares of June 1991. The unique features of the present simulation are: (i) the disturbances are originated at the coronal base (1R _s) and their propagation through inhomogeneous ambient solar wind is simulated out to 1.5 AU; (ii) as a background for the transients, the global steady-state solar wind structure inferred from the 3-D steady-state model (Usmanov, 1993c) is used. The parameters of the initial pulses are prescribed in terms of the near-Sun shock velocities (as inferred from the metric Type II radio burst observations) relative to the preshock steady-state flow parameters at the flare sites. The computed parameters at the Earth's location for the period 1–18 June, 1991 are compared with the available observations of the interplanetary magnetic field, solar wind velocity, density, and with variation of the geomagnetic activityK _pindex.     

Effects of the external temperature-dependent heat sources on the unsteady free convective and mass-transfer hydromagnetic flow in the stokes problem

There have been considered the effects of external temperature-dependent heat sources and mass transfer on free convection flow of an electrically conducting viscous fluid past an impulsively starting infinite vertical limited surface in presence of a transverse magnetic field as considered. Solutions for the velocity and skin-friction, in closed form are obtained by using the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),M (Hartmann number), andS (Strength a Source or Sink) are given in graphical form. The paper is concluded with a discussion on the obtained results.