P. A. Sturrock

An Optimization Approach to Reconstructing Force-free Fields

A new method for reconstructing force-free magnetic fields from their boundary values, based on minimizing the global departure of an initial field from a force-free and solenoidal state, is presented. The method is tested by application to a known nonlinear solution. We discuss the obstacles to be overcome in the application of this method to the solar case: the reconstruction of force-free fields in the corona from measurements of the vector magnetic field in the low atmosphere.

Force-free magnetic fields - The magneto-frictional method

The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.

Evaporative Cooling of Flare Plasma.

Abstract : We investigate a one-dimensional loop model for the evaporative cooling of the coronal flare plasma. The important assumptions are that conductive losses dominate radiative cooling and that the evaporative velocities are small compared to the sound speed. We calculate the profile and evolution of the temperature and verify that our assumptions are accurate for plasma parameters typical of flare regions. The model is in agreement with soft x-ray observations on the evolution of flare temperatures and emission measures. The effect of evaporation is to greatly reduce the conductive heat flux into the chromosphere and to enhance the EUV emission from the coronal flare plasma. (Author)

Chromospheric Magnetic Reconnection and Its Possible Relationship to Coronal Heating

Coronal heating is clearly related to the coronal magnetic —eld. This may be due to a passive role of the magnetic —eld in modifying wave propagation and dissipation or to an active role resulting from the liberation of magnetic energy by reconnection or in some other way. The purpose of this article is to examine the consequences of reconnection at the chromospheric level rather than in the corona. We note that the chromosphere is indeed a favorable site for reconnection to occur, since the resistivity is greatest in that regionspeci—cally at the temperature-minimum location. Chromospheric reconnection can lead to coronal heating by Joule heating, by the generation and subsequent dissipation of high-frequency and magnetacoustic waves, or by the response of the coronal magnetic —eld to a sudden change Alfvec n in connectivity. The second process could also contribute to heating of the solar wind, since high- frequency waves can be absorbed by cyclotron damping. We note also that chromospheric recon- Alfvec n nection could inject sufficient chromospheric gas into the corona to balance the known steady down—ow of coronal gas through the transition region. It is also possible that chromospheric reconnection plays a role in the —rst ionization potential eUect. Subject headings: MHDSun: coronaSun: magnetic —elds

The possible role of MHD waves in heating the solar corona

The possible role of waves in the heating of the solar corona has been investigated. A general dispersion relation has been derived for waves propagating in a homogeneous plasma subject to dissipation by viscosity and thermal conduction. The dissipation mechanisms have been incorporated self-consistently into the equations, and no assumptions about the strength of the damping have been made. Solutions of the sixth-order dispersion relation provide information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. We provide a detailed comparison to the standard approach, which is to solve for the wave quantities in the absence of dissipation and then to use these quantities in expressions for the heating due to viscosity and thermal conduction.

The Waiting-Time Distribution of Solar Flare Hard X-Ray Bursts

A waiting-time distribution is constructed for 8 yr of solar flare hard X-ray bursts observed by the ICE/ISEE 3 spacecraft. The observed distribution is compared with a simulated waiting-time distribution produced by a time-dependent Poisson process constructed using rates estimated from the observations. The observed distribution shows an overabundance of short waiting times (10 s-10 minutes) in comparison with the simulation. This result implies that the hard X-ray bursts are not independent events. The implications of this result for the existence of sympathetic flaring and to models of flare statistics are discussed, and the result is compared with previous determinations of waiting-time distributions for solar hard X-ray events.

Centrifugal instability of the jovian magnetosphere and its interaction with the solar wind

Abstract The outer regions ( r > 2.3 R j ; R j = radius of Jupiter) of the magnetosphere of Jupiter will systematically accumulate plasma. If sufficient plasma accumulates, the field lines must open to allow the plasma to escape. Available energy sources appear able to supply plasma at a high enough rate to keep the field lines constantly open beyond about 60 R J . We suggest that the solar wind interaction with Jupiter may be essentially different from that with the Earth, with the Jovian magnetosphere opening up to form a planetary wind.

Metastable Magnetic Configurations and Their Significance for Solar Eruptive Events

Solar flares and coronal mass ejections (CMEs) involve the sudden release of magnetic energy that can lead to the ejection from the Sun of large masses of gas with entrained magnetic field. In dynamical systems, such sudden events are characteristic of metastable configurations that are stable against small perturbations but unstable to sufficiently large perturbations. Linear stability analysis indicates whether or not the first requirement is met, and energetic analysis can indicate whether or not the second requirement is met: if a magnetic configuration that is stable against small perturbations can make a transition to a lower energy state, then it is metastable. In this paper, we consider a long twisted flux tube, anchored at both ends in the photosphere and restrained by an overlying magnetic arcade. We argue from a simple order-of-magnitude calculation that, for appropriate parameter values, it is energetically favorable for part of the flux tube to erupt into interplanetary space, even when the configuration is stable according to linear MHD stability theory. The properties of metastable magnetic configurations may be relevant to CMEs and to other explosive astrophysical events such as solar flares.

MAGNETIC-FIELD STRUCTURE ASSOCIATED WITH CORONAL STREAMERS.

An interesting coronal structure was observed during the solar eclipse of May 30, 1965. This comprised a series of bright arches centered approximately on a quiescent prominence. A bright ray originated near the top of one of the arches and pointed almost radially away from the photosphere. The ray could be followed for 1.5 solar radii and was deflected towards a direction parallel to the equatorial plane.By comparing the photographs with Fraunhofer maps and magnetograms, the following interpretation of the structure was obtained. The prominence lies above the neutral line of an extended bipolar magnetic region. The bright arches coincide with flux tubes arising from small photospheric regions of enhanced magnetic-field strength. The ray represents a projection view of a thin region of enhanced plasma density in the neighborhood of a current sheet which separates two flux tubes of opposite polarity. The ray is interpreted as a coronal streamer, and it is suggested that all streamers are related to current sheets.

Rotational Signature and Possible r-Mode Signature in the GALLEX Solar Neutrino Data

Recent analysis of the Homestake data has yielded evidence that the solar neutrino flux varies in time—more specifically, that it exhibits a periodic variation that may be attributed to rotational modulation occurring deep in the solar interior, either in the tachocline or in the radiative zone. Here we present a spectral analysis of the GALLEX data that yields supporting evidence for this rotational modulation. The most prominent peak in the power spectrum occurs at the synodic frequency of 13.08 yr (cycles per year) and is estimated to be significant 21