D. S. Spicer

An Unstable Arch Model of a Solar Flare

The theoretical consequences of assuming that a current flows along flaring arches consistent with a twist in the field lines of these arches are examined. It is found that a sequence of magneto-hydrodynamic (MHD) and resistive MHD instabilities driven by the assumed current (which we refer to as the toroidal current) can naturally explain most manifestations of a solar flare.The principal flare instability in the proposed model is the resistive kink (or tearing mode in arch geometry) which plays the role of thermalizing some of the field energy in the arch and generating X-configured neutral points needed for particle acceleration. The difference between thermal and nonthermal flares is elucidated and explained, in part, by amplitude-dependent instabilities, generally referred to as overlapping resonances. We show that the criteria for the generation of flare shocks strongly depend on the magnitude and gradient steepness of the toroidal current, which also are found to determine the volume and rate of energy release. The resulting model is in excellent agreement with present observations and has successfully predicted several flare phenomena.

A numerical model of a solar flare based on electron beam heating of the chromosphere

There are two parts to this paper. In the first we calculate the hydrodynamic response of the solar atmosphere to the injection of an intense beam of electrons in a numerical simulation of a solar flare. In the second we predict the spectroscopic consequences of the hydrodynamic behaviour calculated in the first part. The hydrodynamics is predicted by solving the equations of conservation of mass, momentum, and energy. The latter is expressed as two temperature equations; one for the electrons and the other for the neutral atoms and positive ions of hydrogen. The equations are solved in one dimension and the geometric form is of a semi-circular loop having its ends in the photosphere. The results show how the loop is filled at supersonic speed with plasma at temperatures characteristic of flares. At the same time a compression wave is predicted to propagate down towards the photosphere. After the heating pulse stops, the plasma that has risen into the loop, starts to decay and return to the condition it was in before the pulse started. In predicting the spectrum that would be emitted by such a plasma calcium was chosen for illustration. The first and main part of this calculation was setting up and solving the time-dependent equations of ionization/recombination. In order to provide a standard for comparison the same ionization and recombination rate coefficients are used to predict the steady-state distribution of populations of ionization stages. This is then compared with the distribution found from the time-dependent solution and shows that there is a negligibly small time lag predicted by the time-dependent result. However the more significant comparisons to make are between the temperatures of the peak abundances of the various ions under the assumptions of steady-state and time-dependent ionization. For the particular circumstances chosen here the temperature differences are predicted to be in the neighbourhood of 10% or less and in view of the overall accuracy of the atomic data are not significant. It would appear therefore that the much simpler assumption of steady-state ionization balance leads to results of acceptable accuracy for the particular case considered.

Loop models of solar flares: Revisions and comparisons

Due to developments in solar flare observations which appear to show that a particular class of solar flares result from instabilities occurring in magnetic loops we re-examine the Alfvén-Carlqvist flare model to show that it is workable and we update the Spicer loop model of a flare. It is noted that the Alfvén-Carlqvist model of necessity requires an external current driver which must maintain the current driven instability at marginal stability during the duration of the flare. In addition, it is argued that if the Alfvén-Carlqvist model is to work the current density must rise in a time shorter than an MHD or resistive tearing mode time scale. Otherwise, the dominant flare mechanism must be an ideal MHD or tearing type instability. Further, the distinctions between the two models are highlighted and a new hybrid model of the Alfvén-Carlqvist and Spicer models is introduced.

Electrostatically unstable heat flow during solar flares and its consequences

We examine some of the consequences of an electrostatically unstable return current associated with heat conduction during a solar flare. We note that an electrostatically unstable return current will lead to strong hydrodynamic effects and more rapid magnetic field thermalization, if reconnection is the source of primary energy release during a solar flare.

First phase heating and particle acceleration during solar flares by fast tearing modes

We develop a simple, but physically consistent, model of heating and particle acceleration by fast tearing modes, for modeling compact loop flares or erupting prominences. It is shown that there is a slow preheating, over many e -foldings of the instability, after which a rapid heating takes place in approximately one e-folding. The role of anomalous resistivity excited by the induced electric field during tearing is discussed, and how both thermal conduction and plasma expansion may play a role in cooling. Estimates for the total number of thermal and non-thermal electrons generated by one fast tearing mode are given, and it is argued that collisional tearing modes give rise to a primarily thermal plasma.

The stark broadening mechanism in an unstable plasma

We consider a beam driven unstable plasma and estimate the turbulent electric fields which may be excited by this beam. We then estimate the Stark broadening due to such fields.

Longitudinal friction and intermediate Mach number collisionless transverse magnetosonic shocks

It is shown that for collisionless transverse magnetosonic shocks, there exists an intermediate range of Mach numbers between the maximum Mach number for transverse resistivity and the onset of significant ion reflection. In this intermediate range, the structure is dominated by a breakdown of the quasineutrality approximation, and longitudinal friction is a simple fluid model for the dissipation mechanism which forms the shock. Applications are discussed for laboratory shocks as well as the Earth’s bow shock.

On line tying

We discuss the claim frequently found in the solar physics literature that line tying in the photosphere is capable of stabilizing certain classes of both ideal and resistive MHD instabilities. Our approach is to present a picture of the physical origins of line tying and how resistive effects will affect it.

A comment on the acceleration of charged particles in the presence of micro-turbulence as related to solar flares

In this note we clarify the conditions in which charged particles may be accelerated by a DC electric field in the presence of plasma micro-turbulence.

Coronal heating and photospheric boundary conditions

We present a simple model that demonstrates that regions of high current density cannot exist within the solar atmosphere in a quasi-stationary state if they do not already exist at the photospheric boundary. This result demonstrates that theoretical treatments of coronal heating by electrodynamic processes must take proper account of the photospheric spatial distribution of the forces that generate the currents (or equivalently waves) and not just the power contained in those waves that result in coronal heating.