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Astron. Astrophys. 353, 729-740 (2000)

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1. Introduction

The association of energetic particle signatures (radio, HXR and [FORMULA]-ray) with the impulsive phase of solar flares has resulted in decades of discussion of whether or not non-thermal particle beams play a role in flare energy transport. In particular, the fact that if HXR bursts are interpreted in terms of the collisional thick target electron beam model (Brown 1971), the inferred beam power is sometimes of the same order as the flare power has led to much work on electron beam models of flare heating. Though this model is attractive and receives wide support and use, there have been arguments against it (see e.g. review by Simnett 1995). These include for example the fact that some flares have no, or weak, HXR signatures or exhibit no tight correlation between the light curves of HXRs and various thermal signatures (Feldman et al. 1980). In addition, the model raises several theoretical concerns. First, how likely are acceleration processes to result in preferential deposition of energy in electrons rather than ions (Simnett 1995). Second, how likely is it that a large fraction of magnetic energy release results in acceleration rather than heating? - a question that applies to any non-thermal beam model for flare energy transport. Thirdly, in the electron beam model, the beam number flux is also very large. This fact means that the accelerator must be capable of acting on a large fraction of the particle population in a typical coronal loop. Also, as the beam propagates, its large current electro-dynamically generates an electric field which drives a neutralising return current in the background plasma. This is sometimes misinterpreted as `having to invoke' a return current to `get around a problem with the model' whereas it is an inevitable physical consequence of the propagation of any beam involving charged particles, as we discuss further below.

Because of these objections to the electron beam model, some authors (e.g. Simnett 1995, Simnett & Haines 1990) have proposed that flare energy transport may instead (or also) involve proton or neutral (p+,e-) beams, and suggested that HXRs are a by-product of these. Various observations have been proposed as favouring proton or neutral beams though the inferences are still somewhat ambiguous. These include H[FORMULA] impact polarisation (cf. Henoux et al. 1990, Fletcher & Brown 1995, 1998) and [FORMULA]-ray lines produced by few-MeV ions (cf. Ramaty et al. 1995, Emslie et al. 1997). One of the key issues for such beam models involving protons is how the flare HXR burst is produced, and this is the main issue we address here.

Heristchi (1986, 1987) pointed out that HXRs of (say) 50 keV can be produced by a proton beam of 100MeV as the protons collide with ambient electrons (p-e bremsstrahlung which is equivalent to e-p bremsstrahlung in the proton frame). This can produce a typical HXR burst with a beam power equal to that required in an electron beam model but with a beam flux [FORMULA] times smaller. The model fails, however, because the very high proton energies needed would result in [FORMULA]-ray flare fluxes far in excess of those observed (Emslie & Brown 1985). Models invoking heating by protons or neutral beams of lower particle energy (typically 1-10MeV) have to date offered no quantitative model of how [FORMULA]50 keV HXRs would result. Before we discuss that further, some further remarks on return currents and neutral beams are in order. When protons are accelerated directionally the current they carry must also result electrodynamically in a neutralising return current if the beam is to propagate. If a proton beam is injected into a dense background plasma, the resulting electric field will result in a neutralising drift of (negative) plasma electrons along the beam direction. This drift current can be dense and slow, compared to the beam velocity, but excited at the beam head through a rapidly increasing volume of the plasma as the beam propagates. In the case of the sun, however, a proton beam is not injected from a gun but is accelerated inside the plasma itself. In this acceleration region the accelerated protons have the same density as the local electrons and the return current may take the form of all the electrons moving at the same longitudinal speed of the protons, the electrons being electrostatically dragged by the protons as soon as they separate by a Debye length. Because the densities are the same, the proton acceleration will essentially result in a neutral beam of proton electron pairs emerging from the acceleration region, essentially as in the models of Martens (1988) and Litvinenko & Somov (1995). As we will see in Sect. 5, the initial stages of neutral beam production and propagation are crucial in the viability of the HXR production process we discuss.

The problem of how such a neutral beam propagates through a background plasma or gas has been discussed in Simnett & Haines (1990) and by Brown et al. (1998a) in relation to how HXR bursts might result. The key effect is that collisions with the background produce a larger deceleration on the beam electrons than on the protons, causing the electrons to lag behind and producing an electric field. Under certain conditions, which we discuss more fully in Sect. 5, and certainly in the case of a mostly unionised background plasma, or of a background plasma that is not much denser than the beam, the beam charge separation and associated electric field persist and the beam electrons continue to be dragged by the protons. Simnett & Haines (1990) have pointed out that this electric field is large enough to accelerate background electrons to high enough energies for HXR production. However, Brown et al. (1998a) conclude that the runaway electron flux can only be very small compared to the beam flux since, if it were not, it would very rapidly neutralise the electric field creating it and quench itself. Brown et al. (1998a) conclude that this runaway mechanism is completely inadequate to yield electron beam fluxes sufficient for HXR burst production.

In this paper we consider an effect, hitherto neglected, in the neutral beam propagation problem, which results in HXR production. Though, as we shall see, it does not suffice to solve the flare HXR problem; it is a process which does result in significant HXR production, and is therefore of interest as a flare neutral beam diagnostic and also in more general astrophysical situations involving neutral beams. In the Simnett & Haines (1990) and Brown et al. (1998a) analyses, only 1D motion was considered in the collisional energy transfer process. Brown et al. concluded that, in this case, beam electron motion only comprises longitudinal oscillations, about the beam protons, of very small amplitude and speed. But in reality collisions with the background also scatter the beam electrons, converting beam longitudinal energy into random transverse motion which is not affected by the charge separation field. As the beam propagates we expect the magnitude of this collisionally produced transverse electron energy to grow. In Sect. 2, we present particle simulations which indeed show the initial development of this process. In Sect. 3 we evaluate its full development using an analytic approximation, and in Sect. 4 we discuss the resulting bremsstrahlung radiation signature, and its relevance to flare HXR bursts. In Sect. 5 we discuss the effect of free electrons in the background plasma. In Sects. 3 and 4, however, we assume background conditions are such that they do not much affect the charge separation electric field. For simplicity, however, we treat collisions using the rates appropriate to an ionised plasma, those for a unionised gas differing only by factors of 2-3, within the orders of magnitude effects with which we are concerned here.

We emphasise that this is the first treatment of this particular effect in neutral beams and is aimed at illustrating its potential importance in flare HXR production, so the analysis is deliberately kept as simple as possible. In particular the following assumptions /idealisations are made: (a) by a beam we mean, in common with previous flare beam modelling, a well collimated particle distribution - i.e one which has [FORMULA]; (b) the beam is initially `cold' - i.e. [FORMULA] though as it propagates the electron component becomes `hot'; (c) the beam is very tenuous compared to the background gas density; (d) the beam kinetic energy density is larger than the thermal energy of the background gas so the latter is significantly heated by it but because of (c) never to a high enough temperature to produce HXRs or to modify our analysis of beam collisions; (e) the mean free path of beam particles is long compared to all relevant gradient lengths and the beam duration is long compared with the particle stopping time. Consequently the interaction of beam and gas is treated kinetically and as a quasi-steady spatially extended structure, rather then a fluid boundary interaction (shock) problem; (f) the interaction is described purely in terms of mean particles with no coherent effects considered; (g) for simplicity we consider the problem basically in terms of monoenergetic injection spectra discussing other spectra merely by summing contributions from different energies.

These last assumptions (f) and (g) are those which most need further investigation. In a purely neutral background gas they are quite reasonable but in the ionised coronal region of initial beam propagation it is possible that coherent generation of plasma waves will modify the beam behaviour from our purely collisional description. This is certainly the case for monoenergetic charged beams propagating in an ionised background, as widely discussed for Type III radio burst production (McLean & Labrum 1985), and also under some background plasma conditions even for beams with monotonic decreasing injection spectra (Emslie & Smith 1984). However both theoretically and even moreso observationally (Melrose 1980, Benz 1993) the effects in these cases, if any, are mainly to redistribute energy among beam electrons rather than to extract much energy from the beam. For this reason coherent effects have, following Brown (1971), commonly been neglected in modelling of HXR production by electron beams. In the present case their importance is even less clear since the beam itself has nett neutrality. We note furthermore that most of the collisional heating of beam electrons, which lies at the heart of our model, occurs well along the beam column density path where the background is substantially neutral. Thus while the issue of coherent effects does need addressing for the neutral beam model we do not address it in the present paper for the neutral beam.

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© European Southern Observatory (ESO) 2000

Online publication: December 17, 1999