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Astron. Astrophys. 331, 1147-1156 (1998)

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1. Introduction

Fast particle beams play a very important role in many physical processes observed in space, e.g. in solar flares (Kundu et al., 1989) and cosmic jets (Benford 1985, Blandford, Begelman and Rees 1982). Such beams can be registered directly by particle detectors in interplanetary space (Lin et al. 1986), or indirectly through their electromagnetic emissions. Beams can be charged (electron, proton and ion beams) or ionised but neutral, having both electron and proton components of the same density and velocity. An important aspect of such a neutral beam is that it does not constitute an electric current, with possible implications for the global electrodynamics of the acceleration process (e.g. Martens 1988). Partly for this reason neutral beams have been invoked as playing a central role in some outstanding astrophysical problems. In particular Simnett and Haines (1990) have claimed that injection of a neutral beam whose energy flux is initially in the ions may lead to hard X-ray bremsstrahlung production by acceleration of runaway electrons in an electric field generated by collisional separation of charges in the beam. Secondly Lesch et al (1989) have proposed that similar charge separation effects, resulting from injection of a fast neutral flow into a cool gas ring around a galactic centre, constitute a current which creates a magnetic field and that this may answer the fundamental cosmic problem of production of a seed magnetic field for dynamo action (cf. also Biermann 1950). Other astrophysical applications may include the interaction of galactic (AGN) and stellar (T-Tauri jets) with their ISM/IGM environments. Though we do not address the issue here, a key question is how such jets manage to remain collimated and rectilinear so far from their sources. While these ideas are interesting and stimulating, in none of these analyses is the electrodynamics treated self consistently. This is in part because the complexity of real cosmic situations demands approximations and estimates. It is clear, however, that improvement in our understanding of neutral beam propagation is essential to these important astrophysical problems.

In this paper we shed light on these problems by examining the behaviour of neutral beams in some simplified situations to enable progressive insight into real situations. In particular we obtain solutions for a series of idealised situations both by analytic and particle simulation treatments (using an electrostatic particle code) and compare the results of these two approaches with those claimed earlier by others. One element which we take care to include is the displacement current term which is frequently ignored, since it can play a central role in the transient behaviour which can be crucial to the nature of any final quasi-steady state reached as was noted by Brown and Bingham (1984) in relation to return current neutralisation of charged beams (cf. Miller 1982, Oss and van den Oord 1995).

Due to more effective collisional deceleration of the electron component of the neutral beam, compared to the protons, electric fields are generated which act against the collisional electron-deceleration force. Intuitively, the appearance of this electric field E can usually be viewed as being generated by a non-zero charge density or, equivalently, by the displacement current. However, in an infinite homogeneous beam, for which the charge density is everywhere zero, there exists an E field due to the commonly neglected displacement current [FORMULA], where the current density j is due to the differing beam electron and proton velocities due to collisions. In this case, the charge density picture is intuitively confusing, but in some sense it can be understood that the E -field is generated by charges at infinity. No magnetic fields are involved, as shall be proved below.

In our treatment we start by examining the behaviour of electrons, ions and electric fields generated by the interaction of a neutral `beam' with a dense background plasma whose particles are `immobile' so that it provides collisional drag on the beam particles but does not produce a background current in response to the electric field. This case corresponds very closely to that of an unionised gas, the only difference being in the constants appearing in the collisional term. We shall refer to this artificial background as an unresponsive plasma. First we consider the homogeneous situation in which the `beam' exists everywhere, electrons and ions being `launched' initially with the same speed. Then we consider a true `injection' problem where the beam is semi-infinite and beam head effects appear explicitly. Next, we consider a realistic background plasma which responds to the electric field by producing a plasma current which can significantly modify the system's behaviour as noted by Simnett and Haines (1990). In our analytic treatment of these problems the beam is treated as having unique particle speeds, so a test particle approach is required to treat electron runaway. However, our particle simulations have some randomisation of speeds and therefore should exhibit the runaway effects proposed by Simnett and Haines (1990).

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998