Field-aligned conductance values estimated from Maxwellian and kappa distributions in quiet and disturbed events using Freja electron data

We study the question of what di€erence it makes for the derived ®eld-aligned conductance (K) values if one uses Maxwellian or kappa distributions for the ®tting of low-orbiting satellite electron ̄ux spectra in the auroral region. This question has arisen because sometimes a high-energy tail is seen in the spectra. In principle, the kappa ®ts should always be better, because the kappa distribution is a generalization of the Maxwellian. However, the physical meaning of the parameters appearing in the Maxwellian is clearer. It therefore makes sense to study under which circumstances it is appropriate to use a Maxwellian. We use Freja electron data (TESP and MATE) from two events. One of the events represents quiet magnetospheric conditions (stable arc) and the other represents disturbed conditions (surge). In these Freja events, at least, using kappa rather than Maxwellian ®tting gives a better ®t to the observed distribution, but the di€erence in K values is not large (usually less than 20%). The di€erence can be of either sign. However, sometimes even the kappa distribution does not provide a good ®t, and one needs a more complicated distribution such as two Maxwellians. We investigate the relative contributions of the two Maxwellians to the total ®eld-aligned conductance value in these cases. We ®nd that the contribution of the highenergy population is insigni®cant (usually much less than 20%). This is because K is proportional to n=  Ec p , where n is the source plasma density and Ec is the characteristic energy. Key words. Field-aligned conductance á Maxwellian distribution á Kappa distribution á Freja electron data 1 Introduction Electron ̄ux energy spectra measured by satellites in the auroral region contain information of the source plasma properties (density Ne, characteristic energy Ec) and the acceleration region (the accelerating voltage V ). In this paper we are mainly interested in the ®eld-aligned conductance K (Weimer et al., 1987) which depends on the source plasma properties. Traditionally, one has estimated these parameters by ®tting an accelerated Maxwellian distribution to the data (Evans, 1974) . In the Maxwellian case the ®eld-aligned conductance is proportional to Ne=  Ec p (Lundin and Sandahl, 1978; Fridman and Lemaire, 1980). However, sometimes one observes a high-energy tail in the electron ̄ux energy spectra, which can not be ®tted well by an accelerated Maxwellian (Vasyliunas, 1968; Sarris et al., 1981; Christon et al., 1988). These authors have used the kappa distribution (Vasyliunas, 1968) to describe these situations. The purpose of this paper is to investigate how sensitive the ®eld-aligned conductance K is to the choice of distribution function. The accelerated Maxwellian particle ̄ux is given by Evans (1974): F M ˆ 1 p Ne  2pme p E E c eÿ EÿeV Ec … † ; …1† where Ne is the source plasma density, me is the electron mass, E is the particle energy, Ec is the characteristic energy (source plasma temperature in energy units) and V is the accelerating potential. The accelerated kappa distribution particle ̄ux is given by F j ˆ 1 p Ne  2pme p E E c C…j† C…jÿ 1=2†  j p