## 2. Weak electric field accelerationThe electron energy gain in the current sheet is defined by the potential drop experienced by a particle: Here is the electron Lorentz
factor, and where is the reconnecting magnetic field. It is likely that the electric field acceleration will produce beams of electrons, possibly moving with an angle with respect to the magnetic field lines. In this case the energy loss rate will decrease by a factor of , and the loss length will increase by a factor of . Since the minimum length given by Eq. (2) is already on the order of the jet length, smaller synchrotron losses would be too weak to determine the acceleration length. The reconnection geometry in Fig. 1 suggests that the electrons are accelerated along the electric field and perpendicular to the reconnecting magnetic field outside the current sheet, so that indeed and the loss length is determined by Eq. (2). The influence of the magnetic field inside the sheet on the particle motion is ignored in the one-dimensional model.
Postulating that and taking G and according to observations (Meisenheimer et al. 1997), one obtains the electric field required in the model The large cm from Eq. (2)
requires the electric field to be very small. A conventional measure
of the field strength is the reconnection Alfvén Mach number
, where
is the inflow speed as measured by
the drift speed into the sheet,
cm s The weak electric field model is an attractively simple approach to the problem of electron acceleration in the jets by the DC electric field. More importantly, it can be used to explicitly relate the properties of the accelerated particles to the characteristics of the energy release by virtue of magnetic reconnection (Lesch & Birk 1998). In spite of these advantages, the model has several unappealing features. First, the energy release rate in a single current sheet is very small. The Poynting flux into the current sheet determines its luminosity which is only erg s Allowing for the possibility that the acceleration length is different for different particles, let us introduce the average value . The next section will show that this possibility is realized in reconnecting current sheets with a nonzero magnetic field. In any case, since the magnetic field energy is converted into the particle kinetic energy in the sheet, the Poynting flux in Eq. (4) should be equal to the product of the particle influx to the sheet, , and the average particle energy gain, . Equating the product of these two quantities to the Poynting flux gives the following self-consistency relation: (Alfvén 1968; Vasyliunas 1980). Using
statvolt/cm together with the
previous values for and © European Southern Observatory (ESO) 1999 Online publication: September 2, 1999 |