Magnetic Cloud; Constant Alpha Force-Free Field Model.

The magnetic field configuration in a magnetic cloud is approximately force-free [Goldstein, 1983; Marubashi, 1986]. A useful analytical approximation for the magnetic field configuration is the static, constant-alpha (where J =B), force-free, cylindrically symmetric configuration [Burlaga, 1988] given by the Lundquist solution [Lundquist, 1950]. More accurate models must consider that magnetic clouds expand as they move away from the sun [Burlaga et al., 1981; Klein and Burlaga, 1982]. Models of expanding magnetic clouds are reviewed by Burlaga [1995], and we note the recent work of Farrugia et al, [1992, 1995]; Osherovich et al. [1993, 1995]; and Vandas et al., [1995]. Magnetic clouds can interact with other flows [Burlaga, 1995]; in particular, the magnetic cloud that is the subject of this paper was being overtaken by a corotating stream. The theory of such interactions remains to be developed. The global form of a magnetic cloud on a 1 AU scale is illustrated in Figure 2 from Burlaga et al. [1990], based on an analysis of multi-spacecraft data. The geometry is that of a large flux-rope. The magnetic field lines are helices whose pitch angle increases with increasing distance from the axis of the magnetic cloud. A detailed analysis of one magnetic cloud showed that the magnetic field lines can extend continuously from the sun through the magnetic cloud to the lobe of the geomagnetic tail [Farrugia et al, 1993c]!

Fitting the Lundquist solution to the observations using the method of Lepping et al. [1990] gives the results in Figure 3. The fit is to the magnetic field data for the 30 hour interval beginning at 291.791 (see Figure 1). The front boundary is well-defined (as discussed in the next section), but there is uncertainty in the position of the rear boundary (see below). The rear boundary could have occurred as early as 292.954 (the first interface marked in Figure 1) or as late as 293.068 when the elevation angle drops abruptly to near 0⁰. The top three panels of Figure 3 show that the fit (solid curves) describes the observations (dots) of the three components of the magnetic field rather well. The reduced chi-squared to the fit, ²/(3N - n) where N = 30 is the number of points and n = 5 is the number of parameters in the fit, is only 0.019. Extending the fit another 2 hours gives a reduced chi-squared equal to 0.029, suggesting that the shorter interval better identifies the magnetic cloud. The variation of the magnetic field strength is not modeled accurately, in part because of the interaction with a corotating stream that produced an enhancement of the magnetic field by both a corotating shock which entered the magnetic cloud and a compression of the rear of the magnetic cloud, and possibly because of the age of the cloud. Theoretical studies are needed to explain this profile. The bottom two panels of Figure 3 show that, despite the unusual magnetic field strength profile, the constant-alpha force-free model provides an excellent fit to the variation of the direction of the magnetic field, indicating that the "force-free flux-rope" geometry was not destroyed by the interaction.

The axis of the magnetic cloud is estimated to be in the direction = -10⁰, = 291⁰, i.e., close to the ecliptic and 69⁰ from the radial direction, which is rather typical [Lepping et al., mmmm1990], and the magnetic cloud was right-handed. The spacecraft nearly intercepted the axis of the magnetic cloud, yo/Ro being 0.087, where yo is the closest approach distance to the magnetic cloud and Ro is its radius. This result is consistent with the observation of an extended interval of negative Bz followed by a similar interval of positive Bz. The diameter was 0.27 AU, which is typical for magnetic clouds at 1 AU. However, the duration of the passage of the magnetic cloud ( 1230 hours) is relatively long owing to its moderate speed, so that the geomagnetic effects should be prolonged.