Consequences of the force-free model of magnetic clouds for their heliospheric evolution

We examine the implications of the widely used, force-free, constant-alpha flux rope model of interplanetary magnetic clouds for the evolution of these mesoscale (fraction 1 AU) structures in the heliosphere, with special emphasis on the inner (<= 1 AU) heliosphere. We employ primarily events observed by the Helios 1 and 2 probes between 0.3 and 1 AU in the ascending and maximum phases of solar cycle 21 and by Wind at 1 AU in a similar phase of solar activity cycle. We supplement these data by observations from other spacecraft (e. g., Voyagers 1 and 2, Pioneers 10 and 11, and others). Our data set consists of 130 events. We explore three different approaches. In the first, we work with ensemble averages, binning the results into radial segments of width 0.1 AU in the range 0.3 <= r(h) <= 1 AU. Doing this, we find that in the inner heliosphere the modeled average central axial field strength, [B-0], varies with heliospheric distance r(h) as [B-0] [nT] = 18.1 . r(h)(-1.64) [AU], and the average diameter increases quasi-linearly as [D] [AU] = 0.23 r(h)(1.14). The orientation of the axis of the underlying magnetic flux tube in our data set is generally found to lie along the east-west direction and in the ecliptic plane at all values of r(h), but there is considerable scatter about these average directions. In the second, we monitor the evolution of magnetic clouds in snapshot fashion, using seven spacecraft alignments. The results are in broad agreement with the statistics reported under step 1. In the final approach, we obtain the functional dependence of B0 and D predicted by an analytic expression for a freely expanding Lundquist flux tube. We find D to vary linearly with r(h), broadly similar to that obtained under approach 1. The maximum field strength scales as (--)(r)2 compared to a r(h)(-1.3) dependence obtained from statistics. We compare our findings with those of Bothmer and Schwenn (1998), who used a different methodology. The results obtained form a good background to the forthcoming Solar Terrestrial Relations Observatory (STEREO) and Sentinels missions and to multispacecraft studies of magnetic clouds.