[1] We examine the implications of the widely used, force-free, constant-a 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 ·rh -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 By 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 h -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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006JA011940

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

[1] The one-point probability density functions (PDFs) obtained from the Wind spacecraft observations of the magnitude of total magnetic field (B) and the solar wind quasi-invariant (QI) are investigated at 1 AU during the years 1995 and 1998. It is known from previous studies that the distributions follow in a rather good approximation a lognormal distribution. This indicates that the underlying random multiplicative processes are skewed, the PDFs are nonsymmetric. The concept of kappa distributions generating PDF tails closer to the observed values is introduced. The skewness, characteristic for the multiplicative processes in the solar wind, is treated on the basis of log-kappa distributions, introduced here for the first time. Normal and lognormal distributions are related in a similar way to each other as the kappa and log-kappa distributions, although the statistics is based on extensive physics in the former and nonextensive physics in the latter cases. We show that log-kappa PDFs describe the observed distributions in the solar wind more accurately than the lognormal PDFs. In particular, the tails of PDFs corresponding to extreme values of the considered parameters B and QI are better modeled in terms of the nonextensive approach. It indicates that, for the theoretical explanation of the complexity of multisource fluctuations present in 1 year solar wind magnetic and plasma data, both the extensive and the nonextensive physical description is needed. The variation of the values of kappa obtained from the log-kappa fits can serve as a quantitative measure describing the changing balance between these two distinct physical processes during the solar cycle.

Introducing log-kappa distributions for solar wind analysis

Change of solar wind quasi-invariant in solar cycle 23-Analysis of PDFs

The solar wind quasi-invariant (QI) is defined as the ratio of the solar wind magnetic energy density to the plasma kinetic energy density (i.e., the inverse square of the Alfven Mach number). Previous work has found this quantity to be a good proxy for solar activity, correlating very well with the sunspot number at various heliospheric distances. It has the advantage of being locally determined from in situ measurements and can thus function as a heliospheric index of solar activity. Using STEREO A, STEREO B, and Wind data we obtain the distribution of QIs during the current solar activity minimum (March to December 2007). (1) We investigate whether this minimum is indeed weaker than previous ones by comparing this QI distribution with those during two other solar activity minima: 1995, using Wind data, and 1974, using Helios data at 1 AU. We find that, on average, QI(2007) is lower than during the previous two minima, indicating weaker solar activity. It also implies weaker MHD effects in solar wind flow around planetary magnetospheres, which, in turn, alters the solar wind’s interaction with them. (2) In all three solar cycle minima considered we find that the QI distributions are reasonably well represented by a log-normal distribution, for which we give the respective mean and standard deviations. These values are used in comparing the QIs over the three solar minima.

/pdf/the-solar-wind-quasi-invariant-observed-by-stereo-a-and-b-at-32e22lzl47.pdf

The solar wind Quasi-Invariant observed by Stereo A and B at solar minimum 2007 and comparison with two other minima

Deep Solar Activity Minimum 2007-2009: Solar Wind Properties and Major Effects on the Terrestrial Magnetosphere

The relative distribution of the magnetic and plasma kinetic energy densities in the inner heliosphere (< 1 AU)

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The relative distribution of the magnetic and plasma kinetic energy densities in the inner heliosphere (< 1 AU)