Context. Observations of magnetic clouds (MCs) are consistent with the presence of flux ropes detected in the solar wind (SW) a few days after their expulsion from the Sun as coronal mass ejections (CMEs). Aims. Both the in situ observations of plasma velocity profiles and the increase of their size with solar distance show that MCs are typically expanding structures. The aim of this work is to derive the expansion properties of MCs in the inner heliosphere from 0.3 to 1 AU. Methods. We analyze MCs observed by the two Helios spacecraft using in situ magnetic field and velocity measurements. We split the sample in two subsets: those MCs with a velocity profile that is significantly perturbed from the expected linear profile and those that are not. From the slope of the in situ measured bulk velocity along the Sun-Earth direction, we compute an expansion speed with respect to the cloud center for each of the analyzed MCs. Results. We analyze how the expansion speed depends on the MC size, the translation velocity, and the heliocentric distance, finding that all MCs in the subset of non-perturbed MCs expand with almost the same non-dimensional expansion rate (ζ). We find departures from this general rule for ζ only for perturbed MCs, and we interpret the departures as the consequence of a local and strong SW perturbation by SW fast streams, affecting the MC even inside its interior, in addition to the direct interaction region between the SW and the MC. We also compute the dependence of the mean total SW pressure on the solar distance and we confirm that the decrease of the total SW pressure with distance is the main origin of the observed MC expansion rate. We found that ζ was 0.91 ± 0.23 for non-perturbed MCs while ζ was 0.48 ± 0.79 for perturbed MCs, the larger spread in the last ones being due to the influence of the solar wind local environment conditions on the expansion.

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Context. A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Aims. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. Methods. We analyze MCs observed by the Ulysses spacecraft using in situ magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called ζ. We derive the value of ζ from the in situ velocity data. Results. We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (ζ = 1.05 ± 0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (ζ = 0.91 ± 0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (ζ = 0.28 ± 0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size, mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion).

Context. Significant quantities of magnetized plasma are transported from the Sun to the interstellar medium via interplanetary coronal mass ejections (ICMEs). Magnetic clouds (MCs) are a particular subset of ICMEs, forming large-scale magnetic flux ropes. Their evolution in the solar wind is complex and mainly determined by their own magnetic forces and the interaction with the surrounding solar wind. Aims. Magnetic clouds are strongly affected by the surrounding environment as they evolve in the solar wind. We study expansion of MCs, its consequent decrease in magnetic field intensity and mass density, and the possible evolution of the so-called global ideal-MHD invariants. Methods.In this work we analyze the evolution of a particular MC (observed in March 1998) using in situ observations made by two spacecraft approximately aligned with the Sun, the first one at 1 AU from the Sun and the second one at 5.4 AU. We describe the magnetic configuration of the MC using different models and compute relevant global quantities (magnetic fluxes, helicity, and energy) at both heliodistances. We also tracked this structure back to the Sun, to find out its solar source. Results. We find that the flux rope is significantly distorted at 5.4 AU. From the observed decay of magnetic field and mass density, we quantify how anisotropic is the expansion and the consequent deformation of the flux rope in favor of a cross section with an aspect ratio at 5.4 AU of ≈1.6 (larger in the direction perpendicular to the radial direction from the Sun). We quantify the ideal-MHD invariants and magnetic energy at both locations, and find that invariants are almost conserved, while the magnetic energy decays as expected with the expansion rate found. Conclusions. The use of MHD invariants to link structures at the Sun and the interplanetary medium is supported by the results of this multi-spacecraft study. We also conclude that the local dimensionless expansion rate, which is computed from the velocity profile observed by a single-spacecraft, is very accurate for predicting the evolution of flux ropes in the solar wind.

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