**Publication Date:** 2009.

**Language:** English.

**Abstract:**

Context. A magnetic cloud (MC) is a magnetic flux rope in the solar wind (SW), which, at 1 AU, is observed ∼2-5 days after its expulsion from the Sun. The associated solar eruption is observed as a coronal mass ejection (CME).Aims. Both the in situ observations of plasma velocity distribution and the increase in their size with solar distance demonstrate that MCs are strongly expanding structures. The aim of this work is to find the main causes of this expansion and to derive a model to explain the plasma velocity profiles typically observed inside MCs.Methods. We model the flux rope evolution as a series of force-free field states with two extreme limits: (a) ideal magneto-hydrodynamics (MHD) and (b) minimization of the magnetic energy with conserved magnetic helicity. We consider cylindrical flux ropes to reduce the problem to the integration of ordinary differential equations. This allows us to explore a wide variety of magnetic fields at a broad range of distances to the Sun.Results. We demonstrate that the rapid decrease in the total SW pressure with solar distance is the main driver of the flux-rope radial expansion. Other effects, such as the internal over-pressure, the radial distribution, and the amount of twist within the flux rope have a much weaker influence on the expansion. We demonstrate that any force-free flux rope will have a self-similar expansion if its total boundary pressure evolves as the inverse of its length to the fourth power. With the total pressure gradient observed in the SW, the radial expansion of flux ropes is close to self-similar with a nearly linear radial velocity profile across the flux rope, as observed. Moreover, we show that the expansion rate is proportional to the radius and to the global velocity away from the Sun.Conclusions. The simple and universal law found for the radial expansion of flux ropes in the SW predicts the typical size, magnetic structure, and radial velocity of MCs at various solar distances. © 2009 ESO.

**Author affiliation**: Dasso, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

**Keywords:**
interplanetary medium; Sun: coronal mass ejections (CMEs); Sun: magnetic fields; Boundary pressure; Coronal mass ejection; Cylindrical flux ropes; Expansion rate; Flux ropes; Force free fields; In-situ observations; interplanetary medium; Magnetic clouds; Magnetic energies; Magnetic flux ropes; Magnetic helicity; Plasma velocity; Radial distributions; Radial expansions; Radial velocity; Self-similar; Solar eruption; Sun: coronal mass ejections (CMEs); Sun: magnetic fields; Astrophysics; Boundary layer flow; Energy conservation; Expansion; Fluid dynamics; Magnetic fields; Magnetic flux; Magnetic structure; Magnetohydrodynamics; Ordinary differential equations; Pressure gradient; Solar wind; Sun; Velocity; Velocity distribution; Solar energy.

**Repository:** Biblioteca Digital (UBA-FCEN). Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

**Publication Date:** 2013.

**Language:** English.

**Abstract:**

Context. Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs). One property of MCs is the presence of a magnetic flux rope. Is the difference between ICMEs with and without MCs intrinsic or rather due to an observational bias? Aims. As the spacecraft has no relationship with the MC trajectory, the frequency distribution of MCs versus the spacecraft distance to the MCs' axis is expected to be approximately flat. However, Lepping & Wu (2010, Ann. Geophys., 28, 1539) confirmed that it is a strongly decreasing function of the estimated impact parameter. Is a flux rope more frequently undetected for larger impact parameter? Methods. In order to answer the questions above, we explore the parameter space of flux rope models, especially the aspect ratio, boundary shape, and current distribution. The proposed models are analyzed as MCs by fitting a circular linear force-free field to the magnetic field computed along simulated crossings. Results. We find that the distribution of the twist within the flux rope and the non-detection due to too low field rotation angle or magnitude only weakly affect the expected frequency distribution of MCs versus impact parameter. However, the estimated impact parameter is increasingly biased to lower values as the flux rope cross section is more elongated orthogonally to the crossing trajectory. The observed distribution of MCs is a natural consequence of a flux rope cross section flattened on average by a factor 2 to 3 depending on the magnetic twist profile. However, the faster MCs at 1 AU, with V > 550 km s-1, present an almost uniform distribution of MCs vs. impact parameter, which is consistent with round-shaped flux ropes, in contrast with the slower ones. Conclusions. We conclude that the sampling of MCs at various distances from the axis does not significantly affect their detection. The large part of ICMEs without MCs could be due to a too strict criteria for MCs or to the fact that these ICMEs are encountered outside their flux rope or near the leg region, or they do not contain a flux rope. © 2013 ESO.

**Author affiliation**: Dasso, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

**Keywords:**
Magnetic fields; Solar-terrestrial relations; Sun: coronal mass ejections (CMEs); Sun: heliosphere; Affect detection; Boundary shapes; Current distribution; Decreasing functions; Flux rope model; Flux ropes; Force free fields; Frequency distributions; Heliospheres; Impact-parameter; Interplanetary coronal mass ejections; Large parts; Low field; Magnetic clouds; Magnetic flux ropes; Natural consequences; Non-detection; Parameter spaces; Rotation angles; Solar-terrestrial relations; Spacecraft trajectories; Sun: coronal mass ejection; Uniform distribution; Aspect ratio; Computer simulation; Magnetic fields; Magnetic flux; Planetary surface analysis; Spacecraft; Trajectories; Parameter estimation.

**Repository:** Biblioteca Digital (UBA-FCEN). Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales