Abstract
Magnetic clouds (MCs) are the interplanetary counterpart of coronal mass ejections (CMEs). They transport the magnetic flux and helicity released in CMEs by the Sun. At 1 AU from the Sun, an MC is generally modeled as a static flux rope and its magnetic helicity content can be quantified (Dasso et al., JGR 108, 1362, 2003). However, an MC can be also modeled as an expanding structure when its velocity profile shows evidence of a significant expansion. Here we present a quantification of the global magnitudes for the expanding MC observed by the spacecraft Wind between August 09 (10:48UT) and August 10 (15:48UT), 1999. We use magnetic (Magnetic Field Instrument, MFI) and plasma (Solar Wind Experiment, SWE) data. We analyze here two cylindrical models: (1) a static model that considers the cloud magnetic structure as a linear force free field (i.e., the Lundquist's solution), and (2) a radial expanding selfsimilar model (Farrugia et al., JGR 98, 7621, 1993). In both cases, we derive expressions for magnetic fluxes, helicity, and energy. We apply the minimun variance method to find the cloud orientation and compute the cloud radius for the static model (R_s). For the dynamic model, we fit the initial radius for the expanding model (R_0) and the age of the cloud (T_0) from the observed velocity profile. We also fit the free parameters of each magnetic model using the magnetic observations, and find that the dynamical model better represents the data, since it fits the assymetry caused by the expansion in the cloud. Finally, for both models, we quantify the magnetic fluxes, helicity and energy, as done in Nakwacki et al. (Proc. Solar Wind 11 - SOHO 16, ESA SP-592, 629, 2005). We find a change in the computed helicity and fluxes of less than 30% (comparing static and dynamic models). Considering the range of time in which Wind observes the cloud, and the dynamic model, we find a magnetic energy decay of less than ≈ 12% and a radial expansion of 17%.