The Internal Magnetic Field Structure of ICMEs in the Heliosphere

Interplanetary coronal mass ejections (ICMEs) are major drivers of heliospheric disturbances and space-weather effects. Here we present a multi-spacecraft study of 96 magnetic clouds (MCs) distributed over a broad range of heliocentric distances, and reconstruct their internal magnetic structure with a uniform-twist Gold--Hoyle (GH) flux-rope model. From the fits, we derive the axial field strength B 0, the twist density (turn density) tau, the GH parameter omega, and the integrated twist number n. We find that B 0 and the turn density tau both decrease with increasing heliocentric distance, consistent with expansion and axial stretching during propagation. A key result is that the upper envelope in the tau -- R plane corresponds to a nearly constant boundary in the dimensionless GH parameter omega=2 pi R tau, close to omega about2. Therefore, the inferred upper value of tau is not scale-independent, but follows tau omega/(2 pi R) for a given flux-rope radius. In contrast, the estimated integrated turn number n shows no similarly clear radial organization in the present sample. This study investigates the ICME structure and magnetic field characteristics across heliocentric distances from 0.07 to 5.4 AU, thereby providing observational constraints on the large-scale evolution of interplanetary magnetic flux ropes.