Plasmoids/flux ropes have been observed both at Earth's magnetopause as well as in the magnetotail. Magnetic field measurements of such structures often reveal that rather than a minimum in field strength at their centers as expected from a simple O-type neutral line picture, they exhibit a strong core field. To address this issue, two-dimensional (2-D) and 3-D hybrid simulations are used to investigate the magnetic structure of reconnection layer in general and the formation of the core field within plasmoids in particular. The reconnection layer in the magnetotail is found to be unstable to the fire hose instability. As a result, the region between the lobe and the central plasma sheet is nearly at the marginal fire hose condition. The magnetic signatures of single and multiple X line geometries are contrasted, and it is shown that the interaction of outflowing jets from neighboring X lines leads in general to a highly complex magnetic structure within a plasmoid. The large observed core fields are explained in terms of Hall-generated currents which can naturally lead to core field strengths that even exceed the ambient lobe field in magnitude. Ion beta and the presence of a preexisting guide field are two important factors controlling the Hall-generated fields. In particular, it is shown that the presence of the small ubiquitous cross-tail field component in the magnetotail can under certain conditions lead to a strong unipolar plasmoid core field. There exist significant differences between core fields associated with plasmoids at the magnetopause and those in the tail. This is due to (1) high plasma beta in the magnetosheath and (2) the asymmetry in plasma density across the magnetopause. The former leads to smaller core fields at the magnetopause, whereas the latter leads to differences in the polarity and structure of core fields within magnetopause and magnetotail plasmoids. Such differences are illustrated through examples. ¿ 1999 American Geophysical Union