We have investigated the propagation of a magnetic dipole assuming a simple model of forward and return flow of fast electrons under a condition of plasma-density inhomogeneity by a particle-in-cell simulation. An exact propagating depiction of the dipolar structure is given under the framework of a simplified 'electron magnetohydrodynamic' fluid model (Yadav et al 2008 Phys. Plasmas15 062308; Yadav et al 2009 Phys. Plasmas16 040701; Yadav and Das 2010 Phys. Plasmas17 052306) in a dense plasma. We reproduce this structure in our kinetic calculations. The results indicate that, with a steep plasma density gradient, the structure evolves rapidly toward plasma in a process involving shock formation and rapid dissipation of beam energy, which is consistent with the fluid simulations. In addition, new features are also reported, such as the pinching of the two dipole lobes to form a very strong shear layer, which develops into a Kelvin–Helmholtz instability. The magnetic energy is rapidly converted to kinetic energy of electrons leading to additional plasma heating in inhomogeneous regions, such as the core region in an imploded plasma.