A conceptual study of magnetic flux compression inside a cylindrical coil by an expanding inertial fusion plasma sphere across the magnetic field produced by the coil itself have been performed numerically using a two-dimensional magnetohydrodynamic (MHD) simulations. The concept may find application in inertial fusion energy (IFE) system as a direct energy conversion scheme to convert a part of fusion plasma kinetic energy into pulsed electrical energy. Important theoretical and technical issues that has to be addressed are discussed. Preliminary theoretical analysis are given for the analysis of MHD interchange instabilities of expanding plasma across magnetic field. Overall efficiency of the system is determined numerically for a typical set of initial plasma and system parameters. Ultrahigh coil inter-turn voltages are predicted. Therefore, the application of magnetic self-insulation to avoid coil inter-turn break-down is considered. Also, we have analysed the system performance with different load conditions.