Spatiotemporal Dynamics of Electromagnetic Filamentation Instability in a Collisional Current-Driven Quantum Plasma

The electromagnetic filamentation instability and magnetic field generation in a quantum current-driven plasma are analyzed by introducing a high-order nonlinear transient partial differential equation. This equation is derived using the quantum hydrodynamical model in the diffusion regime and is solved employing an efficient radial basis function (RBF)-based meshless method. The results show the formation of current filaments, the spatiotemporal evolution of the magnetic field, and the electron number density in the current-driven plasma in the presence of quantum effects including the Fermi pressure and the Bohm potential. It is also indicated that the magnetic field and the electron number density profiles gradually converge with increasing the number of RBFs.