AbstractWe present 3-dimensional particle-in-cell simulations for ultra-intense pulse-laser-irradiated plasmas. The self-excited process of large magnetic fields is one of the problems in laser–plasma interactions and in inertial confinement fusion. Weibel instability is known to be a microscopic instability that causes spontaneously growing transverse waves due to an anisotropic temperature. Spontaneously generated large magnetic fields can be generated by ultra-intense laser-irradiation-causing sources, such as anisotropic temperature.