A Q-switched Nd: YAG laser was used to fabricate micro channels in the fused silica substrate by laser-induced plasma. The micro channels were observed with fluorescence microscope, no thermal cracks around the channels and the depth of the channels is up to 4 mm. There are coagulation layers around the inner surface. We studied the ionization mechanism of optical breakdown in solids by nanosecond laser pulses. For the 1064 nm laser, as the intensity of nanosecond pulse is not enough large, plasma formation in optical breakdown is the result of an electron avalanche process. We got the plasma formation model using the breakdown threshold of avalanche ionization and calculated the range of laser plasma based on the model. The theoretical analysis based on the model is shown to be mainly agreement with the experimental observations. The laser-supported detonation wave (LSDW) based on the principle of hydrodynamics was analyzed as well and calculated the characteristic parameters of plasma including the plasma temperature, pressure and velocity. The characteristics of micro channels were analyzed through the parameters. When the plasma passed, the melting quartz solidified with the effect of LSDW and produced the coagulation layers. The ablation of the high temperature and pressure plasma lead to a micro channel of high quality with a relatively smooth internal surface and no thermal cracks.