The formation of permanent periodic structural changes in fused silica induced by the multifilamentation process was investigated. A cylindrical lens was used to focus 800 nm 50 fs pulses with 0.5 - 3 mJ energy down to a line, resulting in a quasi-periodic linear self-arrangement of multiple filaments (MF). The quasi-period of multiple filaments is shown to be uniquely defined by the critical power of the material and the peak intensity on the sample entrance surface. A novel technique to control this spatial self-arrangement of MF is demonstrated based on the use of a binary phase mask. This technique allowed us to decrease the relative variation of spacing between the adjacent tracks of refractive index modifications by a factor of 4 as compared with the case without the phase mask. 3D + time numerical simulations qualitatively reproduce the main features of multiple filament formation obtained in the experiment.