{'fraction_non_alphanumeric': 0.021218343600273786, 'fraction_numerical': 0.0054757015742642025, 'mean_word_length': 5.142857142857143, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Characteristics of the energy-replenishing diffraction-ray tube at the postfilamentation stage of the propagation of femtosecond laser pulses in the air

The results of studies of the femtosecond laser pulses propagation in air in the mode of self-focusing and filamentation are presented. The analysis of the numerical simulation results is carried out based on the method of diffraction-ray tubes. This approach made it possible to evaluate the characteristics of the energy-replenishing diffraction-ray tube, which forms a nonlinear focus, contains energy sufficient for compensation of the beam energy loss throughout the entire life cycle of the filament, and after its completion determines the boundaries of the postfilamentation channel (PFC). It is found that the average power in PFC formed by beams of sub- and millimeter radius is about 0.6-0.9 critical power for self-focusing, and it weakly depends on the initial parameters of the femtosecond laser pulse. In general, the energy consumption of radiation on filamentation decreases with increasing the initial beam radius. The angular divergence of PFC decreases by an order when the initial radius of the laser beam increases from submillimeter to millimeter values. For the last class of beams, the angular divergence of PFC remains approximately constant (20-25 microradians). Dependence of the angular divergence of post-filamentation light channels on the peak pulse power is less pronounced.