Fig. 1. Intensity and phase distribution in the input beam within a 5 mm × 5 mm area.

Fig. 2. SSSF for θ_max = 1 mrad at noise filter contrast 10⁸: (a) noise spectrum (solid curves), gain K(θ) in the linear regime for B = 5 (dashed curve); (b) intensity distribution in the beam for B = 5 within a 5 mm × 5 mm area.

Fig. 3. SSSF for θ_max = 3 mrad at noise filter contrast 10⁸: (a) noise spectrum (solid curves), K(θ) in the linear regime for B = 6 (dashed curve); (b) intensity distribution in the beam for B = 6 within a 2.5 mm × 2.5 mm area.

Fig. 4. SSSF for θ_max = 10 mrad at noise filter contrast 10⁸: (a) noise spectrum (solid curves), K(θ) in the linear regime for B = 11 (dashed curve); (b) intensity distribution in the beam for B = 11 within 2.5 mm × 2.5 mm area (see Silin_supplementmovie1.avi for 0 ≤ B ≤ 11 within a 5 mm × 5 mm area).

Fig. 5. SSSF for θ_max = 10 mrad, no self-filtering: (a) noise spectrum (solid curves), K(θ) in the linear regime for B = 6 (dashed curve); (b) intensity distribution in the beam for B = 6 within a 1 mm × 1 mm area (see Silin_supplementmovie2.avi for 0 ≤ B ≤ 6 within a 5 mm × 5 mm area).

Fig. 6. SSSF for θ_max = 30 mrad at noise filter contrast 10⁸: (a) noise spectrum (solid curves), K(θ) in the linear regime for B = 16 (dashed curve); (b) intensity distribution in the beam for B = 16 within a 1 mm × 1 mm area.

Fig. 7. SSSF for θ_max = 30 mrad at noise filter contrast 10²⁴: (a) noise spectrum (solid curves), K(θ) in the linear regime for B = 27 (dashed curve); (b) intensity distribution in the beam for B = 27 within a 2.5 mm × 2.5 mm area.

Fig. 8. Comparison of noise gain K(θ) in the linear mode obtained using numerical simulation and Equation (8).

Fig. 9. (a), (b) Fraction of radiation power converted into noise, (c), (d) maximum intensity in the beam normalized to mean intensity in the beam, (e) root mean square (RMS) intensity in the beam and (f) RMS phase in the beam as a function of the B-integral. Curves (a), (c), (e) and (f) correspond to the level of input noise of about 0.02% of the beam power, while curves (b) and (d) are for the level of input noise of about 0.002% of the beam power. Self-filtering threshold θ_thr = 4 mrad.

Fig. 10. Example of intensity distribution in a beam shortly before the development of either filamentation or honeycomb instability.