Fig. 1. Schematic diagram of longitudinal steady magnetic field assisted laser powder filling welding

Fig. 2. Combined heat source model. (a) Gaussian surface heat source; (b) cross-section of body heat source

Fig. 3. Curves of thermophysical parameters of welding materials with temperature. (a) Density; (b) thermal conductivity; (c) specific heat; (d) electrical conductivity

Fig. 4. Distribution of magnetic flux density in weld. (a) Longitudinal cross-section; (b) transverse section; (c) top surface; (d) bottom surface

Fig. 5. Temperature and velocity distribution in longitudinal section of molten pool. (a) 0 T; (b) 0.2 T; (c) 0.4 T; (d) 0.6 T; (e) 0.8 T; (f) 1.0 T

Fig. 6. Three-dimensional flow velocity distribution of molten pool. (a) 0 T; (b) 0.2 T; (c) 0.4 T; (d) 0.6 T; (e) 0.8 T; (f) 1.0 T

Fig. 7. Flow velocity curve at point A on surface of molten pool

Fig. 8. Variation curves of cooling rate of molten pool

Fig. 9. Distribution of Lorentz force in molten pool. (a) x component; (b) y component; (c) z component; (d) Lorentz force and velocity vector distribution

Fig. 10. Instantaneous change curves of points in Fig. 9(b) in depth direction

Fig. 11. Simulation and experimental results. (a)(c) Welded joint cross section and simulated temperature; (b)(d) weld morphology and simulated temperature