An oxy-gaseous fuel burner (400, 500) or a solid fuel burner (700) having an annular cavity (404, 504, 704) upstream from and proximate to an outlet plane (416, 516, 716) and a converging (434, 734) or converging-diverging nozzle (537) located upstream from and proximal to the cavity (404, 504, 704). The solid fuel burner (700) also is preferably operated so that the velocity of gas exiting a second annulus (730) is less than the velocity of gas exiting a central conduit (710).