We analyze frontal dynamics of dilute powder snow avalanches sustained by rapid blow-out into the head. Such material injection arises as a weakly cohesive snow cover is fluidized by the very pore pressure gradient that the particle cloud induces within the snowpack. We model cloud fluid mechanics as a potential flow consisting of a traveling source of denser fluid thrust into a uniform airflow. Stability analysis of a mass balance involving snow cover and powder cloud yields relations among scouring depth, head height, frontal speed, mixed-mean density and impact pressure when the avalanche achieves a stable growth rate. We compare predictions with field measurements, show that powder clouds cannot reach steady frontal speed on a uniform snowpack with constant cloud width, and derive a criterion for cloud ignition. Because static pressure is continuous across the mean air-cloud interface, and because shear stress is negligible, the relatively small frontal acceleration is insensitive to local slope, but instead arises from a deficit of flow-induced suction pressure in the wake. We calculate how far a powder cloud travels until its mixed-mean density becomes stable, and show how topographic spread can hasten its collapse. Other information can be found at http://grainflowresearch.mae.cornell.edu/geophysics/suspension_currents/suspension_currents.html