The magnetic field in the photospheric layers of the Sun outside sunspots is found to be in the form of concentrated magnetic flux tubes of 1–2 kG field strength. The model of convective collapse in a thin flux tube, where an instability causes “draining” of the tube and concentration of the magnetic field, has proved useful in attempting to explain the inferred field concentrations. Here we explore the mechanism of convective instability allowing for the inflow of matter in the upper reaches of the tube. ©2000 American Institute of Physics.