An experiment is described to show that anomalous diffusion seems to occur in plasmas, such as an r-f discharge, wher a directed current does not exist. On increasing the static magnetic field, B, it was observed that one passes through a critical value, B/sub c/, above which the flux of ions across the magnetic field no longer decreases but increases for a while. This anomalous rise in diffusion rate is generally accompanied by the commencement of r-f noise of an unknown origin. The product of B/sub c/ and the discharge tube diameter is roughly constant and B/sub c/ increases nonlinearly with pressure. It was also observed that the grid voltage of the r-f oscillator, V/sub g/ reaches an extremum at nearly the same B/sub c/ at which the r-f noise commences. The external and internal ion saturation currents, j/sub ext/sup +, and j/sub int/sup +/, wer e measured, and j/sub ext/sup +/, J/sub int/sup +/, J/sub ext/sup +/, J/ sub int/su p +/ and V/sub g/ are plotted as they vary with B. A second region of critical magnetic field strengths, B/sub c'/, was also observed and is more » plotted. The values of B/sub c/ in hydrogen and argon are plotted for different pressures and different diameters of the discharge tube. (H.D.R.) « less