Effect of Magnetic Field and Collisions on the Ion Current to a Cylindrical Probe

Using a modified pressure theory the parameters of a dc discharge between concentric coaxial cylinders have been calculated with the plasma approximation. Both ion-neutral collisions and a longitudinal magnetic field have been taken into account in this low-and intermediate-pressure plasma. In the limit of large outer to inner radii and electron Debye length much smaller than the probe radius, the results are applicable to a cylindrical Langmuir-type probe in an infinite plasma. In the free-fall limit, the results for ion current and density are shown to agree closely with previous collisionless and no magnetic field theories. Curves are presented which show quantitatively, for the first time, the effect of collisions and a “low” magnetic field on the ion current at the Tonks-Langmuir boundary. Contrary to what has been assumed in the past, the magnetic field is shown to have a considerable effect on the ion current even though the ion gyroradius is assumed to be much larger than the probe dimensions. At the Tonks-Langmuir boundary the Bohm criteria comes as a natural consequence of the theory.