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

Abstract

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.

Finite ion cyclotron radius effects upon the ion probe current

“…For strong fields (r1 2 r ) ions are forced to move in a helix along the lines of force ('Z-magnetization'), and radial and azimuthal transport of ions is possible only by diffusion across B. Collisions come into play even if the mean free paths are large compared with the probe sizes (Ohguchi et al 1969, Shaw and Kino 1969, Sanmartin 1970. A depleted region is formed around the probe, having the shape of a rotational ellipsoid with its long axis parallel to the field.…”

Ion collection by cylindrical Langmuir probes in a strong axial magnetic field

“…The effects of a strong magnetic field upon the motion of positive ions and hence upon the magnitude of the ion current drawn by a collecting electrode have in the past been dismissed as negligible. Recently this assumption has been subjected to close scrutiny, in particular by Shaw and Kino (1969), Cohen (1969), Sanmartin (1970), Brown et a1 (1971), Sat0 (1972a, b) and Niyogi and Cohen (1973), with the result that in a large number of cases it is seen to be unwarranted. It has been demonstrated that the ion current can be influenced by a magnetic field, in both the continuum and the collisionless cases, even though the particle gyroradius is still much larger than the probe dimensions.…”