Effective collecting area of a cylindrical Langmuir probe in magnetized plasma

Abstract

Langmuir probe diagnostic on magnetic plasma devices often encounters more challenges in data processing than in non-magnetized plasmas, the latest itself being far from simple. In this paper, a theory of particle collection by a probe at the plasma potential in collisionless weakly ionized plasmas is constructed, accounting for velocities distributed according to the Maxwell equation and different mechanisms of particle collection depending on their speed. Experimental validation of the presented theory has been done with 2 cylindrical probes (rpr = 75 μm and Lpr = 1 cm and rpr = 0.5 mm and Lpr = 1 cm) parallel to B→ on a linear plasma device Aline, with magnetic fields of 0.0024–0.1 T and plasma densities of 1015–1017 m−3 in helium. Cylindrical probe measurements are compared to data from a planar probe perpendicular to the magnetic field, and the results for electron density, temperature, and plasma potential are presented. The introduced theory is initially constructed for a cylindrical probe but is applicable to various probe sizes, shapes, and orientations. Alongside the main subject, a number of associated issues are addressed with different details: a probe design issue relative to the magnetized environment, the “intersection” method of plasma potential evaluation, and the robustness of the conventional “1st derivative” method, a current bump near the plasma potential, lower limit for electron temperature estimation, and self-consistent calculation of electron temperature and density.

Theory of a cylindrical Langmuir probe parallel to the magnetic field and its calibration with interferometry

“…Specific particle transport in the presence of magnetic field (B) changes the shape of a Langmuir probe IV curve such that the conventional methods of data interpretation become unsuitable, 1,2 especially for a parallel cylindrical probe. Very few attempts [1][2][3] exist on providing a correct theory for density (n) evaluation with such a probe.…”

“…Specific particle transport in the presence of magnetic field (B) changes the shape of a Langmuir probe IV curve such that the conventional methods of data interpretation become unsuitable, 1,2 especially for a parallel cylindrical probe. Very few attempts [1][2][3] exist on providing a correct theory for density (n) evaluation with such a probe. Of those, the Laframboise and Rubinstein calculations 2,3 are hardly applicable in practice 1 and our previous theory 1 contains simplifying assumptions that restrict validity limits.…”

“…Very few attempts [1][2][3] exist on providing a correct theory for density (n) evaluation with such a probe. Of those, the Laframboise and Rubinstein calculations 2,3 are hardly applicable in practice 1 and our previous theory 1 contains simplifying assumptions that restrict validity limits.…”

“…In this paper, we develop an accurate theory describing electron collection by a cylindrical Langmuir probe biased to plasma potential (V pl ) (to avoid sheath) and oriented parallel to the magnetic field. This model is an advancement of our previous work, 1 and it gives an exact formula connecting plasma density and collected current at V pl . Only the case of a parallel probe is considered since for a probe at an arbitrary angle to B an exact analytical solution would be excessively complex.…”

“…Only the case of a parallel probe is considered since for a probe at an arbitrary angle to B an exact analytical solution would be excessively complex. At the end, the applicability limits of the approximate theory 1 are revised.…”