Advances in Langmuir probe diagnostics of the plasma potential and electron-energy distribution function in magnetized plasma

Abstract

Advanced Langmuir probe techniques for evaluating the plasma potential and electron-energy distribution function (EEDF) in magnetized plasma are reviewed. It is shown that when the magnetic field applied is very weak and the electrons reach the probe without collisions in the probe sheath the second-derivative Druyvesteyn formula can be used for EEDF evaluation. At low values of the magnetic field, an extended second-derivative Druyvesteyn formula yields reliable results, while at higher values of the magnetic field, the first-derivative probe technique is applicable for precise evaluation of the plasma potential and the EEDF. There is an interval of intermediate values of the magnetic field when both techniques—the extended second-derivative and the first-derivative one—can be used. Experimental results from probe measurements in different ranges of magnetic field are reviewed and discussed: low-pressure argon gas discharges in the presence of a magnetic field in the range from 0.01 to 0.08 T, probe measurements in circular hydrogen plasmas for high-temperature fusion (magnetic fields from 0.45 T to 1.3 T) in small ISTTOK and CASTOR tokamaks, D-shape COMPASS tokamak plasmas, as well as in the TJ-II stellarator. In the vicinity of the last closed flux surface (LCFS) in tokamaks and in the TJ-II stellarator, the EEDF obtained is found to be bi-Maxwellian, while close to the tokamak chamber wall it is Maxwellian. The mechanism of the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is discussed. Comparison of the results from probe measurements with those obtained from calculations using the ASTRA and EIRENE codes shows that the main reason for the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is the ionization of the neutral atoms.