Evaluation of the scrape-off-layer plasma parameters by a horizontal reciprocating Langmuir probe in the COMPASS tokamak

The scrape-off-layer (SOL) parameters in the COMPASS tokamak are studied by using a Langmuir probe mounted on a horizontal reciprocating manipulator. The radial profiles of the plasma potential, the electron energy distribution function and the electron densities are derived from the measured current-voltage probe characteristics by applying the firstderivative probe technique (FDPT). It is shown that close to the tokamak wall the electron energy distribution function is Maxwellian, while in the SOL, in the vicinity of the last closed flux surface and inside the confined plasma, the electron energy distribution function is bi-Maxwellian with a low-energy electron fraction dominating over a higher energy one. The radial profiles of the electron pressure and the parallel electron power flux density in COMPASS are also presented.


Introduction
The electric probes are simple plasma diagnostic tools allowing one to evaluate quickly and reliably the edge plasma parameters. In magnetized plasma, the interpretation of the electron part of the current-voltage (IV) characteristics above the floating potential still remains difficult [1] because the electron part of the IV characteristics is distorted due to the influence of the magnetic field.
In tokamaks, the assumption for a Maxwellian electron energy distribution function (EEDF) is generally valid. However, experimental evidence does exist suggesting non-Maxwellian distributions in tokamak SOL plasmas [2]. It is clear that the knowledge of the real EEDF is of great importance in understanding the underlying physics in SOL plasma. This fact notwithstanding, only a few experimental works have so far been reported devoted to the EEDF direct measurement. Our investigations on the CASTOR tokamak aimed at evaluating the real EEDF indicated a bi-Maxwellian 4 To whom any correspondence should be addressed. one in the edge plasma [3]. Recent probe measurements in the liquid lithium divertor area of the NSTX also showed a bi-Maxwellian EEDF [4].
In this paper we report results of measurements in the SOL made by a horizontal reciprocating probe in the COMPASS tokamak [5] with D-shaped plasma. The radial distribution of the plasma potential, the electron temperatures and densities are presented and discussed. The radial distributions of the electron pressure and the parallel electron power flux density in COMPASS are also presented.

The first-derivative Langmuir probe technique for evaluating the EEDF in tokamak edge plasma
The FDPT for evaluating the plasma parameters in tokamak edge plasma was published and discussed in detail in [3]. It was shown there that the electron current flowing to a cylindrical probe negatively biased by potential U is given by: where W is the electron energy; e, m and n are the electron charge, mass and density; S is the probe area; U is the probe potential with respect to the plasma potential U pl ( ). The geometric factor γ assumes values in the range of 0.71 ≤ γ ≤ 4/3.
In the presence of a magnetic field B at low gas pressures, the diffusion parameter B) ψ(W = ψ , depends on the Larmor radius B) (W, R L , as well as on probe size and orientation with respect to the magnetic field. As it was shown in [3], for cylindrical probes oriented perpendicular with respect to the magnetic field the diffusion parameter can be written as: where ' L is the characteristic cross-section size of the turbulent structures (blobs), R is the radius of the probe. As the magnetic field intensity increases, so does the value of the diffusion parameter. When 1 >> B) ψ(W, (high value of the magnetic field B), the EEDF is represented by the first derivative of the electron probe current, as was shown in [3,6,7]: Note that in equation (4) the diffusion parameter is inversely proportional to the square root of the energy. This will cause the parameter to diverge at small energies and can cause an artifact in the resulting distribution function. This artifact in the range from zero to the value of the electron temperature (on energy scale) is due to the mathematical approach rather than to physical phenomena [1,3].

Langmuir probe measurements in the COMPASS tokamak edge plasma
To diagnose the edge plasma and the SOL in the horizontal direction in the COMPASS tokamak, the IV characteristics were measured by using a reciprocating Langmuir probe. The graphite cylindrical probe tip (length 1.5×10 -3 m and diameter 8×10 -4 m) was placed perpendicular to the magnetic field lines. Before the shot, the probe was moved to a chosen initial position with respect to the center of the tokamak chamber and, in synchronization with the shot onset, started a fast reciprocation towards the last closed flux surface (LCFS) and back. The maximum extension of the reciprocating probe motion was 0.06 m. A series of reproducible ohmic discharges in hydrogen with D-shape cross-section plasma were performed. We present below results from shot #3908, which is typical for the series.     Figure 3 shows the radial distribution (with respect to the position of the LCFS) of the electron temperature − the triangles represent the temperature of the more populated low-energy electron fraction, while the squares, the temperature of the suprathermal electrons in the bi-Maxwellian EEDF. The dots indicate the temperature of the Maxwellian EEDF. The position of the LCFS evaluated by EFIT is indicated in all figures by a dashed line. We should point out that more detailed theoretical and experimental investigations must be performed to clarify the origin of the lowenergy fraction in the bi-Maxwellian EEDF. In [4], a "heuristic model" accounting for the inelastic collision effects (i.e. excitation and ionization of neutral hydrogen) is proposed to explain this EEDF feature. Indeed, the energy balance of the reaction 2e H e H + → + + for electrons with energy higher by 10 − 15 eV than the energy of ionization (13.6 eV) is in agreement with the energy of the lowtemperature electrons registered. The values of the rate coefficient [8] for electron temperatures in the range 15 − 20 eV are close to the maximum. Performing a detailed energy balance necessitates that ionization through neutral hydrogen excited states be taken into account as well. On the other hand, the energy of the electrons    in the far SOL is ~5 eV and the most probable reactions are dissociation with threshold of 4.5 eV and excitation. The behavior of the electron temperature spatial distribution at the vicinity of the separatrix can be explained by the plasma turbulence and non-local kinetic effects [9,10,11]. The radial distribution of the plasma potential is presented in figure 4. The dots show the values evaluated by the FDPT.

Results and discussion
In figure 5, the electron densities evaluated are represented by the same symbols as used in figure 3. Figure 6 shows the ratio between the electron densities of the two electron groups. The solid symbols represent the data for the reciprocating probe motion from its initial position to its maximum extension. The empty symbols illustrate the data measured during the backward probe motion. It is seen that the density of the high-energy electron group increases from 15% to 43% within a few millimeters after the LCFS.
Using the results for the electron temperatures and densities obtained by probe measurements, we can also calculate other plasma parameters. Figure 7 Figure 5. Radial distribution of the electron densities n e for shot # 3908.   figure 8). Such a profile shape is regularly observed when other probe techniques are used and in most of tokamaks [12]. This is usually interpreted in terms of turbulent structures (blobs) transporting plasma radially away from the LCFS with a roughly constant speed, with the plasma loosing both its density and temperature in parallel with the magnetic field lines by acoustic streaming (determined by the ion sound velocity, or the parallel pressure gradient).

Conclusions
The SOL parameters in the COMPASS tokamak are studied by using a horizontal reciprocating Langmuir probe. Data for the radial distribution of the plasma potential, the electron energy distribution function and the electron densities are derived from the measured current-voltage probe characteristics by applying the first-derivative probe technique. It is shown that close to the wall of the tokamak chamber the energy distribution function of the electrons is Maxwellian, while in SOL, around the last closed flux surface and inside the confined plasma, the electron energy distribution function is bi-Maxwellian with a low energy electron fraction dominating over the higher energy one. The radial profiles of the electron pressure and the parallel electron power flux density in the COMPASS tokamak are also presented.