Characterization of the TJ-II stellarator plasma by means of reciprocating Langmuir probes

Experiments were conducted in deuterium plasma in the TJ-II stellarator by means of swept Langmuir probes mounted on reciprocating probes manipulators. The results were processed using the four-parameter fit, as well as the triple-probe and the first-derivative probe techniques. The parameters determined were the floating potential, the ion saturation current density, the electron temperature and density, and the plasma potential. The results were obtained for two plasma heating techniques – electron cyclotron resonance heating (ECRH) and neutral beam injection (NBI) heating. In the case of ECRH, employing the first-derivative probe technique resulted in finding that the electron-energy distribution function (EEDF) was not Maxwellian, but rather a bi-Maxwellian one with thermal (14-25 eV) and cold (4-5 eV) electrons. In comparison, during NBI heating we found a Maxwellian EEDF with the electron temperature being around 5 eV and slightly increasing in the confined plasma, but always remaining below 15 eV. We present a detailed analysis and discussion of the data for the plasma parameters as acquired by different techniques of using the reciprocating probe manipulator.


Introduction
Knowing the parameters of the plasma near the wall and of that in the confined region is very important for comparisons between experimental and modelling data.A relatively easy approach to following these parameters' variations is the use of probe manipulators.Various ways are being used of extracting the radial profiles of the plasma parameters when employing a reciprocating probe or changing the probe's position between consecutive reproducible discharges.A reciprocating probe is a probe that is mounted on a moving support which allows it to be moved rapidly into and out of the plasma.
The TJ-II apparatus is a heliac-type stellarator with a low magnetic shear and a major radius, R, of 1.5 m and a mean minor radius, r, of ≤ 0.22 m.The magnetic field at the plasma center, B(0) ≤ 1 T, is formed by a set of poloidal, toroidal and vertical coils.The resulting plasma cross-section is of a bean shape, with plasma volume of ~1 m 3 .In addition, the design of the TJ-II provides a broad range of possibilities of modifying the magnetic-field configuration.During the experiments, hydrogen, helium or deuterium plasmas are heated using one or two gyrotrons operating at 53.2 GHz, i.e., the second harmonic of the frequency of the electron cyclotron resonance.Further heating can be achieved by injecting neutral hydrogen atoms accelerated by a couple of tangential neutral-beam injectors (NBI).An overview of recent results and of systems and techniques for plasma diagnostics used on the TJ-II stellarator are presented in detail in [1][2][3].
Two fast reciprocating drives for Langmuir probes are installed on the TJ-II with a speed of displacement ∼1 m/s and at a path length of 0.1 m (providing penetration of ∼10% of the minor plasma radius) [4].At present, several types of probe heads can be mounted on the drives [2].Thus, if the probe is swept, it can provide measurements of the plasma edge parameters -the floating potential, Vfl, the ion saturation current density, jsat, the electron temperature, Te, the electron density, ne, and the plasma potential, Vpl.When several pins are installed on one probe head, different regimes of operation can be used for different purposes, e.g., applying the triple probe technique [5][6][7] for fast turbulent measurements.
In this work, results on the plasma parameters are presented obtained by swept reciprocating probes using the current-voltage characteristics, I-V, as measured for plasma produced using the 100-44-64 magnetic-field configuration [1], (a = 0.192 m, B0 = 0.95 T, i0/2p = 1.56,Vplasma = 1.1 m 3 ) where i0/2p is the on-axis rotational transform.The label "xxx_yy_zz" of the configuration defines the currents in the circular, helical, and vertical coils of the current-free stellarator.In the discharges considered here, where the plasma-edge density and temperature do not exceed, respectively, 10 18 m -3 and several tens of eV, the sizes of the sheaths around the probes are several tens of microns, i.e., significantly smaller than the probe separation distances.
The Langmuir probes are used because of their ability to measure the local plasma parameters.In fusion plasmas, which are highly magnetized, the ion saturation part of the I-V characteristics and the one close to the floating potential are employed to recover the plasma parameters [8][9][10].This "classical" approach presumes a Maxwellian electron-energy distribution function (EEDF.In fusion plasmas, this assumption is generally valid.The first-derivative probe technique (FDPT) allows determination of the actual EEDF, which is proportional to the first derivative of the probe current.In some cases, the real EEDF is non-Maxwellian in fusion devices [11,12].Generally, three probe techniques have been employed to determine plasma parameters -the four-parameter fit [8][9][10], the FDPT and the triple-probe techniques (TPT) [5][6][7].A good agreement between the plasma parameters values is observed when using the four-parameter fit and the FDPT.However, the TPT overestimates the electron temperatures, which is to be expected as found in [7]; the values of the other parameters are in agreement with those obtained by the FDPT.

Probe measurements in the TJ-II stellarator by means of "stairs" probe head
Below we discuss results of measurements with the probe manipulator installed in sector D of the stellarator chamber (see figure 1).
Figure 1 (a) visualizes schematically the probe's position and the last closed flux surface (LCFS) shown by a dotted line.A top view is shown in figure 1 (b).A "stairs" head holding a probe measuring at successive shots was used; to record the current-voltage characteristics, I-Vs, the probe was swept by ±100 V.
The experiments were performed with deuterium as a working gas.The Langmuir probe made of tungsten (two-mm long, a diameter of 0.75 mm) was moved into the plasma to consecutive vertical positions toward the LCFS (see figures 1 and 2).In view of studying the plasma during different discharge phases (ECR and NBI heating), a series of reproducible discharges (#44769 -#44785) were achieved with gas puffing during the discharges.The working gas pressure in the main vacuum chamber was in the order of 10 -5 -4×10 -5 mbar [13].During each discharge, the probe was moved in the plasma at positions, Z, from Z = -27 mm toward the LCFS in the SOL to Z = 21 mm in the confined plasma (the LCFS position defining the zero position).During the discharges first half, heating by electron cyclotron resonance (ECRH, two gyrotrons of 250 kW power at 53.2 GHz, second harmonic, X-mode polarization) was employed resulting in a lineaveraged density of ~5×10 18 m -3 .In the discharge second phase, heating by neutral beam (NBIH, 30 kV, one beam with power of 400 kW power through the port) was employed.This results in significantly higher line-averaged densities (see figure 3).It should be noted here that, in this series, a single cryogenic pellet is injected into each plasma at ~1166 -1167 ms [14].However, the post-injection phase is not considered in the analysis performed here.Also, in the ECRH phase, the densities fluctuate within 18%, whereas in the NBIH phase, one observes a more reproducible part prior to the pellet-induced jumps in the density.Figure 4 (b) displays the radial temperature profiles as measured in consecutive shots by four LPs (a swept one and a triple one) on a fixed manipulator; as seen, in comparison with the swept probe results the TPT yields temperatures (empty triangles) that are ~25% higher outside of the LCFS, and twice as high as in the confined plasma.The TPT overestimates the Te; however, the more interesting result is that the electron-energy distribution function found using FDPT in the case of ECRH is not Maxwellian, but can rather be approximated by a bi-Maxwellian function with thermal electrons (14 -25 eV, red squares) and cold electrons (4 -5 eV, blue triangles).A hypothesis concerning the origin of the cold electrons is proposed in [12], namely, collisions between thermal electrons and neutrals resulting in cold electrons being "born".The TPT results should be referred to the thermal electrons, since the theory of processing the data thus provided assumes a Maxwellian EEDF; i.e., this technique does not detect the cold electrons.
Another reason why the TPT provides higher Te values is that the magnetic field alters the electron branch of the I-V characteristics and moves the floating potential closer to the plasma potential; this has the result of a larger difference between the positive and floating electrodes potentials of the triple probe (V+ -Vfl), the latter being proportional to Te in the TPT.The larger the magnetic field, the greater this overestimation [7].
During NBIH, Te in the SOL is around 5 eV (black solid circles), then slightly increases in the confined plasma, but always remains below 10 eV.
Finally, as illustrated in figure 4 (c), the ion saturation current during ECRH remains higher than in the case of NBIH.The TPT (empty triangles) and the FDPT (solid squares) produce very similar values with good agreement.
In figure 5, the radial profiles of the electron densities are shown as registered by the two techniques using swept data (the four-parameter fit, empty stars, and FDPT, solid signs) during ECRH (figure 5 (a)) and NBIH (figure 5 (b)).The ne values determined by the FDPT are found by integrating the EEDF for each group.It is seen that for a bi-Maxwellian EEDF the density values of both groups of electrons (thermal, red squares, and cold, blue triangles, in figure 5 (a) are comparable in the confined plasma.Outside of the confined plasma, the thermal electrons are dominating, while in the vicinity of the LCFS this tendency is reversed as the cold electron population starts increasing.This observation is in agreement with previous results on TJ-II [12].The total density (the sum of the thermal and the cold electrons, green dots) increases fourfold in the confined plasma with respect to the density in the edge region.During NBIH (figure 5 (b)), the increase in ne is much larger, namely, 10 18 m -3 , or one order of magnitude compared to 10 17 m -3 in the edge region.
To calculate the electron density, the four-parameter fit makes use of the equation [15]: where, ‫ܫ‬ ‫ݐܽݏ‬ ݅ is the ion saturation current, ܿ ‫ݏ‬ = [݇(ܶ ݁ + ܶ ݅ )/݉ ݅ ] 1/2 is the ion acoustic speed, pr A is the projection of the probe on the magnetic field lines, e is the electron charge; cs is calculated for deuterium.The values for ne determined by the four-parameter fit are overestimated.This technique also assumes that the EEDF is Maxwellian and does not detect the cold electrons, so that the determined Te is very similar to that of the thermal electrons for a Maxwellian EEDF.
The final plasma parameter that can be determined by the FDPT is the plasma potential (solid dots in figure 6).Based on the technique, its value is close to the first-derivative minimum of the I-V.This is in agreement with the relation between Te and Vfl (empty stars): ܸ = ܸ + 2.8ܶ [15].In figure 6 (a), one can see that the plasma potential profiles follow the floating potential profiles as far as 20 mm into the confined plasma during NBI heating, when Vpl becomes negative.This result is interesting in view of model calculations or as a comparison and extrapolation of the Vpl profile determined by the heavy ion beam probe diagnostic [16] when measuring in the confined plasma.The observed potential is mainly negative, which is in agreement with our results during NBI heating.
It is known that the plasma potential's first derivative represents the radial electric field.Figure 6 (b) shows plots of the electric field during both types of heating using the experimental data obtained by using the FDPT.As can be seen, the electric field is always negative during NBIH, but exhibits a more complicated behaviour during ECRH -it is generally positive, at the LCFS changes to negative, then in the confined plasma reaches a maximum value around 1 cm off the LCFS, and then decreases.

Conclusions
The experiments presented were carried out using a "stairs" probe-head manipulator mounted on the reciprocating drive-in sector D of the vacuum chamber.The I-V characteristics are measured in consecutive shots.Three diagnostic techniques were employed to determine the plasma parameters during additional heating by ECR and NBI, namely, TPT, and in the case of a swept probe, FDPT and four-parameters fit.The FDPT and the four-parameters fit yielded results in a very good agreement, with the exception of some discrepancies concerning the electron density.The FDPT's advantage of providing information on the EEDF was used again; it was found that in the case of ECR heating it is bi-Maxwellian throughout the profile, while during NBI heating it is Maxwellian with colder electrons -temperatures below 10 -15 eV.
It was further found that the TPT overestimates the electron temperature, in comparison with the values determined using one swept Langmuir probe.The TPT and the four-parameter fit do not detect the cold-electron fraction of bi-Maxwellian EEDFs.The rest of the plasma parameters are in a good agreement.

Figure 1 .
Figure 1.(a) The probe positions and the LCFS (shown by a dotted line) in sector D of TJ-II; (b) a birds-eye view sketch of the TJ-II; the vacuum chamber is seen in grey, and the plasma, as seen through the port holes, in purple.The four quadrants are labelled A through to D and the eight sectors in each quadrant are labelled 1 through to 8.

Figure 3
Figure 3 displays the line-averaged densities of the plasma for this series of reproducible discharges.During the discharges first half, heating by electron cyclotron resonance (ECRH, two gyrotrons of 250 kW power at 53.2 GHz, second harmonic, X-mode polarization) was employed resulting in a lineaveraged density of ~5×10 18 m -3 .In the discharge second phase, heating by neutral beam (NBIH, 30 kV, one beam with power of 400 kW power through the port) was employed.This results in significantly higher line-averaged densities (see figure3).It should be noted here that, in this series, a single cryogenic pellet is injected into each plasma at ~1166 -1167 ms[14].However, the post-injection phase is not considered in the analysis performed here.Also, in the ECRH phase, the densities fluctuate within 18%, whereas in the NBIH phase, one observes a more reproducible part prior to the pellet-induced jumps in the density.

Figure 2 .
Figure 2. Photograph of the "stairs" probes head mounted on the reciprocating manipulator probe D.

Figure 3 .
Figure 3. Line-averaged plasma densities along the TJ-II discharges #44769 -#44785 -a different colour is used for the trace of each discharge.

Figure 4 (Figure 4 .
Figure4(a)-(c) presents, respectively, the radial distributions of the Vfl, Te, and Isat for the TJ-II plasmas of interest during the NBIH phase (in black) and the ECRH phase (in red) as determined by the FDPT (solid symbols) and the TPT (empty triangles)[11,12].The two techniques produce very similar floating potential profiles (figure4 (a)).During ECRH, it remains always positive with some distribution between 15 V and 60 V with a minimal value at the LCFS (dashed line in figure4).During NBI, it has lower positive values below 20 V outside the LCFS and reaches negative values (to -35 V) inside the confined plasma, while monotonically decreasing in outside-to-inside direction.

Figure 5 .
Figure 5. Local electron density radial profiles (a) during ECRH (red); (b) NBIH (black) phases estimated using the FDPT and the four-parameter fit methods.

Figure 6 .
Figure 6.Radial profiles of the (a) plasma potential in ECRH (red) and NBIH (black), using the FDPT and the four-parameter fit and (b) radial electric field as found by the FDPT.