Monte Carlo estimates of edge particle sources in TJ-II plasmas

Three-dimensional calculations of the electron source in plasmas of the TJ-II stellarator (Madrid, Spain) are performed using the Monte Carlo code EIRENE. When possible, the results are compared with diagnostic measurements in equivalent coordinates. Examples are shown for the Hα light evolution during a plasma collapse, CX fluxes, neutrals distributions along diagnostic chords and line radiation emissivities.


Introduction
The evaluation of sources in magnetic confinement fusion devices is a complex task. In most cases, the source terms do not conform to flux surfaces and three-dimensional (3D) calculations are required. Particle sources, e.g., involve the motion of neutrals through the vacuum vessel (VV) and the contained plasma, together with atomic physics and interaction with the first wall. In medium size or large tokamak plasmas, one-dimensional calculations can give a fair approximation of the neutrals distribution and the corresponding electron source [1], although detailed calculations near the divertor demand 3D calculations. Matters are commonly more complicated in stellarators, like the TJ-II Heliac [2], where the plasma-wall interaction is strong in a complicated VV geometry. For instance, in addition to the possible insertion of poloidal limiters, typical TJ-II plasmas are limited by the "hard core", a metallic case that protects the central conductors all along the toroidal coordinate.
In this paper we present calculations that require 3D neutrals distributions inside the VV. They are necessary for comparison with experiments that involve specific geometries, like gas puffing valves, diagnostic chords or solid angles through which radiation is collected. Examples are given for (i) the evolution of Hα light during a radiative collapse following the L-H transition, (ii) CX spectra at a specific time of a discharge, (iii) electron source from ionization of neutrals in relation with electric probe measurements and (iv) helium 667 mm light recorded near a gas-puffing valve in He plasmas.
viewing lines, there are three decisive inputs that come from the plasmas under study: gas puffing, plasma distributions of density and temperature, and ion outflows. The plasma distributions are provided as radial profiles, which means that such magnitudes are flux-surface functions. The outflows, or number of particles per second escaping from the plasma, are then obtained from the ion distribution and the net particle confinement time, τ p . In the TJ-II, this magnitude has been estimated experimentally [5], but in the absence of dedicated experiments it can be also estimated through the use of transport codes coupled with EIRENE if some experimental information, like recycling coefficient [6], Hα [7] or CX spectra [8] can be provided. It is often the case that other sources, like NBI flows, must be taken into account. One difficulty here is that the NBI deposition and shinethrough depend on the neutrals distribution itself, which calls for a coupling of different codes to transport calculations [9]. For TJ-II studies of particle and energy transport, we commonly use transport models for the density evolution that allow reproducing the experimental density profiles.
The particle sources are updated with enough frequency using the evolving plasma profiles, τ p and NBI deposition profiles. In this way, the obtained sources are not only compatible with all the provided experimental information, but also with transport. For example, if the plasma is in steady state, the source and confinement times provided are compatible with such a steady state, which may not happen if the evaluation of sources is decoupled from transport. Figure 1 gives an idea of the geometry of the TJ-II device. It shows the distributions of neutral hydrogen molecules and atoms obtained using parameters from TJ-II discharge #34517, a low-density (~1.1×10 19 m -3 ) NBI plasma without additional gas puffing. The structure of the TJ-II ports can be fairly well seen in the distribution of molecules; and the different TJ-II sub-sectors, eight per each of the four periods, can be seen in both distributions. This stresses the importance of the geometry to evaluate diagnostic measurements as in the examples that follow.  Figure 2.a shows the effect of inserting two poloidal limiters under the conditions of high-density NBI plasma. Two monitors are simulated: one looking at one of the limiters, the other one far from them. When the limiters reach the LCFS position (vertical line) the monitors behave oppositely. The signal increases considerably for the monitor oriented towards one limiter, while it decreases for the other monitor due precisely to the plasma flow intercepted by the limiters. Figure 2.b shows the atom density along the top line of the perpendicular CX diagnostic for identical calculations except that the coating is changed from B to Li. The electron density along the chord is also shown to give an indication of the portion of the chord intersecting the plasma. The higher recycling inherent to B-coating is manifested mainly in the atom density near the LCFS on the diagnostic side of the chord.

Sources and diagnostics in NBI plasmas
Calculations that include particle sources from NBI require a previous estimate of the spatial distribution of neutrals. These distributions are then used to take CX losses into account in Monte Carlo methods [11] for NBI beams, again adapted to the TJ-II (see [12] and references therein), so the corresponding particle source is included in a consistent way despite possible uncertainties, such as gas desorption from direct impact on the NBI protection tiles [13]. Once the neutrals distribution is obtained (e.g. figure 1), the NBI contribution to the net particle source can be calculated. Figure 3 shows that the deposition of particles coming from the neutral beams is small in comparison with the recycling sources. The behavior of Hα emissivity as recorded by different monitors during the radiative collapse can be explained based on the calculated sources as explained above. Figure 4.a shows the time trace of the Hα monitor located in sector A3 of the TJ-II device in a discharge similar to the one in figure 3, where an L-H transition happens close to the radiative collapse due to the increasing density (see [8] for details). The simulated evolution of the intensity for the same Hα monitor matches approximately the experimental one: it decreases at the L-H transition, but the cooling produced by the almost immediate collapse makes the neutrals density grow giving rise to a large increment of Hα light. CX spectra were recorded during the discharge, so that a comparison with calculated values could also be performed ( figure 4.b). In this case, two thermal populations were required to explain the curved energy distribution in a logarithmic scale: 0.4% of the ions have a temperature ~ T e , close to three times the bulk ion temperature.

Edge sources and probes
Recent work has shown bi-Maxwellian distributions of electrons in the edge of tokamak and stellarator plasmas [14]. One population seems to be the expected thermal component while the other, cooler, is found with energies in the order of ~ 5 eV, but with a higher density. The calculation of neutrals distribution in the sector where the electric probe is inserted (arrow in figure 5.a) shows an approximate flux-surface distribution of the source density term except near the hard-core region, where the plasma is limited by the wall. The flux-surface averaged source density is plotted in figure  5.b, together with the measured electron density that corresponds to each of the two populations mentioned above: high (squares) and low (triangles) temperature. Figure 5.c represents the atom and molecule distributions along a vertical chord passing through the probe. For reference, the electron density is also given for the same chord in the plasma region (between vertical dashed lines). A small shady rectangle indicates the range covered in figure 5.b. Note that the molecule density decreases as the chord approaches the LCFS from outside the plasma, opposite to the atom density.

Line radiation emissivities
Finally we show a first comparison with measurements taken by a tangential camera set so as to collect the emissivity of He-lines from the plasma region above the helium-puffing valve. Appropriate ratios of He lines are related with the electron density and temperature -this technique can provide their spatio-temporal evolution [15]. The data in figure 6 were collected in ECRH TJ-II plasma where He was puffed at 2 cm from the LCFS (r = a). The figure corresponds to the emissivity of the 667 nm  He-line received in viewing lines that pass vertically above the gas puffing valve. We overplot the emissivities calculated for the equivalent numerical diagnostic using the experimental density and temperature profiles as input for EIRENE. The experimental emissivities are not calibrated; they were rescaled to match the calculated values. Therefore the confinement time in the calculation is not critical and it was fixed to a reasonable value, 5 ms. Ongoing research is dedicated to refine the measurements and calculations similar to those shown here, due to their importance to magnetic fusion research. The development of new numerical diagnostics that require neutral distributions, such as Hα spectral analysis [16,17], is encouraged.

Conclusions
Calculations that require 3D distributions of neutrals around the plasma-edge region are calculated, based on coupled transport and Monte Carlo codes, for the plasma parameters and geometry of the TJ-II stellarator. They are compared with experimental results (evolution of Hα light during a radiative collapse following the L-H transition, CX spectra, helium 667 mm light recorded near a gas-puffing valve in He plasmas) or used to interpret data (Hα emissivities in different monitors, neutrals densities along diagnostic chords, electron source from ionization of neutrals in relation with electric probe measurements).