On the applicability of three and four parameter fits for analysis of swept embedded Langmuir probes in magnetised plasma

Abstract

The problem of power exhaust is one of the grand challenges of nuclear fusion research today. In order to understand the physics phenomena occurring in the scrape-off layer and the divertor regions of tokamaks, it is essential to correctly determine the divertor plasma parameters, which are often measured by swept Langmuir probes. While the construction and operation of this diagnostic can be straightforward, the data analysis using 3- or 4-parameter fits presents a challenge and can potentially lead to erroneous values of electron temperature and ion saturation current. In this work, we present modelling and experiments aimed at determination of conditions for proper analysis of swept Langmuir probes using these two fitting models. Particle-in- cell modelling was employed to evaluate the sheath-expansion effects for particular probe geometry and plasma conditions, yielding a semi-empirical rule capable of predicting its magnitude. Experiments with unusually wide range of swept voltage in the divertor of the COMPASS tokamak explored the magnitude of voltage range required for successful analysis with either three or four-parameter fitting. With the use of our new semi-empirical rule, it is possible to improve the four-parameter fit reliability in situations where the available voltage range is limited. In addition, we introduce the tangent method - an independent and fast method of electron temperature estimation, which allows to reliably determine the available voltage range and as such assist the more complex method of probe analysis.

Experimental evidence of very short power decay lengths in H-mode discharges in the COMPASS tokamak

“…The divertor probe measurements allow us to calculate the upstream T ue using the two point model as where T t is the downstream electron temperature, q ||,t is the downstream parallel peak heat flux and κ 0 is the S-H electron heat conduction constant (κ 0 = 2000 eV 7/2 W m −1 ) [22]. A further analysis of the dataset showed T te ∼ 50 eV at the outer divertor target (note that these high values were recently confirmed by analysis of swept LP [23]). As a consequence, the first term in the r.h.s.…”

ELM temperature in JET and COMPASS tokamak divertors

“…⋆ The overall voltage range 170 V must be larger than T e div , as discussed in [16]. We estimated the limit of credibility of the ELM peak T e div to be below 170 eV, as demonstrated by the green dashed linear line in figure 5(a).…”

“…All IV-characteristics were fitted by both three and four parameters. To enable a better estimate of the parameter errors, the bootstrap technique was applied [16]. Each IVcharacteristic is fitted a hundred times, each time with the same number of randomly selected points, meaning that some points are randomly excluded or repeated.…”

“…This yields a spread of all possible parameters, whose confidence interval (containing two thirds of the data) may be asymmetric, which is the main advantage of the bootstrap method and is further used. This is particularly important for temperatures near and above the available voltage span or for scattered data, where often the maximum possible fit temperature is undetermined [16], whilst the minimum is still relatively precise. Figures 3(c In figure 4, the entire ELM time evolution obtained from CAV is compared to the same quantities measured at a much higher rate (1 µs resolution) with the BPP-LP array and only then averaged into the red curve.…”

Embedded-probes diagnostics for the COMPASS upgrade tokamak: a concept

“…In many tokamaks, such as Tore-Supra [16], Castor [14], DIII-D [17] and [18], this technique of processing probe data has been applied successfully and with very good results; this is why we intend to employ it for the analysis of the probes embedded in COMPASS-U.…”