New diagnostic tools for transport measurements in the scrape-off layer (SOL) of medium-size tokamaks

We present a new diagnostic tool for the determination of various plasma parameters in the edge region of medium-size tokamaks (MST) and stellarators (specifically Wendelstein 7-X) which is under development under the EUROfusion project task force MST2 and S1. This will be a probe head (called the new probe head-NPH) which will carry two cold Langmuir probes, one electron-emissive probe (EEP), two retarding field analysers (RFA) facing upstream and downstream and two magnetic pickup coils. By various adaptors, the same NPH will be used on all three European MSTs (ASDEX Upgrade, TCV and MAST-U) and on Wendelstein 7-X. For the first time the plasma potential in the edge region of MSTs and comparable toroidal fusion experiments will be directly determined by an EEP that will be permanently heated during the measurements. After the introduction and the theoretical background especially of the EEP, the NPH and its components are described in detail. The NPH will be able to measure electron and ion temperature, electron and ion density, cold floating potential, plasma potential and magnetic fluctuations in all three directions of space at two radial positions.


Introduction
Understanding turbulence in the edge region of toroidal magnetised plasmas is one of the key issues in modern fusion research. Great experimental and theoretical efforts are devoted to understand and quantify radial particle and energy losses and radial transport of poloidal momentum (see e.g. [2][3][4]). This transport is dominantly turbulent and intermittent and is mainly caused by strong filamentary structures originating from the edge of magnetically confined plasmas. They become elongated along the magnetic field and propagate radially towards the chamber walls. These structures are observed in both low-confinement and high-confinement modes (Land H-mode) of tokamaks and are referred to as plasma blobs. Also in stellarators such phenomena have been observed (see e.g. [5][6][7]).
Comprehensive and accurate investigations of blobs require diagnostics which can measure several parameters simultaneously, locally and with high temporal resolution. The most important parameters are plasma potential, Φ pl , electron and ion temperature, T e,i , and electron and ion densities, n e,i . For the determination of Φ pl , T e and n e the best suited diagnostic tools are plasma probes [8,9]. However, conventional cold Langmuir probes (CLP) are not sufficient, primarily since Φ pl and T e can only be derived indirectly from the current-voltage characteristics and thus with low temporal resolution. While Φ pl can in principle also be derived from the floating potential, V fl , of a CLP, this is also of no avail since the difference between V fl and Φ pl depends on T e [10][11][12][13][14] (see below). The electron temperature has, however, strong gradients and fluctuations especially in the edge region of magnetised toroidal plasmas and cannot be determined with sufficient accuracy and good temporal resolution.
We have developed probes whose floating potential is close, or ideally equal to Φ pl , so that this important parameter can be measured directly and thus with high temporal resolution [14]. Such plasma potential probes (PPP) are either electron-emissive probes (EEP), operable in all types of plasma [13,15], or electron screening probes (ESP) drawing on the difference of the gyroradii of electrons and ions in magnetic fields [12,16,17]. In both cases the floating potential V fl,ppp of such probes is a good approximation of the plasma potential [14]. With arrays of PPPs, electric field components can be determined with much higher reliability than with CLP since V fl,ppp does ideally not depend on T e . On the other hand, from the difference between the floating potential of a CLP and the plasma potential the electron temperature can be determined (see below). This can be realised by one CLP and one PPP mounted closely by each other on one probe head. More details on the EEP and the ESPs developed recently in our group will be presented in forthcoming papers [13,14].
For comprehensive investigations of blobs in the edge region of toroidal magnetic fusion experiments a new probe head (NPH) has been developed which combines two CLPs, an EEP and two retarding field analysers (RFA) for ion energy distribution measurements [18][19][20]. The NPH also carries two magnetic pickup coils (MPC) to measure magnetic field fluctuations on two radial positions [21,22]. The NPH will be robust enough to withstand the strong plasma heat and particle fluxes in the edge regions of toroidal magnetic fusion experiments and will make it possible to simultaneously measure plasma potential, electron and ion temperature, electron and ion density and magnetic fluctuations.
In this research note the NPH will be described which will be used in all three present European medium-size tokamaks (MST) for comparative measurements of transport parameters:  [25].
Also in Wendelstein 7-X of the Max-Planck-Institute for Plasma Physics in Greifswald, Germany, [26] the application of the NPH is envisaged to compare the measurements of transport parameters with those of MSTs.
To avoid mounting and dismounting the same NPH on the various probe manipulators of the three MSTs and the Wendelstein 7-X, several identical probe heads will be constructed and employed. In AUG two NPHs will be employed and operated simultaneously, one on the mid-plane manipulator (MEM-from German 'Mittel-Ebenen-Manipulator'), and one on the X-point reciprocator (XPR).

Theoretical considerations
Whereas (cold) probes were used in plasmas even long before the famous works by Mott-Smith and Langmuir [8, 9, see also 14], until about the end of last century they were employed almost exclusively in laboratory plasmas and small toroidal fusion experiments; all these probes were what we now conveniently call CLPs. Due to the much higher plasma temperatures, the use of probes in MST and larger stellarators with typical discharge lengths of several seconds has long been considered hardly feasibly since the probes would be damaged and destroyed quickly. Moreover, the sputtered-off or evaporated probe material will subsequently contaminate the plasma and/or might deposit on other plasma-facing components (PFCs) possibly leading to undesirable leakage currents or even short circuits.
However, the application of probe manipulators made it possible to use probes at least in the edge region of toroidal fusion experiments, mainly in the scrape-off layer (SOL) up to almost the last closed flux surface largely without these detrimental effects. To increase the versatility it has become customary to combine several probes on so-called probe heads (see e.g. [4,[27][28][29][30][31]). By mounting the probe heads on manipulators the heads are then inserted into the SOL for several strokes of about 100ms at most each time during one discharge.
Although Langmuir has also used EEPs already [32] their use was even more restricted to special applications in laboratory plasmas. Only recently EEPs were also found useful in small tokamaks [10,33], while now they are envisaged also for MSTs. For more information on CLPs and EEPs see [13,14].

CLPs versus EEP
In this section we would like to give a brief summary of the most important features and equations relevant for CLPs and EEPs.
For a CLP the basic, simplified relation between its floating potential V fl,cp and the plasma potential Φ pl reads [10,13,14,33]: Here I es and I is are the electron and ion saturation currents, respectively, impinging from the plasma onto the probe, T e is electron temperature in energy units and e is the electron charge (T i will be the ion temperature). Since in almost all types of plasmas I es ?I is , inevitably V fl,cp <Φ pl , and the difference between V fl,cp and Φ pl depends also on T e [10,12,14]. This dependence can be circumvented if we succeed to make the second term of equation (1) zero, i.e. if we make the argument of the logarithm one. This goal can be reached by adding a current to the ion probe current I is until numerator and denominator of the argument of the logarithm are equal in magnitude. This can be achieved by an electron emission current I em from the probe into the plasma since such a current will have the same sign as I is . Equation (1) for the floating potential V fl,em of an EEP will then read: Since I is is almost negligible compared to I es , this means that the magnitude of the emission current I em must be almost as large as that of I es . This derivation is simplified insofar as we have neglected the possible formation of space charges in front of an EEP [34]. There is an ongoing discussion on the question whether a strongly emitting EEP can really float on the plasma potential, but a detailed treatment of an EEP lies beyond the scope of this paper (see our forthcoming paper [13,14]). A discussion of the limits and restrictions of this simplified derivation and the requirements for its usage in SOL plasmas can be found in [13,14,33].
In a realistic experiment the procedure to verify that the emission current is sufficient for shifting V fl,em as close as possible to Φ pl is to measure V fl,em as function of the EEP heating power P heat . It is very helpful that for increasing heating power the transition from the cold floating potential V fl towards Φ pl (being more positive than V fl by a few time T e -equation (1)) is usually rather abrupt and that above a certain value of P heat the value of V fl,em almost saturates (see for instance [10,30,35,36]). Also figure 1 illustrates the rather abrupt transition of the floating potential of an unheated, or only slightly heated EEP from that of a CLP (horizontal blue line) to that of an EEP, being close to the plasma potential Φ pl (horizontal red line). This result was obtained with an EEP similar as that one shown below in figure 2, however with a tip of LaB 6 , in an unmagnetized argon plasma with a density of approximately 10 17 m -3 and an electron/ion temperature of around 2eV/0.2eV [37].
Above the threshold of P heat (which in case of figure 1 is around 175W) the actual value of the heating power is therefore not very critical since V fl,em remains constant very close, or even slightly above Φ pl [38]. Hence for the determination of spatial or temporal variations of V fl,em ≅Φ pl it suffices to adjust P heat at a sufficiently high value above the threshold.
We would like to point out that if we have the possibility to measure the floating potential V fl,cp of a CLP and the plasma potential Φ pl simultaneously on the same position, by turning around equation (1) we can deduce the electron temperature T e : . Drawing on equation (4) we can measure Φ pl with an EEP. Therefore, if we have a CLP and an EEP nearby, we can determine T e with a certain limited spatial resolution given by the distance between the two probes.

Robust strong EEPs for the NPH
In [13] also a detailed description of the robust, strong EEP to be used on the NPH is provided (see also [37,39]). Here only a brief summary is given: The greatest problem in constructing a sufficiently robust EEP, obviously being required to produce a strong emission current, was to find a material that, on one side, has a low work function, guaranteeing a high emission current according to the law of Richardson and Dushman, while, on the other side, has to withstand the high plasma temperatures and particle fluxes in the SOL of a typical MST. In the deep SOL typical electron and ion temperatures can go up to 50eV at densities of around 10 19 m -3 and electron current densities up to 4×10 6 A m −2 .
Usually lanthanum hexaboride (LaB 6 ) would be considered as the best suited electron emitter for such purposes since it combines good chemical and thermal stability with a relatively low work function of 2.66eV [40,41]. For the purposes of an EEP to withstand the harsh conditions of a MST SOL, however, surprisingly it turned out that the melting and sublimation temperature of LaB 6 (2482K) is too low. Our research showed that titanium carbide (TiC) will be better suited. Although it has a higher work function of 3.35eV (thus producing lower electron emission for the same temperature as LaB 6 ), its far higher thermal stability than that of LaB 6 (up to 3420K) compensates this disadvantage. See table 1 for a comparison between LaB 6 and TiC, including graphite and tungsten, the most frequently employed materials for an EEP in laboratory experiments. For further comparison this table also shows a typical current density |j es |-|j is | (electron/ion saturation current density) in the deep SOL of an MST with T e ≅ T i = 50eV and a density of around 10 19 m -3 . For a detailed discussion of this problem see [13].
The EEP for the NPH will therefore consist of a 1 mm diameter graphite pin coated with a thin film of TiC. Another important feature of the EEP is that it will be constructed of highly oriented pyrolytic graphite which will ensure that only the bridge between the two legs will be heated to the necessary temperatures for electron emission. More details of this EEP will be presented in our forthcoming paper [13]. Figure 2 shows a schematic presentation of the EEP that will be inserted into the NPH.

The housing and shroud of the NPH
Graphite is the most favourite material for anything to be inserted into a hot plasma since it has a very high thermal stability (up to 4023K) and is relatively insensitive to sputtering. Moreover, if sputtering occurs and carbon atoms enter the plasma, the relatively low atomic number of 6 keeps the Bremsstrahlung losses in an acceptable range. On the other hand, as mentioned above, sputtered-off graphite might deposit on other PFCs possible causing unwanted conductive layers.
Therefore the cylindrical shroud of the NPH for TCV, AUG, MAST-U and W 7-X, which encases the diagnostics, consists of graphite. The overall length of the probe is 208mm, its diameter 25mm. The latter dimension is determined by the maximum possible diameter of probe heads in TCV. The NPH carries on its top (right-hand side) two CLPs of pyrolytic graphite (PG) and one EEP also of PG, coated with TiC, as described in section 2.2. and shown in figure 2. Also on top there are two RFAs back to back, thus facing upstream and downstream. 40mm behind the top two MPCs will be inserted into the NPH to record magnetic fluctuations in all three directions of space [21], on two radial positions. Figure 3 shows a schematic view of the entire NPH. For AUG a shroud of 50mm diameter will be used for the NPH which will be coated by tungsten.

The diagnostics
The three probe pins of 1mm diameter each and a protruding length of 3mm consist of graphite and will be mounted in a row, slanted by 10°with respect to the total magnetic field in the edge region to avoid mutual shadowing. While the two outer probe pins will not be heated, thus acting as conventional CLPs, the centre pin will, as mentioned above, be The blue arrows suggest the strongly different electric resistivity of HOPG in the two main directions of the graphite crystal lattice. The red arrow shows the direction of high heat conductivity from the HOPG 'loop' upward to the actual probe pin whose tip will be covered by a layer of titanium carbide. See also [13].  [13] coated by TiC and heated externally (see section 2.2. and figure 2), thus acting as an EEP [13]. Figure 4 shows more details of the top of the NPH. Without heating the EEP the three probes can be used as triple probe for direct measurements of T e [42].
3.2.1. Retarding field analysers (RFA). The two RFAs will be facing upstream and downstream to record the ion energy distributions [19], whereof the ion temperatures T i,up and T i,down can be deduced (see figure 5) [43]. The entrance slit of the RFAs has a width of 20-30μm, the length of the slit is  2.5mm. The thickness of the tungsten slit plate is 0.1mm. The expected transmission of the entire grid system is 0.5%. The biasing scheme of the RFA grids is the usual one for recording the ion energy distribution, as shown for instance in figure 6 (from [43]). The negatively biased 'slit plate' repels the plasma electrons, the swept 'grid 1' is used to scan the energy distribution function of the ions. The negatively biased 'grid 2' repels secondary electrons released from the 'collector' by the impinging ions. Only about 0.5% of the plasma ions, gyrating along the magnetic field lines, arrive at the collector.
One prototype of such an RFA was tested in the linear magnetic plasma device (LMPD) at the Jožef Stefan Institute in Ljubljana at a magnetic field strength of 320mT and a typical density of 10 17 m -3 with T e ≅3eV. The results showed that the actually measured current transmission (0.49%) agreed very well with the above-mentioned expected value. Figure 7 shows an example of an ion energy distribution measured in the LMPD. From this characteristic we can deduce an ion temperature of about 0.2eV. As assumed in table 1, in a typical MST SOL the temperatures will be T e ≅T i ≅ 50 eV at a density of around 10 19 m -3 . The expected ion current in a typical SOL will therefore be in the range of several tens of μA.

Magnetic pickup coils.
The two MPCs will be contributed by the group at ENEA-RFX in Padua [21,22]. Figure 8 shows a schematic of the two MPCs and a photo of   one coil for comparison with a scale. The corpus of such a triaxial MPC consists of PEEK ® carrying three coils obtained by winding a 0.12mm diameter wire around a small parallelepiped-shaped support (8×8×8mm 3 ). The bandwidth for magnetic measurements is above 1 MHz with −3 dB cutoff at 1.1MHz.

Heat-stress simulations
Since the NPH will be inserted into rather hot plasma its heat resistance had to be investigated. To this end heat flux and stress simulations have been carried out. A detailed description of the modelling approach with the simulation results is given in [44]. Here a few first results are summarised. Further results will be published in a later publication [45].
The NPH will be cooled to the outside only by thermal radiation. For the simulations the temperature of the outer radiating surfaces of the graphite shroud was set to 100°C. The outside domain that should approximate the tokamak walls was modelled as a cylinder with a height of 1m and a diameter of 1.5m and a temperature of also 100°C. The heat sink for the heat conduction represents the bottom surface of the metal shaft with a fixed temperature of 100°C. The initial temperature of the probe at the start of the transient is also set to 100°C. The probe and the outside space are meshed by the hybrid mesh consisting of 0.385 million tetra and hexa elements. The meshing of the NPH and the outside domain is shown in figure 9.
The problem was approached from two sides. First the heat transfer model for steady state was solved and then also  3.3.1. Steady state simulation. First a steady state case with a linear axial distribution of isotropic heat flux q(x) onto the NPH's shroud was assumed. Naturally this case is not very relevant since under no circumstances could any probe stay in the SOL during an entire discharge of an MST. Nevertheless, such a simulation can give us a first idea of the general behaviour of the NHP in the SOL of an MST. For this initial simulation a rather low value of q(x)≅ 10MW m −2 was chosen on the top of the NPH, down to 0.1MW m −2 at the lowest part of the shroud still immersed in plasma, which was estimated to be lying 5cm lower. The solver balances between the heat source and the sinks with the residual target of 10 -5 using auto-timescale. The results are presented in figure 10.
As can be seen in the top left graph in figure 10, the graphite shroud would reach temperatures above its sublimation point (around 4000°C). However, even at such temperatures, the supporting holder made of VESPEL ® SP1 would not heat to temperatures above 300°C, as shown in the top right graph of figure 10. The parts made of VESPEL ® are the most critical parts of the probe, as their temperature should stay below 300°C (VESPEL ® sublimation point)    figure 10 shows that the supporting function of this VESPEL ® part would not be compromised even for the case where the NPH would be stuck at a completely extended position. Nevertheless, as can be seen in the bottom right graph of figure 10, the inside VESPEL ® part would reach temperatures much higher than 300°C.
3.3.2. Transient case simulation. A more realistic case is of course the transient case, where the probe is only briefly exposed to heating from plasma for a short time. Here preliminary results of a simulation of a single plunge of the probe are presented, exposing it to plasma for 0.1 s. In this case a conservative assumption of the heat flow was used, being uniformly distributed along the top 5cm of the NPH shroud of q 0 = 10MW m −2 . The initial temperature of the NPH is set to 25°C in this case. In the top right graph of figure 11 we see that the VESPEL ® support would almost not heat up at all, while the bottom right graph shows that the inner VESPEL ® part would stay below the critical temperature of 300°C. The estimated temperature of the shroud after one plunge is assumed to not exceed 400°C.

Possible measurements
As a summary, table 2 presents a list of plasma parameters which can be measured either simultaneously or with various methods for comparative purposes with the NPH. We would like to point out that the simultaneous determination of electron and ion temperature in the SOL would be especially relevant for getting a better insight into the formation and the propagation of blobs. Especially valuable will be that identical NPHs will be available at various MSTs, which will make it possible to directly analyse and compare the results and to draw generalised conclusions. At AUG, in particular, two NPHs will used simultaneously on the MEM and the XPR, thus in the toroidal mid plane and at the X-point, yielding new insights into the transport from the LFS mid plane towards the divertors. In addition measurements with the NPH will also deliver valuable instruments to compare and benchmark the experimental data with the results of edge plasma simulations codes for mid plane transport such as the HESEL code [46].

Conclusion
We have developed a diagnostics tool for the measurement of various relevant plasma parameters in the edge region of toroidal fusion experiments. This is a probe head combining two CLPs, one EEP, two RFAs and two MPCs. Identical types of this probe head shall be used on three European MSTs and Wendelstein 7-X. We are confident that by comparative investigations we will be able to contribute to a better understanding of blobs, their origin and propagation through the edge region. We hope for a better insight into the problem of plasma losses across the magnetic field of toroidal fusion experiments.