Experiments with reduced single pass absorption at ASDEX Upgrade – instrumentation and applications

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Introduction
The electron cyclotron resonance heating system (ECRH) at ASDEX Upgrade (AUG) has been extended to eight Gyrotrons in total. Each Gyrotron operates at 105 and 140 GHz and is designed for up to 1 MW millimetre wave output power. Experimental topics at AUG include variations of the main magnetic field strength in the plasma and conditions with high plasma densities, potentially above the X-2 cut-off at 140 GHz, e.g. [1]. New ECRH schemes have been proposed [2] which can cope with the demand, at the cost of reduced single pass absorption, however. It is necessary to design reflecting gratings [3] and install them into the heat shield, i.e. the inner column inside AUG's vacuum vessel. The gratings are designed for 140 GHz, they are refocussing and redirecting each beam towards the plasma centre, thereby increasing the second-pass absorption and the total heating efficiency.
Part of the heat shield inside AUG consists of the steel W1.4901. Four of the gratings were manufactured out of this steel and a thin tungsten coating was applied, which is a newly developed technique. In order to monitor the position of each ECRH beam on the corresponding grating, thermocouples were installed. The fast response of the thermocouples opens the possibility to measure the local beam intensity after the first pass through the plasma with short pulses. Since experimental data on X-3 absorption at 140 GHz are rare, it was decided to try this measurement. The * Corresponding author: experimental setup uses the two available frequencies: (a) 105 GHz at different power levels and with nearly perfect absorption at the X-2 resonance in order to vary the central plasma electron temperature. (b) 140 GHz for the probing beam, where only the X-3 resonance is present in the plasma and the shine-through can be measured at the heat shield, using the thermocouples. The results on X-3 absorption are presented in a separate contribution to this conference.
In a more general approach to study the beam properties after the first pass through the plasma, we started to measure the local beam intensity as a function of the launching direction, in a set of reproducible and similar plasma discharges using the O-2 mode polarisation. Putting the measurements of several AUG experiments together, a kind of 2D image of the beam cross-section can be generated.

Two-pass scheme at ASDEX Upgrade
The design criteria were already written down [3] and the scheme has now been completed for all ECRH launchers (figure 1). We would like to point out that the oblique geometry is necessary in order to maximize the O-2 absorption [2]. For each launcher (figure 2) there is a corresponding reflecting grating (figure 3) and it is necessary that the unabsorbed beam power after the first pass is located on the corresponding grating, as long as the absorption is incomplete. Consequently, the heating geometry is fixed and no large variations of the launching direction are allowed.  Middle: Single launcher in segment 8. Right: Segments 7,6,5 (from left to right) with the large port of the neutral beam input in segment 7, the single ECRH launcher in segment 6, and the four launchers in segment 5. The robust surfaces of the auxiliary limiters left of the launcher mirrors in segments 14, 8, and 6 are the design end points after the second pass. The launcher highlighted with a white circle in segment 5 (right photo) was used for the experiments described in section 4.
The inner column of AUG's vacuum vessel consists of tiles (figure 3). Two tiles at the corresponding position were merged into a double tile, to make the reflecting gratings sufficiently large. The heat shield around the midplane consists of W1.4901 steel, which concerns the gratings in segments 7 and 13 (figure 3). The other ones were machined out of graphite.
With tungsten coating, mm-wave power absorption of the grating can be reduced to approx. 0.5% [4]. For graphite, this coating is established at AUG for a long time, while for W1.4901 steel this had to be developed. Figure 4 shows the depth profile measured by glow discharge optical emission spectroscopy (GDOES) of a successful coating. A thin coating of up to 10 µm can be applied to this steel using a molybdenum interlayer.  GDOES is sputtering the sample and is, thus, destructive.

Thermocouple measurement
Fast thermocouples can be used to monitor ECRH beam positions in scenarios with potential shine-through [2], and this technique has been developed continuously [5]. We chose a NiCr-Ni (type K) thermocouple with an outer diameter of 0.25 mm [6]. Sensitivity 40.96 µV/K and maximum specified temperature approx. 1200 ºC. The jacket of the thermocouple is made of Inconel 600 and it is connected to a flexible cable within a cylindrical joint with outer diameter 4 mm and a length of 25 mm. We have tested different mount options and found that the best compromise between longevity and signal amplitude is achieved in a flush mount (figure 5).

Flush mount
Several tools have been developed in order to facilitate the flush mount, cf. figure 6. We have put emphasis on sufficient protection and shielding of the cables in order to prevent damage during operation with mm-waves. Bottom: Flush mount, the borehole goes through the surface and the TE is partly exposed to the mm-wave. The On/Off time of the power is of the same order as the relaxation time of the thermocouple. If the total heat capacity of the absorbing material is comparable, then the total temperature rise after the last pulse plus relaxation time is also comparable (double sided arrows on the right).

Fig. 6.
Left: Transparent CAD view of two double tiles with built-in channels for the cables. Right: Tools which ensure a precise flush mount. During the attachment procedure, the opening of the borehole at the plasma exposed surface is temporarily blocked (upper right photo). This opening is normally located on the bottom of a groove of the grating. The view onto the rear side (lower right) shows the mechanics used to fixate cables and cylindrical joints. In the manufacturing process the thermocouples are attached to the tile with a graphite glue, which is a mixture of graphite powder and phenolic resin. The tile including thermocouples and cables is baked, until the graphite glue is sufficiently stable. After complete assembly, tile and grating are inspected (figure 7). If the flush mount was successful, then within each borehole the tip of the thermocouple is clearly visible.
During the recent AUG experimental campaigns we did not encounter thermocouple sensor failures specific to the flush mount. In the AUG case, the specified temperature ranges of the thermocouple sensor and jacket [6] are not exceeded. This should be regularly checked, depending on the planned application.

Evaluation model
During experiments with applied mm-wave power, Gyrotron On/Off times are recorded with a precision better than 0.1 milliseconds (ms) by directional couplers in the transmission line. The thermocouple signals are filtered with a 300 Hz Bessel low-pass and recorded with 1 ms time resolution. Taking into account the relevant transit times and the transfer function of the filter, we observe a characteristic time delay of typically 10 ms between the mm-wave power arriving at the borehole and the start of the signal rise in the recorded thermocouple signal. The relaxation time of the signal, when the mm-power is switched off, is of the same order. This indicates that, when evaluating short pulses, the model should be comprehensive enough to account for the effect of these time constants.
Thermocouples, which are not hit by the mm-wave, show a continuous, uniform, and slow rise of the temperature due to the background heat load from the plasma. The rise time is larger than the relaxation time of the thermocouple. We therefore model this background heat load pbg homogeneously across the tile, based on the direct measurement from those thermocouples.
When evaluating pulsed mm-wave power similar to figure 5 (bottom), we use a simplified 2D model around each thermocouple in order to account for the dynamics of the heat exchange between the absorbing surface and the thermocouple sensor, which is located several 10 µm below the surface [6], see also figure 8. Fig. 8. Schematic visualisation of model temperature zones around and inside a thermocouple. Left: The entire tile with total heat capacity CB and exposed surface area Atl. Cylindrical zones around the thermocouple, which expand into the depth: near bulk ANB (grey) and intermediate bulk fIB Atl (fraction of Atl dark green). Right: side view of the thermocouple cross section [6]. Absorbing surface area ASM with heat capacity CSM. The metal-metal joint with the heat capacity CM is the position of the temperature measurement TM and it is located several 10 µm below the surface [6]. The heat flux has to cross insulating material with model heat conductances kSM and kMN.
The model has three grid points in radial direction parallel to the tile surface, and one additional grid point in the depth, where the measurement TM takes place (figure 8). The three radial grid points are: (i) absorbing tip of the thermocouple with surface area ASM, heat capacity CSM, temperature TSM , (ii) the near bulk with surface area ANB = fNB Atl, temperature TNB, and (iii) the intermediate bulk with surface area AIB = fIB Atl, temperature TIB.
Both near and intermediate bulk are characterized as fractions fNB and fIB of the entire tile, i.e. with heat capacities CNB= fNB CB, and CIB= fIB CB, respectively.
We introduce heat conductances: kSM between the thermocouple tip and the measurement sensor (CM, TM), kMN between the sensor and the near bulk, and kNB between near and intermediate bulk. For simplicity, we allow heat transfer from TNB to TIB (via kNB) as a loss term for TNB, but we set TIB as a boundary condition, which changes its value only due to the heat flux from the surface, ignoring the incoming radial transfer from the near bulk. In doing so, we assume that at this position, the incoming heat flow from the near bulk is small compared to the flow from the surface, and we end up with a system of three coupled differential equations for TSM, TM, TNB, and a separate equation for TIB: In this system pA is the absorbed mm-wave intensity, pbg is the (homogeneous) background intensity, measured by the distant thermocouples, and the term rIB·pA is to model the heat flux to the intermediate bulk as a fraction of the mm-wave intensity. The fraction rIB had to be introduced in order to correct the baseline of the signal, whenever the incoming mm-wave intensity is zero for a duration longer than the relaxation time of the thermocouple. It is an indication, that the beam width is indeed smaller than the dimensions of the tile.
A cooling term can be included in each equation, which is due to the fact, that the tile is mounted on a cooling channel, see figure 6, CAD drawing on the left: the vertically elongated, blue structure is in fact a tube with cooling water. The cooling time constant is of the order of several minutes and was measured, using long acquisition times. Within the short pulse analysis of our experiments, it can be neglected.
The system of equations (1-4) can be solved in time, using a Runge-Kutta fourth order scheme, depending on the parameter values. The Runge-Kutta solver is a subroutine to an optimizer [7], which does a least square fit of the model TM to the measured signal, using as free parameters: the absorbed intensity pA, most of the material constants (except CB, ASM, Atl, which can be measured) and the fractions fNB and rIB (fIB is indeed irrelevant due to our choice to ignore the incoming radial transfer from the near bulk).

Experimental results
In this paper we restricted the evaluation to a short pulse analysis, assuming the absorbed mm-wave intensity pA constant during each pulse. It is necessary to calibrate the system in vacuum, measuring the thermocouple response with respect to a well-defined incoming beam power. We neglect the influence of the incoming wave polarisation, because (a) the gratings are optimized to be independent on the polarisation [2] and (b) the reflection geometry and, thus, the angles of incidence are nearly constant. The possible dependency on the polarisation is, therefore, expected to be small.

Launcher sweep and vacuum calibration
It is possible that the beam will be deflected due to beam refraction in the plasma, and therefore we continuously scan the beam across the thermocouple. For that purpose, we use one of the fast steerable launchers of AUG in segment 5 (cf. figure 2). During one sweep of the launcher mirror, we apply 5 pulses of Gyrotron power, which end up on different positions across the thermocouple (figure 9). This sweep is large enough to clearly identify the maximum response of the thermocouple to the applied mm-wave power, in both cases with and without plasma (e.g. figure 10). According to the TORBEAM simulation [8], the vertical beam refraction is more important than the horizontal one. A fast horizontal sweep is technically not possible with this launcher.
The signal quality in the vacuum case (figure 10) is very good, such that the free parameters (section 3.2) can be fitted together with the pulse amplitudes. The parameter values of the fit result seem reasonably consistent: e.g. CSM/kSM = 30 ms, corresponding to the main time constant of the thermocouple measurement. Fig. 10. Measured signal response to pulses of mm-wave power without plasma, compared with the modelling. Pulse amplitudes (bottom row) are the fit results. The main part of the residual (middle row) can be understood from the fact, that the model intensity amplitude is assumed to be constant within one pulse. In reality, during the fast launcher sweep for example in the second pulse (at approx. 0.15 sec) the absorbed mm-wave intensity increases during the measurement. The model fits an average value and, therefore, the residual, which is model minus measurement, is positive during the first part of the pulse. The observer should keep in mind, that there is a time lag between the mm-wave power and the measurement. The data was recorded as AUG experiment #39744.
The fitted quantity kSM /ASM =15000 W/(K m 2 ) can be approximated by λ/d where λ is the specific heat conductivity and d the distance between the absorbing surface and the measurement position (TM). In the case of a typical insulator with λ approx. 1 W/(K m) this corresponds to d of the order 10 -4 m, which is consistent with the specification of the thermocouple [6].
An additional fitted signal delay of the order of 1 ms of the thermocouple measurement with respect to the power improves the fit quality. It should also be mentioned, that the fit of parameters, which are related to material constants, is part of the calibration. When evaluating a measurement, only beam related quantities should be fitted again, i.e. pulse amplitudes pA and the fraction to the intermediate bulk rIB.

Absorption measurement X-3
Experiments were carried out to measure the plasma absorption at the X-3 resonance as a function of the plasma electron temperature. We show an exemplary overview of experimental data in figure 11. Heating and X-3 probing geometry are visualized in figure 12. For further evaluation see the contribution by J. Stober [9]. The signal evaluation as described in section 4.1 yields the results of figure 13. The material constants from the vacuum calibration are used. Fit results are: pA (one value for each pulse) and rIB (only one value for the entire time interval). If the absorbed power during one pulse is not constant, then deviations between model and measurement can be observed in the residual, e.g. during the longer pulse at t approx. 4.9 sec, where the background plasma (cf. figure 11) seems to be transient.
In order to evaluate the X-3 absorption, the fitted pA with plasma (figure 13) are normalised by the launched Gyrotron power of Gyrotron 6 (figure 11) and the five pulses during one launcher sweep are summed up. The same procedure is done in the vacuum case, where in particular the launched Gyrotron power was different. The shine through is evaluated by the ratio of the plasma measurement versus the vacuum measurement. Fig. 11. Comprehensive overview of AUG discharge #39747 with total ECRH power data, evolution of plasma density and plasma current on top, individual Gyrotron power signals in the middle row, and Launcher 6 push-rod scans, as well as stray radiation signals in the bottom row. The blue density signals on top are line-integrated interferometry data. Middle row: the purpose of the group of 105 GHz Gyrotrons is to vary the plasma heating such, that different levels of plasma electron temperature exist. Bottom row: Stray radiation, in particular which is measured by the ECE, is significant only during the 140 GHz X-3 pulses and increases with decreasing plasma electron temperature, as expected. Fig. 12. Cross section, AUG #39747 showing the geometry [8] of the 105 GHz X-2 heating (left) and the 140 GHz probing (right). The main magnetic field strength was chosen such, that for 140 GHz only the X-3 resonance is present in the plasma. The heating beams (left) were launched with a toroidal angle, so that the Doppler shifted resonance is closer to the centre. The amplitudes of the model temperature TSM are much larger and not shown for simplicity. Second row: residual = model temperature minus measurement. The residual is subject to minimization in the fit procedure using the pA as fit parameters. The resulting pA are shown in the bottom row. The parameter rIB was also fitted, but assumed constant during the experiment.

Shine-through power in O-2 polarisation
The evaluation model described in section 3.2 was developed very recently. Earlier, the amplitude of the pulse response of one thermocouple to the pulsed mmwave power in O-Mode was recorded as a function of the launching direction ( figure 14). . The plot on the left was generated using Delauney triangulation and corresponding visualization [7] for irregularly gridded data. Individual measurements are plotted in orange (2017 campaign) and blue (2019 campaign). Points connected with a dashed line are from a launcher sweep as described in section 4.1. The inset on the right is a contour plot of the same data, with contour levels 0.9, 1.8, 2.7 and 3.6. Within the plot range of a [mm], the centre of the beam moves approx. 10 cm on the heat shield, and approx. 7 cm within the plot range of β. The coordinates are only approximatively corresponding to the vertical and horizontal directions, because the geometry is oblique (cf. figure 9). This was repeated in a particular plasma experiment called "Standard H-mode", which is carried out frequently and considered reproducible. Short pulses (approx. 30 ms) of Gyrotron no. 8 (Elisey 3M) were used for these experiments. Vacuum calibration data were not measured. Figure 14 shows data from the 2017 and 2019 experimental campaigns. With the thermocouple position being fixed, it should be possible to transform the variation of the launching direction into a cross section of the shine-through beam. This needs beam tracing and reliable plasma kinetic profiles in order to evaluate the shine-through power. We propose to use the simplified analysis as shown in figure 14 in order to verify the launcher setting.

Summary
The thermocouple mount and the corresponding evaluation model were developed further in order to provide a measuring tool to study mm-wave deposited power on the heat shield of ASDEX Upgrade with high time resolution. A local monitoring of shine-through intensity was demonstrated exemplarily. A systematic comparison of the beam geometry and size with beam tracing predictions seems possible.
Careful mechanical work by H. Schütz is gratefully acknowledged. Photos in figures 6 and 7 as well as the launcher CAD model ( figure 9) are also courtesy of H. Schütz. This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 -EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.