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SINGLET BREAKDOWN OPTIMISATION TO A DOUBLET PLASMA CONFIGURATION ON THE TCV TOKAMAK

B.P. DUVAL1*, H. REIMERDES1, J. SINHA1,2, S. CODA1 AND J-M. MORET1 1Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland 2Presently: ITER Organisation, Cadarache, France *Email: basil.duval@epfl.ch

Abstract

TCV has long used its extensive set of close-to-plasma poloidal shaping coils to examine a wide range of plasma configurations. Covering a wide range of divertor configurations and main plasma shapes, TCV has explored the possibility of creating multipole configurations with more than one current carrying core. The paper presents a fresh approach to creating a so-called Doublet configuration commencing with two simultaneous, but separate, current carrying cores of similar magnitude. Doublet configurations were, historically, predicted to provide enhanced stability over an equivalently elongated single core configuration, to stabilise turbulence and MHD through configuration shear, and provide a natural divertor solution. TCV has demonstrated a clear double plasma breakdown and plasma current ramp that followed an extensive study of the breakdown and plasma current formation of a single current core performed over the full TCV vessel height. Preliminary attempts to control the two current lobes separately of a doublet configuration using directed resonant ECH heating are reported that have shown surprising heat transport behaviour. In general, together with its potential for improving plasma performance, this configuration also provides a huge challenge to existing ideas and models of plasma confinement and divertor operation.

1. INTRODUCTION

TCV is equipped with a full grid of poloidal shaping coils that have been employed in creating and controlling a wide range of plasma configurations. Together with a full range of in-vessel poloidally and toroidally distributed magnetic pickup coils and a DML (Diamagnetic Loop), magnetic reconstruction of the plasma configuration is particularly advanced [1]. More recently, TCV was equipped with a digital control system that is able to react non-linearly to a wide range of integrated plasma diagnostic inputs to affect the plasma evolution [2]. Finally, TCV has long been equipped with steerable second harmonic (X2) lateral ECH heating/current drive that is also under computer surveillance and control. This combination of components is directly applicable to the well-known concept of a doublet divertor configuration for Tokamak-like plasmas where the divertor of one current channel leads to the divertor of a second current carrying plasma channel through a common X-point in a “figure of eight” poloidal shape. Both current carrying channels generate their own, Tokamak-like, poloidal field for confinement. This concept first culminated experimentally with the construction of the Doublet III device where, although the literature remains sparse, after several years of operation only a transitory configuration was obtained [3] culminating in the conversion of the machine to the DIII-D Tokamak device in 1984. Before the question of divertor power management was more generally understood, the Doublet configuration was predicted to feature improved MHD stability limits over a similarly elongated single core plasma such that the large expenditure necessary to generate the high toroidal field in a Tokamak could be more efficiently employed [4]. Furthermore, an intrinsic zone of negative shear was hoped to, at least partially, stabilise turbulence and thus improve the energy confinement. The main difficulty in obtaining this configuration is twofold. In the presence of a single loop voltage, both plasma channels (lobes) carry current in the same direction and will attract finally resulting in a single current channel. The two current channels also have high mutual inductance. If one channel starts to lose power (through confinement or radiation etc.) its temperature decreases, thus its conductivity decreases and with a closely coupled adjacent current channel, the current will transfer to the other lobe thus decreasing its temperature further etc. In both cases, the two current lobes will effectively merge into a single channel i.e. a standard Tokamak [5,6,7].

TCV Doublet experiments were first attempted in the mid 1990s with several doublet creation scenarios examined. In the most successful experiments, a Pear-Shaped configuration was programmed to evolve into an hourglass (the same “figure of eight” configuration described in this paper) but disrupted early through what was thought might be a q=2 limit resulting from a poor plasma current profile [8,9]. It was there noted that a direct hourglass breakdown with direct ECH controlled plasma current control might be possible. These ideas were revisited in 2010 where a double breakdown was achieved in TCV using X2 ECH heating at two locations

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[5]. That work examined the Doublet’s instabilities and potential but, although a double breakdown and current build up was inferred, was unable to progress farther due to instabilities in the burn-through phase resulting in rapid plasma termination. This paper describes a doublet formation starting from two separate plasma breakdown channels and plasma current build-ups, without ECH heating, that are then approached vertically to form the desired doublet configuration (see below). Before this method could be attempted, it proved necessary to re-visit gas breakdown and plasma current formation in the TCV tokamak. As with many machines, once plasma breakdown is followed by a successful plasma current ramp to a desired value, little further analysis nor physics interest remains in this process. On TCV, with a highly conducting continuous metal vacuum vessel (designed to improve plasma vertical stability), large currents in the machine vessel affect strongly the magnetic field profiles early in the discharge. This problem is exacerbated strongly when attempting to simultaneously achieve two, more or less, similar gas breakdowns and plasma current build-ups whilst keeping the plasma lobes separate. In the first part of the paper, the TCV machine with the most relevant diagnostics is presented together with assessments and improvements of the single-core breakdown scenarios at several locations within the TCV vessel. The understanding and tools thus developed are then applied to a two-core breakdown scenario. Finally, to extend the achieved plasma duration, ECH heating was applied to each lobe with a separately aimed gyrotron in an attempt to control the plasma current ratio between the lobes to avoid the thermal collapse of the weaker lobe, as described above.

2. TCV SINGLE-CORE CURRENT BREAKDOWN CONFIGURATION

Gas breakdown on TCV was, initially, feared to be challenging due to the break-less (45µOhm impedance) vacuum vessel limiting the available breakdown electric field. TCV is a medium sized, highly elongated Tokamak with a 1.5m vessel height, 0.25m minor and 0.88m major radii a nominal 1.5T on axis toroidal field and a 1MA plasma current capability. The main coil arrangement and magnetic pickup coil positions, projected into a poloidal plane, are shown in figure 1. For this paper, that will mainly consider the first 100ms of the discharge, gas breakdown, with a loop voltage ~10V, was rarely a problem. Following the Townsend breakdown model [6], this electric field was enough to cause visible gas breakdown over a tractable range of neutral gas pressures in H and D although often more troublesome for a pure He pre-fill. Thus the real question, and the main cause of plasma initiation problems on TCV is during the plasma current ramp up phase where several phenomena can result in failure to establish the desired discharge. The standard breakdown scenario is portrayed in Figure 2.

Equation 1: 𝐴𝑝!𝑒!!!!!! = !

! ∇!"!!

Simplified Townsend model for Fig 3, the threshold for avalanche (breakdown) for a given gas takes this form φ/p toroidal/poloidal directions, !"#

!" inversely proportional to the field line connection length Leff (A,B constants for gas and

pn the neutral gas pressure)

FIG 1a) Poloidal Coils and the OH coil (A,B,C,D) FIG 1b) Magnetic pickup coils in poloidal plane inside the

TCV vessel

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The currents in the OH and Toroidal field coils are ramped from 250ms before the breakdown and a pre-fill gas puff initiated into the empty vessel from 100ms before breakdown. An established near constant OH current is sharply reverse ramped providing a loop voltage ~10V for gas breakdown. (a small vertical field, not shown, is applied before breakdown to avoid any pre-breakdown). It should be mentioned that short toroidally orientated tungsten filaments at the top and bottom of the TCV vessel are heated and biased to supply thermo-electrons to start the breakdown avalanche sequence. It is important to understand the limitations in plasma breakdown control on TCV. The poloidal coil currents are set to compensate for the currents in the vessel. On TCV, this amounts to several hundred amperes through a vessel that contains many non-symmetric features such as large ports and holes for diagnostics that are neither toroidally nor poloidally evenly distributed. There is no vessel gap across which the vessel currents can be estimated with shunts as is done for the coil currents. Furthermore, the poloidal coils are outside the vessel and, although their power supplies can be switched every ms, the penetration time of their fields changes is 10-20ms. Thus, through the breakdown and early current rise phases, the gas breaks down and the plasma current grows only through pre-programmed temporal coil trajectories.

Initially, breakdown occurs where the parallel connection length L (distance of field line to termination at the vessel wall) is greatest. To obtain breakdown, this value must exceed a threshold that depends on the gas, its pressure, and the applied electric field, Fig 3. The null is calculated using a “breakdown code” [5,6,7] to occur at t=0ms by compensating for the vessel currents and accounting for field penetration etc. from the poloidal coils. This procedure is further described in detail in a paper in preparation at the time of writing and details more of the verification steps employed to reach the conclusions described below [7].

From the start of this exercise, several problems became apparent. TCV plasma startup had, over the years, been notoriously “moody”- Although shot attempts without breakdown (i.e. no Dalpha light) are rare, varying the pre-fill pressure was mostly used to obtain a successful discharge i.e. defined as gas burn-through and plasma current formation. As was mentioned above, most of the shaping and induction currents are preprogramed until 10ms into the discharge at which time the Dalpha emission is close to peak intensity (highest ionisation rate) so that the plasma is already well ionised. Failure of the plasma current often occurs between 10ms and 50ms into the discharge following which the operator often tweaked only the pre-fill gas once all other systems had been verified. Two main situations were common. With too much gas, the ionisation fraction remained insufficient and the gas was insufficiently ionised by the end of the high Vloop phase. The main, and recurring, problem was, however, that the plasma current grew far more quickly than anticipated. Here, when the feedback system was engaged at 10ms, the estimated plasma current was compared to its preprogramed value resulting in the feedback control reducing the loop voltage after which the plasma did not survive. Furthermore, the horizontal position estimator that is proportional to the plasma current is also false resulting in the control system suddenly pushing the plasma radially when position feedback is applied, again reducing the chances of a successful plasma current build-up. The aforementioned “moodiness” displayed by TCV breakdowns becomes clearer. The operator, once convinced that the coil configuration and poloidal field were the same as for a successful plasma

FIG 2 TCV breakdown sequence showing current in OH, loop voltage, Toroidal field and working gas flux

FIG 3 Townsend breakdown thresholds for three effective connection lengths from the null to the vessel. (Equation 1: deuterium gas with A = 3.9 Pa-1m-1 and B = 97 VPa-1m-1)

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initiation, tweaked the gas fill to be just below the value that would douse the plasma formation and not low enough to result in an excessive current ramp that would be quenched by the control system’s reaction. Since gas fill is a function of wall conditioning that, in turn, depends on recent and long term machine operating history, this delicate tweaking was prone to error.

3. DIAGNOSTICS

Before listing the optimisation parameters that were explored to rectify this situation, it is pertinent to mention the, relatively few, diagnostics available to the short period of low plasma temperature and densities of these plasma initiation experiments.

As mentioned above, the main diagnostic was the magnetic coil array coupled with the LIUQE Grad-Shafranov equilibrium solver to estimate the poloidal field evolution. This system is already part of TCV’s real-time non-linear control system and will be further employed below. To estimate the poloidal field around breakdown where the vessel currents affect strongly the poloidal field employed the so called “breakdown code” that strives to estimate the field ensemble at the time of gas breakdown, here defined as the time at which the main plasma current estimator exceeds its noise floor i.e. shows a toroidal current is flowing. The vertically viewing 14 radial chord FIR interferometer proved invaluable in estimating the radial plasma position. Each chord measures the integrated electron density across a vertical chord with a better than 2kHz temporal resolution. This was complemented by TCV’s high spatial resolution Thomson scattering system providing electron temperature and density measurements along a vertical chord through TCV. Although the lasers’ repetition rates were 20ms, the three lasers of the system could either be staggered by 1ms providing 3 measurements for one discharge and/or Thomson profiles could be obtained as a function of time by firing the laser at different times for a sequence of reproducible discharge breakdowns (here the 3 lasers were often fired together to reduce measurement noise). For vertical breakdown estimation, a fast visible camera viewing the plasma column tangentially provided a poloidal-like light emission profile as a function of time. Its central location in the vessel made it particularly sensitive to vertical plasma movement in the partially ionised phase of the plasma column formation. A set of discrete, horizontally and radially viewing photodiodes equipped with Dalpha filters also provided rapid estimations of changes of the location and strength of the ionisation rate.

4. SINGLE-CORE CURRENT BREAKDOWN OPTIMISATION

The initial plasma null is produced by using four, (two LFS and two HFS), poloidal coils in a quadrupole arrangement with all the coils performing field compensation to zero the coil and vessel current generated field. As was noted above, the current ramp rate, its value compared to pre-shot expectations and the reaction of the control system all contribute to reduce the probability of a successful plasma formation. Furthermore, a systematic difference between the predicted and experimental positions of the initial breakdown (and hence null position) was discovered that would also cause the control system to react wrongly to pre-calculated references. A breakdown database of ~10000 discharges was constructed to investigate the distribution of breakdown failures and a set of experiments performed to investigate possible corrections to the above errors and their importance in affecting the plasma formation likelihood. The following changes were investigated:

FIG 4 Typical breakdown curves for a single plasma core breakdown and current build-up. Top curve shows Ne density contours estimated from the FIR and the pre-shot request (dashed line). The plasma current is similarly shown in the second curve. Here Ip rises more quickly than anticipated and the breakdown radial position is wrong resulting in a strong radial excursion when the control system starts reacting at 0.01s. An MHD-like oscillation on the pickup coil (lower trace) is often observed together with similar fluctuations on the vertical Dalpha signal.

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— The offset in the reconstructed poloidal field was improved by re-evaluating the magnetic compensation matrix. The evaluated and measured breakdown position differences were much reduced.

— The plasma current (Ip) ramp rate was reduced by reducing the loop voltage or modifying the quadrupole gradient around the breakdown null. Although the Ip control problems were improved, the loop volt reduction acted to reduce the strength, and thus the probability, of the breakdown.

— The Ip feedback was enabled earlier in the breakdown and for a range of gains (thus changing the amplitude of the feedback’s reaction when turned on). As above, this reduced the Ip feedback reaction problems and the MHD-related oscillations that were seen on the Dalpha trace, but the improvement was tempered by a lower eventual Ip and further problems with the radial position control.

— The digital control system was used to generate a so-called “bump-less” transition in the plasma current and radial position control systems at the feedback control switch on time. Here, the observation parameters were tracked from breakdown and their values allowed to evolve only slowly to their correct values using an additional calculated error term that smoothly dissipated within a programed time (varied from 10 to 70ms). This approach reduces the feedback system’s oscillations but allows both the plasma current and radial position to not be as projected for longer, but retains the control system’s final target.

— One simple approach was to let the predicted control system’s reference calculation use a higher Ip ramp rate than before. Here, when the feedback is turned on, the real and predicted values agree better, reducing the tendency to oscillate. Paradoxically, this resulted in the breakdown plasma staying closer to the central column, as programmed, thus reducing the plasma current bore and reducing the plasma current ramp rate. This was a clear demonstration of the role of the Ip ramp rate link to the plasma radial position through the current channel bore modifying the plasma column’s loop resistance.

With these tools implemented, the considerably more reliably controlled breakdown position was employed to create single column breakdown scenarios at +/- 0.4m from the vessel centre [6]. Several of the techniques listed above were employed and these configurations form the basis of the doublet configuration that starts with two simultaneous, yet completely separately located, breakdowns and initial current ramps.

5. MULTICORE PLASMA CURRENT CONFIGURATION

In the first approach to a doublet, TCV was symmetrically divided into upper and lower halves with two quadrupoles, again using two pairs of poloidal coils for each (8 coils in total). Fig 6a shows the poloidal coil currents, poloidal field and poloidal flux contours calculated at t=0ms. Fig 6b plots the resulting plasma parameters using a modified LIUQE reconstruction that accepts two separate current lobes and a double filament model previously used to model the discharge initiation and equilibrium stability. Although two separate lobes with similar plasma currents are initiated, they appear to coalesce 20ms into the discharge. The plasma ramp rate in the top lobe rolls off after 10ms and the extra current appears in the lower lobe. Both lobes are also 0.05 to 0.07m further out than intended, which is also seen on the FIR data.

The most interesting result is from Thomson scattering whose laser trajectory almost crosses the shared X-point and reveals two clear temperature peaks with a dip at the X-point where the plasma density is highest (Fig 7).

FIG 5a: TCV signals for z=+0.4 single core breakdown.

Green cross is requested location, solid lines poloidal flux and dashed lines poloidal field contours (mT)

FIG 5b: Same curves for a z=-0.4 core breakdown request. In both cases, the experimental result is close to the request

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Three highly reproducible discharges were used to measure the plasma profiles as a function of time after breakdown. As the lobes coalesce, the temperature of the upper lobe decreases with the X-point density rising significantly (Fig 7). The doublet plasma consists of relatively small, but highly elongated, current-carrying cores surrounded by a large mantle defined by closed flux surfaces that do not appear to contain much plasma i.e. that do not carry the plasma current that heats the ionised plasma. TCV’s vertical control system features internal “fast” coils arranged to control fast vertical displacements. These, however, are not able to affect the lobe separation since they act identically on both current lobes. Vertical control to maintain lobe separation is only possible through the external poloidal shaping coils that had little time to react for these plasmas in view of the long penetration time of their field into the plasma compared to the relatively short ~20ms plasma duration.

This scenario indicates clearly that the difference in Ip ramp rates between the lobes is causing one to finally extinguish as described in the introduction. The reason for the vertical displacement of the upper lobe, alone, remains unclear but the lobes become vertically close at ~20ms where the discharge disrupts for reasons that are, again, not yet clear.

FIG 6a Poloidal field magnetic reconstruction for doublet scenario, with coil currents in [kA] and the two sets of coils used to generate the quadrupole nulls in red.

FIG 6b Plasma currents and positions of two lobes following a twin Ohmic breakdown. After 10ms the top lobe starts to fade and move down to the lower lobe

FIG 7 Three Ne and Te Thomson profiles across an Ohmic doublet configuration formation. Two clear hot plasma cores with a dip around the X-point are seen. All profiles taken before the plasma current in the top lobe, (that clearly descends), cedes to the lower lobe.

FIG 8 Two lobe plasma currents and positions with separate X2 heating for each lobe. Although the currents and lobe heights are close to request (dashed lines), they are radially ~5cm further to the LFS than intended.

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6. DOUBLET CONTROL AND PERFORMANCE

In the last experiments described here, separate gyrotrons were aimed at each lobe to attempt to control their temperature, and thus their resistivity, and thus their currents. The initial idea was that a feedback on the relative ECH power deposited in each lobe could be used to keep any difference between the currents in each lobe from increasing. A secondary effect would, of course, be to add heat to the Ohmic discharges described above that may also increase the configuration stability by improving the overall power balance in favour of a strong plasma channel. At the low initial plasma densities, (see Fig 7), X2 beam diffraction was not problematic so ECH aiming was always reliable. Fig 8 shows the plasma current and position evolution for a discharge heated with two gyrotrons, from breakdown onset, as a function of discharge time. The doublet discharges seemed better balanced with ~20% more ECH power to the upper lobe, a result supported by LIUQE reconstruction that also evaluated a lower plasma current in the upper lobe. Although the upper lobe’s vertical position initially evolved from 0.26m to 0.21m from t=10ms to t=20ms, the two lobes always appear to remain vertically stable. Here again, the top lobe appear to be performing less well and, again, for unclear reasons the discharge terminates abruptly near 30ms but now with a combined plasma current approaching 300kA (the current record on TCV). The electron temperature with such strong ECH is now ~1300eV as compared to ~200eV for Ohmic heating alone (Fig 9).

A strong temperature gradient was observed between the mantle plasma and the current carrying cores with only a sharp temperature drop in close proximity to the X-point. The Te and Ne profiles in Fig 9, also show the positions of the lobe limits from magnetic reconstruction compared to the Thomson laser path that indicate a slight vertical offset between the Thomson measurements and the LIUQE reconstruction. The sharp temperature drop at the X-point is not accompanied by a similar density variation with the density profiles, at least at this spatial resolution, remarkably flat. The data does, however, appear to imply that the current only flows through the lobes themselves with the mantle, lying within closed flux surfaces, effectively inert.

Somewhat surprisingly, the improved doublet performance did not seem to depend on where the ECH power was deposited showing that, although heat was being deposited as aimed, that the doublet’s lobe currents could not be controlled separately using the double X2 Gyrotron arrangement. This phenomenon is demonstrated in Fig 10 where the Thomson profiles are plotted for four different ECH deposition profiles. Although the deposited power is more or less efficiently transferred to the plasma, whether heating the lower or upper lobe

FIG 9 ECH assisted doublet Ne and Te profiles at 17ms

into discharge (during Ip ramp). The reconstructed lobe extremity positions are shown by vertical lines indicating a slight Reconstruction/Thomon position mismatch. Two clear hot lobes are distinguished with very low pressure across the entire mantle

FIG 10 ECH assisted doublets for a range of heating positions (intercept of indicated beam lines with radial position of common X-point). For all heating locations, the electron temperature and density profiles are very similar indicating a strong heat sharing between doublet lobes for all heating schemes.

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alone (Fig 10a,b) or close to the X-point (Fig 10c) or far from the X-point (Fig 10d), the resulting temperature and density profiles are remarkably self similar. This result negates localised ECH heating as a control actuator, and is hard to explain. Clearly the heat transport between the lobes is sufficient to, alone, equilibrate the temperatures of the lobes and maintain a doublet configuration.

Although the Thomson coverage is not complete below z=-0.4m, the profiles do not indicate that the mantle is responsible for this transport but, since the lobes only communicate at their common X-point, that has no direct volume, a strong heat transfer channel, most probably in the immediate region just outside the X-point, is likely to be responsible. What looks like a strong transport barrier surrounding the doublet may be due to the negative magnetic shear that was one of the original hopes for this configuration.

7. CONCLUSION

Following a complete revisit of the TCV breakdown scenarios that included a database of several thousand discharge initiations, several issues were discovered and approaches developed to deal with the strong TCV vessel currents’ contribution to the breakdown and plasma current formation period. TCV was shown to have little problem with the initial breakdown itself but showed several problems with plasma current ramping that were often due to the reaction of the plasma control system to the experimental plasma ramp rate being higher than anticipated. This expertise, to be detailed in a further upcoming publication [7], was employed to set up reliable plasma formation at +/-0.4m in the TCV vessel. This was then used to obtain an Ohmic doublet configuration that displayed two separate hot plasma cores but where the top plasma lobe tended to cede its current to the lower lobe whilst losing power and coalescing with the lower lobe. The initial control approach of adding separate and independently controlled, X2 localised ECH power to each lobe to compensate for mismatches between the current lobes generated a surprising result. The power, resulting in a temperature increase from ~200eV up to ~1300eV did stabilise the doublet with their combined current ramping to ~300kA with, again, two separate hot cores measured by Thomson scattering. Following initial observations that changing the heat ratio deposited between the lobes did not appear to have the expected effect, a scan of the power deposition showed an extremely high heat transport between the lobes that thus seemed to stabilise themselves against any thermal quenching of one lobe. A clear and reproducible doublet scenario is now available to TCV. As the mantle surrounding the doublet cores showed both low temperature and density, the strong heat transport is concluded to lie in the region around their shared X-point. An explanation for this, an examination of the divertor properties of this configuration, together with ideas to lengthen the plasma duration beyond the ~30ms so far achieved, will be the subject of a new research line on TCV in the coming years.

ACKNOWLEDGEMENTS

The authors wish to particularly acknowledge F. Hoffman and F. Piras who pioneered doublet discharges on TCV. The whole TCV team, and this over more than one generation, has directly contributed to reaching this new stage in Doublet investigations. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work was supported in part by the Swiss National Science Foundation

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