On the possiblity of direct electrical power extraction from scrape-off layer currents in tokamaks

Scrape-off layer currents (SOLCs) have been detected in a number of contemporary tokamaks [1–5]. They can be either stationary or linked to intermittent events, such as edge localised modes (ELMs) [2, 6] or MHD activity [7]. The most common driving mechanism of the SOLCs is the thermoelectric effect, which appears when each divertor target has a different electron temperature, therefore a different magnitude of the sheath potential drop and consequently a different value of potential at the sheath entrance [8]. In such case, the particles flowing along the magnetic field lines are experiencing a parallel electric field, which drives the SOL current. The current is closed through the divertor plates and the vessel between the two targets. Another driving mechanism for SOLCs are the Pfirsch–Schlüter flows [9, 10] which arise in locations of high radial pressure gradient, typically close to the last closed flux surface.

The SOLCs have been intensively studied in the past for two reasons: intermittent SOLCs driven by the thermoelectric effect occurring during ELMs, were suspected to cause stochastization of the magnetic equilibrium and consequently ejection of hot and dense plasma from the pedestal region into the SOL and divertor [11]. The steady-state SOLCs have been investigated with hopes that they could be manipulated by divertor biasing in order to control transport in the edge plasma and e.g. mitigate ELMs [12, 13].

In this work we revisit the SOLCs from a new perspective: we will address the question whether such currents could be extracted from the machine and used as an non-thermal mean of electricity production in future thermonuclear reactors. Unlike the traditional way of power extraction via heat conversion, this method is attractive as it does not suffer from poor efficiency of the conversion. We will base our report on dedicated experiments at the COMPASS tokamak, where such extraction has been attempted.

The divertor of the COMPASS tokamak [14] has been equipped with a specially designed segmented tile, which consists of 5 radially separated graphite segments placed on an insulating bed made of boron nitride (see figure 1). Two 2 cm wide segments (no. 2 a and 4) are placed on radial locations where the strike-points are typically situated (R = 480–500 mm and 418–438 mm respectively), the middle segment (no. 3) covers the private flux region and the remaining segments (no. 1 and 5) cover the far SOL on low field side (LFS) and high field side (HFS) respectively. The segments are radially separated by gaps of 1 mm between each other and toroidally by 1 cm from the neighbouring tiles, which are conductively connected to the vessel (grounded). The segmented tile occupies 1/32th fraction of the total divertor area. The toroidal lengths of the segments increase towards the LFS, with segment 2 being approximately 6 cm long. The areas of top surfaces of segments 1–5 are 9124, 805, 1726, 724 and 2934 mm² respectively.

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Similar tiles were installed in the past on a number of tokamaks in order to characterise the SOLCs [3, 6]. The novelty of our approach is that each segment is connected to a feedthrough and further to the dedicated electronics located outside the vessel. This electronics was developed to allow fast switching between two different regimes: (i) Floating regime, where the segments are electrically disconnected from the vessel and (ii) Grounded regime, where the segments are connected to the vessel and current flowing through the circuit is measured. The change of regime can be controlled by a trigger signal and was typically performed every 5 ms during a discharge, so that both the floating potential V_float and the current to the grounded tile I₀ (shunt current) could be measured during the flat top of the discharge. This setup allowed for initial characterisation of the SOLCs in different plasma regimes.

Preliminary estimations of the magnitude of the currents revealed that currents induced during disruptions could reach several hundreds of amperes. Such currents may damage the cables inside the vessel and most importantly the feedthrough, which could in the worst case lead to a loss of pressure in the vacuum. Therefore, a robust feedthrough capable of carrying up to 180 A (in steady state) through each lead was installed. Disruptions may induce large voltage differences between floating segments and the vessel, which could drive arcing and damage of the vessel. For this reason, the segments were located on a 2 cm thick boron-nitride bed and additional kapton insulation was placed between the cables and the vessel beneath the tile.

First measurements with the segmented tile were performed during a so-called standard discharge, which is a simple ohmic discharge performed at the beginning of every experimental day at COMPASS (R = 0.56 m, a = 0.18 m, I_plasma = −180 kA, B_T = −1.15 T, n_e = 4 × 10¹⁹ m⁻³, q₉₅ = 4, κ = 1.76, β_n = 1.0, ∇B drift pointing toward the target). The measured shunt currents and floating potentials of each segment are shown in figure 2. The shunt currents flowing through the segments can reach magnitude of several amperes and have opposite sign on the LFS and HFS target. This is in qualitative agreement with results reported from COMPASS-D [4]. The total current is, however, not zero, which indicates that the segmented tile has insufficient radial coverage to collect all the currents flowing through the targets. The sign of the floating potentials reflect the direction of the currents flowing in the segments.

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In order to cross-check the validity of the segmented tile measurements, a comparison with divertor probes [15] was attempted, as shown in figure 3. The divertor probes consist of a single poloidal array of 56 Ball-pen probes (whose floating potential V_float,BPP is close to the plasma potential) and two poloidal arrays of protruding Langmuir probes, measuring the ion saturation current I_sat and floating potential V_float,LP respectively. The electron temperature can be derived from the difference of the two potentials as

$$\begin{eqnarray}&&{T}_{e}=({{eV}}_{{\rm{float}},{\rm{BPP}}}-{{eV}}_{{\rm{float}},{\rm{LP}}})/\alpha ,\end{eqnarray} \tag{ 1 }$$

where the value of coefficient α has been experimentally determined as 1.4 [15]. The probe array covers the entire poloidal cross-section of the divertor; however, the interpretation of probe measurements on the HFS is not resolved at the time of writing, therefore only measurements from the LFS target are used in this work. The parallel current density for each segment is calculated as

$$\begin{eqnarray}&&{j}_{0,\parallel }={I}_{0}/{A}_{{\rm{seg}}}/\sin {\alpha }_{B},\end{eqnarray} \tag{ 2 }$$

where α_B is an average angle of impact of magnetic field line with respect to the top surface for each segment (ranging typically from 0.5° to 3° depending on the distance from the strike points) as calculated by the magnetic equilibrium reconstruction code EFIT and A_seg is the area of the top surface of the segment.

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The comparison of floating potentials measured by the tile segments and the Langmuir probes (figure 3(B)) is straightforward, but only qualitative agreement could be assessed due to different radial resolution of the probes and segments. The comparison of parallel current density j_0,∥ requires some assumptions on the electron and ion current, since the divertor probe array does not measure the shunt current directly. Using the ideal Langmuir probe theory [16], it is possible to reconstruct the full I–V characteristics and subsequently to determine the current at zero bias, assuming that the plasma potential is above zero. According to the three-parameter probe model the total current I_p should depend on probe potential V_p as:

$$\begin{eqnarray}&&{I}_{p}({V}_{p})={I}_{{\rm{sat}}}(1-{{\rm{e}}}^{({{eV}}_{p}-{{eV}}_{{\rm{float}}})/{T}_{e}}).\end{eqnarray} \tag{ 3 }$$

The grounded probe has V_p = 0 and therefore the shunt current is simply

$$\begin{eqnarray}&&{I}_{0,{\rm{ideal}}}={I}_{{\rm{sat}}}(1-{{\rm{e}}}^{-{{eV}}_{{\rm{float}}}/{T}_{e}}).\end{eqnarray} \tag{ 4 }$$

Unfortunately, this model is generally valid only for V_p < V_float, as the electron current can be significantly reduced in the presence of magnetic fields, especially if the biased surface is at grazing angle of incidence with respect to the magnetic field [17]. Dedicated measurements with the divertor probe array [15] have revealed a ratio of ion and electron saturation current ${R}_{\exp }=| {I}_{{\rm{sat}}}^{-}/{I}_{{\rm{sat}}}^{+}| =7$, instead of the theoretical value of R_theor=17. This information can help us to modify the model presented in equation (3). We assume that the electron current drawn by the segment is reduced either by electron reflection in the magnetic pre-sheath of the nearby tiles [18] or by flux tube charging [19] and employ a correction to the electron current driven by the segment—the current follows the Langmuir theory only until it becomes limited by a value dictated by the value of R_exp. In the following text, we dub this model the limited model, while the original model based on Langmuir theory as the ideal model

$$\begin{eqnarray}&&{I}_{0,{\rm{limited}}}={I}_{{\rm{sat}}}(1-\max ({R}_{\exp }-1,{{\rm{e}}}^{-{{eV}}_{{\rm{float}}}/{T}_{e}})).\end{eqnarray} \tag{ 5 }$$

An illustration of the two models is shown in figure 4. In order to verify the applicability of the limited model for the conditions in COMPASS divertor, dedicated measurements were performed, in which every odd Langmuir probe was directly connected to ground via a resistor, measuring the shunt current (instead of I_sat). These currents were compared to the expected shunt currents calculated by equation (5), based on measurements of the even probes sets (as shown in figure 5) for L-mode and ELM-free H-mode. It can be seen that the limited model yields a reasonable agreement with the measurements; however it overestimates the shunt current in far-SOL in the case of L-mode discharge. This corresponds to the results obtained in figure 3(A)-the expected shunt current (shown by dashed blue and cyan lines for segments 1 and 2 respectively) agrees with the measured value for segment 2 (near SOL) but overestimates the value for segment 1. Since the value R_exp may be in principle dependent of specific plasma conditions, predictions of the limited model are shown for a span of values from 5 to 9. Actually, the predictions are rather insensitive to the precise value of R_exp since the local non-ambipolarity is typically not pronounced enough to reach I_e > − R_exp I_sat. The source of discrepancy in L-mode is not fully understood, however it is at least partially caused by a non-monotonous profile of Isat, which shows a local maximum at the radial location of the discrepancy. This feature has been already observed in COMPASS-D [4] and has been attributed to the presence of strong E × B drifts in the SOL.

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In the experiments dedicated to power extraction, currents I₀ from segments 1 and 2 were totalled to form I_SOL and measured against the tokamak ground. In principle, one could also measure the current flowing between the inner and outer target; however, measurements presented in figure 2(A) show that the tile is not reaching far enough on the HFS to capture the whole current flowing to the inner target, and this would limit the current extracted in such a setup. In order to characterise the plasma as a source of current and voltage, a circuit element equivalent to a variable resistance R_z was required. In laboratory conditions, this setup is typically achieved by a potentiometer; however the magnitude of SOLCs and the required temporal rate of change of the resistance was incompatible with a mechanical solution. Instead, an additional controlled source of current was introduced in the circuit, which acted against the current driven by plasma.

Measurements were again performed during a standard shot. The time traces of the current, voltage and variable load R_z are shown in figure 6(A). Measurements between t = 1160 and 1180 ms were combined to produce averaged dependence of the extracted power P_out on the equivalent resistance R_z, as shown in figure 6(B). It can be seen that the maximum extracted power of 12 W is achieved for R_z ∼ 10 Ω (which corresponds to 384 W if the current was drawn from the entire outer target). Finally, figure 6(C) shows the current-voltage characteristics of plasma, which is in the first approximation linear and as such represents an ideal power source. The slope of the characteristics yields the plasma internal resistance R_i ∼ 12 Ω. This is in agreement with the general rule that maximum power can be extracted from the power source when R_z ∼ R_i. The working point with maximum P_out (marked by magenta symbol) is located at approximately half the current and voltage. The maximum extracted power P_{out, max} can be related to I_SOL and V_float as

$$\begin{eqnarray}&&{P}_{{\rm{out}},\max }={c}_{p}{V}_{{\rm{float}}}{I}_{{\rm{SOL}}},\end{eqnarray} \tag{ 6 }$$

where the constant c_p is a priori not known but can be determined experimentally, as shown in figure 7, where an approximate value 0.27 ± 0.01 was found. The V_float and I_SOL are not independent but linked by equation (5). Assuming only a moderate degree of local non-ambipolarity, one can obtain

$$\begin{eqnarray}&&{P}_{{\rm{out}},\max }=-0.27\pm 0.01{I}_{{\rm{SOL}}}{{kT}}_{e}{\rm{ln}}(1-{I}_{{\rm{SOL}}}/{I}_{{\rm{sat}}}).\end{eqnarray} \tag{ 7 }$$

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In this particular discharge, the electron temperature measured by the divertor probes (averaged over the radial extend of near SOL) was 37 eV and the equivalent I_sat 1.7 A, which yields P_out of 15 W, in reasonable agreement with the value measured at the segmented tile.

In order to demonstrate the practicality of power extraction, a demonstration experiment was performed, replacing the dedicated electronics with a light bulb with resistance of 1 Ω (note that the resistance of the bulb wire increases approx. tenfold when it heats up). A recording of the visible camera confirmed that the electrical power from the SOLCs was successfully converted into light [20].

In this section we attempt to address the problem of scaling of the magnitude of P_out and possible extrapolation to next-step devices, such as ITER. Considering equation (7), the problem is reduced to the scaling of I_SOL.

One possible approach would be to predict the magnitude of I_SOL using analytical models, which describe the underlying mechanisms. The thermoelectric current was first studied by Harbour [21] and his model was later extended by Staebler [8] to account for finite plasma conductivity. It allows to calculate I_SOL based on the knowledge of T_e at both targets and the plasma conductivity. However, there is no analytical model to predict the divertor temperatures and their ratio. Similarly, the Pfirsch–Schluter current was addressed by a model developed by Schaffer [9] for JET conditions; however, it requires knowledge of radial pressure gradient in the edge plasma, which again cannot be determined a priori. Moreover, Silva has demonstrated [4], that in COMPASS-D the SOL current is driven by a combination of the two mechanisms, which makes any analytical prediction even more arduous. Instead, we attempt to derive a scaling of I_SOL experimentally, using results of series of measurements in COMPASS.

We have assembled a set of measurements from a series of attached L-mode discharges performed during the CC20.01 campaign in 2018, where the floating tile was in operation. The I_SOL data points were extracted as averaged values of 10-20 ms long intervals, where the discharges were quasi-stationary. I_SOL was determined either by measurements of segment 1 or combined current from segments 1 and 2, depending on the location of the outer strike point in the particular discharge. This series of discharges contained a range of plasma currents between 150 and 330 kA (corresponding to P_Ohm between 150 and 400 kW) at B_T between −1.15 and −1.5 T, resulting in span of q₉₅ between 2.5 and 5.0. In some discharges the NBI heating with power delivered to plasma of up to 400 kW was applied.

The standard deviations of the measured signals were used to estimate the errors. Figure 8 shows the dependence of the SOL current I_SOL on the plasma current I_plasma (representing a scan in q₉₅ between 2.5 and 5.5, with values of B_T between −1.15 T and −1.5 T), maximum electron temperature T_e,div,max measured at the outer target by probes [15], the LFS gas puff particle flux Γ_D2 and the Greenwald fraction (calculated as ${f}_{{\rm{gw}}}={n}_{{\rm{int}}}\pi {a}^{2}/{I}_{{\rm{plasma}}}$ using the line-averaged density n_int measured by the interferometer). A scaling model derived for intra-ELM SOLCs at AUG [3] (the only scaling of SOLCs known from literature) is shown in figure 8(D).

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It can be seen that neither of these variables are very good scaling factors for I_SOL. The ELM current scaling also does not seem to describe the data very well for low Greenwald fractions. It is also possible to assume a combined scaling with the ratio of maximum temperature target temperature (representing the magnitude of the thermoelectric effect) and the line averaged density (which is linked to the collisionality in the SOL). Unfortunately such scaling is strongly nonlinear (as shown in figure 9) and moreover exhibits a dependence on I_plasma.

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The strongest variation of I_SOL is with the gas puff intensity; however, there is a large scatter for a number of discharges where the gas puff was completely turned off. An example of how intensively the gas puff influences edge plasma is shown in figure 10. It can be seen that the gas puff does not only provokes a decrease in the target temperature but also reduces the upstream temperature measured by the Thomson scattering diagnostics at the separatrix T_e,sep. The values of T_e,sep were obtained from vertical profiles of T_e by fitting data points between 0.9 < ψ_n < 1.1 with an exponential decay (similarly to analysis at AUG [22]) and interpolating the fit to ψ_n = 1. The profile of ψ_n was obtained from the magnetic equilibrium reconstruction code EFIT. Note that the location of LFCS is known to have limited precision, so a systematic offset in T_e,sep may occur [23]. Separatrix temperature appears to be the best scaling parameter for I_SOL, the dependence determined by nonlinear fitting being ${I}_{{\rm{SOL}}}[A]=0.35\pm 0.09{({T}_{e,{\rm{sep}}}[{eV}])}^{0.64\pm 0.06}$, as shown in figure 11. For tokamaks in conduction-limited regime, T_e,sep can be determined from the two-point model [24] and depends mostly on the power crossing the separatrix P_sep, which in turn depends on the heating power (for a fixed value of plasma current, which sets the power decay length [25]). This scaling parameter is, therefore, favourable with respect to the burning scenarios in next-step devices, where the heating power should be dominated by alpha heating P_α (and which should lead to an increase of T_e,sep).

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There are two major questions related to the possibility of direct power extraction from SOL currents:

• 1.  
  The impact of the power extraction on the plasma operation. In the experiments described in this work, no such effect was observed (e.g. on confinement or even divertor heat flux footprint). One has to note that the extracted power of 12 W is very small compared to the plasma heating. The ohmic power delivered to plasma P_Ω in this particular discharge was 200 kW, P_sep = 50 kW. This ordering would remain valid even if the extraction was performed from the entire divertor (the segmented tile covers 1/32 of the divertor area, leading to some 380 W of possible total extracted power).
• 2.  
  Prediction of the magnitude of extracted power on next-step devices, such as ITER. In principle it is possible to use the scaling of the magnitude of I_SOL derived in the previous section to simply extrapolate it (assuming T_e,sep ∼ 200 eV [26], divertor parameters T_e = 10 eV, n_e = 6 × 10²⁰ m⁻³ [27] and accounting for the size difference between the machines). The extremely high electron density results in a small ratio of I_SOL to I_sat in equation (7) and subsequently in a very small value of the floating potential ($| {V}_{{\rm{float}}}| \lt 5$ V). The resulting extracted power is therefore negligible, however we suspect that single-machine measurement are insufficient to resolve all important parametric dependencies and to produce a reliable prediction. Moreover, ITER will be operating in conditions, which are rather different to most contemporary machines: (i) it will be fuelled by pellets and NBIs, (not by gas puff) and (ii) it will operate in real-time controlled partial detachment, which will also affect T_e at both targets. Experimental results from JT60-U show that under detachment the SOLCs are probably no longer driven by thermoelectric effect and are larger than expected [5]. In principle it would be also possible to optimise the discharge scenario to deliver maximum power via the SOLCs, which is clearly not considered in the current baseline scenario for ITER. While some room for this optimisation can be envisaged (such as preferentially detaching one target to increase the temperature difference between the two targets), it would have to respect the stringent conditions regarding plasma performance and material limits of the divertor PFCs.

For these reasons we believe that the estimate of the extracted power in ITER cannot be based only on COMPASS and more dedicated measurements in dedicated ITER-like plasmas on larger devices would be necessary. An alternative approach could make use of fluid modelling of edge plasma with drifts in codes such as SOLPS-ITER [28]. Such simulations are, however, due to its complexity outside the scope of this work.

We have demonstrated a possibility to intercept parallel currents flowing in the SOL and use them to extract electrical power from the plasma in a dedicated proof-of-concept experiment at the COMPASS tokamak. The COMPASS plasmas act as an ideal power source with low internal resistance of 10 Ω and allow to extract electrical power which is very small compared to the input power. The magnitude of the SOL currents scales approximately as a square root of the upstream separatrix temperature, at least in the series of L-mode discharges, which were analysed. The strongest actuator on the SOL currents is the gas puff, which affects both the upstream and target temperature. More experiments or dedicated modelling are needed to reliably predict the amount of extracted power for next-step devices, such as ITER.

MK would like to thank K Jirakova for corrections of the manuscript. This work was supported by the Czech Science Foundation project GA16-14228S and co-funded by MEYS project CZ.02.1.01/0.0/0.0/16_013/0001551 and #LM2015045.