EX/P1-2 Experimental studies in support of equilibria calculations during AC transition in the ISTTOK

A. Malaquias 1, M. Hole 2, R.L. Dewar 2 C. Michael 2, and R.B. Henriques 1 1Instituto de Plasmas e Fusão Nuclear, Inst. Sup. Técnico, Univ. de Lisboa, 1049-001 Lisboa, Portugal 2Research Sch. of Phy. and Engineering Australian National University Canberra ACT 0200, Australia

Abstract: The present paper presents an initial step towards the development of a deeper understanding of the equilibria and current profile during the AC transition in ISTTOK. The goal of the present study is to identify based on experimental pressure-like measurements and matched current profiles, the existence (or not) of antiparallel currents during transition. An alternative scenario exploits the existence of runaways or fast electrons and their role during the current ramp-up. There is experimental indication that these electrons may play an important role during the stages of the discharge close to the current transition.

1. Introduction In order to achieve successful AC operation in a technically enabled tokamak the control of external parameters such as vertical and horizontal fields, external heating (where available), chamber conditioning and gas puff are of key importance. How this external control determines the internal evolution of the current transition is not sufficiently understood for proposing a universal recipe that could guide the optimization of the AC transition. The reason for this is because the internal status of plasma during transition is poorly diagnosed due to the relatively low signals it generates. The control of AC discharge is conducted mostly based on empirical experimentation. Several papers have reported numerical solutions for the equilibrium evolution during AC transition where two opposite plasma current columns co-exist and evolve during the AC transition. This paper deals with a collection of experimental data in order to investigate the validity of this hypothesis in ISTTOK. Recent AC experimental studies performed in the ISTTOK tokamak have shown that a link between the different external actuators and the plasma discharge response could be established [1]. However, empirical optimization of the external actuators in view of such response did not contributed significantly for the repetitive success of AC transition, particularly at higher than 4 kA plasma currents. Except for the case that (and this may be of later relevance) after many discharges repetitions the regular AC operation is achieved. This observation is systematic indicating that the conditioning of the chamber plays a fundamental role during the current transition once the other external parameters had been experimentally optimized (i.e. maintaining full AC transition cycles in a reproducible way). The way this observation can be linked to plasma AC dynamics is via reducing impurity content (impurities released by the wall decreases as the number of discharges increases). In order to achieve a more predictive control of the AC transition it would be useful to develop a first principles model based on plasma dynamics which captures the underlying physics and can explain the experimental observations. Such model would need to combine the electro-technical properties of the tokamak during AC operation with experimental discharge data and calculations on the equilibria and stability evolution. The goal of the present paper is to analyse the plasma pressure profile evolution, and the current profile evolution during the AC transition based on data provided by the Heavy Ion Beam Diagnostic (HIBD). This data is used to investigate which is the most likely transition scenario based on a comparison of equilibrium calculations and experimental data from other AC enabled .

2. The AC transition phases In Figure 1 is presented the time evolution of the nσ(r) profile as measured by the HIBD ( n(r) is plasma density and σ is the ionization effective cross section, a function of plasma temperature, T(r) ). The nσ(r) is a pressure-like quantity, amplified by the non-linear dependence of σ with T(r) . It can be taken directly for local plasma pressure fluctuations characterization. For obtaining an absolute pressure profile it requires the knowledge of the plasma temperature profile.

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Figure 1 – The pressure-like profile measured by the Heavy Ion Beam Diagnostic during an AC plasma current transition from positive to negative.

The AC transition can be divided in three main phases ( Figure 2). The phase I corresponds to the moment the primary current is imposed to change sense; the plasma current decays but still maintaining rotational transform and equilibria balance up to certain values of Ip > 0. In phase II the plasma current is close to zero (Ip ~ 0 A) corresponding to a situation where the plasma is cold (few eV) and the density has dropped about 6 x fold from the flat-top phase. In approaching phase II experimental data as shown that the discharge produces runaway electrons that can be manifested in several beams or in a larger beam representing probably around 50% of the discharge current [1]. This phase is typically characterised by large neutral composition co-existing with quiescent plasma and possibly overshooting fast electrons or run-aways. The nature of this quiescent plasma is one of the aspects this paper intends to clarify. The phase III corresponds to the ramp-up of the following cycle. In this phase one would expect that the conditions in phase II would be of paramount importance in determining a successful burn-through and ramp-up of the following semi-cycle. In this line of though, the control of phase I is key importance to reach phase II with the appropriated background conditions that could ensure a reliable transition to phase III.

Figure 2 – The three phases of an AC discharge: 1 – current decay from flat-top to near Ip ~ 0 A, 2 – quiescent plasma phase around Ip ~0 A, 3 - ramp-up from Ip ~ 0 A till flat-top

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As was mentioned above past experiments performed in ISTTOK allowed for observe some plasma behaviour that is useful to remind:

Edge Electrode Biasing – Was used to increase the plasma density (~40%) during the current transition phase (Ip ~ 0 A). However, the reliability of AC operation did not seem to have systematically improved with the quiescent plasma density increase. It has been observed that the plasma gets cooler when density is increased by this method (particle density improves but total energy is constant therefore temperature drops). The action of electrode biasing is such that it could impose such low levels of collisionality (below some critical threshold) that the low temperature electrons are accelerated by Vloop to form preferably a runaway discharge during ramp-down, in addition to the conversion of plasma current magnetic energy into electromotive force.

Role of fast and run-away electrons – It was observed an inverse correlation between the number of runaway events (measured with x-ray detector outside the vacuum chamber) during the transition phase and the success of subsequent semi-cycles. In addition, some experimental results showed a correlation in the observed plasma ramp-up pressure-like oscillations and the presence of runaway bursts (x-ray detector).

Gas puff experiments – When more gas puffs are used before or during the transition more successful transitions occur. It was also observed an apparent reduction of runaway generation with more puffs. However, if too much puff is used the discharges do not start, probably due to a combination of neutral pressure and Vloop that could not sustain an avalanche chain leading to a burn-through phase of the discharge.

Plasma column control – The tuning of the V-H fields is in general considered as one key parameter to the success of the AC transition. However, once a minimum level of current rump-up is achieved (probably just after the burn through phase) the experiments showed that radial and vertical maladjustments leading to the offset of the plasma column were well tolerated and do not determine unsuccessful semi-cycles. One open question is how important is the role of V-H fields during the transition phase near Ip = 0 A, particularly in the presence of fast or run-away electrons.

2.1 Characterizing Phase I

In order to determine how the absolute plasma pressure profile evolves during the current decay it is necessary to investigate the profile evolution of the quantity nσ as retrieved by the HIBD. Using constraints from the interferometer average density and plasma resistivity measurements, and via HIBD simulations it is possible to identify the contribution of the density and temperature profiles in shaping the nσ profile. This is an important assessment in order to be able to select the possible density and temperature profiles that combined can agree with the experimental nσ measurements. The first step is to estimate the plasma average temperature. One first approach is using Spitzer resistivity calculated from Vloop and I p,

eq. 1)

One second alternative way is to use the product average quantity (taken from the measured profile) divided by the average interferometer density, . The result is the function (approximatly), which is an explicit function of electron temperature. This method requires the evaluation of the sistematic error associated with the approximation used as the . (product of the averages) is the correct quantity to be used for this estimation (unfortunately, it is not measured). The range of values for the systematic error

EX/P1-2 with this approximation can be from 7% for more flat or hollow-like nσ profiles up to 30% - 40% for the more peaked nσ profiles (note that the systematic error does not depend much on the absolute temperature or density values but rather on the shape of the functions under consideration). As HIBD measures the nσ profile one can correct for the corresponding offset. The average temperature estimations are presented in Figure 3 and both diagnostics have a good agreement on the average temperature. A linear fit for the temperature given by the Spitzer resistivity is required due to the large spikes in V loop . One interesting observation is that the plasma average temperature decreasing rate is much slower than the current decay rate during the current ramp-down.

Figure 3 – average temperature evolution determined by HIBP (in red) and by Spitzer resistivity (in blue broken line).

The plasma average temperature plays an important role in determining the contribution of the density and temperature individual profiles contribution for the nσ profile. The HIBD numerical modelling results indicate that for the average temperatures of our plasma (20 eV) the density, n, and temperature, T, profiles play an identical role in shaping the nσ profile. This would mean to take the profiles for n and T as similar to each other, and similar to nσ. The profiles chosen are also bounded to the average values of temperature and density (via interferometer) as given above. Selecting a combination of possible profiles is possible to construct the plasma pressure profile during the phase 1 ( Figure 4). Additionally, the Spitzer resistivity along the minor radius can be determined in order to obtain the plasma current profile ( Figure 5) from Ohm’s Law (the integral of current density is equal to the total plasma current, as expected).

Figure 4 – Absolute values of plasma pressure profile Figure 5 – Current density profile derived from temperature profile and Spitzer resistivity

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In Figure 6 are plotted the average values for average β and q in the edge. As the discharge approaches the Ip = 0 zone the safety factor raises much faster than the decay of plasma current and plasma pressure. This behaviour raises the possibility that at this point in time the discharge is sustained by a current (max. 500 A) of low collisional fast electrons (beam-like) just before reaching phase II. This point will be investigated in more detail in a future work.

Figure 6 – Average discharge parameters (to read on the left axis, except for the red line)

2.2 Characterizing Phase II

Several numerical calculations [2][3][4] and experiments have been done to describe the behaviour of the plasma near the AC transition (Ip ~0 A). For the HT-7 tokamak [5] it is indicated that about 25% of the nominal plasma current is present during the AC transition in the form of two radially displaced counter currents (Ip ~ 0 A; + 40 kA and – 40 kA). This is a substantial amount of current that for ISTTOK would mean co-existing about +1 kA and -1 kA counter currents during AC transition (if the confinement properties were the same). In the CT-6B tokamak [6] (with parameters closer to ISTTOK) it was measured the current profile evolution during AC transition. The results indicate that the two counter currents co-exist for 15% of the nominal plasma current (around + 0.35 kA and -0.35 kA). If to scale these results for ISTTOK we would expect to find signatures of these counter currents at around 0.6 kA. In some ISTTOK discharges one of the observations that support this scenario is the freezing of the toroidal shift of the HIBD primary beam [1]. This can occur by a combination of counter poloidal field direction due to the opposite sense of the currents. However, this frozen of the toroidal beam shift is not always observed. For several AC transitions in ISTTOK the nσ profile does not show the evolution as expected by the above experiments. Based on the above scenarios description one should see the formation of the new current channel immediately after the decay of the previous current channel (in particular for the HIBD geometry in ISTTOK, which is probing the vertical diameter of the plasma). One would expect to see a relative short duel time and observe symmetric features (around Ip = 0 A) in the global plasma current evolution. By contrast, we observe in many characteristic discharges the formation of a hollow profile during the first current decay (phase I) and then a formation of a peaked current channel on the second semi-cycle (phase III). The time delay between the ‘apparent’extinguish of the first current semi cycle and the formation of the subsequent semi-cycle is around 0.5-0.7 ms, more than the 0.2-0.3 ms for particle confinement in ISTTOK. Therefore we seek for an alternative explanation for the observed signals during AC transition. In (Figure 7) are depicted several plasma signals obtained during the AC transition.

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Figure 7 – Normalized values of plasma parameters during AC transition from positive (left) to negative (right) current (ns is the background 2D signal where the left scale represents plasma radius).

Two points to note on this figure:

• The visible emission has the minimum when Ip = 0 A (corresponding to the plasma temperature minima) • Average density measured by the interferometer has the minimum (1.6x10 18 m-3) at about 0.2 ms after Ip = 0 A

In the moment the plasma current is zero we observe the existence of a quiescent plasma with very low temperature (few eVs) but with a density level that only decays to its minimum (not to zero) 0.2 ms after the instant of Ip = 0 A. We speculate that fast electrons or runaway electrons are generated during the positive cycle ramp-down. These electrons are ‘overshot’ into the negative cycle by inertia and are responsible to keep the quiescent plasma. This mechanism would be different than a positive/negative counter-current scenario equilibrium evolution. A hand calculation indicates that a 10 keV electron beam (or beam-like electron population) would take about 0.07 ms to drift to the walls (in ISTTOK). However, one needs to consider two additional aspects. During transition ISTTOK horizontal and vertical fields are applied and would be possible to find a combination that sustains this beam of electrons longer in the chamber (this is speculative at this moment as numerical simulations are required). One other point is that while propagating this beam of electrons will generate secondary electrons in the background gas that get accelerated in the opposite direction (as Vloop has changed sense). The velocity of this beam is also retarded by Vloop, in 0.250 ms it would have been stopped (if only inertia was taking into account). As the beam is retarded the ionization process is more efficient and more primary electrons are produced but at the same time recombination for the remaining of the original beam is more likely to occur as the negative current plasma forms. In addition, the gradB and curvature drifts could lead to charge separation in the absence of effective rotational transform. According to Mitarai [] during Ip ~ 0 A it is proposed that electron currents short-circuiting through the vessel or limiter could provide charge balance for the tenth of micro-seconds during which rotational transform does not exist. The consideration of all these mechanisms into a model for AC transition calls for a more deep analysis and simulations. Nevertheless, the equilibria model proposed during AC transition in other devices does not seem to explain a large fraction of the results observed in ISTTOK. As we propose, the present results are more likely to be in agreement with a scenario where overshooting of electrons plays the role of keeping the current close to zero by generating secondary ions that are accelerated in the opposite direction sustaining a significant

EX/P1-2 amount of plasma density before they die out by deceleration and recombination (inducing a minimum in plasma density 0.2 ms after the AC transition). The HIBD operates at around 150-180 kHz in a pulsed mode enabling effective noise subtraction. In (Figure 8) is presented the raw data in the cells overlapped with the chopping signal. The figure is a zoom into the AC transition phase II. From the raw data it was generated the nσ profile presented in Figure 9.

Figure 8 – HIBD raw signal overlapped with beam chopping signal. The semi-periods when the beam is off are used to evaluate the noise and subtract to the semi-periods when the beam is on. Yellow rectangles are signatures of plasma during the AC transition.

50 0.5

0.4

0.3 0 0.2 radius (mm) radius 0.1

0 -50

31.7 31.8 31.9 32 32.1 32.2 Time (ms)

Figure 9 – nσ signature as measured by the HIBD during AC transition. The yellow rectangles are signatures of plasma, or more exactly signatures of the presence of electrons (the dynamic colour scaling is reduced in this choice of contrast mainly to highlight the presence of plasma).

What is observed around Ip ‰ 0 A is that a distributed cloud of electrons exists just before the current transition (at 31.85 ms) and immediately after this instant there are signatures of electrons (coldest plasma) more on the top first and then on top and bottom of the chamber. In a later instant (after 32.2 ms) the top signature vanishes and the electron cloud is now more located on the bottom of the chamber, where the second semi-cycle plasma forms. The flashing-like evolution of the electron signature during the transition (particularly visible on the bottom half of the plasma) can be compatible with the formation of local pressure-like osilations due to islands evolving during current revearsal transition or some sort of instablity that we are not able to identify at this stage.

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2.3 Characterizing Phase III

During the initiation of the second semi-cycle the current rumps-up to relatively high values while the density remains near its minimum (Figure 7 at around 32.5 ms). At the same time the visible emission increases significantly from the Ip = 0 A time instant. This could be an indication that a cold population of seeded electrons could be present just after the AC transition with inefficient collision energy to ionize the plasma and/or the presence of impurities that get brighter as the electrons are accelerated. Since the density remains at the levels of AC transition for as long as 0.5 ms after Ip=0 it seems that the plasma current raises mainly due to plasma heating and not by a density increase.

3. Conclusions

The measurements done with the HIBD in ISTTOK allowed to determine the plasma pressure and current density profiles evolution during the current ramp-down of AC discharges. Several works and experiments indicate that the mechanism of current reversal can be explained by equilibrium considerations and numerical solutions of the GS equation. The present results in ISTTOK seem to point for different explanation for the existence of a plasma during the AC transition when Ip ~ 0 A. The time scales involved are in a first approach compatible with the hypothesis of a current of fast or runaway electrons being overshoot due to inertia into the negative cycle (for ~ 0.1-0.2 ms around Vloop transition). These electrons could generate the cloud of electrons that are accelerated in the opposite direction and produce a cancelling effect in the plasma current during AC transition. The future work consists in developing detailed simulations and analyse more data in order to produce more solid interpretation of the experimental results References: [1] “Investigation of the transition of multicycle AC operation in ISTTOK under edge electrode biasing”, A. Malaquias, et al., Nucl. Fusion 57 (2017) 116002 (13pp), https://doi.org/10.1088/1741-4326/aa7c9c

[2] “Tokamak Equilibria with Reversed Current Density” A. A. Martynov, et al. Phys. Rev. Lett. 91, 085004, 2003, DOI: 10.1103/PhysRevLett.91.085004

[3] “Vacuum Poloidal Magnetic Field of Tokamak in Alternating-Current Operation”, Guo Wei et al., Plasma Science and Technology, V.12, N.6, Dec 2010

[4] “Tokamak Equilibria with Strong Current Reversal” G. O. Ludwig et al., Nucl. Fusion 53 (2013) 053001 (20pp) doi:10.1088/0029-5515/53/5/053001 [5] “Quasi-steady-state ac plasma current operation in HT-7 tokamak” Jiangang Li, et al, Nucl. Fusion 47 (2007) 1071–1077, doi:10.1088/0029-5515/47/9/001

[6] “The plasma current profile during current reversal in AC operation of the CT-6B tokamak”, Jianguo Huang, et al., , Vol. 40, No. 12

Aknowledgments: IPFN activities received financial support from “Fundação para a Ciência e Tecnologia” through project UID/FIS/50010/2013 and grant SFRH/BSAB/135071/2017