Overview of disruptions with JET-ILW

The JET-ILW upgrade was completed in late 2010 [30]. The first commissioning pulse #79 856 was executed on 30/03/2011 with the first plasma pulse #80 128 on 24/08/2011. The total number of JET shots with at least one powered poloidal field (PF) or toroidal field (TF) coil was 12 649 in pulse range #79 856–#92 504. In the present analysis, a shot is treated as a relevant plasma shot if the plasma current |I_p| ≥ 0.8 MA for at least 0.25 s, figure 1. Accordingly, the number of plasma pulses during JET-ILW operation was 9686, which corresponds to 77% of the total number of shots. In this study, we defined disruption criteria based on reliable magnetic diagnostics with simple quantitative criteria, which we then used to build the JET disruption database. The magnetic diagnostic quantities, which are recorded at a 5 kHz sampling rate, have been used to identify the disruptive shots and define the time of disruption (T_dis). The quantities are two toroidally opposite average plasma current measurements (I_p), plasma current vertical centroid position (Z_p) and their derivatives, and toroidal loop voltages, which are measured at two poloidal locations on the inner wall of JET vessel, figure 2. In this paper a left-hand coordinate system was chosen for disruption analyses, hence I_p is positive.

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The loss of the poloidal magnetic flux due to the large MHD events causes the electromagnetic circuit of the plasma to respond with a positive spike in the plasma current. The induced negative current which flows in the vessel manifests itself as a large negative impulse in the toroidal full flux loops, V_rru and V_rrl, see flux loop locations in figure 2. The following disruption criteria have been used to build the disruption shot list:

• (i)  
  Fast drop of the plasma current, d|I_{p_2}|/dt > 20 MA s⁻¹, so it does not detect the fast I_p spike but only the start of a CQ, where I_{p_2} is two toroidally opposite plasma current measurements, which are averaged and ± 2 ms triangular smoothed;
• (ii)  
  Normalised average toroidal voltage V_rrAN = (V_rru + V_rrl)/2I_p < −13 V MA⁻¹, figure 3;

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The averaging of the two toroidally opposite I_p measurements is necessary to eliminate the n = 1 (i.e. 3D) effect. The smoothing removes fast transient I_p oscillations. Both criteria (i) and (ii) indicate an ongoing disruption. The pulse is treated as a disruption pulse if at least one of the criteria are met. The somewhat arbitrary choice of the numerical criteria has been justified by manual analyses of the numerous disrupted pulses. The adequacy of this disruption criteria is demonstrated in figure 4 which presents each disrupted pulse by a single point on the plane of maximum values of d|I_{p_2}|/dt derivative and normalised average toroidal voltage V_rrAN, where the blue lines indicate the two disruption criteria. A typical non-disruptive pulse has d|I_{p_2}|/dt ∼ 0.1 MA s⁻¹ with a noise level ∼ ± 0.2 MA s⁻¹ across I_p ramp-down phase. The normalised loop voltage V_rrAN is about zero value with a noise level ∼ ± 1 V, (hence a typical safe I_p ramp-down is nearby origin but outside the figure 4 plot area). A special criterion has been used to label a VDE pulse, where the loss of vertical plasma position control will result in a CQ: |ΔZ_p| > 0.225 m (∼a/4), where ΔZ_p is displacement respect of the steady-state prior to CQ, a is minor plasma radius.

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All MGI deliberately induced disruptions satisfied both criterion (i) and (ii). In case of plasma pulses with multiple subsequent disruptions (which are very common) the maximum presented values of d|I_{p_2}|/dt and V_rrAN correspond to the first major disruption, see the next section for how the first major disruption was defined.

It is worth mentioning that criterion (ii) and the VDE criterion are not used in the real time (RT) JET disruption detection system. The RT disruption detection is outlined in the next section 2.2.

During #80 128–#92 504 JET-ILW operation there were 1951 disruptive shots, including 466 with deliberately induced disruptions. 431 out of the 466 induced disruptions belong either to MGI (massive gas injection), or to VDE and EFCC (error field correction coil) experiments (i.e. intentional disruptions). The rest (35) of the induced disruptions were caused by various human errors or specific hardware/software tests or faults (however, such occurrences could equally be in the 'un-intended' category). Hence the total number of unintended disruption pulses was 1951–466 = 1485 and the average disruption rate of unintended disruption was 1485/(9686–466) = 16.1% overall for JET-ILW pulses, figure 5.

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The noticeable drop in disruption rate in figure 5 in the range #83 623–#83 794 belongs to a special experiment ('H-mode experiments for wall retention studies and long term sample analysis'), when 149 H-mode nearly identical and reliable pulses were executed [21, 43] (we believe that in [21] and [28], the amount of 'nearly identical plasma discharges' includes erroneously a few faulty plasma pulses). Nevertheless, five shots (3.3%) were disrupted, thus reflecting the lowest disruption rate during JET-ILW exploitation. It can be seen in figure 6 that the total bolometer power (P_rad) increases at 11 s and T_{e max} drops from 13 s in one such disrupted pulse. The electron temperature continues to decrease at 14 s after NBI was turned off and the Cu19 line (273.36 Å) emission increases in intensity during this temperature decrease; the plasma passes through the most emissive temperature range for the line (figures 6 and 7). It is thought that the plasma is polluted by copper from NBI. Copper is used in an internal component of the NBI system, hence NBI could deliver the copper to the plasma. The main message from these 149 near identical primitive plasma pulses is that there are some uncontrolled causes which lead to disruptions.

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The disruption rate significantly increases in the last group of pulses from #91 960 to #92 442, as shown in figure 5. This can be attributed to exploration of the operational space for high performance plasmas and optimisation in preparation for the upcoming JET DT campaigns going significantly outside the operational boundaries explored so far.

Disruption criteria (i) and (ii) and the VDE criterion are used to create the disruption shot list. Plasma pulses with multiple subsequent disruptions are very common. A special criterion is used to determine the major disruption in these cases:

If d|I_p|/dt < −1.0 MA s⁻¹ between two sequential voltage spikes with V_rrAN < −13 V MA⁻¹, then the disruption is defined to start at the first voltage spike. Should d|I_p|/dt > −1.0 MA s⁻¹ occur for the whole time between two sequential voltage spikes, then the disruption is defined to start at the second voltage spike. If d|I_p|/dt < − 1.0 MA s⁻¹ does not occur between any of the voltage spikes, then the last voltage spike with I_p > 0.8 MA defines the disruption; an example is shown in figure 8. In this example, the plasma re-heats after the first major disruption event at ∼13.3 s.

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On JET in RT, the plasma current derivative alone was used to register disruption events and to estimate a disruption time $(T_{dis}^{RT}$) with the condition of 100 kA step in 2 ms (namely −d|I_p|/dt > 50 MA/s). We are almost certain that this $(T_{dis}^{RT}$) quantity was used to build the early JET disruption database which has been analysed for example in [13]. The use of plasma current derivative alone has a disadvantage, since $T_{dis}^{RT}$ is late with respect to the sharp I_p rises and the toroidal voltage drops (which are manifested the start of the TQ and the MHD phase) by a few milliseconds.

The post pulse analyses can use a more sophisticated and reliable algorithm to build a disruption database. Namely, the I_{p_2} (two toroidally opposite plasma current measurements, which are averaged and ±2 ms triangular smoothed), V_rrAN (for non-VDE) and ΔZ_p (for VDE) waveforms are analysed to extract a disruption time, T_dis. The disruption time is defined as when d|I_{p_2}|/dt is maximum and/or V_rrAN < −13 V MA⁻¹ (whichever is sooner). Then the T_dis calculated float value is rounded down to the nearest millisecond and that is what is recorded in the database, see figure 9.

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In the case of VDEs, ΔZ_p and its derivative are used to calculate T_dis, with conditions |ΔZ_p| > 0.225 m and |dZ_p/dt| > 20 m s⁻¹ must be simultaneously satisfied, figure 10. This definition of the T_dis of VDEs was chosen to define the time 'just' before the CQ. Other researchers may consider using other criteria since there is no solid scientific definition of the VDE 'disruption time'. In this study, the selected VDE thresholds were seen to be justified for all detected JET-ILW VDE pulses.

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The pre-disruptive plasma parameters are as follows: current $I_p^{\rm dis}$ ≡ I_p(T_dis) = (0.82–3.38) MA and toroidal field $B_T^{\rm dis}$ ≡ B_T (T_dis) = (0.98–3.4) T. The pre-disruptive equilibrium parameters were taken from 5 kHz EFIT [44, 45] data which was available for 1420 out of 1485 unintended disruptive pulses. They are as follows: safety factor q₉₅ = (1.53–9.1); plasma internal inductance l_i = (0.58–1.77), where dimensionless internal inductance l_i ≡l_i(3); normalized beta β_N ≤ 2.91 (% · m · T/MA) [46]; poloidal beta β_p ≤ 1.27 and plasma configuration (either X-point or limiter). The plasma has an X-point configuration prior to disruption for 720 pulses (∼50%) out of 1420 pulses. EFIT pre-disruptive plasma parameters are calculated as an average in the time window [T_dis − 5 ms: T_dis—1 ms].

In the majority of unintended disruptive pulses (∼96% from 1485 disruptions), the protection system detected an abnormal event such as a LM, impurity radiation, density limit, etc prior to disruption. The majority of the undetected unintended disruptions belong to hollow electron temperature collapse which is followed by disruption.

At disruption the Greenwald density limit fraction FGWL is in the (0.04–1.61) range, where FGWL is the line-averaged density divided by the Greenwald-density, ${n_G} = {I_p}/$($\pi {a^2}$) in (MA, m, 10²⁰ m⁻³) [47]. The line-average density is measured by the Thomson scattering diagnostics (HRTS and LIDAR) and mapped to a horizontal principal chord. The final available measurement of FGWL prior to disruption has been used to plot the distribution of pre-disruptive FGWL which significantly varies across disruption database, figure 11. For normal operation we would expect a Greenwald fraction of 0.4 to 1.0. However, a failure of the gas fuelling system can result in very low Greenwald fractions, and conversely during current ramp-down the Greenwald fraction sometime rises up to 1.6. Figure 11 shows that normalised Greenwald density largely varies over a large range prior to disruption, hence it cannot be used as reliable disruption predictor alone.

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Using three quantities, dI_p/dt, V_rrAN and ΔZ_p, the disruptions were sorted into four categories, specifically:

• i.  
  Fast d|I_{p_2}|/dt drop (> 20 MA s⁻¹) and large negative toroidal voltage spike (< −13 V/MA), 76.5% of disruptions, such as in figure 3;
• ii.  
  Slow |I_{p_2}| drop and large negative toroidal voltage spike, 11.7% of disruptions, such as in figure 12 (I);
• iii.  
  Fast |I_{p_2}| drop and small negative toroidal voltage spike, 5.8% of disruptions, such as in figure 12 (II);
• iv.  
  VDE, 5.9% of disruptions, such as in figure 10.

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The empirical stability l_i−q(a) diagram is widely used to present permissible values of l_i and q(a) [9, 48, 49], usually with the interpretation that the lower bound is due to ideal external kink modes and the upper bound is due to resistive kinks. For example, Cheng concluded that TFTR MHD-stable plasma current profiles tend to maintain itself inside the permissible values of l_i and q(a) [48]. The JET-ILW dimensionless internal inductance l_i and safety factor q₉₅ are presented for all disruptions in the database in figure 13, showing a diffused cloud of the pre-disruptive data. From this it follows that that traditional l_i−q diagram does not specify the non-disruptive domain for JET-ILW. It is worth mentioning that the present definition of internal inductance l_i ≡l_i(3) differs from references [9, 48, 49], hence a direct quantitative comparison is not straightforward.

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There is some separation of the (i)–(iii) disruption categories: category (i) disruption has an extended cloud of points, while category (iii) disruptions are characterised by flat current profile and moderate safety factor. The physical reason for some separation of (i)–(iii) categories is an outstanding issue, which will be the subject of a future study.

MGI has been routinely used in protection mode both to terminate pulses when the plasma is at risk of disruption, and to mitigate the potentially damaging impact of disruptions on the vessel and the PFC [18, 19, 50, 51]. During JET-ILW plasma operations (from #80 128 up to #92 504), in total 896 shots were ended by MGI, using typically an optimum gas mixture of 90% D2 + 10% Ar (which corresponds to 95.7% D atoms + 4.3% Ar atoms). The amount of injected gas varies from 1.6 bar · l (6.8 · 10²²D atoms + 3.8 · 10²¹ Ar atoms) to 10.7 bar · l (4.5 · 10²³D atoms + 2.5 · 10²² Ar atoms) for DMV3 (Disruption Mitigation Valve #3, named 'Top,S' in [51]) and from 1.9 bar · l (2.3 · 10²³D atoms + 1.3 · 10²² Ar atoms) to 26.3 bar · l (3.2 · 10²⁴D atoms + 1.8 · 10²³ Ar atoms) for DMV2 (Disruption Mitigation Valve #2, named 'Midpl' in [51]). It is worth mentioning that the quantity of injected atoms at 1.6 bar · l exceeds the total number of electrons in pre-disruptive plasma by approximately a factor 2.

In the majority of the mitigated disruptions, the MGI was triggered by a n= 1 LM amplitude exceeding its threshold (523 shots) or by the disruption itself, specifically by dI_p/dt (207 shots) or by the toroidal loop voltage (145 shots). There are 21 exceptional cases when a MGI was triggered by other causes including pick up of an n= 2 mode oscillation by the plasma vertical control system (14 shots), and various other tests and faults. Moreover, 249 disruption shots were dedicated for MGI experiments, where MGI was triggered at a pre-programmed time.

The High Voltage (HV) JET systems, which includes the auxiliary heating (NBI, ICRH, LH) and some diagnostics (Li-beam, NPA, VUV spectroscopy, etc) have to be in a safe state when large gas quantities arrive in the vessel, hence the HV systems impose a delay before the MGI is fired. The MGI puts high pressure gas in the vessel where some of the HV systems operate. High voltage in high pressure gas will create breakdown and arcs which must be avoided in the machine.

The initial MGI usage had a conservative HV delay of up to 60 ms; however later the requested HV delay was reduced to as low as ∼10 ms, figure 14. The decrease in delay time is due to the implementation of a check on whether the NBI or RF power supplies have turned off. Figure 14 presents a specific property of the MGI usage on JET, but it also points out that, in general, tokamak HV in-vessel systems require some delay of MGI/SPI firing after triggering MGI/SPI for an emergency pulse suppression.

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MGI increases plasma radiation, which has the effect of reducing both the thermal load and CQ duration, which additionally helps to reduce thermal loads on PFC [20]. The CQ duration is described by τ_80-20, which is a time linearly extrapolated from the time taken to quench from 80% to 20% of $I_p^{\rm dis}$. The value of τ_80-20 for JET should be in the region of (10–27.5) ms, with the lower threshold given by force loads on the machine [52] and the upper threshold justified by minimisation of thermal loads.

The CQ duration strongly depends on the injected gas amount and pre-disruptive plasma current (figures 15 and 16, where IQAN is the amount of gas in the DMV reservoirs). Also, the two main MGI systems, DMV2 and DMV3 (DMV1 was replaced by SPI during the 2016–18 shutdown) have different geometrical parameters [51] and to deliver the same amount of gas DMV2 must operate at ∼3 times higher pressure than DMV3. Thus, the efficiency of DMV2, in terms of τ_80-20, is a factor of ∼2 higher than DMV3, figure 15. The CQ duration increases with the pre-disruptive plasma current, which may reflect the dependence of τ_80-20 on the plasma current magnetic energy to be dissipated. The data presented in figures 15 and 16 have been used to justify the gas amount which are needed to achieve the target value of τ_80-20 for JET of (10–27.5) ms. In figure 16 the CQ duration for high gas amount, IQAN2 = (23.4–26.5) bar · l shows weak dependence with the increasing I_p, however such gas amount outside the practical interest for JET.

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For MGI-induced disruptions the distribution of measured CQ time is shifted towards low CQ time and is much narrower in comparison with natural disruptions, figure 17; this is consistent with modelling where MGI boosts MHD instabilities, which enhance the penetration of the gas into the plasma [53, 54], and thus the overall rate of the energy loss from the plasma is boosted.

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The MGI effect on CQ duration for three different plasma conditions, (i) normal ('healthy') i.e. not prone to disruption, (ii) off-normal (affected by LM) pre-disruptive plasma and (iii) post-disruptive plasma is presented in figure 18. In cases of normal plasma MGI is triggered at a pre-programmed time, named 'MGI experiment' in figure 18. In cases of off-normal pre-disruptive plasma, MGI is triggered by LM amplitude. In cases of post-disruptive plasma, MGI is triggered by dI_p/dt, product of the toroidal voltages, V_rru · V_rrl, or LM amplitude, which detect a major disruption. The V_rru · V_rrl product can also detect the start of VDE. It can be seen in figure 18 that there are small differences in the CQ duration; it is surprising that the distribution of measured CQ time shifts slightly towards lower CQ times for MGI experiments, when the gas is fired into normal ('healthy') plasma.

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Electro-magnetic (EM) loads arise during the CQ when currents are driven in machine conductive structures [20, 22, 23, 39]. It should be noted that the observed large forces on the JET vessel only occur during the CQ. The JET vessel axisymmetric oscillatory deformations and vessel reaction vertical forces mainly depend on ${\left( {I_p^{\rm dis}} \right)^2}$ hence deformations and forces are not relevant to the TQ.

Due to the EM loads, the JET vessel experiences oscillatory deformations with main axisymmetric roll and asymmetrical sideways vessel movement modes [55] (see also schematic illustration—figure 14 in [20]), while vessel displacements and vertical reaction forces (F_V) are measured. Figure 19 shows three shots: a VDE, a MGI terminated pulse and a central disruption (i.e. a disruption where the TQ appears before any significant vertical motion of the plasma occurs) followed by large plasma displacement during the CQ, where the vertical force waveforms are denoted as F_V and peak-to-peak force is denoted as F_Z. Figure 19 demonstrates that axisymmetric vessel reaction forces, F_V, and axisymmetric vessel motion, Roll, are not affected by MGI. On the other hand, an asymmetrical sideways vessel displacement is significantly lower for the MGI mitigated disruption (see section 4).

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The dependence of F_Z on pre-disruptive plasma current is presented in figure 20. In general, the F_Z vessel reaction vertical forces for MGI mitigated disruptions (green points in figure 20) are below non-mitigated VDEs (red points) and below the upper bound of non-mitigated disruptions (yellow points). However, there are several non-MGI cases in which F_Z is lower than with MGI for the same plasma current. The scatter in each subset of the points (MGI, VDE, neither MGI nor VDE) could be caused by the inappropriate behaviour of the plasma vertical position control system during the CQ or other effects, i.e. variation in plasma shape, which mask the MGI efficiency. We believe that the (33–40)% reduction in F_Z due to MGI in [51] was obtained for a very specific subset of the pulses and, in general, a quantitative effect of MGI on F_Z is less evident, see figure 20.

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