1. Introduction
One feature of tokamak devices is the large current in the toroidal direction. Thermal and magnetic energy associated with this current (up to several megajoules in larger devices) is lost during a disruption on a millisecond time scale, leading to heat and electromagnetic loads, and the formation of runaway electrons. The runaway electrons are generated during the thermal and current quenches by a significant increase in loop voltage produced according to Lenz’s law in order to maintain the plasma current. The induced voltage exceeds the loop voltage applied to sustain the plasma current by a factor of 10–100 and could accelerate electrons up to relativistic energies. It generates a beam of electrons with energies of tens of megaelectronvolts and a carried current of several tens of per cent of the initial current. If the runaway beam impacts onto the wall, its whole stored energy will be deposited within a small area and may cause serious damage to plasma-facing components. Therefore, runaway electrons present an extreme danger for large-sized tokamaks.
Recent modelling for ITER indicates that approximately 70 % of the initial current
$I_{p}=15$
MA will be converted into runaway electrons, the duration of the runaway electron pulse will be approximately 150–250 ms, the runaway energy content 50 MJ, and the peak deposited energy
$15{-}65~\text{MJ}~\text{m}^{-2}$
(Hender et al.
Reference Hender, Wesley, Bialek, Bondeson, Boozer, Buttery, Garofalo, Goodman, Granetz and Gribov2007). This would lead to the melting of both tungsten and beryllium plasma-facing components, in the optimistic case, and their melting and ablation in the pessimistic case (Hender et al.
Reference Hender, Wesley, Bialek, Bondeson, Boozer, Buttery, Garofalo, Goodman, Granetz and Gribov2007).
There is no well-developed disruption theory that satisfactorily describes the variety of tokamak disruptions. Therefore, experiments aiming to investigate processes and plasma conditions during disruptions in order to benchmark existing theories and models are crucially important.
1.1. Generation of runaway electrons
The primary generation of runaway electrons in an electric field occurs due to the nature of the friction force exerted on electrons and is referred to as the Dreicer mechanism (Dreicer Reference Dreicer1959, Reference Dreicer1960). The friction force in the range of small energies is linearly proportional to the electron energy. Here, the electrons undergo frequent collisions and their energy is effectively lost. The friction force in the range of high energies is proportional to the electron speed as
$v^{-2}$
. In this range, the electrons increase in energy over the course of time, suffer fewer and fewer collisions, and finally run away.
The friction force in Dreicer’s work has no limitation on the minimum electric field required to accelerate the particles. The magnitude of the electric field determines only the acceleration rate. Therefore, the high-energy particles in the tail of the Maxwellian distribution already run away at an arbitrarily low electric field. The depletion of the high-energy tail is compensated due to diffusion of the particles in velocity space. To allow the runaway of electrons with thermal energy, the electric field must be equal to or larger than the so-called Dreicer field:
$$\begin{eqnarray}E_{D}=\frac{n_{e}e^{3}\ln {\it\Lambda}}{4{\rm\pi}{\it\varepsilon}_{0}^{2}}\frac{1}{T_{e}},\end{eqnarray}$$
where
$\ln {\it\Lambda}$
denotes the Coulomb logarithm and
$T_{e}$
is the electron temperature expressed in units of energy. For
$n_{e}=10^{20}~\text{m}^{-3}$
and
$T_{e}=1~\text{keV}$
, the Dreicer field is
$E_{D}\approx 10~\text{V}~\text{m}^{-1}$
.
Speeds close to the speed of light and very weak electric fields are beyond the validity of Dreicer’s model. The influence of relativistic effects on runaway generation has been analysed by Connor & Hastie (Reference Connor and Hastie1975). The relativistic description of electron scattering in Coulomb collisions leads to a minimum electric field required to enable electrons to run away:
$$\begin{eqnarray}E_{c}=\frac{n_{e}e^{3}\ln {\it\Lambda}}{4{\rm\pi}{\it\varepsilon}_{0}^{2}}\frac{1}{m_{e}c^{2}}=\frac{T_{e}}{m_{e}c^{2}}E_{D}\approx 5.2\times 10^{-22}n_{e}\quad (\text{V}~\text{m}^{-1}).\end{eqnarray}$$
For
$n_{e}=10^{20}~\text{m}^{-3}$
the critical field amounts to
$E_{c}\approx 5.2\times 10^{-2}~\text{V}~\text{m}^{-1}$
.
In contrast to the friction force determined by Dreicer, which decreases to zero in the high-energy limit, the friction force taking into account relativistic effects remains larger than zero even for relativistic electrons, preventing their acceleration under the applied electric field if it is lower than
$E_{c}$
.
The primary mechanism of runaway electron generation affects a relatively small part of the high-energy tail with a slow runaway rate due to diffusion in the velocity space (Dreicer generation) and/or due to conversion of the high-energy particles into the runaways (the so-called hot tail generation (Harvey et al. Reference Harvey, Chan, Chiu, Evans, Rosenbluth and Whyte2000; Smith et al. Reference Smith, Helander, Eriksson and Fulop2005; Smith & Verwichte Reference Smith and Verwichte2008)). Large tokamaks exhibiting an increased duration of the disruption and an enhanced induced electric field will additionally generate runaway electrons through collisions at small impact parameter, resulting in knock-out of the encountered electrons into the runaway region while the seed electrons do not significantly lose their energy and thus remain runaways. This mechanism of runaway multiplication is referred to as the secondary or avalanche generation.
A detailed investigation of avalanche generation (Jayakumar, Fleischmann & Zweben Reference Jayakumar, Fleischmann and Zweben1993) taking into account relativistic effects (Connor & Hastie Reference Connor and Hastie1975) and pitch angle scattering (Fussmann Reference Fussmann1979) has been performed by Rosenbluth & Putvinski (Reference Rosenbluth and Putvinski1997). In that work the critical field
$E_{c}$
was generalised for the case of partially ionised and neutral gas atoms as
$$\begin{eqnarray}E_{c}=\frac{(n_{e}+0.5n_{b})e^{3}\ln {\it\Lambda}}{4{\rm\pi}{\it\varepsilon}_{0}^{2}}\frac{1}{m_{e}c^{2}}\approx 5.2\times 10^{-22}\left(n_{e}+\frac{n_{b}}{2}\right)\quad (\text{V}~\text{m}^{-1}),\end{eqnarray}$$
where
$n_{e}$
and
$n_{b}$
are the densities of free and bound electrons, respectively. With the speed of seed electrons close to the speed of light, the bound electrons in atoms have to be taken into account with a weight factor
$1/2$
derived from the ratio of Coulomb scattering cross-sections for free and bound electrons. The critical density
$n_{c}=n_{e}+n_{b}/2$
relative to the critical electric field
$E_{c}$
is known as the Rosenbluth density. The runaway generation (including avalanche generation) is suppressed if the total electron density is above the Rosenbluth density.
The avalanche generation limits the energy of runaway electrons. According to the calculations in Rosenbluth & Putvinski (Reference Rosenbluth and Putvinski1997), the average energy of runaway electrons is approximately 10–15 MeV.
The avalanche mechanism of runaway electron production becomes the major mechanism in large tokamaks, with multiplication factors of
$e^{5}$
for JET and
$e^{50}$
for ITER, resulting in a conversion of up to 70 % of the initial plasma current into runaway current (Rosenbluth & Putvinski Reference Rosenbluth and Putvinski1997).
1.2. Suppression of runaway electrons
The generation of runaway electrons is one of the negative consequences of disruptions with serious damage potential. The other threats to tokamak integrity are electromagnetic and heat loads. In order to preserve machine integrity, all three hazards have to be mitigated or suppressed by the application of suitable mitigation techniques.
The major idea of massive gas injection (MGI) as a mitigation technique is the injection of a large amount of particles (
$\text{H}_{2}$
,
$\text{D}_{2}$
, noble gases He, Ne, Ar, or their mixture) and the consequent effectively uniform radiation of plasma thermal and magnetic energies. The suppression of runaway electron generation can also be achieved by the injection of additional particles. The increase in density is supposed to result in a sufficient increase in the friction force and hence the suppression of runaway generation due to Coulomb collisions.
However, the mitigation of electromagnetic and heat loads, and the suppression of runaway electrons require noticeably different amounts of added particles. In disruption mitigation experiments using the injection of frozen solid particles (‘killer pellets’), the mitigation of electromagnetic and heat loads has been quite successful. A reduction of thermal flux onto the divertor plates of up to 90 % and a reduction of halo current of up to 70 % have been observed (Pautasso et al. Reference Pautasso, Buchl, Fuchs, Gruber, Herrmann, Lackner, Lang, Mast, Ulrich and Zohm1996; Evans et al. Reference Evans, Kellman, Humphreys, Schaffer, Taylor, Whyte, Jernigan, Hyatt and Lee1997; Yoshino et al. Reference Yoshino, Kondoh, Neyatani, Itami, Kawano and Isei1997; Taylor et al. Reference Taylor, Kellman, Evans, Gray, Humphreys, Hyatt, Jernigan, Lee, Leuer and Luckhardt1999). The amount of introduced particles sufficient for the mitigation of electromagnetic and heat loads is by far not enough for the suppression of runaway generation. As a drawback, the formation of runaways has been routinely observed in these killer pellet experiments (Yoshino et al. Reference Yoshino, Kondoh, Neyatani, Itami, Kawano and Isei1997; Taylor et al. Reference Taylor, Kellman, Evans, Gray, Humphreys, Hyatt, Jernigan, Lee, Leuer and Luckhardt1999).
Owing to the limited applicability of killer pellet injection, most investigations of disruption mitigation and runaway suppression on present machines focus on MGI. The mitigation of electromagnetic forces of up to 75 % and maximum mitigation of thermal loads have been shown in MGI experiments on TEXTOR (Finken et al. Reference Finken, Mank, Krämer-Flecken and Jaspers2001), DIII-D (Taylor et al. Reference Taylor, Kellman, Rice and Humphreys1996; Whyte et al. Reference Whyte, Jernigan, Humphreys, Hyatt, Lasnier, Parks, Evans, Rosenbluth, Taylor and Kellman2002, Reference Whyte, Jernigan, Humphreys, Hyatt, Lasnier, Parks, Evans, Taylor, Kellman and Gray2003; Hollmann et al. Reference Hollmann, Jernigan, Groth, Whyte, Gray, Austin, Bray, Brennan, Brooks and Evans2005), Alcator C-Mod (Granetz et al. Reference Granetz, Whyte, Izzo, Biewer, Reinke, Terry, Bader, Bakhtiari, Jernigan and Wurden2006), ASDEX-U (Pautasso et al. Reference Pautasso, Coster, Eich, Fuchs, Gruber, Gude, Herrmann, Igochine, Konz and Kurzan2009), JT-60U (Bakhtiari et al. Reference Bakhtiari, Kawano, Tamai, Miura, Yoshino and Nishida2002, Reference Bakhtiari, Tamai, Kawano, Kramer, Isayama, Nakano, Kamiya, Yoshino, Miura and Kusama2005b ; Kawano et al. Reference Kawano, Yoshino, Neyatani, Nakamura, Tokuda and Tamai2002) and JET (Lehnen et al. Reference Lehnen, Alonso, Arnoux, Baumgarten, Bozhenkov, Brezinsek, Brix, Eich, Gerasimov and Huber2011, Reference Lehnen, Arnoux, Brezinsek, Flanagan, Gerasimov, Hartmann, Hender, Huber, Jachmich and Kiptily2013).
No runaway electrons have been observed in plasma discharges terminated by the injection of 1–10 mbar l of He at Tore Supra (Martin et al.
Reference Martin, Sourd, Saint-Laurent, Bucalossi and Eriksson2004). In further experiments with the injection of 0.05–5 bar l of He, Ne, Ar and a He/Ar mixture (95/5 %) (Reux et al.
Reference Reux, Bucalossi, Saint-Laurent, Gil, Moreau and Maget2010; Saoutic et al.
Reference Saoutic, Abiteboul, Allegretti, Allfrey, Ané, Aniel, Argouarch, Artaud, Aumenier and Balme2011), a strong reduction of the number of runaway electrons has been obtained with injected amounts above 0.2 bar l of He and a He/Ar mixture. On the other hand, the injections of pure Ar or Ne have not prevented runaway generation on Tore Supra. A significantly reduced rate of runaway electron generation in the disruptions caused by the injection of a He mixture with 1 % of Ar, Kr, Xe has been observed at JT-60U (Bakhtiari et al.
Reference Bakhtiari, Tamai, Kawano, Kramer, Isayama, Nakano, Kamiya, Yoshino, Miura and Kusama2005b
). No runaways have been detected in MGI experiments with pure
$\text{D}_{2}$
, He and
$\text{D}_{2}$
mixtures at JET (Lehnen et al.
Reference Lehnen, Alonso, Arnoux, Baumgarten, Bozhenkov, Brezinsek, Brix, Eich, Gerasimov and Huber2011). At the same time, the injections of pure Ne and Ar have not suppressed the runaway generation on JET. In low-density runaway discharges at TEXTOR terminated using a He puff in an amount of 10 mbar l, the runaway electrons have been successfully removed from the discharges (Finken et al.
Reference Finken, Mank, Krämer-Flecken and Jaspers2001). On TEXTOR, disruptions induced by Ar MGI have been free of runaway electrons only in the case of a large amount of injected particles
$(15\times 10^{21})$
; runaway electrons have not been detected after the injection of He or a
$\text{D}_{2}/\text{Ar}$
mixture (5 %, 10 %, 20 %) (Bozhenkov et al.
Reference Bozhenkov, Lehnen, Finken, Jakubowski, Wolf, Jaspers, Kantor, Marchuk, Uzgel and Van Wassenhove2008).
The shallow penetration of impurities into the plasma by a few centimetres without affecting the plasma centre has been reported at DIII-D (Whyte et al.
Reference Whyte, Jernigan, Humphreys, Hyatt, Lasnier, Parks, Evans, Rosenbluth, Taylor and Kellman2002; Hollmann et al.
Reference Hollmann, Jernigan, Groth, Whyte, Gray, Austin, Bray, Brennan, Brooks and Evans2005, Reference Hollmann, Jernigan, Parks, Boedo, Evans, Groth, Humphreys, James, Lanctot and Nishijima2008; Hender et al.
Reference Hender, Wesley, Bialek, Bondeson, Boozer, Buttery, Garofalo, Goodman, Granetz and Gribov2007), Alcator C-Mod (Granetz et al.
Reference Granetz, Whyte, Izzo, Biewer, Reinke, Terry, Bader, Bakhtiari, Jernigan and Wurden2006, Reference Granetz, Hollmann, Whyte, Izzo, Antar, Bader, Bakhtiari, Biewer, Boedo and Evans2007; Whyte et al.
Reference Whyte, Granetz, Bakhtiari, Izzo, Jernigan, Terry, Reinke and Lipschultz2007) and Tore Supra (Reux et al.
Reference Reux, Bucalossi, Saint-Laurent, Gil, Moreau and Maget2010; Saoutic et al.
Reference Saoutic, Abiteboul, Allegretti, Allfrey, Ané, Aniel, Argouarch, Artaud, Aumenier and Balme2011). Furthermore, the amount of lightweight particles successfully mixed into the plasma has been found to be relatively larger than the amount of high-
$Z$
impurities. For example, helium injection added at least three times more free electrons (up to
$2\times 10^{21}$
) into the plasma than argon injection (Reux et al.
Reference Reux, Bucalossi, Saint-Laurent, Gil, Moreau and Maget2010; Saoutic et al.
Reference Saoutic, Abiteboul, Allegretti, Allfrey, Ané, Aniel, Argouarch, Artaud, Aumenier and Balme2011). The efficiency of plasma fuelling by impurities (defined as the ratio of impurities assimilated by the plasma to all injected impurities) has been determined in previous works to amount to 20–40 % for He, 5–20 % for
$\text{H}_{2}$
,
$\text{D}_{2}$
, Ne and Ar in DIII-D (Hollmann et al.
Reference Hollmann, Jernigan, Parks, Boedo, Evans, Groth, Humphreys, James, Lanctot and Nishijima2008), 35–55 % for He and Ne in ASDEX (Pautasso et al.
Reference Pautasso, Mank, Mlynek, Beck, Weisbart, Bernert, Gruber, Herrmann and Sertoli2011), and 3 % for Ar, 15 % for
$\text{Ar}/\text{D}_{2}$
and 40 % for He in TEXTOR (Bozhenkov et al.
Reference Bozhenkov, Lehnen, Finken, Jakubowski, Wolf, Jaspers, Kantor, Marchuk, Uzgel and Van Wassenhove2008).
The investigation of the suppression of runaway electron generation by MGI allows cautious optimism but has not yet provided sufficient certainty. In order to achieve the above-mentioned Rosenbluth density, the plasma density must increase by a factor of 100 after the MGI. It is still questionable if such powerful and fast gas injection could be realised. Work on such systems has just begun, and a design for an ITER MGI valve for runaway suppression has been published recently (Czymek et al. Reference Czymek, Giesen, Charl, Panin, Hiller, Nicolai, Neubauer, Koslowski and Sandri2015).
According to the observed experimental evidence, helium is considered to be a promising candidate for runaway generation suppression by MGI. In this paper the investigation of runaway electron generation suppression in TEXTOR by helium MGI after deliberately induced disruptions is presented. Disruptions are very fast events and suitable diagnostics are required for their characterisation. Especially, the measurement of the electron density is an important task. For this purpose, a dispersion interferometer has been used (Bagryansky et al. Reference Bagryansky, Khilchenko, Kvashnin, Lizunov, Voskoboynikov, Solomakhin and Koslowski2006; Dreier et al. Reference Dreier, Bagryansky, Baumgarten, Biel, Lambertz, Lehnen, Lizunov and Solomakhin2011). This is an advanced tool allowing reliable measurement of line-integrated electron density during the disruption and post-disruption stages with a high time resolution. The knowledge of electron density during disruptions provides a key for the comparison of theoretical predictions on runaway electron generation suppression with experimental results.
2. Description of massive gas injection experiments
2.1. Experimental set-up
The primary aim of MGI is to inject a large particle quantity in a short period of time. For that task, a series of fast valves operated by eddy currents have been designed, built and successfully used at TEXTOR. Such a fast valve is named in the following a disruption mitigation valve (DMV).
(a) Scheme of the disruption mitigation valve DMV-30: 1, valve body; 2, gas filling tube; 3, working volume with a spacer; 4, piston; 5, coils inducing eddy currents; 6, spring. (b) TEXTOR top view showing the toroidal locations of diagnostics and experimental equipment.
Two DMVs have been used in the present MGI experiments. The first valve has a designed volume of
$320~\text{cm}^{3}$
, a maximum gas pressure of up to 35 bar, and an orifice of 10 mm (hence this valve is named DMV-10) (Savtchkov, Finken & Mank Reference Savtchkov, Finken and Mank2002; Bozhenkov et al.
Reference Bozhenkov, Finken, Lehnen and Wolf2007). In the MGI experiments, DMV-10 was only used to trigger a disruption. Therefore, its volume was reduced using the set of spacers to
$27~\text{cm}^{3}$
, and its operating pressure was set to 1 bar.
Traces of plasma current
$I_{p}$
, loop voltage
$U_{loop}$
, electron temperature
$T_{e}$
, magnetic fluctuations
$\text{d}B/\text{d}t$
, soft X-ray radiation (SXR) and line-integrated electron density
$\langle n_{e}l\rangle$
during the disruption caused by the injection of 27 mbar l of argon using the DMV-10 at
$t=1.5~\text{s}$
.
The second DMV has a designed reservoir volume of
$360~\text{cm}^{3}$
, reduced by a spacer to
$111~\text{cm}^{3}$
to adjust it to TEXTOR conditions, an orifice of 30 mm (hence this valve is named DMV-30, see figure 1
a for details), and a maximum gas pressure of up to 100 bar. The DMV-30 is used several milliseconds after the DMV-10 to inject gas in order to suppress the runaway electrons which would otherwise develop after the DMV-10 injection.
The following plasma conditions have been chosen for the experiments on runaway electron generation suppression: a low-density plasma favourable for the disruption experiments, a relatively high plasma current and a high toroidal magnetic field to overcome the
${\rm\delta}B/B_{t}$
threshold for runaway electron generation (Lehnen et al.
Reference Lehnen, Bozhenkov, Abdullaev and Jakubowski2008; Zeng et al.
Reference Zeng, Koslowski, Liang, Lvovskiy, Lehnen, Nicolai, Pearson, Rack, Jaegers and Finken2013) (
$\langle n_{e}\rangle =1.5\times 10^{19}~\text{m}^{-3}$
,
$I_{p}=350~\text{kA}$
,
$B_{t}=2.4~\text{T}$
,
$T_{e}=1~\text{keV}$
).
The disruptions were always deliberately induced by a gas injection of 27 mbar l at time
$t=1.5~\text{s}$
using the DMV-10. The typical disruption scenario is shown in figure 2. The MGI causes the collapse of plasma confinement, the fast loss of plasma thermal energy over a time scale of 1 ms during the thermal quench (TQ), and the much longer process of plasma current dissipation over a time scale of 10 ms. The runaway current is approximately 30 % of the initial current before the current quench (CQ).
A convenient set of diagnostics for MGI experiments are as follows: (i) fast plasma current measurements by a Rogowski coil, (ii) loop voltage using a toroidal flux loop, (iii) electron temperature by an electron cyclotron emission (ECE) radiometer, (iv) magnetic fluctuations
$\text{d}B/\text{d}t$
detected by a set of Mirnov coils, (v) soft X-ray radiation (SXR) measured by an array of pin diodes (Liang et al.
Reference Liang, Koslowski, Kraemer-Flecken and Zimmermann2004; Donné et al.
Reference Donné, de Bock, Classen, von Hellermann, Jakubowska, Jaspers, Barth, van der Meiden, Oyevaar and van de Pol2005), and (vi) line-integrated electron density measured with a dispersion interferometer (Bagryansky et al.
Reference Bagryansky, Khilchenko, Kvashnin, Lizunov, Voskoboynikov, Solomakhin and Koslowski2006; Dreier et al.
Reference Dreier, Bagryansky, Baumgarten, Biel, Lambertz, Lehnen, Lizunov and Solomakhin2011) (see figure 1
b for the location details).
The ECE signals (Waidmann et al.
Reference Waidmann, de Vries, Kraìmer-Flecken, Eulenberg and Huxhagen1997) indicate the onset of a disruption by a drop in the edge electron temperature. The electron temperature normalised to the pre-disruptive value is used for a qualitative description of the disruption because the ECE signals from the plasma core are often cut off during disruptions due to the large density increase. However, the ECE signal can be well used in the case of small amounts of injected gas. The injection of 27 mbar l of noble gas, assuming single ionisation and uniform gas distribution, leads to an increase in plasma frequency
$f_{pe}$
up to 60 GHz, while the applied second extraordinary ECE harmonic has cut-offs at 100 GHz (low-field side) and 125 GHz (plasma core) (Krämer-Flecken Reference Krämer-Flecken2006). To back up the ECE measurements, the detection of magnetic fluctuations indicates the collapse of magnetic surfaces and the onset of the thermal quench.
The measurement of the plasma current provides information about the duration of the current quench and the magnitude of the runaway plateau. In principle, the plasma current could also be used for the observation of runaway losses. However, the SXR signal better suits the task of runaway loss observation. It consists of contributions originating from line radiation, recombination and bremsstrahlung caused by the interaction between runaway electrons, background plasma and mobilised dust. The SXR signals increase when deceleration and loss of runaway electrons occur.
The loop voltage is used for the calculation of the toroidal electric field
$E_{t}$
reaching up to
$5~\text{V}~\text{m}^{-1}$
in TEXTOR during disruptions. The
$E_{t}$
field determines the critical density
$n_{c}$
required for the suppression of runaway electron generation according to the Connor–Rosenbluth theory.
Measurements of line-integrated electron density
$\langle n_{e}l\rangle$
are performed by the dispersion interferometer at
$R=1.63$
m (for TEXTOR,
$R_{0}=1.75~\text{m}$
,
$a=0.46~\text{m}$
). The dispersion interferometer has a high time resolution of
$2~{\rm\mu}\text{s}$
and reliably follows the line density with a rate of change of up to
$1.75\times 10^{19}~\text{m}^{-2}~{\rm\mu}\text{s}^{-1}$
.
Measurements of the neutral particle pressure are not possible using the regular set of vacuum gauges due to their saturation during the MGIs. Therefore, vacuum gauges designed for the engineering monitoring of the pressure inside the TEXTOR chamber are used. This leads to a significant reduction of the time resolution of neutral pressure measurements from 10 ms down to 1 s and would be the major source of errors. Therefore, the data from the vacuum gauge are used only as a reference to benchmark the straightforward estimation of the neutral pressure based on the ratio of the injected gas amount to the total volume of the TEXTOR vessel of
$17~\text{m}^{3}$
.
Traces of plasma current
$I_{p}$
, core electron temperature
$T_{e}$
, magnetic fluctuations
$\text{d}B/\text{d}t$
and soft X-ray radiation (SXR) during disruptions caused by the injection of 27 mbar l of helium, neon or argon using the DMV-10 at
$t=1.5~\text{s}$
. The plasma current plateau and the strong SXR clearly indicate the generation of runaway electrons in the disruption caused by argon injection and their absence in the cases of helium and neon injections.
2.2. Disruption mitigation valve characterisation
MGI by DMV-10 reliably causes tokamak disruptions, but the generation of runaway electrons is observed only under specific conditions. According to our experience, the use of argon not only causes a disruption but also leads to reliable runaway electron generation. The traces of plasma current
$I_{p}$
and soft X-ray radiation intensity during disruptions induced by the injection of 27 mbar l of helium, neon and argon by DMV-10 are shown in figure 3.
A clear runaway electron plateau and strong SXR emission (with the spikes caused by runaway losses and well correlated with the decreases in plasma current) are observed only for the case of argon injection and are not seen in the injections of helium or neon. The presence of runaway electrons in the disruption caused by argon injection can be explained by its low fuelling efficiency (the ratio of the particles delivered inside the plasma column to all injected particles), which is approximately 3 %, compared to the fuelling efficiency of helium and neon, which reaches up to 40 % according to Bozhenkov et al. (Reference Bozhenkov, Lehnen, Finken, Jakubowski, Wolf, Jaspers, Kantor, Marchuk, Uzgel and Van Wassenhove2008) and Pautasso et al. (Reference Pautasso, Mank, Mlynek, Beck, Weisbart, Bernert, Gruber, Herrmann and Sertoli2011). This means that, even at the lowest possible amount of gas injection by DMV-10, helium and neon perform too effectively, penetrating well into the plasma. This suggests that the destroyed confinement and the likely perturbed magnetic surfaces do not allow the formation of runaway current. In addition, despite the early arrival of helium at the plasma edge, seen by the start of edge plasma cooling, the onset of the current quench takes place significantly later than in the cases of neon or argon injections (see the edge electron temperature and magnetic fluctuation signals in figure 3). This can be explained by the relatively late onset of the thermal quench (delayed by approximately 2 ms) because of the low plasma cooling capability of helium.
One important question is the reaction time of the DMVs. The DMV-10 starts to open within 0.3–0.5 ms after the trigger signal and is fully open within 1 ms according to observations by a fast camera/photomultiplier (Savtchkov et al.
Reference Savtchkov, Finken and Mank2002; Bozhenkov et al.
Reference Bozhenkov, Finken, Lehnen and Wolf2007). The DMV-30 has the same reaction time to the trigger signal and is fully open within 1.4 ms at the maximum coil voltage of 2 kV (Lehnen Reference Lehnen2012). However, for the full valve reaction time, the gas propagation time from the valve to the plasma needs to be considered. The DMV-10 is placed on the top of TEXTOR, and gas reaches the plasma by means of a 1 m tube with a 40 mm diameter. The total distance to the last closed flux surface is approximately 1.5 m. The DMV-30 is placed in the equatorial plane of TEXTOR on the low-field side at a distance of 10 cm from the plasma. The gas delivery time can be estimated using a simple model of ideal gas propagation into a semi-infinite space at the speed of sound
$c_{s}$
and consideration of one-dimensional gas expansion into a vacuum in an infinite tube with the formation of a shock front with the speed
$c_{sh}$
:
$$\begin{eqnarray}c_{s}=\sqrt{\frac{{\it\gamma}kT}{m}},\quad c_{sh}=\frac{2c_{s}}{{\it\gamma}-1}.\end{eqnarray}$$
Here
${\it\gamma}$
is the adiabatic index (
${\it\gamma}=5/3$
for a monatomic gas),
$k$
is the Boltzmann constant,
$T$
is the absolute temperature and
$m$
is the mass (kg) of a single atom/molecule. The speeds of sound for He, Ne and Ar are
$1010$
,
$448$
and
$320~\text{m}~\text{s}^{-1}$
, respectively, under normal conditions. The propagation times of He, Ne and Ar and the full valve reaction times for DMV-10 and DMV-30 are summarised in table 1.
Estimation of the gas propagation time
${\it\tau}$
from a DMV into the plasma and the full valve reaction time
${\it\tau}^{full}$
. The measured full valve reaction time is denoted as
${\it\tau}^{\ast full}$
. Times are given in milliseconds.
A more accurate result for the total valve reaction time can be obtained experimentally from the observation of the plasma edge temperature at the low-field side. The plasma cooling onset indicates the arrival of the gas front. Such measurements have been performed in several shots using the injection of He, Ne and Ar by DMV-10 using a pressure of 1 bar and a trigger at
$t=1.5~\text{s}$
. The plasma edge cooling starts with a delay of 1.5, 2.3 and 2.7 ms, respectively, after the trigger signal for He, Ne and Ar injections (see figure 4 and table 1). The resulting spikes in the electron temperature are connected with the loss of plasma confinement and/or with the presence of suprathermal electrons. Similar observations of the plasma core temperature show that the core cooling starts within 2.4, 3.6 and 4.2 ms, and has a duration of 4.2, 0.8 and 0.4 ms, for He, Ne and Ar injections, respectively. Two different shots with Ar injection using the same shot parameters are shown in figure 4 in order to check the reproducibility of an experiment; the results obtained for Ar are consistent within an accuracy of 0.1 ms. There is a noticeable difference between the estimated and experimental values. This fact could be explained by a more complex flow of the real gas in the tube and by the transition between propagations in the tube and in the vessel.
Plasma edge cooling as an indication of the reaction time of the DMV-10 and DMV-30 valves. The cooling is caused by disruptions due to the injection of 27 mbar l of helium, argon and neon by DMV-10 and 0.555 bar l of argon (#120449) by DMV-30. The trigger signal is at 1.5 s. The electron temperature is normalised to the pre-disruptive values.
The same approach has been used to obtain the parameters of DMV-30. For that reason, the injection of Ar at 5 bar pressure and
$t=1.5~\text{s}$
has been carried out. It is shown in figure 4 that the plasma temperature at the edge drops with a 0.7 ms delay after the valve triggering (the plasma core cooling starts 1 ms later). The DMV-30 opens nearly directly into the plasma (10 cm distance). Therefore, further investigation of other gases and pressures are not possible because the time resolution of the ECE radiometer is below the expected difference in propagation times.
Summarising the results obtained, the full reaction time of DMV-30 is 0.7 ms, and it is independent of the gas species within an accuracy of 0.1 ms; the full reaction times of DMV-10 are 1.5, 2.3 and 2.7 ms for He, Ne and Ar injections, respectively. Taking this and the chosen step of valve triggering of 1 ms into account, one can conclude that the minimum reasonable delay for the DMV-30 is 4–5 ms, otherwise its gas arrives at the same time or even before the gas injected by DMV-10.
3. Results
3.1. Injection amount and delay scans
To find the threshold of the runaway electron generation suppression by MGI, a scan of the amount of helium injected was performed. The experiments followed the scheme described above: a disruption with the generation of runaways was caused by the injection of 27 mbar l of argon by DMV-10 at
$t=1.5~\text{s}$
. After this, the injection of helium was performed by DMV-30 with a 5 ms delay, which is the minimum time satisfying the condition that the helium arrives at the plasma edge after the argon. The amount of helium injected was varied in the range 0–5 bar l (
$1~\text{bar}~\text{l}=2.5\times 10^{22}$
particles). The results are presented by the traces of plasma current and soft X-ray signal in figure 5. The runaway plateau shown in the figure becomes smaller and/or shorter compared to the unmitigated disruption, and it is not observed with injections above 2.5 bar l. The SXR signal indicates the clear change in the population of runaway electrons and in the behaviour of runaway losses. The strong interactions between the runaways and the background plasma without helium injection become much smaller as the amount of injected gas increases, with several separated SXR bursts indicating the runaway losses, and, at injections above 2.5 bar l, the runaway electrons are lost at a high rate in the very beginning of the disruption. Therefore, the threshold for runaway electron suppression is in the range of 2.5–3.0 bar l of helium injection.
Plasma current
$I_{p}$
and SXR emission during the current quench after the helium injections by DMV-30 in the range of 0–5 bar l. The trigger of DMV-30 has a 5 ms delay compared to the trigger of DMV-10, causing the disruption at
$t=1.5~\text{s}$
.
To find the influence of the helium injection delay on the runaway electron generation suppression, the helium injection was performed by DMV-30 with 5 and 6 ms delays after the DMV-10 trigger. The amounts injected were 1.9 bar l and 5.0 bar l – slightly below and significantly above the found threshold between 2.5 and 3.0 bar l. The results are presented by the traces of plasma current and soft X-ray signal in figure 6. The increased delay in the case of 1.9 bar l injection causes a very long runaway plateau: approximately 70 ms versus 45 ms in the case without helium injection. Surprisingly, the level of SXR emission is reduced by a factor of 2–3, which may indicate even less runaway losses than in the unmitigated case. We have no explanation for this behaviour, but should note that there is always a large variation in the reproducibility of runaway tails. The injection significantly above the determined threshold but with a 1 ms longer delay shows the clear existence of runaways: a 10 ms runaway plateau and strong runaway losses during the runaway electron (RE) phase. Nevertheless, the slope of the RE plateau even in the case of late injection, but above the threshold, is noticeably steeper than the slopes in the case of an unmitigated disruption or early injection below the threshold. This result indicates the remaining capability of runaway suppression in the case of late injection of a significant amount of gas but also highlights the high importance of proper timing and fast injection.
Plasma current
$I_{p}$
and SXR emission during the current quench at different times and with different amounts of helium injection by DMV-30. The disruption is caused by DMV-10 at
$t=1.5~\text{s}$
.
The injection of a small amount of gas (0.3 bar l) with a 4 ms delay is presented in figure 6 to show the completely different behaviour in the case of overlapping injections by DMV-10 and DMV-30: the runaway electron generation is completely suppressed. The injections with more than a 6 ms delay are not presented in figure 6, because they do not show any further difference in the observed behaviour of runaway current. See, for example, the injection of 1.1 bar l helium with a 9 ms delay (
$=8~\text{ms}$
delay in terms of the present paper) in Koslowski et al. (Reference Koslowski, Zeng, Lehnen, Lvovskiy and Wongrach2014). This injection occurs well after the onset of CQ, at the stage of the RE plateau. It shows no effect on the RE current, and the course of the disruption is very similar to the picture observed after the injection of 1.9 bar l of helium with a 6 ms delay in the present paper.
The different runaway suppression effectiveness for the early and late (compared to the development of the disruption) MGIs may have the following nature. Thermal electrons must be accelerated by the loop voltage increase during the disruption to become runaways. The formation of a seed runaway population via diffusion in velocity space is a relatively slow process with a low gain coefficient. Therefore, with early MGI, the electrons cannot gain enough energy between collisions and do not become runaways due to the increased collision rate. On the other hand, in the case of late injection, the already accelerated electrons are nearly not affected by the density increase due to the low friction force at high electron energies. In other words, the MGI is able to suppress the generation of primary runaway electrons but can only weakly decelerate or scatter the already existing runaways. Such runaway electrons can be only de-confined, for example, by strong magnetic fluctuations. From this point of view, a suppression of avalanche generation by MGI after the formation of seed runaway electrons (for example, in the end of CQ in the case of Dreicer/hot-tail generation) is much less effective than the suppression of primary generation. We should note that another possible factor limiting the effectiveness of MGI in the case of late injection is the change of gas–plasma mixing during the CQ.
Critical density
$n_{crit}$
required for the runaway electron generation suppression calculated using
$E_{t}$
(grey circles) and density of free and bound electrons (black markers). The squares show the total density assuming uniform distribution of non-ionised helium atoms over the vessel, the triangles are used for the assumption of penetration of 50 % non-ionised particles into the plasma, and the diamonds are for taking into account only singly ionised ions. The shaded area in the plot denotes the experimentally observed range of runaway electron generation. The dashed lines are only to guide the eye.
3.2. Comparison of the experimentally determined density threshold with the Rosenbluth density
The experimentally observed threshold for the runaway electron generation suppression is between 2.5 and 3.0 bar l. The Connor–Rosenbluth theory states that the combined density of free and bound electrons must overcome the so-called critical (Rosenbluth) density
$n_{c}<n_{e}+n_{b}/2=n_{tot}$
for the suppression of runaways. The required critical density
$n_{c}$
is determined by the toroidal electric field,
$n_{c}~(10^{21}~\text{m}^{-3})=2E_{t}~(\text{V}~\text{m}^{-1})$
, which was obtained from the loop voltage measurements. The toroidal electric field in TEXTOR during disruptions is approximately
$3{-}5~\text{V}~\text{m}^{-1}$
. The corresponding critical density
$n_{c}$
is in the range
$(5{-}10)\times 10^{21}~\text{m}^{-3}$
, and it is shown in figure 7 by grey circles. The density of the free electron component
$n_{e}$
is provided by the line-integrated measurements of the dispersion interferometer. The free electron density for helium injection of 0.5–5 bar l varies in the range
$(10{-}100)\times 10^{19}~\text{m}^{-3}$
at the beginning of disruptions.
The necessity to also take bound electrons into account is shown by the following estimations. For the given conditions of the experiment (
$\langle n_{e}\rangle =1.5\times 10^{19}~\text{m}^{-3}$
,
$I_{p}=350~\text{kA}$
,
$B_{t}=2.4~\text{T}$
,
$T_{e}=1~\text{keV}$
), the plasma thermal energy
$W_{th}=3\int nkT\,\text{d}V$
is approximately 50 kJ, the magnetic energy
$W_{mag}=0.5I_{p}^{2}L_{p}$
is approximately 270 kJ (
$L_{p}={\it\mu}_{0}R[\ln (8R/a)-2+l_{i}/2]$
, and
$l_{i}$
is typically 1.2 for sawtoothing ohmic discharges in TEXTOR). The first ionisation energy for helium is 24.6 eV, and 54.4 eV for the second electron (Lide Reference Lide2003). Assuming that all the plasma energy is used for helium ionisation, 3 bar l of injected helium could be ionised in the case of only single ionisation or 1 bar l in the case of double ionisation. In reality, both ionisation stages will occur and the ionised amount will be in between. However, most of the plasma energy during the induced disruptions is lost through radiation, convection and multiple ionisation–recombination events (up to 70–90 %). This will reduce the available energy for the production of free electrons and thus reduce their number and density. Therefore, the presence of bound electrons already starts to play the major role in the collisional suppression of runaway generation at a rather low amount of injected particles.
The bound electrons can be associated with neutral atoms and with partially ionised particles. Without fast and unsaturated diagnostics of neutral pressure, the density of neutral particles can be estimated by the ratio of the injected particle amount to the vessel volume. The combined density of free and bound electrons
$n_{tot}$
is shown in figure 7 by black markers.
The minimum estimation of the total density relevant for runaway suppression
$n_{tot}=n_{e}+n_{b}/2$
was performed using only the electron density measurement by the dispersion interferometer without taking into account non-ionised helium atoms. Under the assumption that the measured increase in the free electron density is caused by the corresponding penetration of impurities, and under the condition of single ionisation, one obtains the density of bound electrons as
$n_{b}=(Z-1)n_{e}$
. Thus, the total density takes the form
$n_{tot}=n_{e}+0.5(Z-1)n_{e}$
. The primary injection of argon is not taken into account because it delivers only 3 % of electrons into the plasma compared with the secondary helium injection in the investigated range according to the measurements by the dispersion interferometer. In this approach, the density of bound electrons associated with neutral particles is neglected. It cannot be measured directly; such an assumption would require the complex simulation of every shot. The diamonds in figure 7 show the total density calculated completely based on the measurements by the dispersion interferometer. In this case, the total density is 12–14 times lower than the critical density in the threshold area of 2.5–3 bar l helium injection.
The maximum estimation of the total electron density considers that those of helium atoms which remained non-ionised are uniformly distributed over the vessel. The total density takes the form
$n_{tot}=n_{e}+0.5n_{e}+0.5\times 2\times (N_{inj}/V-n_{i})$
, where
$N_{inj}$
is the number of injected particles,
$V$
is the volume of the TEXTOR vessel and
$n_{i}=n_{e}$
. This estimation of the total density is shown by square markers in figure 7. It is below the critical density over almost the full range of helium injection and starts to overlap only at 5.0 bar l injection. This finding has to be related to the experimental observation showing no runaway electrons above the injection of 2.5 bar l. In the range of 2.5–3 bar l, the total density achieving runaway generation suppression is approximately two times lower than the theoretical critical density for avalanche suppression.
The maximum estimation assumes that all injected particles reaching the plasma edge would penetrate into the plasma over the disruption time scale. This result has never been achieved in the past, neither in experiments nor in modelling. The amount of helium impurities penetrating into the plasma has been determined to be 20–50 % of injected particles in DIII-D, ASDEX-U and Tore Supra (Hollmann et al. Reference Hollmann, Jernigan, Parks, Boedo, Evans, Groth, Humphreys, James, Lanctot and Nishijima2008; Reux et al. Reference Reux, Bucalossi, Saint-Laurent, Gil, Moreau and Maget2010; Pautasso et al. Reference Pautasso, Mank, Mlynek, Beck, Weisbart, Bernert, Gruber, Herrmann and Sertoli2011).
Both given estimations emphasise the important role of bound electrons, especially those associated with the neutral atoms. Therefore, the difference between the estimations based on the uniform penetration of non-ionised impurities into the plasma, and those based on the account of only free electrons and singly ionised atoms, reaches a factor of 7. To place additional points in between the two extremes, some information about neutral penetration into the plasma is required. Such analysis has been performed in Bozhenkov et al. (Reference Bozhenkov, Lehnen, Finken, Bertschinger, Koslowski, Reiter and Wolf2011). As a result, 50 % of helium impurity penetration into the plasma has been stated. Therefore, the intermediate estimation of the total electron density includes the bound electrons associated with 50 % of injected particles reaching the plasma and takes the form
$n_{tot}=n_{e}+0.5n_{e}+0.5\times 2\times (0.5N_{inj}/V-n_{e})$
. The result is shown in figure 7 by triangles. It is approximately four times below the theoretical value.
4. Discussion
One possible explanation for the significant difference between the theoretical predictions and the experimental results could be the fact that classic theory does not take into account any additional runaway losses or runaway energy limitations. This could be caused, for example, by synchrotron or bremsstrahlung radiations.
The power of synchrotron radiation
$P_{s}$
is proportional to the particle energy as
$W^{2}$
and inversely proportional to the particle mass as
$\text{m}^{-4}$
. Therefore, losses of particle energy are significant for ultra-relativistic lightweight particles. This effect severely limits the acceleration rate for electrons at high energies. Numerical simulations (Martin-Solis et al.
Reference Martin-Solis, Alvarez, Sanchez and Esposito1998, Reference Martin-Solis, Sanchez and Esposito2010) show a decrease in the critical density when taking into account the synchrotron radiation compared to the critical density determined by Rosenbluth. A decrease in the critical density due to synchrotron losses has been observed experimentally in FTU (Martin-Solis et al.
Reference Martin-Solis, Sanchez and Esposito2010). The critical density has been found to be approximately a factor of 2 below the density predicted by the classic Rosenbluth value.
An investigation of the influence of bremsstrahlung radiation on the runaway electron energy limit has been carried out in Bakhtiari et al. (Reference Bakhtiari, Kramer, Takechi, Tamai, Miura, Kusama and Kamada2005a
). According to the modelling, the energy limit
$W$
decreases with increasing ion charge
$Z$
. However, the dependence of runaway energy limitation on the gas species used has not been observed in experiments on JT-60U (Bakhtiari et al.
Reference Bakhtiari, Kramer, Takechi, Tamai, Miura, Kusama and Kamada2005a
).
It is interesting to compare the results obtained with investigations of the runaway electron growth threshold under quasi-steady-state conditions. In low-density but disruption-free experiments, the plasma density is slowly changed at the Ohmic flat-top phase during the shot or from shot-to-shot. In that quiescent regime free from transients, magnetohydrodynamic and beam instabilities, the measurement of plasma parameters, analysis of the RE transition and comparison with theory are relatively easier. However, the extension of conclusions of such an analysis to processes of runaway electron generation and losses during disruptions must be cautious. In an International Tokamak Physics Activity (ITPA) experiment joining the results from DIII-D, TEXTOR, C-Mod, FTU and KSTAR, the density threshold for the suppression of RE generation has been found to be significantly lower than the theoretical critical density (Granetz et al. Reference Granetz, Esposito, Kim, Koslowski, Lehnen, Martin-Solis, Paz-Soldan, Rhee, Wesley and Zeng2014). The measured threshold is 10–12 times below the theoretical one on TEXTOR and DIII-D, 8.5 times below on FTU, and 4.5–5 times below on C-Mod and KSTAR. The shift of RE orbits from the magnetic surfaces and the diffusive losses of runaways due to magnetic fluctuations have been proposed as possible explanations (Paz-Soldan et al. Reference Paz-Soldan, Eidietis, Granetz, Hollmann, Moyer, Wesley, Zhang, Austin, Crocker and Wingen2014).
Further detailed investigation of the mechanisms of additional runaway electron losses and explanation of the gap between the classic theory and the experimental results are required. Another open question is the impurity penetration determined by the balance between magnetic field pressure and the gas jet pressure, which may lead to barely possible penetration of the gas jet into the ITER plasma centre.
Nonetheless, even without further developed theory, the reduction of critical density by several times gives cautious optimism that runaway electron generation suppression could be realised in ITER with lower requirements on the MGI.
5. Summary and conclusions
Runaway electrons are reliably generated in deliberately induced disruptions in TEXTOR due to the injection of a small amount of argon. However, no runaway electron phase has been observed in the case of consecutive massive helium injection by a fast valve with an amount above 2.5 bar l. This result is valid for the injection of helium no later than 5 ms after the triggering of a disruption. Injections above the threshold with 6 ms delay do not completely suppress the runaway electrons but only shorten the runaway plateau and increase the slope of its decay compared to the early but below-threshold injections. The experimentally observed density threshold is up to one order of magnitude below the critical value predicted by the Connor–Rosenbluth theory. The finding of a reduced density threshold remains valid even for the density estimation assuming uniform distribution of all non-ionised particles in the plasma. This issue could be explained by the absence of any additional mechanisms of runaway losses in the theory, such as the effects caused by a magnetic field. The result obtained is consistent with the density thresholds determined in experiments under quiescent conditions, which are below the theoretical value by a factor of 5–12. The significantly weakened condition on the critical density reduces the requirements on the MGI system for ITER.
