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Modelled plasma density (in colour) and flow contours (lines) after the pellet injection for (a) a 1.0 mm pellet and (b) a 2.1 mm pellet injected with a velocity of 100 ms −1 at the outer midplane of a DIII-D ITER-like plasma.  

Modelled plasma density (in colour) and flow contours (lines) after the pellet injection for (a) a 1.0 mm pellet and (b) a 2.1 mm pellet injected with a velocity of 100 ms −1 at the outer midplane of a DIII-D ITER-like plasma.  

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Edge localized mode (ELM) triggering by pellet injection in the DIII-D tokamak has been simulated with the non-linear MHD code JOREK with a view to validating its physics models. JOREK has been subsequently applied to evaluate the requirements for ELM control by pellet injection in ITER. JOREK modelling results for DIII-D show that the key paramete...

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... Previous studies on DIII-D [2,3], ASDEX Upgrade [4] and JET [5,6] have explored pellet ELM pacing in regimes with high collisionality [7] in the pedestal region, ν * ped > 2, due to the difficulty of achieving low density edge plasma conditions while injecting pellets. It is the general understanding that pellets trigger ELMs by providing a pressure perturbation in the plasma [1,8]. Therefore, it is beneficial for pellet ELM triggering to operate close to the ballooning stability limit. ...
... Hence, larger pellets are needed to trigger an ELM on the high field side. This is different from experiential observations in JET and JOREK simulations for higher pedestal collisionality [6,8]. While the next section will show the significance of pedestal collisionality on thresholds for pellet ELM triggering, clearly, more studies are needed here to fully understand the dynamics. ...
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In ITER, pellets are calculated to require more than 8 times the mass than currently planned to reliably trigger edge-localized modes (ELMs). Unmitigated heat flux impulses from ELMs are intolerable in ITER at full power and current. Therefore, ITER operation relies on multiple approaches to control ELM heat fluxes. One method is pellet ELM pacing to instigate small rapid ELMs with low heat flux. Predicting the performance of pellet pacing is critical for ITER, which is expected to operate in a regime with a low-collisionality, peeling-limited pedestal. However, to trigger ELMs the local pressure increase in the expanding pellet cloud pushes the equilibrium over the ballooning stability limit. In this work, linear and nonlinear M3D-C1 simulations are used to predict pellet mass thresholds in DIII-D discharges and ITER scenarios with peeling-limited pedestals. It is found that the distance of the equilibrium’s operational point from the ballooning branch of the pedestal stability boundary strongly changes thresholds. Linear M3D-C1 simulations find a strong dependence of the pellet mass threshold on the poloidal injection location for ITER’s 15 MA, Q = 10 scenario. The required pellet mass at the planned injection locations is 8 to 17 times larger than currently considered. However, such linear simulations do not include pellet ablation physics or time evolution of density and temperature. A new scheme of 2D nonlinear simulations, coupled with linear stability analysis at various steps throughout the nonlinear time evolution, was developed to include such physics and improve on the linear results. These new nonlinear-to-linear simulations confirm previous findings. This result suggests that pellet ELM triggering in ITER could require pellets much larger than those currently planned, which makes ELM-pacing operationally challenging. On the other hand, fueling pellets injected from the high-field side will likely not unintentionally trigger ELMs in an otherwise ELM-stable plasma.
... [4] As a key tool for providing a deep fueling, PI technology has been widely recognized to be more suitable for future fusion devices. [5][6][7][8] It is commonly used in current magnetic confinement fusion devices, such as DIII-D, [9] JT-60U, [10] HL-2A, [11] Tore Supra, [12] Alcator C-mod, [13] and EAST. [14,15] In 2012, a pellet fueling system with a frequency of 10 Hz was successfully developed for the EAST tokamak. ...
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... The realm of theoretical simulations has also made substantial contributions to PI studies. The non-linear MHD code JOREK has been utilized in DIII-D [11] and JET [12]. As shown in figure 10 of [12], the local high-density region caused by pellet ablation expands simultaneously along parallel and perpendicular magnetic field lines, with the parallel expansion velocity approaching the local ion sound speed C s0 . ...
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... The normal expectation is that the parallel transport of impurity ions is driven by the plasma power flux from the surrounding high-temperature but low-density plasmas into the much colder and denser pellet ions. Since previous studies have mostly used fluid or MHD models, the plasma power flux is usually modeled by Braginskii closures, with possibly flux limiting in the initial hightemperature phase to approximate the long-mean-freepath effect on heat flux [16,17]. However, recent work reveals the subtle parallel transport physics that can regulate the plasma power flux reaching the impurity ions and thus affect the surrounding plasma cooling [18,19], the essential complication of which is indicated by various fronts in Fig. 1 (notice that an artificial boundary that mimics the radiative pellet cloud was previously used in Ref. [18,19]). ...
... Therefore, the impurity front would stay behind the cooling front. Equation (16) also reveals that the impurity front speed is actually dominated by the electron temperature, and hence the key problem is how the electron temperature is developed at and behind the impurity front, which will be discussed in next section. Before answering this question, we first show the numerical verification of the self-similar solution in Fig. 7 and Table I, where the relative error between the impurity front speed from the simulations and the self-similar solutions is within 25%. Figure 7 also reaffirms that the impurity front propagates nearly steadily. ...
... This mechanism can be quantified if we consider again Eq. (9) and assume linear profiles of ln(n e ) and ln(T e∥ ), where 25% of the domain near the impurity front contributes 50% of the integral forc s . Therefore, bothc s and c s (IF) are dominated by the surrounding hot plasmas and so is the impurity front speed as seen from Eq. (16). ...
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The assimilation of ablated high-Z impurities into the hot surrounding plasma along the magnetic field is investigated by first-principles kinetic simulations. It is found that the assimilated impurity ions, primarily driven by the ambipolar electric force, propagate steadily into the surrounding plasmas. The high-Z impurities in different charge states are mostly aligned due to the strong collisional friction among them so that the averaged impurity ions chargeZ is a deciding factor. Such assimilation is led by an impurity front that is behind the cooling front due to a smaller charge-mass-ratio of the impurity ionsZ/m I. With the help of a self-similar solution, the speed of the impurity front U s is shown to be primarily set by the hot surrounding plasma temperature T 0 with a weak dependence on the pellet plasma temperature, underscoring the collisionless nature of the impurity assimilation process. Specifically, U s ∼ Z T 0 /m I. The ambipolar-constrained electron conduction flux from the hot plasma is primarily responsible for the collisionless impurity assimilation process.
... The obtained result differs quantitatively from earlier obtained results [8] but it is the same in principle. It is seen that, in the significant fraction of the working window with τ p /τ E > 1.7 for α ELM = 0.2 and with τ p /τ E > 1. Estimates of the size of LFS pellets required for reliable initiation of ELMs (for example, [26]) by the method described in [23] give the value of ~1.0 mm 3 . This agrees with modern experimental data from JET, DIII-D, and ASDEX Upgrade [23]. ...
... Of the experimental data accessible in open literature, only the results from Alcator C-Mod [31,32] can be compared with the DEMO-FNS and ITER facilities. Estimates of the size of LFS pellets required for reliable initiation of ELMs (for example, [26]) by the method described in [23] give the value of~1.0 mm 3 . This agrees with modern experimental data from JET, DIII-D, and ASDEX Upgrade [23]. ...
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Modeling the D and T fluxes in Fusion Neutron Source based on a tokamak fuel cycle systems was performed consistently with the core and divertor plasma. An indirect integration of ASTRA, SOLPS4.3, and FC-FNS codes is used. The feedback coupling is realized between the pumping and puffing systems in the form of changes in the isotopic composition of the core and edge plasma. In the ASTRA code, instead of electrons, ions were used in the particle transport equations. This allows better estimates of the flows of the D/T components of the fuel that have to be provided by the gas puffing and processing systems. The particle flows into the plasma from pellets, required to maintain the target plasma density = (6–8) × 1019 m−3 are 1022 particles/s. In the majority of the working range of parameters, additional ELM stimulation is necessary (by ~1-mm3-size pellets from the low magnetic field side) in order to maintain the controlled energy losses at the level δWELM~0.5 MJ. For the starting load of the FC and steady-state operation of the facility, up to 500 g of tritium are required taking into account the radioactive decay losses.
... This effect should tend to vanish in the large neon mixture-ratio limit due to the reduction of the local pressure peak by radiation [46]. Further, we also expect the H mode pedestal to be strongly destabilized by the vanguard fragments [47], this would likely to cause premature thermal energy loss before deep fragment penetration. On the other hand, whether we will really perform SPIs into a full H-model in reality is uncertain, as significant thermal energy loss would likely occur already in the pre-TQ phase of disruptions, and many disruptive discharges would see the transition back to L-mode before the SPI system is triggered [48]. ...
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Recent studies suggest significant time delay between the Shattered Pellet Injection (SPI) fragment arrival and the temperature radiative collapse could exist in ITER, depending on the impurity assimilation and the plasma thermal reservoir. Hence in some cases the fragments could reach the core even before the edge radiative collapse occurs and triggers strong stochastic transport. This could be beneficial for heat load mitigation and hot-tail runaway electron suppression. To investigate the expected assimilation and radiation, thus the MHD response after SPIs in 3D, we carry out simulations of collisional-radiative impurity mixed SPIs into ITER L-mode equilibrium. Localized cooling around the fragments is found to cause current perturbations which destabilize MHD modes. Meanwhile, slower injections are found to result in stronger and more complete radiative collapse, thus stronger MHD amplitude. Due to the $q=1$ surface enclosing a significant volume, the $1/1$ resistive kink mode is shown to couple with outer modes to bring global stochasticity and convective core density mixing, although a transport barrier outside of the $q=1$ surface prevents immediate temperature relaxation over the whole plasma. The impact of various physical assumptions and numerical treatments, such as the use of the flux-averaged ambient plasma parameters for ablation calculation, the exclusion of the magnetic constraining effect in ablation, the localization of the density source and the use of constant parallel thermal conduction instead of the Braginskii one and different injection velocities are also investigated. In general, stronger and more localized ablation results in stronger radiation, faster radiative collapse and a more violent MHD response, while the assimilation changes little due to a self-regulation effect.
... The pellet is presently assumed to move along a straight line with constant velocity, and its particle content (and physical size) is evolved according to the ablation. The toroidal extension δφ c of the ablation cloud in simulations is typically far larger than in reality due to limited toroidal resolution, but tests shown in Ref. [87] for a Deuterium pellet found that for a sufficiently small δφ c , JOREK results converge, i.e. MHD dynamics becomes independent of δφ c . ...
... A lot more verification work can be found in the literature. E.g., the JOREK pellet model has been successfully benchmarked, for a Deuterium pellet, with a dedicated code by B. Pégourié, as can be seen in Fig. 2 of Ref. [87]. Note that all the validation against experiments is included along with the physics studies in Sections 5-7. Figure 12 shows an example to demonstrate that the finite element solutions are G 1 continuous and (if resolved well) smooth. ...
... These strong perturbations are associated to a pellet triggered ELM crash and induce losses from the plasma. Re-print from Ref. [87]. ...
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JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.
... A more refined treatment of the ablation physics is investigated separately from this work. For an in-depth description of the pellet module used, the reader is referred to Ref. [28]. ...
... Further relevant simulations with JOREK include: spontaneous ELMs with realistic plasma background flows [20], RMP penetration [29,30], investigation of ELM-RMP interactions [31], Quiescent H-Mode [32], triggering of ELMs by vertical magnetic kicks [33], and a direct comparison of the divertor heat fluence caused by spontaneous ELMs to experimental scaling laws [21]. Pellet ELM triggering has also been studied with JOREK before, providing an explanation for the mechanism of pellet ELM triggering by a localised increase of the pressure in the re-heated ablation cloud and including experimental comparisons to JET and DIII-D [34,28,35]. An overview of ELM related non-linear MHD simulations worldwide is given in Ref. [36]. ...
... The relative difference between the ELM-related thermal energy lost between the ELM crash simulated with n = 0 − 3 − 15 and n = 0 − 3 − 30 was found to be ∼ 4 %. When simulating pellet injection, it is not possible to use a "periodicity" greater than 1 because the n = 1 toroidal mode number is always needed and typically observed to be dominant [28,35]. As a result, the toroidal discretisation in JOREK must contain the entire mode spectrum, i.e., the entire torus has to be simulated. ...
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Injecting frozen deuterium pellets into an ELMy H-mode plasma is a well established scheme for triggering edge localized modes (ELMs) before they naturally occur. This paper presents non-linear simulations of spontaneous type-I ELMs and pellet-triggered ELMs in ASDEX Upgrade performed with the extended MHD code JOREK. A thorough comparison of the non-linear dynamics of these events is provided. In particular, pellet-triggered ELMs are simulated by injecting deuterium pellets into different time points during the pedestal build-up described in A Cathey et al (2020 Nuclear Fusion 60 124007). Realistic ExB and diamagnetic background plasma flows as well as the time dependent bootstrap current evolution are included during the build-up to accurately capture the balance between stabilising and destabilising terms for the edge instabilities. Dependencies on the pellet size and injection times are studied. The spatio-temporal structures of the modes and the resulting divertor heat fluxes are compared in detail between spontaneous and triggered ELMs. We observe that the premature excitation of ELMs by means of pellet injection is caused by a helical perturbation described by a toroidal mode number of n = 1. In accordance with experimental observations, the pellet-triggered ELMs show reduced thermal energy losses and a narrower divertor wetted area with respect to spontaneous ELMs. The peak divertor energy fluence is seen to decrease when ELMs are triggered by pellets injected earlier during the pedestal build-up.
... The density source is poloidally localised to a narrow area, and it is stretched to span a user-defined toroidal arc. The adiabatic density source moves with the pellet position, and its time-dependent amplitude results from the neutral gas shielding ablation model as described in [27]. For a given time point this model describes the number of particles that are ionised and become part of the bulk plasma. ...
... Further relevant simulations with JOREK include: spontaneous ELMs with realistic plasma background flows [20], RMP penetration [28,29], investigation of ELM-RMP interactions [30], Quiescent H-Mode [31], triggering of ELMs by vertical magnetic kicks [32], and a direct comparison of the divertor heat fluence caused by spontaneous ELMs to experimental scaling laws [21]. Pellet ELM triggering has also been studied with JOREK before, providing an explanation for the mechanism of pellet ELM triggering by a localised increase of the pressure in the re-heated ablation cloud and including experimental comparisons to JET and DIII-D [33,27,34]. An overview of ELM related non-linear MHD simulations worldwide is given in Ref. [35]. ...
... When simulating pellet injection, it is not possible to use a "periodicity" greater than 1 because the n = 1 toroidal mode number is always needed and typically observed to be dominant [27,34]. As a result, the toroidal discretisation in JOREK must contain the entire mode spectrum, i.e. the entire torus has to be simulated. ...
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Injecting frozen deuterium pellets into an ELMy H-mode plasma is a well established scheme for triggering edge localized modes (ELMs) before they naturally occur. Based on an ASDEX Upgrade H-mode plasma, this article presents a comparison of extended MHD simulations of spontaneous type-I ELMs and pellet-triggered ELMs allowing to study their non-linear dynamics in detail. In particular, pellet-triggered ELMs are simulated by injecting deuterium pellets into different time points during the pedestal build-up described in [A. Cathey et al. Nuclear Fusion 60, 124007 (2020)]. Realistic ExB and diamagnetic background plasma flows as well as the time dependent bootstrap current evolution are included during the build-up to capture the balance between stabilising and destabilising terms for the edge instabilities accurately. Dependencies on the pellet size and injection times are studied. The spatio-temporal structures of the modes and the resulting divertor heat fluxes are compared in detail between spontaneous and triggered ELMs. We observe that the premature excitation of ELMs by means of pellet injection is caused by a helical perturbation described by a toroidal mode number of n = 1. In accordance with experimental observations, the pellet-triggered ELMs show reduced thermal energy losses and narrower divertor wetted area with respect to spontaneous ELMs. The peak divertor energy fluency is seen to decrease when ELMs are triggered by pellets injected earlier during the pedestal build-up.
... The secondary ELM control scheme in ITER relies on the control of the ELM frequency by pellet injection [44,62,71]. This is expected to require up to 30-60% of the total throughput since the estimated pellet size for ELM triggering is ∼1-2 × 10 21 DT atoms/pellet [44] and the triggering of ELMs reduces the fueling ef ciency of pellets [72]. ...
... The secondary ELM control scheme in ITER relies on the control of the ELM frequency by pellet injection [44,62,71]. This is expected to require up to 30-60% of the total throughput since the estimated pellet size for ELM triggering is ∼1-2 × 10 21 DT atoms/pellet [44] and the triggering of ELMs reduces the fueling ef ciency of pellets [72]. Integrated edge-core plasma simulations including ELM control by pellet pacing have been carried out taking into account HFS pellet injection for core plasma fueling, LFS pellet injection for ELM control and gas and impurity fueling for divertor power load control [74]. ...
Article
The tritium aspects of the DT fuel cycle embody some of the most challenging feasibility and attractiveness issues in the development of fusion systems. The review and analyses in this paper provide important information to understand and quantify these challenges and to define the phase space of plasma physics and fusion technology parameters and features that must guide a serious R&D in the world fusion program. We focus in particular on components, issues and R&D necessary to satisfy three ‘principal requirements’: (1) achieving tritium self-sufficiency within the fusion system, (2) providing a tritium inventory for the initial start-up of a fusion facility, and (3) managing the safety and biological hazards of tritium. A primary conclusion is that the physics and technology state-of-the-art will not enable DEMO and future power plants to satisfy these principal requirements. We quantify goals and define specific areas and ideas for physics and technology R&D to meet these requirements. A powerful fuel cycle dynamics model was developed to calculate time-dependent tritium inventories and flow rates in all parts and components of the fuel cycle for different ranges of parameters and physics and technology conditions. Dynamics modeling analyses show that the key parameters affecting tritium inventories, tritium start-up inventory, and tritium self-sufficiency are the tritium burn fraction in the plasma ( f b ), fueling efficiency ( η f ), processing time of plasma exhaust in the inner fuel cycle ( t p ), reactor availability factor (AF), reserve time ( t r ) which determines the reserve tritium inventory needed in the storage system in order to keep the plant operational for time t r in case of any malfunction of any part of the tritium processing system, and the doubling time ( t d ). Results show that η f f b > 2% and processing time of 1–4 h are required to achieve tritium self-sufficiency with reasonable confidence. For η f f b = 2% and processing time of 4 h, the tritium start-up inventory required for a 3 GW fusion reactor is ∼11 kg, while it is <5 kg if η f f b = 5% and the processing time is 1 h. To achieve these stringent requirements, a serious R&D program in physics and technology is necessary. The EU-DEMO direct internal recycling concept that carries fuel directly from the plasma exhaust gas to the fueling systems without going through the isotope separation system reduces the overall processing time and tritium inventories and has positive effects on the required tritium breeding ratio (TBR R ). A significant finding is the strong dependence of tritium self-sufficiency on the reactor availability factor. Simulations show that tritium self-sufficiency is: impossible if AF < 10% for any η f f b , possible if AF > 30% and 1% ⩽ η f f b ⩽ 2%, and achievable with reasonable confidence if AF > 50% and η f f b > 2%. These results are of particular concern in light of the low availability factor predicted for the near-term plasma-based experimental facilities (e.g. FNSF, VNS, CTF), and can have repercussions on tritium economy in DEMO reactors as well, unless significant advancements in RAMI are made. There is a linear dependency between the tritium start-up inventory and the fusion power. The required tritium start-up inventory for a fusion facility of 100 MW fusion power is as small as 1 kg. Since fusion power plants will have large powers for better economics, it is important to maintain a ‘reserve’ tritium inventory in the tritium storage system to continue to fuel the plasma and avoid plant shutdown in case of malfunctions of some parts of the tritium processing lines. But our results show that a reserve time as short as 24 h leads to unacceptable reserve and start-up inventory requirements. Therefore, high reliability and fast maintainability of all components in the fuel cycle are necessary in order to avoid the need for storing reserve tritium inventory sufficient for continued fusion facility operation for more than a few hours. The physics aspects of plasma fueling, tritium burn fraction, and particle and power exhaust are highly interrelated and complex, and predictions for DEMO and power reactors are highly uncertain because of lack of experiments with burning plasma. Fueling by pellet injection on the high field side of tokamak has evolved to be the preferred method to fuel a burning plasma. Extrapolation from the DIII-D penetration scaling shows fueling efficiency expected in DEMO to be <25%, but such extrapolations are highly uncertain. The fueling efficiency of gas in a reactor relevant regime is expected to be extremely poor and not very useful for getting tritium into the core plasma efficiently. Gas fueling will nonetheless be useful for feedback control of the divertor operating parameters. Extensive modeling has been carried out to predict burn fraction, fueling requirements, and fueling efficiency for ITER, DEMO, and beyond. The fueling rate required to operate Q = 10 ITER plasmas in order to provide the required core fueling, helium exhaust and radiative divertor plasma conditions for acceptable divertor power loads was calculated. If this fueling is performed with a 50–50 DT mix, the tritium burn fraction in ITER would be ∼0.36%, which is too low to satisfy the self-sufficiency conditions derived from the dynamics modeling for fusion reactors. Extrapolation to DEMO using this approach would also yield similarly low burn fraction. Extensive analysis presented shows that specific features of edge neutral dynamics in ITER and fusion reactors, which are different from present experiments, open possibilities for optimization of tritium fueling and thus to improve the burn fraction. Using only tritium in pellet fueling of the plasma core, and only deuterium for edge density, divertor power load and ELM control results in significant increase of the burn fraction to 1.8–3.6%. These estimates are performed with physics models whose results cannot be fully validated for ITER and DEMO plasma conditions since these cannot be achieved in present tokamak experiments. Thus, several uncertainties remain regarding particle transport and scenario requirements in ITER and DEMO. The safety standard requirements for protection of the public and release guidelines for tritium have been reviewed. General safety approaches including minimizing tritium inventories, reducing tritium permeation through materials, and decontaminating material for waste disposal have been suggested.