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Conceptual design study of pellet fueling system for DEMO
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Conceptual design study of pellet fueling system for DEMO S. Tokunaga ∗ , A. Matsuyama, Y. Someya, H. Utoh, Y. Sakamoto, N. Asakura, K. Tobita, Joint Special Team for Fusion DEMO Rokkasho Fusion Institute, National Institutes for Quantum and Radiological Science and Technology (QST), Aomori, Japan
h i g h l i g h t s • A conceptual design of pellet fueling system for JA-DEMO is presented. Requirements are assessed from viewpoints of both plasma response and restriction of device.
• Simulation study of simple fusion output control by fueling pellet using transport code is demonstrated to estimate the requirements for fuel particle source.
• Massive parameter scan of pellet ablation and drift simulation is carried out to evaluate effects of pellet speed, injection angle, pellet mass on deposition depth.
• Dominant impact of pellet guide tube layout on critical velocity for pellet survivability is shown. Specifications of fueling system for DEMO consistent for both plasma and device are given at last.
a r t i c l e
i n f o
Article history: Received 4 October 2016 Received in revised form 15 February 2017 Accepted 22 February 2017 Available online xxx Keywords: DEMO Pellet Fueling Control
a b s t r a c t Requirements for pellet injection system for a Japanese DEMO concept are comprehensively assessed in order to elucidate direction and target of R&D. A fusion output control simulation study using 1.5D transport code is carried out to estimate requirement of fuel particle source. Next, multivariable parameter dependence survey of the fuel deposition source on pellet speed, poloidal injection angle, pellet mass and pedestal height is performed. The conditions to achieve the target fueling depth derived from the output control study are shown. The AUG calibrated relation is referred to consider spatial restriction of tokamak geometry which relates maximum pellet velocity to curvature of pellet guide tube. Then the restriction is collated to the results of multivariable survey to find the most advantageous pellet speed, injection angle, and pellet mass which is consistent with both output control and tokamak geometry. Consequently, a conceptual design of fuel pellet injection system as the R&D target toward to DEMO is proposed. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Robust fusion output power controllability is one of the essential requirement for DEMO reactor. Fuel supply is expected as the most promising robust control knob of the fusion output. And pellet injection is considered as the primary fueling technique in DEMO as well as ITER [1]. Main difference of requirement for fueling system in DEMO from ITER comes from demand for the larger fusion output. It consequences requirement of more fueling efficiency to obtain higher fuel density under the conditions of density limit as well as sufficient purity against to the larger He ash generation.
Furthermore, in DEMO, necessity of self-sustaining tritium breeding and severe heat and neutron load results thicker in-vessel components (blanket and shielding structure) than ITER. It leads to larger major radius Rp of plasma. If we fix the q95 , the larger Rp leads to lower Ip , it means lower Greenwald density limit. Therefore, the density limit in DEMO tends to become tighter condition even compared to ITER. The fuel pellet injector in DEMO has to be designed so as to satisfy such a tighter edge density condition, the larger demand of fusion output and sufficient particle throughput to avoid He dilution, simultaneously.
2. Fusion output control simulation ∗ Corresponding author. E-mail address: [email protected] (S. Tokunaga).
In order to translate such demands for DEMO fueling system, to quantitative request specification of pellet injection system, we
http://dx.doi.org/10.1016/j.fusengdes.2017.02.079 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
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start from the consideration of response of burning plasma to fuel pellet. We used a rather simple 1.5D transport code (ATLAS) for fusion output control simulation. The ATLAS is being developed in QST aiming to be used as a fusion plant control simulator. At this moment, simple transport model based on the mixed Bohm/gyroBohm (BgB) model [2] is implemented. It solves particle and energy transport for each species (e, D, T and He in this study). In addition, an artificial mechanism to mimic pedestal formation at the empirical power threshold of L-H transition, by shrinking mixing length in the Bohm-like term of BgB into gyro-Bohm-like one which is proportional to Larmor radius with a tuning factor is implemented. The factor is tuned to reproduce assumed HH98y2 factor. Particle diffusivity D is also determined by BgB formulation. Particle pinch v profile is also given by input in the form of v˜ ≡ v/(aD) to reproduce given assumed peaking rate (1.3 in the following) if there is no particle source in the plasma column. Profile control is beyond of the scope of the present study. The fuel pellet appears as particle source with fixed profile. The profile is computed from given peak position, number of atom and melting time. In this study, the melting time of pellet dominates time step size of the transport calculation, and is set as 25 ms (much longer than typical actual time scale, 1 ms) for convenience. The 1 ms of melting time results more than 25 times longer computation time (a few days per a case). It is unacceptably inconvenient for this conceptual design study. The other fast mechanism, e.g., MHD, micro-instabilities and so on are not modeled either. Temporal evolution shown in this section should be regarded as smoothed variation averaging these fast behaviors. The fusion output control is assigned to DT pellet with simple ON/OFF feedback control logic based on neutron measurement. Decision of injection is made every 0.1 s based on neutron detector signal. Simply, if the detected fusion output is lower than the given target value at the moment, the fuel particle source appears during the melting time. The edge density is cared by D puff to be kept at least 70% of the Greenwald limit. Non-inductive current drive is controlled by On-axis 1 MeV D-NBI power. These settings are arranged to separate the role of each actuator as much as possible by minimizing side effects for simple and robust control. The calculation is based on a JA-DEMO concept parameters, Pfus = 1.5 GW, major radius Rp = 8.2 m, minor radius ap = 2.56 m, elongation = 1.70, 98(y,2)
Ip = 14.6 MA, HH = 1.25, ne =5.9 × 1019 m−3 , Greenwald density limit nGW = 7 ×1019 m−3 , the plasma volume V = 1800 m3 and expected He dilution rate He = 0.07. For a rough understanding of particle confinement time scale, let us consider the 0D particle balance for Helium. Based on the above parameters, from rela∗ = 3.55 × 1020 P tions nHe /ne ≤ He and V nHe /He fus [GW ] , we ∗ can obtain He 200He = 14 s. Extremely torrent throughput is demanded from the viewpoint of particle balance. Fig. 1 shows waveform from a fusion output control simulation of (A) currents, (B) fuel supply by pellet, (C) volume averaged densities and (D) fusion output. The pellet mass is 2.0E+21 atom/pel (D:T = 25%:75%), which is corresponding to ∼2% of the total stored particle inside separatorix. It starts after the Ip reaches flattop by induction. The plasma starts with almost D 100%, and the density at r/a ∼ 0.9 is controlled to be 70% of Greenwald limit by D-puff. It is approach from the safety side for divertor. The target value of fusion output is raised step by step as shown by blue line in Fig. 1(D). It can be also regarded as steps of power ascension testing scenario. The L-H transition takes place at t ∼ 220 s. Density ETB formation consequences sudden reduction of needed fuel supply (Fig. 1(B)). The feedback control of NBI power starts from t ∼ 300, and achieves steady state at t ∼ 330 s (Fig. 1(A)). The good controllability of fusion output by pellet fueling absorbing effect of the improvement of confinement and the modification of current drive power is apparently shown. In case with D:T ratio always fixed to 50%:50% for all sources, i.e., renouncing the degree of freedom of D:T ratio as control knob, the fusion output is more strongly coupled with these
Fig. 1. Temporal evolution (A) current, (B) fuel source by pellet, (C) density and (D) fusion output power in reference case.
effects. Particle confinement time p∗ depends on transport, exhaust rate and distribution of particle source itself. The exhaust rates for each species are presumed as 2% for D and T, 1% for He in this calculation. They should be changed depending on structure of divertor in future works. The weight of particle source is temporally varying. Increase of the pellet source with shallow deposition shortens p∗ . The increase of temperature also shortens p∗ by making position of ionization of puffed or recycled particle be shallower. Although it is difficult to know appropriate p∗ for fuel particle with large discrete source like pellet, the confinement time of He as a measure of ∗ ∼8 s at t = 180, ∼25 s at t = 300 particle confinement changes as He and ∼22 s at t = 540. The longer confinement time than 0D estimation could be affected by the ne which exceeds the expected value and peaking rate of He ∼1.65 which is larger than one of DT ∼1.4. The pellet injection frequency in the flattop phase (Pfus = 1.5 GW) is ∼5 Hz (1.0E+22 atom/s) in this case. Fig. 2 shows results from another case with pellet mass Mpel = 4.0E+21 atom/pel (∼4% of total stored particle) and deposition peak at r/a=0.9 (∼ pedestal top) (Fig. 2(A)). In this case, the oscillation of fusion output during flattop (Pfus = 1.5 GW) is 2.5∼3
Fig. 2. (A) pellet deposition profile with Mpel =4E+21 atom/pel and deposition peak at r/a = 0.9. Profile variation during a fusion output oscillation period of (B) electron density, (D) ion temperature and (D) number of He generation. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
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times larger than one in the case with Mpel = 2.0E+21. Such oscillation of output is caused by delayed response of fusion output with the control logic. In this simulation, the delay of response was resulted by 2 reasons, (1) delay of core density response from the particle supply to the edge and (2) plasma cooling effect by pellet (phase shift of temperature from density). The former reason should not be changed by pellet mass with the current transport model. The latter cooling effect causes not only delay but also decrease of fusion output. Fig. 2 (B, C, D) show responses of electron density, ion temperature and He generation (number of DT fusion reaction) integrated over each flux tube, during one period of fusion output oscillation. The time slices are indicated by red line (injection start) at first, then advance to yellow (stop of injection), green (transport to core) then blue (total output becomes less than target) at last. Fig. 2(D) looks like the bottom half is red, and upper half is green∼blue. Thus the boundary between red and blue is close to profile with targeted fusion output. The fusion output decreases when pellet injection starts, then overshoot after it stopped. Such overcooling-overshoot cycle becomes larger when the background ion temperature is lower or the pellet is larger. It is deduced that such cooling effect of the larger pellet could cause 2.5∼3 times larger fluctuation with 2 times larger pellet. The current ON/OFF pellet control logic continues injection as long as the fusion output response is delayed. It consequences too large deviation of density profile from the favorable profile (Fig. 2(B)). These results provide insights of requirements for fueling. (1) Importance to minimize overcooling effect for output control. Disadvantage of large pellet and shallow deposition is emphasized from this. (2) Development of smart control logic considering the delay of fusion output is needed. Furthermore, there are several expected physics issues related to fueling that are not considered in the present transport model, e.g., confinement degradation due to density limit, ELM trigger by deposition on pedestal, and stiffness of core temperature profile response dropping with pedestal temperature. They come down to the (3) importance to deposit fuel inside of pedestal top and to reduce deposition on pedestal region as much as possible, (4) and also importance of predicting radial width of deposition profile. As the consequence of the above consideration we set the target depth of fuel pellet deposition peak as r/a = 0.85 for the following sections.
Fig. 3. Tokamak geometry including TFC, vacuum vessel (VV), back plate (BP), tritium breeding blanket (BLK) and plasma. Spatial relationships between target flux tube and injection point, pellet guide tube curvature radius Rc and injection angle () are shown. Pink filled area is closed by TFC. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
peak position is shown in Fig. 4. It is noted that the lower pedestal temperature tends to result in shallower deposition. It is because, the higher background temperature drives pellet drift stronger. In DEMO plasma with several keV pedestal temperature, effect of drift is dominant than ablation. The lower pedestal is not favorable for fueling. Considerable dependence on injection angle is shown. The difference between = 105–120 is significant in every plot. = 105 gives insufficient deposition depth in many case even with 3000 m/s. The speed and angle dependence are stronger in lowpedestal cases, because the ablation becomes relatively important
3. Pellet ablation-drift simulation It is easily shown by NGS Scaling [3] that reaching r/a ∼ 0.85 as ablation profile is difficult. Then pellet drift [4,5] must be utilized to achieve the target. It means injection from high-field side (HFS) is mandatory. Z-coordinate of the magnetic axis of plasma equilibrium of current JA-DEMO is shifted upward to secure the sufficient space for divertor. It immediately leads to conclusion that fuel injection from Upper-HFS is the most rational choice. Hence, it is different from ITER. Fig. 3 indicates the geometry. The pellet cloud drifts horizontally to +R direction. Upper and lower edge of the flux tube corresponding to the target depth are indicated by orange lines. Z-coordinate of the injection point on plasma surface must locate in-between the lines. Apparently, the injection angle is spatially restricted by the geometry. In order to evaluate the requirements to achieve the target depth r/a = 0.85, we have carried out a massive scan simulation survey of the pellet deposition by the use of pellet ablation-drift simulation code HPI2 [6]. The background data are imported from the transport simulation. Scan calculation are done for 4 pellet injection speeds 1000, 1500, 2000, 3000 m/s, 4 injection poloidal angles 105, 120, 135, 150 degrees (Fig. 3), 3 pellet sizes corresponding to the number of atoms 2E+21, 4E+21, 6E+21, and 3 kinds of pedestal temperature 3, 6, 9 keV, 144 cases in total. The scan results of deposition
3
Fig. 4. Scan results of peak position of pellet deposition profile.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
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Table 1 Critical velocity vc for each 3different injection angles and pellet sizes. Mpel [atm/pel]
2E+21
4E+21
6E+21
Lpel [mm] vc (Rc = 10 m, = 120) [m/s] vc (Rc = 1 m, = 135) [m/s]
2.0 2571 813
2.8 2173 687
5.1 1610 509
in these cases. The pellet size dependence is also stronger in lowpedestal temperature cases due to the same reason. Gray hatched area is explained in the next section. 4. Discussion In order to think of the consistency between the tokamak geometry and the requirement for pellet, we introduce useful empirical formulation: AUG Calibrated Relationship [7], vc [m/s] = 1150 Rc [m]/Lpel [mm], where, Rc is curvature radius of pellet guide tube (PGT) in metre, Lpel is diameter length of pellet in millimetre. It enables to estimate trade-off relationship between available speed and angle coupled by curvature of PGT layout. The 3 pellet sizes 2e+21, 4e+21, 6e+21 atom/pel are corresponding to about 2.0 mm, 2.8 mm, 5.1 mm, respectively. The poloidal injection angle and PGT curvature are intimately related as shown in Fig. 3. Now corresponding PGT curvature radii for = 120 and = 135 are estimated as 10 m and 1 m, respectively. The evaluated critical speed is shown in Table 1. Strong disadvantage of small curvature radius is apparently shown. Tight limitation of critical speed for Large (6E+21 atom) pellet is also apparent. Based on these estimation of the critical speed, unavailable area for combination of the pellet speed and angle are roughly depicted in the Fig. 4 as grayhatched area. In these hatched areas, pellet cannot be delivered to plasma without breaking apart. Such PGT layout appears as the strongest constraint for pellet deposition depth. As a consequence of the above considerations, it is concluded that, = 120 degrees, pellet mass 4 × 1021 atom/pel should be the most favorable conditions for the current geometry of DEMO regardless to the pedestal temperature. Then about 2∼3 Hz of frequency for the corresponding pellet size is required. The pellet speed faster than 2000 m/s should be necessary to reach the target depth r/a = 0.85. Each of these values is not unrealistic, but enough imaginable from the currently available foresighted technologies [8]. In consideration of the range of needed injection speed, double-pneumatic gun is regarded as the promising acceleration technology. Supposing the duration of in-situ production of pellet ice in gun-barrel as 30 s (0.033 Hz), 3 Hz of injection frequency needs 90 barrels. Since the number of the injection route into VV is restricted by number of TFC (16∼20), multi-barrel injector [9] technology will be useful. Sophisticated fuel circulation system will be also the essential engineering subject to minimize tritium inventory [10]. Supplementarily, it is important to stress that the STRAIGHT pellet injection route does completely contradict to requirement for neutron shielding. The injection route needs straight “embrasure” on shielding structure (Fig. 3). As the rough estimation, suppose a point source (flux) of neutron 1014 at first wall and the embrasure with 2 cm × 2 cm cross section and 120 cm of length, neutron
flux of 2 × 109 [n/cm2 /s] on VV is obtained. It is 1-order higher than the allowable level. Additional neutron shielding structure must be equipped on VV around the embrasure. It is also concerned that the AUG calibrated relationship is based on experiments with pure D2 pellet. The critical velocity of tritium-mixed pellet would be different [11]. It would affect the optimized relationship between injection speed and angle. It is stressed that the bottle-neck of the injection speed is the PGT curvature and plasticity of pellet, not the accelerating technology. Dope of the other element to enhance pellet plasticity [12] may be beneficial technique from such a viewpoint. 5. Summary Conceptual design study of pellet injection system for JA-DEMO has been carried out. Comprehensive consideration about requirements for fueling system including plasma response and spatial restriction from tokamak geometry was presented. Requirements for the fuel source from the viewpoint of plasma response were studied by fusion output control simulation using a 1.5D transport code. It was shown that delay of fusion output response caused by cooling effect can result fluctuation of fusion power. Setting target depth of the pellet deposition peak as r/a = 0.85, a massive parameter scan survey using pellet ablation-drift code was performed in order to estimate the required pellet injection speed, angle and mass. It was shown that lower pedestal temperature tend to result shallower deposition of the pellet. The spatial restriction of PGT curvature was considered by the use of AUG Calibrated Relation. As the consequence of above considerations, concept of the DEMO fueling system as the development target has been estimated as following. Injection from Upper-HFS with speed faster than 2000 m/s, 120 degrees of poloidal angle, pellet mass 4E+21 atom/pel, 10 m PGT curvature radius, 3 Hz of injection frequency as the whole system, which will be consist of 90 barrels of double pneumatic guns. Acknowledgements The author ST acknowledges Prof. R. Sakamoto for fruitful discussions. This work was supported by the Broader Approach and JSPS Grant-in-Aid for Scientific Research; KAKENHI No. 25889068. A number of calculations were enabled by HELIOS supercomputer at International Fusion Energy Research Centre. References [1] L.R. Baylor, et al., Nucl. Fusion 47 (2007) 443–448. [2] M. Erba, et al., Plasma Phys. Control. Fusion 39 (1997) 261; T. Tala, et al., Nucl. Fusion 46 (2006) 548–561. [3] L.R. Baylor, A. Geraud, et al., Nucl. Fusion 37 (1997) 445. [4] P.T. Lang, et al., Phys. Rev. Lett. 79 (1997) 1487. [5] L.R. Baylor, et al., Phys. Plasmas 7 (2000) 1878. [6] B. Pegourie, et al., Nucl. Fusion 47 (2007) 44. [7] P.T. Lang, et al., Fusion Eng. Des. 96 (2015) 123–128. [8] S. Sudo, M. Kanno, H. Kaneko, et al., 15th Symposium on Fusion Energy (Cape Cod, U.S.A.), 1993, 1-PA-3. [9] A. Frattolillo, et al., Rev. Sci. Instrum. 69 (1998) 2675. [10] B. Ploeckl, et al., Fusion Eng. Des. 96 (2015) 155–158. [11] W. Fisher, ORNL/TM-11781, Oak Ridge National Laboratory, June 1991. [12] L.A. Alekseeva, et al., Phys. Solid State 48 (2006) 1513; L.A. Alekseeva, Czech. J. Phys. 46 (Suppl. S1) (1996) 519.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
ARTICLE IN PRESS
FUSION-9149; No. of Pages 4
Fusion Engineering and Design xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Conceptual design study of pellet fueling system for DEMO S. Tokunaga ∗ , A. Matsuyama, Y. Someya, H. Utoh, Y. Sakamoto, N. Asakura, K. Tobita, Joint Special Team for Fusion DEMO Rokkasho Fusion Institute, National Institutes for Quantum and Radiological Science and Technology (QST), Aomori, Japan
h i g h l i g h t s • A conceptual design of pellet fueling system for JA-DEMO is presented. Requirements are assessed from viewpoints of both plasma response and restriction of device.
• Simulation study of simple fusion output control by fueling pellet using transport code is demonstrated to estimate the requirements for fuel particle source.
• Massive parameter scan of pellet ablation and drift simulation is carried out to evaluate effects of pellet speed, injection angle, pellet mass on deposition depth.
• Dominant impact of pellet guide tube layout on critical velocity for pellet survivability is shown. Specifications of fueling system for DEMO consistent for both plasma and device are given at last.
a r t i c l e
i n f o
Article history: Received 4 October 2016 Received in revised form 15 February 2017 Accepted 22 February 2017 Available online xxx Keywords: DEMO Pellet Fueling Control
a b s t r a c t Requirements for pellet injection system for a Japanese DEMO concept are comprehensively assessed in order to elucidate direction and target of R&D. A fusion output control simulation study using 1.5D transport code is carried out to estimate requirement of fuel particle source. Next, multivariable parameter dependence survey of the fuel deposition source on pellet speed, poloidal injection angle, pellet mass and pedestal height is performed. The conditions to achieve the target fueling depth derived from the output control study are shown. The AUG calibrated relation is referred to consider spatial restriction of tokamak geometry which relates maximum pellet velocity to curvature of pellet guide tube. Then the restriction is collated to the results of multivariable survey to find the most advantageous pellet speed, injection angle, and pellet mass which is consistent with both output control and tokamak geometry. Consequently, a conceptual design of fuel pellet injection system as the R&D target toward to DEMO is proposed. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Robust fusion output power controllability is one of the essential requirement for DEMO reactor. Fuel supply is expected as the most promising robust control knob of the fusion output. And pellet injection is considered as the primary fueling technique in DEMO as well as ITER [1]. Main difference of requirement for fueling system in DEMO from ITER comes from demand for the larger fusion output. It consequences requirement of more fueling efficiency to obtain higher fuel density under the conditions of density limit as well as sufficient purity against to the larger He ash generation.
Furthermore, in DEMO, necessity of self-sustaining tritium breeding and severe heat and neutron load results thicker in-vessel components (blanket and shielding structure) than ITER. It leads to larger major radius Rp of plasma. If we fix the q95 , the larger Rp leads to lower Ip , it means lower Greenwald density limit. Therefore, the density limit in DEMO tends to become tighter condition even compared to ITER. The fuel pellet injector in DEMO has to be designed so as to satisfy such a tighter edge density condition, the larger demand of fusion output and sufficient particle throughput to avoid He dilution, simultaneously.
2. Fusion output control simulation ∗ Corresponding author. E-mail address: [email protected] (S. Tokunaga).
In order to translate such demands for DEMO fueling system, to quantitative request specification of pellet injection system, we
http://dx.doi.org/10.1016/j.fusengdes.2017.02.079 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
G Model FUSION-9149; No. of Pages 4
ARTICLE IN PRESS S. Tokunaga et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
2
start from the consideration of response of burning plasma to fuel pellet. We used a rather simple 1.5D transport code (ATLAS) for fusion output control simulation. The ATLAS is being developed in QST aiming to be used as a fusion plant control simulator. At this moment, simple transport model based on the mixed Bohm/gyroBohm (BgB) model [2] is implemented. It solves particle and energy transport for each species (e, D, T and He in this study). In addition, an artificial mechanism to mimic pedestal formation at the empirical power threshold of L-H transition, by shrinking mixing length in the Bohm-like term of BgB into gyro-Bohm-like one which is proportional to Larmor radius with a tuning factor is implemented. The factor is tuned to reproduce assumed HH98y2 factor. Particle diffusivity D is also determined by BgB formulation. Particle pinch v profile is also given by input in the form of v˜ ≡ v/(aD) to reproduce given assumed peaking rate (1.3 in the following) if there is no particle source in the plasma column. Profile control is beyond of the scope of the present study. The fuel pellet appears as particle source with fixed profile. The profile is computed from given peak position, number of atom and melting time. In this study, the melting time of pellet dominates time step size of the transport calculation, and is set as 25 ms (much longer than typical actual time scale, 1 ms) for convenience. The 1 ms of melting time results more than 25 times longer computation time (a few days per a case). It is unacceptably inconvenient for this conceptual design study. The other fast mechanism, e.g., MHD, micro-instabilities and so on are not modeled either. Temporal evolution shown in this section should be regarded as smoothed variation averaging these fast behaviors. The fusion output control is assigned to DT pellet with simple ON/OFF feedback control logic based on neutron measurement. Decision of injection is made every 0.1 s based on neutron detector signal. Simply, if the detected fusion output is lower than the given target value at the moment, the fuel particle source appears during the melting time. The edge density is cared by D puff to be kept at least 70% of the Greenwald limit. Non-inductive current drive is controlled by On-axis 1 MeV D-NBI power. These settings are arranged to separate the role of each actuator as much as possible by minimizing side effects for simple and robust control. The calculation is based on a JA-DEMO concept parameters, Pfus = 1.5 GW, major radius Rp = 8.2 m, minor radius ap = 2.56 m, elongation = 1.70, 98(y,2)
Ip = 14.6 MA, HH = 1.25, ne =5.9 × 1019 m−3 , Greenwald density limit nGW = 7 ×1019 m−3 , the plasma volume V = 1800 m3 and expected He dilution rate He = 0.07. For a rough understanding of particle confinement time scale, let us consider the 0D particle balance for Helium. Based on the above parameters, from rela∗ = 3.55 × 1020 P tions nHe /ne ≤ He and V nHe /He fus [GW ] , we ∗ can obtain He 200He = 14 s. Extremely torrent throughput is demanded from the viewpoint of particle balance. Fig. 1 shows waveform from a fusion output control simulation of (A) currents, (B) fuel supply by pellet, (C) volume averaged densities and (D) fusion output. The pellet mass is 2.0E+21 atom/pel (D:T = 25%:75%), which is corresponding to ∼2% of the total stored particle inside separatorix. It starts after the Ip reaches flattop by induction. The plasma starts with almost D 100%, and the density at r/a ∼ 0.9 is controlled to be 70% of Greenwald limit by D-puff. It is approach from the safety side for divertor. The target value of fusion output is raised step by step as shown by blue line in Fig. 1(D). It can be also regarded as steps of power ascension testing scenario. The L-H transition takes place at t ∼ 220 s. Density ETB formation consequences sudden reduction of needed fuel supply (Fig. 1(B)). The feedback control of NBI power starts from t ∼ 300, and achieves steady state at t ∼ 330 s (Fig. 1(A)). The good controllability of fusion output by pellet fueling absorbing effect of the improvement of confinement and the modification of current drive power is apparently shown. In case with D:T ratio always fixed to 50%:50% for all sources, i.e., renouncing the degree of freedom of D:T ratio as control knob, the fusion output is more strongly coupled with these
Fig. 1. Temporal evolution (A) current, (B) fuel source by pellet, (C) density and (D) fusion output power in reference case.
effects. Particle confinement time p∗ depends on transport, exhaust rate and distribution of particle source itself. The exhaust rates for each species are presumed as 2% for D and T, 1% for He in this calculation. They should be changed depending on structure of divertor in future works. The weight of particle source is temporally varying. Increase of the pellet source with shallow deposition shortens p∗ . The increase of temperature also shortens p∗ by making position of ionization of puffed or recycled particle be shallower. Although it is difficult to know appropriate p∗ for fuel particle with large discrete source like pellet, the confinement time of He as a measure of ∗ ∼8 s at t = 180, ∼25 s at t = 300 particle confinement changes as He and ∼22 s at t = 540. The longer confinement time than 0D estimation could be affected by the ne which exceeds the expected value and peaking rate of He ∼1.65 which is larger than one of DT ∼1.4. The pellet injection frequency in the flattop phase (Pfus = 1.5 GW) is ∼5 Hz (1.0E+22 atom/s) in this case. Fig. 2 shows results from another case with pellet mass Mpel = 4.0E+21 atom/pel (∼4% of total stored particle) and deposition peak at r/a=0.9 (∼ pedestal top) (Fig. 2(A)). In this case, the oscillation of fusion output during flattop (Pfus = 1.5 GW) is 2.5∼3
Fig. 2. (A) pellet deposition profile with Mpel =4E+21 atom/pel and deposition peak at r/a = 0.9. Profile variation during a fusion output oscillation period of (B) electron density, (D) ion temperature and (D) number of He generation. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
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times larger than one in the case with Mpel = 2.0E+21. Such oscillation of output is caused by delayed response of fusion output with the control logic. In this simulation, the delay of response was resulted by 2 reasons, (1) delay of core density response from the particle supply to the edge and (2) plasma cooling effect by pellet (phase shift of temperature from density). The former reason should not be changed by pellet mass with the current transport model. The latter cooling effect causes not only delay but also decrease of fusion output. Fig. 2 (B, C, D) show responses of electron density, ion temperature and He generation (number of DT fusion reaction) integrated over each flux tube, during one period of fusion output oscillation. The time slices are indicated by red line (injection start) at first, then advance to yellow (stop of injection), green (transport to core) then blue (total output becomes less than target) at last. Fig. 2(D) looks like the bottom half is red, and upper half is green∼blue. Thus the boundary between red and blue is close to profile with targeted fusion output. The fusion output decreases when pellet injection starts, then overshoot after it stopped. Such overcooling-overshoot cycle becomes larger when the background ion temperature is lower or the pellet is larger. It is deduced that such cooling effect of the larger pellet could cause 2.5∼3 times larger fluctuation with 2 times larger pellet. The current ON/OFF pellet control logic continues injection as long as the fusion output response is delayed. It consequences too large deviation of density profile from the favorable profile (Fig. 2(B)). These results provide insights of requirements for fueling. (1) Importance to minimize overcooling effect for output control. Disadvantage of large pellet and shallow deposition is emphasized from this. (2) Development of smart control logic considering the delay of fusion output is needed. Furthermore, there are several expected physics issues related to fueling that are not considered in the present transport model, e.g., confinement degradation due to density limit, ELM trigger by deposition on pedestal, and stiffness of core temperature profile response dropping with pedestal temperature. They come down to the (3) importance to deposit fuel inside of pedestal top and to reduce deposition on pedestal region as much as possible, (4) and also importance of predicting radial width of deposition profile. As the consequence of the above consideration we set the target depth of fuel pellet deposition peak as r/a = 0.85 for the following sections.
Fig. 3. Tokamak geometry including TFC, vacuum vessel (VV), back plate (BP), tritium breeding blanket (BLK) and plasma. Spatial relationships between target flux tube and injection point, pellet guide tube curvature radius Rc and injection angle () are shown. Pink filled area is closed by TFC. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
peak position is shown in Fig. 4. It is noted that the lower pedestal temperature tends to result in shallower deposition. It is because, the higher background temperature drives pellet drift stronger. In DEMO plasma with several keV pedestal temperature, effect of drift is dominant than ablation. The lower pedestal is not favorable for fueling. Considerable dependence on injection angle is shown. The difference between = 105–120 is significant in every plot. = 105 gives insufficient deposition depth in many case even with 3000 m/s. The speed and angle dependence are stronger in lowpedestal cases, because the ablation becomes relatively important
3. Pellet ablation-drift simulation It is easily shown by NGS Scaling [3] that reaching r/a ∼ 0.85 as ablation profile is difficult. Then pellet drift [4,5] must be utilized to achieve the target. It means injection from high-field side (HFS) is mandatory. Z-coordinate of the magnetic axis of plasma equilibrium of current JA-DEMO is shifted upward to secure the sufficient space for divertor. It immediately leads to conclusion that fuel injection from Upper-HFS is the most rational choice. Hence, it is different from ITER. Fig. 3 indicates the geometry. The pellet cloud drifts horizontally to +R direction. Upper and lower edge of the flux tube corresponding to the target depth are indicated by orange lines. Z-coordinate of the injection point on plasma surface must locate in-between the lines. Apparently, the injection angle is spatially restricted by the geometry. In order to evaluate the requirements to achieve the target depth r/a = 0.85, we have carried out a massive scan simulation survey of the pellet deposition by the use of pellet ablation-drift simulation code HPI2 [6]. The background data are imported from the transport simulation. Scan calculation are done for 4 pellet injection speeds 1000, 1500, 2000, 3000 m/s, 4 injection poloidal angles 105, 120, 135, 150 degrees (Fig. 3), 3 pellet sizes corresponding to the number of atoms 2E+21, 4E+21, 6E+21, and 3 kinds of pedestal temperature 3, 6, 9 keV, 144 cases in total. The scan results of deposition
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Fig. 4. Scan results of peak position of pellet deposition profile.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079
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FUSION-9149; No. of Pages 4
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Table 1 Critical velocity vc for each 3different injection angles and pellet sizes. Mpel [atm/pel]
2E+21
4E+21
6E+21
Lpel [mm] vc (Rc = 10 m, = 120) [m/s] vc (Rc = 1 m, = 135) [m/s]
2.0 2571 813
2.8 2173 687
5.1 1610 509
in these cases. The pellet size dependence is also stronger in lowpedestal temperature cases due to the same reason. Gray hatched area is explained in the next section. 4. Discussion In order to think of the consistency between the tokamak geometry and the requirement for pellet, we introduce useful empirical formulation: AUG Calibrated Relationship [7], vc [m/s] = 1150 Rc [m]/Lpel [mm], where, Rc is curvature radius of pellet guide tube (PGT) in metre, Lpel is diameter length of pellet in millimetre. It enables to estimate trade-off relationship between available speed and angle coupled by curvature of PGT layout. The 3 pellet sizes 2e+21, 4e+21, 6e+21 atom/pel are corresponding to about 2.0 mm, 2.8 mm, 5.1 mm, respectively. The poloidal injection angle and PGT curvature are intimately related as shown in Fig. 3. Now corresponding PGT curvature radii for = 120 and = 135 are estimated as 10 m and 1 m, respectively. The evaluated critical speed is shown in Table 1. Strong disadvantage of small curvature radius is apparently shown. Tight limitation of critical speed for Large (6E+21 atom) pellet is also apparent. Based on these estimation of the critical speed, unavailable area for combination of the pellet speed and angle are roughly depicted in the Fig. 4 as grayhatched area. In these hatched areas, pellet cannot be delivered to plasma without breaking apart. Such PGT layout appears as the strongest constraint for pellet deposition depth. As a consequence of the above considerations, it is concluded that, = 120 degrees, pellet mass 4 × 1021 atom/pel should be the most favorable conditions for the current geometry of DEMO regardless to the pedestal temperature. Then about 2∼3 Hz of frequency for the corresponding pellet size is required. The pellet speed faster than 2000 m/s should be necessary to reach the target depth r/a = 0.85. Each of these values is not unrealistic, but enough imaginable from the currently available foresighted technologies [8]. In consideration of the range of needed injection speed, double-pneumatic gun is regarded as the promising acceleration technology. Supposing the duration of in-situ production of pellet ice in gun-barrel as 30 s (0.033 Hz), 3 Hz of injection frequency needs 90 barrels. Since the number of the injection route into VV is restricted by number of TFC (16∼20), multi-barrel injector [9] technology will be useful. Sophisticated fuel circulation system will be also the essential engineering subject to minimize tritium inventory [10]. Supplementarily, it is important to stress that the STRAIGHT pellet injection route does completely contradict to requirement for neutron shielding. The injection route needs straight “embrasure” on shielding structure (Fig. 3). As the rough estimation, suppose a point source (flux) of neutron 1014 at first wall and the embrasure with 2 cm × 2 cm cross section and 120 cm of length, neutron
flux of 2 × 109 [n/cm2 /s] on VV is obtained. It is 1-order higher than the allowable level. Additional neutron shielding structure must be equipped on VV around the embrasure. It is also concerned that the AUG calibrated relationship is based on experiments with pure D2 pellet. The critical velocity of tritium-mixed pellet would be different [11]. It would affect the optimized relationship between injection speed and angle. It is stressed that the bottle-neck of the injection speed is the PGT curvature and plasticity of pellet, not the accelerating technology. Dope of the other element to enhance pellet plasticity [12] may be beneficial technique from such a viewpoint. 5. Summary Conceptual design study of pellet injection system for JA-DEMO has been carried out. Comprehensive consideration about requirements for fueling system including plasma response and spatial restriction from tokamak geometry was presented. Requirements for the fuel source from the viewpoint of plasma response were studied by fusion output control simulation using a 1.5D transport code. It was shown that delay of fusion output response caused by cooling effect can result fluctuation of fusion power. Setting target depth of the pellet deposition peak as r/a = 0.85, a massive parameter scan survey using pellet ablation-drift code was performed in order to estimate the required pellet injection speed, angle and mass. It was shown that lower pedestal temperature tend to result shallower deposition of the pellet. The spatial restriction of PGT curvature was considered by the use of AUG Calibrated Relation. As the consequence of above considerations, concept of the DEMO fueling system as the development target has been estimated as following. Injection from Upper-HFS with speed faster than 2000 m/s, 120 degrees of poloidal angle, pellet mass 4E+21 atom/pel, 10 m PGT curvature radius, 3 Hz of injection frequency as the whole system, which will be consist of 90 barrels of double pneumatic guns. Acknowledgements The author ST acknowledges Prof. R. Sakamoto for fruitful discussions. This work was supported by the Broader Approach and JSPS Grant-in-Aid for Scientific Research; KAKENHI No. 25889068. A number of calculations were enabled by HELIOS supercomputer at International Fusion Energy Research Centre. References [1] L.R. Baylor, et al., Nucl. Fusion 47 (2007) 443–448. [2] M. Erba, et al., Plasma Phys. Control. Fusion 39 (1997) 261; T. Tala, et al., Nucl. Fusion 46 (2006) 548–561. [3] L.R. Baylor, A. Geraud, et al., Nucl. Fusion 37 (1997) 445. [4] P.T. Lang, et al., Phys. Rev. Lett. 79 (1997) 1487. [5] L.R. Baylor, et al., Phys. Plasmas 7 (2000) 1878. [6] B. Pegourie, et al., Nucl. Fusion 47 (2007) 44. [7] P.T. Lang, et al., Fusion Eng. Des. 96 (2015) 123–128. [8] S. Sudo, M. Kanno, H. Kaneko, et al., 15th Symposium on Fusion Energy (Cape Cod, U.S.A.), 1993, 1-PA-3. [9] A. Frattolillo, et al., Rev. Sci. Instrum. 69 (1998) 2675. [10] B. Ploeckl, et al., Fusion Eng. Des. 96 (2015) 155–158. [11] W. Fisher, ORNL/TM-11781, Oak Ridge National Laboratory, June 1991. [12] L.A. Alekseeva, et al., Phys. Solid State 48 (2006) 1513; L.A. Alekseeva, Czech. J. Phys. 46 (Suppl. S1) (1996) 519.
Please cite this article in press as: S. Tokunaga, et al., Conceptual design study of pellet fueling system for DEMO, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.02.079