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Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation
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Fusion Engineering and Design xxx (2016) xxx–xxx
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Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation J.S. Kang a , L. Jung b , C.-S. Byun a , D.H. Na a , Y.-S. Na a , Y.S. Hwang a,∗ a b
Seoul National University, Seoul 151-742, Republic of Korea National Fusion Research Institute, Daejeon, Republic of Korea
h i g h l i g h t s • • • •
One-dimensional current density and its optimization for the K-DEMO are explored. Plasma current density profile is calculated with an integrated simulation code. The impact of self and external heating profiles is considered self-consistently. Current density is identified as a reference profile by minimizing heating power.
a r t i c l e
i n f o
Article history: Received 1 September 2015 Received in revised form 19 December 2015 Accepted 1 February 2016 Available online xxx Keywords: K-DEMO Integrated system code Steady-state operation Current drive configuration Optimization
a b s t r a c t Concept study for Korean demonstration fusion reactor (K-DEMO) is in progress, and basic design parameters are proposed by targeting high magnetic field operation with ITER-sized machine. High magnetic field operation is a favorable approach to enlarge relative plasma performance without increasing normalized beta or plasma current. Exploration of one-dimensional current density profile and its optimization process for the K-DEMO steady-state operation are reported in this paper. Numerical analysis is conducted with an integrated plasma simulation code package incorporating a transport code with equilibrium and current drive modules. Operation regimes are addressed with zero-dimensional system analysis. Onedimensional plasma current density profile is calculated based on equilibrium, bootstrap current analysis, and thermal transport analysis. The impact of self and external heating profiles on those parameters is considered self-consistently, where thermal power balance and 100% non-inductive current drive are the main constraints during the whole exploration procedure. Current and pressure profiles are identified as a reference steady-state profile by minimizing the external heating power with desired fusion power. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Strategic plan for the fusion demonstration reactor program of Korea has been evolving in the frame of a fast-track approach, and recently a two-stage development plan has been under discussion as a baseline approach. [1] With this approach, Korean demonstration fusion reactor (K-DEMO) is designed not only to demonstrate a net electricity generation and a self-sustained tritium cycle, but also to be used as a component test facility. At its second stage, a net electric generation in the order of 500 MWe may be pursued with major upgrades to provide sufficient data for the competitiveness in the cost of electricity.
∗ Corresponding author. E-mail address: [email protected] (Y.S. Hwang).
It is essential to show the possibility of stable steady-state operations in technological aspect as well as physics for the demo design. Steady-state and efficient operations could be addressed in the exploration of current drive configuration since efficiency is a key property to commercialize fusion power plant. Preliminary K-DEMO current drive studies with one-dimensional steady-state parallel current density distribution were recently reported. [2] In this paper, current drive configuration optimization processes are firstly explored to deduce a methodology of minimizing recirculating power for efficient K-DEMO operation. Description of analyzing tool is given in Section 2. Zero-dimensional system analyses of fusion reactor models along with the K-DEMO design concept and operation regime are described in Section 3. Optimization procedures of current drive configuration related to the reactor models are described and discussed in Section 4, proposing potential current density profiles for K-DEMO. Conclusion and future work of this study are presented in Section 5.
http://dx.doi.org/10.1016/j.fusengdes.2016.02.011 0920-3796/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
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Table 1 List of modules. OD
0d system analysis
EQ TR WF WR NB
Fixed boundary 2d Grad-Shafranov solver 1D Transport Neoclassical & Anomalous transport models Full wave analysis Ray tracing method Neutral Beam Injection analysis
Table 2 K-DEMO design parameters. Major/minor radius
6.8/2.1 m
Aspect ratio Toroidal magnetic field Elongation fGreenWald ˇN Fusion power Plasma current
3.23 7.5T 2.0 <1 <4 ∼2000 MW ∼12 MA
Fig. 1. Procedure of determining the K-DEMO operation regime. (1) Draw density and temperature limit. (2) Determine target fusion power line. (3) Solve power balance equation. Select density & temperature with the lowest Pext .
2. Analysis tool An integrated numerical package named as Korean system-code is prepared to deduce the K-Demo parameters and current drive configurations where multi-dimensional codes from 0d to 2d are incorporated. The conceptual design variables, operation regime, and current drive scenario are primary calculation results. The numerical package is composed of different modules such as 0d system analysis code, 1d transport code and 2d equilibrium & current drive codes. The list of modules implemented is given in Table 1. Zero dimensional system analysis code analyzes conceptual design parameters and operation regimes with physics and technological constraints. ESC [3], a fixed boundary equilibrium code, calculates two dimensional MHD equilibria. The ASTRA code [4] is selected as a main transport solver for particle, heat, and current on each magnetic flux surface. TORAY-GA [5] for ECH (Electron Cyclotron Heating), TORIC for ICH [6] (Ion Cyclotron Heating), and LSC [7] for LH (Lower hybrid Heating) are utilized to the integrated simulation system [8] to estimate the current drive efficiency and power absorption. TORAY and LSC are ray tracing codes and TORIC is a full wave code. The neutral beam (NB) driven current and power are calculated from the ASTRA-NB sub-module. The Korean system code will be upgraded to a platform-based flexible code. The platform plays a role of framework combining various plasma simulation codes with a standardized interface. Standardization of the data model establishment is under consideration to couple input and output data from each module. 3. K-DEMO design parameters and operation regime 3.1. Design parameters Basic design features of the K-DEMO reactor models come from technical as well as physical aspects. Although tokamak performance, such as the energy confinement scaling, favors larger machine size, the size of K-DEMO is limited to that of ITER to minimize the construction cost and the engineering risks. To incorporate the plasma physics accumulated from KSTAR and ITER operations, the aspect ratio of K-DEMO shall be in a similar range of 3–3.5. High magnetic field operation is a favorable way to increase relative plasma pressure without enlarging normalized beta or plasma current. So, operational regimes of the K-DEMO reactor are pursued by extrapolating ITER steady-state operation scenarios [9] (Pf = 250MW IP = 8MA ˇN = 2.7) to the high magnetic field regime in advanced tokamak operations.
Fig. 2. Initial density and temperature profiles.
The device size is represented by the major radius at a given aspect ratio. Major radius of R = 6.8 m is considered to be similar to that of ITER (R = 6.2 m). Aspect ratio is set to be around 3.2 to reflect KSTAR and ITER operation experiences. High magnetic field on axis is a key design feature of K-DEMO. By using high performance Nb3 Sn-based superconducting cable currently available, a high magnetic field of more than 7T at the plasma center (with the maximum field of 16T) is chosen [2] (Table 2). 3.2. Operation regime Operation regime analyses are performed to find a proper operation density and temperature in the aspect of the global thermal power balance. Before applying to K-DEMO, the 0d analysis scheme is validated with KSTAR reference H-mode shot #7081. [10] Plasma parameters calculated with the 0d routine such as density, temperature, stored energy and normalized beta values are found to be consistent with the experimental values. Fig. 1 shows the process to find an appropriate operation regime with physics constraints in K-DEMO. The list of constraints is as following; Pf ≥ 1.5GW, 0.85 ≤ fGW ≤ 1, H98 ≤ 1.5, ˇN ≤ 4, IP = 12 ∼ 13MA, fBS > 0.6. These operation regimes are the constraints as well as calculation domains. The Greenwald density fraction and the normalized beta limits draw boundary lines in the density and temperature space, and minimally required fusion power sets the other calculation boundary which is presented with the dashed black circle in Fig. 1. The global power balance equation is solved to select the operation density and temperature regime with the lowest external heat-
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
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Fig. 3. (a) ITER weak shear safety factor profile [9]. (b) ARIES-AT safety factor profile [13].
ing power. The NB current drive power is assumed to be the only external heating power in this analysis. 4. Current drive configuration 4.1. Simulation setup Zero dimensional analysis provides the guideline to onedimensional and two-dimensional calculations. Various initial conditions are prepared to start detailed analyses such as the pressure profile, the safety factor profile, the transport model, and the current drive power. From the operation regime analysis, the line-average electron density is assumed to be the same as the Greenwald density and average temperature is around 20 keV. The initial pressure profile is set to have a linear shape with a pedestal region. The pedestal model is benchmarked from the ITER case [11] and 120% enhanced temperature height is assumed. Density profile is assumed to be flat inside the pedestal region. The temperature gradient is assumed to be limited by the Ion Temperature Gradient (ITG) stability limit and set to the highest value of 5. [12]
T0 = exp a/R R/LTcrit ≈ 5 Tped
(1)
where LTcrit is the critical temperature gradient scale length. Fig. 2 shows initial density and temperature profiles with these assumptions. Two safety factor profiles are benchmarked. One is from the ITER weak-shear steady-state scenario [9] and the other is from the ARIES-AT study [13]. ITER profile is chosen to extrapolate ITER physics level to Demo, and ARIES profile is representing the configuration with high bootstrap current drive fraction Fig. 3.
The NB injection is selected as a reference current drive tool in this study for external current drive. The beam energy is set to be 1 MeV to reflect the ITER specification. The heat transport is solved by using two kinds of anomalous transport models in addition to the neoclassical contribution [14]. One is the Weiland model (a theory-based transport model) [15] and the other is ITER ITB diffusivity model [9]. The Weiland model is based on the ITG/TEM (Trapped Electron Mode) theory, applied to the analyses of various existing devices [16–18]. On the other hand the ITER model would represent the technological level at the ITER steady-state phase. The particle transport is not solved in this work for simplicity. Alpha particle density profile and relative magnitude are from ITER weak-shear scenario values. [9] The boundary condition is given at rho = 0.94 assuming the constant pedestal. The toroidal rotation is assumed to be zero and the poloidal rotation is solved using a neoclassical model [19]. Zeff is assumed to be 1.6 with a flat profile. The bremsstrahlung and the synchrotron radiation are considered.
4.2. Optimization process With pressure and safety factor profiles, fixed boundary equilibrium and bootstrap current analysis can suggest a target of the externally-driven current profile by subtracting bootstrap current profile from total current profile Fig. 4 illustrates this procedure. By varying external neutral beam heating configuration, Jext = JNB conditions are classified. Scanned parameters are beam power, position, width, height, and beam number. Since broad current drive characteristics of NB, a 5% uncertainty of aligning current density profile is assumed. Fig. 5 shows the optimizing iteration routine. Density profile is fixed in whole simulation procedure. Variations of heating profile
Fig. 4. Drawing target external current density profile Jext = JTOT –JBS .
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Fig. 5. Optimization process diagram.
Fig. 6. (a) Pressure profile, (b) diffusivity of Weiland transport model (WL ) diffusion coefficient required to sustain pressure profile at the initial condition. (exp ).
lead to pressure profile differences with thermal transport. Pressure profile modification also makes total current density profile and bootstrap profile change. Eventually the amount of required external heating is changed. Those three steps are iterated equally. The lowest external heating power satisfying thermal power balance and 100% non-inductive current fraction is selected after the iteration process.
Fig. 7. K-DEMO High performance pressure profile (a) and current density profile (b).
drive. Finally, a fusion power multiplication factor Q = 25 is obtained with this external heating configuration. 5. Conclusion and future work
4.3. Exploration of current density profile First, the ITER weak-shear safety factor profile and Weiland transport model are used to maintain less extrapolation from the present physics level. Fig. 6 shows the pressure profile and diffusivity profile of weak shear scenario calculations with the Weiland transport model. Total plasma current of 12MA and fusion power of 1420 MW are obtained. External neutral beam power totals 105MW and positions are adjusted to form the required external current density profile. However, the gap of diffusivity profiles shown in Fig. 6-(b) is too large to sustain the pressure profile. Pressure profile may not be sustained especially in the off-axis region. As a result, pressure profile collapses without reaching 2000 MW thermal fusion power. Advanced safety factor profile and ITB diffusivity model are utilized to overcome previous weaknesses. Steady-state current density profile is derived within 5% margin of calculation uncertainty. Overall density slope is modified to maximize self-driven current by benchmarking ARIES density profiles [13]. Fig. 7(a) presents pressure and current density profiles. An improved transport behavior makes a high temperature configuration. As a result, such a high performance profile, HH98 = 1.42 and Pfus = 2000 MW, is deduced even with the ITER level ˇN = 2.8. Total plasma current of 12 MA and bootstrap current of 10.5 MA are achieved, showing 87.5% bootstrap fraction. The self-driven current contributes overall current density profile formation. Neutral beam configuration is optimized by adjusting total current profile and thermal power balance. On-axis and off-axis neutral beams are injected to drive current. Two beams, with a total power of 80MW, are launched: 60 MW to core and 20 MW to the outboard region. Since most plasma heating is provided by alpha heating for the K-DEMO level fusion power, the role of neutral beam heating is mostly for current
The K-DEMO concept with the recent progress of magnet technology is suggested, which leads to the level of fusion demonstration with an ITER-size machine. Operation regime and one-dimensional current density configurations are studied to resolve steady-state operation. An integrated numerical analysis system is used to analyze current density profiles and will be developed as a new system code. Plasma equilibria with high bootstrap current fraction have been used in order to minimize recirculating power and the required current density profile to be driven externally is obtained by substracting bootstrap current profile from the target equilibrium current density profile. Current drive for KDEMO should have low recirculating power but also steady-state properties. Two kinds of transport models are investigated with a little extrapolation from the ITER phase technology. When weak shear calculation with the Weiland transport model is applied as a realistic case with current technology level, it does not sustain a stable pressure distribution due to severe transport loss. The ITER diffusivity model enhances overall transport property, where the steady-state pressure profile is achieved with improved off-axis confinement and the current density profile with high bootstrap fraction is also obtained with relatively sharp pressure gradient. Current drive configuration optimization process is conducted to find advanced steady-state current density profile. Such a highperformance current and pressure profiles are derived and the minimum heating power configuration is presented for an efficient steady-state profile of K-DEMO. Further transport and stability studies on the advanced profile are crucial to demonstrate the advanced current density profile as a K-DEMO steady-state operation scenario. Stability of pressure and safety factor profiles are not guaranteed in this study. MHD stability analyses would be conducted for
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
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the K-DEMO’s own safety factor distribution by solving equilibrium and stability self-consistently. Various current drive methods other than NB may be considered as well. On-axis current drive could be replaced by fast wave or electron cyclotron wave and offaxis by lower hybrid wave. Optimization process is planned to be improved by mixing various current drive methods to find the best self-consistent external heating configuration considering progress and prospects of current drive technology. Acknowledgments This work was supported by the R&D Program through the National Fusion Research Institute of Korea (NFRI) funded by the Government funds.
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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L.E. Zakharov, et al., Phys. Plasmas 6 (1999) 4693. G., Pereverzev, MPI fur PP Report ZB:IPP 5–98 (2002). K. Matsuda, IEEE Trans. Plasma Sci. 17 (1989) 6. M., Brambilla, IPP 5/66 (1996). D. Ignat, et al., Nucl. Fusion 34 (1994) 837. Y.-S., Na, et al., 23th IAEA Fusion Energy Conference (Daejeon, Korea, 2010), THS/P 2–04. M. Murakami, et al., Nucl. Fusion 51 (2011) 103006. H.-S. Kim, et al., Nucl. Fusion 54 (2014) 083012. S. Saarelma, et al., Nucl. Fusion 52 (2012) 103020. J.A. Baumgaertel, et al., Phys. Plasmas 20 (2013) 022305. S.C. Jardin, et al., Fusion Eng. Des. 80 (2006) 25. C. Angioni, et al., Phys. Plasmas 7 (2000) 1224. G. Gateman, et al., Phys. Plasmas 5 (1998) 1793. Y.S. Na, et al., Nucl. Fusion 46 (2006) 232. Y.S. Na, et al., Nucl. Fusion 49 (2009) 115018. H.-S., Kim, et al., 24th IAEA Fusion Energy Conference (San Diego, USA, 2012), EX/P 7–19. P. Hirshman, et al., Nucl. Fusion 21 (1981) 1079.
References [1] K., Kim, et al., 27th SOFT, September 24–28(2012) Liege Belgium. [2] K. Kim, et al., Nucl. Fusion 55 (2015) 053027.
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ARTICLE IN PRESS
FUSION-8528; No. of Pages 5
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation J.S. Kang a , L. Jung b , C.-S. Byun a , D.H. Na a , Y.-S. Na a , Y.S. Hwang a,∗ a b
Seoul National University, Seoul 151-742, Republic of Korea National Fusion Research Institute, Daejeon, Republic of Korea
h i g h l i g h t s • • • •
One-dimensional current density and its optimization for the K-DEMO are explored. Plasma current density profile is calculated with an integrated simulation code. The impact of self and external heating profiles is considered self-consistently. Current density is identified as a reference profile by minimizing heating power.
a r t i c l e
i n f o
Article history: Received 1 September 2015 Received in revised form 19 December 2015 Accepted 1 February 2016 Available online xxx Keywords: K-DEMO Integrated system code Steady-state operation Current drive configuration Optimization
a b s t r a c t Concept study for Korean demonstration fusion reactor (K-DEMO) is in progress, and basic design parameters are proposed by targeting high magnetic field operation with ITER-sized machine. High magnetic field operation is a favorable approach to enlarge relative plasma performance without increasing normalized beta or plasma current. Exploration of one-dimensional current density profile and its optimization process for the K-DEMO steady-state operation are reported in this paper. Numerical analysis is conducted with an integrated plasma simulation code package incorporating a transport code with equilibrium and current drive modules. Operation regimes are addressed with zero-dimensional system analysis. Onedimensional plasma current density profile is calculated based on equilibrium, bootstrap current analysis, and thermal transport analysis. The impact of self and external heating profiles on those parameters is considered self-consistently, where thermal power balance and 100% non-inductive current drive are the main constraints during the whole exploration procedure. Current and pressure profiles are identified as a reference steady-state profile by minimizing the external heating power with desired fusion power. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Strategic plan for the fusion demonstration reactor program of Korea has been evolving in the frame of a fast-track approach, and recently a two-stage development plan has been under discussion as a baseline approach. [1] With this approach, Korean demonstration fusion reactor (K-DEMO) is designed not only to demonstrate a net electricity generation and a self-sustained tritium cycle, but also to be used as a component test facility. At its second stage, a net electric generation in the order of 500 MWe may be pursued with major upgrades to provide sufficient data for the competitiveness in the cost of electricity.
∗ Corresponding author. E-mail address: [email protected] (Y.S. Hwang).
It is essential to show the possibility of stable steady-state operations in technological aspect as well as physics for the demo design. Steady-state and efficient operations could be addressed in the exploration of current drive configuration since efficiency is a key property to commercialize fusion power plant. Preliminary K-DEMO current drive studies with one-dimensional steady-state parallel current density distribution were recently reported. [2] In this paper, current drive configuration optimization processes are firstly explored to deduce a methodology of minimizing recirculating power for efficient K-DEMO operation. Description of analyzing tool is given in Section 2. Zero-dimensional system analyses of fusion reactor models along with the K-DEMO design concept and operation regime are described in Section 3. Optimization procedures of current drive configuration related to the reactor models are described and discussed in Section 4, proposing potential current density profiles for K-DEMO. Conclusion and future work of this study are presented in Section 5.
http://dx.doi.org/10.1016/j.fusengdes.2016.02.011 0920-3796/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
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Table 1 List of modules. OD
0d system analysis
EQ TR WF WR NB
Fixed boundary 2d Grad-Shafranov solver 1D Transport Neoclassical & Anomalous transport models Full wave analysis Ray tracing method Neutral Beam Injection analysis
Table 2 K-DEMO design parameters. Major/minor radius
6.8/2.1 m
Aspect ratio Toroidal magnetic field Elongation fGreenWald ˇN Fusion power Plasma current
3.23 7.5T 2.0 <1 <4 ∼2000 MW ∼12 MA
Fig. 1. Procedure of determining the K-DEMO operation regime. (1) Draw density and temperature limit. (2) Determine target fusion power line. (3) Solve power balance equation. Select density & temperature with the lowest Pext .
2. Analysis tool An integrated numerical package named as Korean system-code is prepared to deduce the K-Demo parameters and current drive configurations where multi-dimensional codes from 0d to 2d are incorporated. The conceptual design variables, operation regime, and current drive scenario are primary calculation results. The numerical package is composed of different modules such as 0d system analysis code, 1d transport code and 2d equilibrium & current drive codes. The list of modules implemented is given in Table 1. Zero dimensional system analysis code analyzes conceptual design parameters and operation regimes with physics and technological constraints. ESC [3], a fixed boundary equilibrium code, calculates two dimensional MHD equilibria. The ASTRA code [4] is selected as a main transport solver for particle, heat, and current on each magnetic flux surface. TORAY-GA [5] for ECH (Electron Cyclotron Heating), TORIC for ICH [6] (Ion Cyclotron Heating), and LSC [7] for LH (Lower hybrid Heating) are utilized to the integrated simulation system [8] to estimate the current drive efficiency and power absorption. TORAY and LSC are ray tracing codes and TORIC is a full wave code. The neutral beam (NB) driven current and power are calculated from the ASTRA-NB sub-module. The Korean system code will be upgraded to a platform-based flexible code. The platform plays a role of framework combining various plasma simulation codes with a standardized interface. Standardization of the data model establishment is under consideration to couple input and output data from each module. 3. K-DEMO design parameters and operation regime 3.1. Design parameters Basic design features of the K-DEMO reactor models come from technical as well as physical aspects. Although tokamak performance, such as the energy confinement scaling, favors larger machine size, the size of K-DEMO is limited to that of ITER to minimize the construction cost and the engineering risks. To incorporate the plasma physics accumulated from KSTAR and ITER operations, the aspect ratio of K-DEMO shall be in a similar range of 3–3.5. High magnetic field operation is a favorable way to increase relative plasma pressure without enlarging normalized beta or plasma current. So, operational regimes of the K-DEMO reactor are pursued by extrapolating ITER steady-state operation scenarios [9] (Pf = 250MW IP = 8MA ˇN = 2.7) to the high magnetic field regime in advanced tokamak operations.
Fig. 2. Initial density and temperature profiles.
The device size is represented by the major radius at a given aspect ratio. Major radius of R = 6.8 m is considered to be similar to that of ITER (R = 6.2 m). Aspect ratio is set to be around 3.2 to reflect KSTAR and ITER operation experiences. High magnetic field on axis is a key design feature of K-DEMO. By using high performance Nb3 Sn-based superconducting cable currently available, a high magnetic field of more than 7T at the plasma center (with the maximum field of 16T) is chosen [2] (Table 2). 3.2. Operation regime Operation regime analyses are performed to find a proper operation density and temperature in the aspect of the global thermal power balance. Before applying to K-DEMO, the 0d analysis scheme is validated with KSTAR reference H-mode shot #7081. [10] Plasma parameters calculated with the 0d routine such as density, temperature, stored energy and normalized beta values are found to be consistent with the experimental values. Fig. 1 shows the process to find an appropriate operation regime with physics constraints in K-DEMO. The list of constraints is as following; Pf ≥ 1.5GW, 0.85 ≤ fGW ≤ 1, H98 ≤ 1.5, ˇN ≤ 4, IP = 12 ∼ 13MA, fBS > 0.6. These operation regimes are the constraints as well as calculation domains. The Greenwald density fraction and the normalized beta limits draw boundary lines in the density and temperature space, and minimally required fusion power sets the other calculation boundary which is presented with the dashed black circle in Fig. 1. The global power balance equation is solved to select the operation density and temperature regime with the lowest external heat-
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
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Fig. 3. (a) ITER weak shear safety factor profile [9]. (b) ARIES-AT safety factor profile [13].
ing power. The NB current drive power is assumed to be the only external heating power in this analysis. 4. Current drive configuration 4.1. Simulation setup Zero dimensional analysis provides the guideline to onedimensional and two-dimensional calculations. Various initial conditions are prepared to start detailed analyses such as the pressure profile, the safety factor profile, the transport model, and the current drive power. From the operation regime analysis, the line-average electron density is assumed to be the same as the Greenwald density and average temperature is around 20 keV. The initial pressure profile is set to have a linear shape with a pedestal region. The pedestal model is benchmarked from the ITER case [11] and 120% enhanced temperature height is assumed. Density profile is assumed to be flat inside the pedestal region. The temperature gradient is assumed to be limited by the Ion Temperature Gradient (ITG) stability limit and set to the highest value of 5. [12]
T0 = exp a/R R/LTcrit ≈ 5 Tped
(1)
where LTcrit is the critical temperature gradient scale length. Fig. 2 shows initial density and temperature profiles with these assumptions. Two safety factor profiles are benchmarked. One is from the ITER weak-shear steady-state scenario [9] and the other is from the ARIES-AT study [13]. ITER profile is chosen to extrapolate ITER physics level to Demo, and ARIES profile is representing the configuration with high bootstrap current drive fraction Fig. 3.
The NB injection is selected as a reference current drive tool in this study for external current drive. The beam energy is set to be 1 MeV to reflect the ITER specification. The heat transport is solved by using two kinds of anomalous transport models in addition to the neoclassical contribution [14]. One is the Weiland model (a theory-based transport model) [15] and the other is ITER ITB diffusivity model [9]. The Weiland model is based on the ITG/TEM (Trapped Electron Mode) theory, applied to the analyses of various existing devices [16–18]. On the other hand the ITER model would represent the technological level at the ITER steady-state phase. The particle transport is not solved in this work for simplicity. Alpha particle density profile and relative magnitude are from ITER weak-shear scenario values. [9] The boundary condition is given at rho = 0.94 assuming the constant pedestal. The toroidal rotation is assumed to be zero and the poloidal rotation is solved using a neoclassical model [19]. Zeff is assumed to be 1.6 with a flat profile. The bremsstrahlung and the synchrotron radiation are considered.
4.2. Optimization process With pressure and safety factor profiles, fixed boundary equilibrium and bootstrap current analysis can suggest a target of the externally-driven current profile by subtracting bootstrap current profile from total current profile Fig. 4 illustrates this procedure. By varying external neutral beam heating configuration, Jext = JNB conditions are classified. Scanned parameters are beam power, position, width, height, and beam number. Since broad current drive characteristics of NB, a 5% uncertainty of aligning current density profile is assumed. Fig. 5 shows the optimizing iteration routine. Density profile is fixed in whole simulation procedure. Variations of heating profile
Fig. 4. Drawing target external current density profile Jext = JTOT –JBS .
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Fig. 5. Optimization process diagram.
Fig. 6. (a) Pressure profile, (b) diffusivity of Weiland transport model (WL ) diffusion coefficient required to sustain pressure profile at the initial condition. (exp ).
lead to pressure profile differences with thermal transport. Pressure profile modification also makes total current density profile and bootstrap profile change. Eventually the amount of required external heating is changed. Those three steps are iterated equally. The lowest external heating power satisfying thermal power balance and 100% non-inductive current fraction is selected after the iteration process.
Fig. 7. K-DEMO High performance pressure profile (a) and current density profile (b).
drive. Finally, a fusion power multiplication factor Q = 25 is obtained with this external heating configuration. 5. Conclusion and future work
4.3. Exploration of current density profile First, the ITER weak-shear safety factor profile and Weiland transport model are used to maintain less extrapolation from the present physics level. Fig. 6 shows the pressure profile and diffusivity profile of weak shear scenario calculations with the Weiland transport model. Total plasma current of 12MA and fusion power of 1420 MW are obtained. External neutral beam power totals 105MW and positions are adjusted to form the required external current density profile. However, the gap of diffusivity profiles shown in Fig. 6-(b) is too large to sustain the pressure profile. Pressure profile may not be sustained especially in the off-axis region. As a result, pressure profile collapses without reaching 2000 MW thermal fusion power. Advanced safety factor profile and ITB diffusivity model are utilized to overcome previous weaknesses. Steady-state current density profile is derived within 5% margin of calculation uncertainty. Overall density slope is modified to maximize self-driven current by benchmarking ARIES density profiles [13]. Fig. 7(a) presents pressure and current density profiles. An improved transport behavior makes a high temperature configuration. As a result, such a high performance profile, HH98 = 1.42 and Pfus = 2000 MW, is deduced even with the ITER level ˇN = 2.8. Total plasma current of 12 MA and bootstrap current of 10.5 MA are achieved, showing 87.5% bootstrap fraction. The self-driven current contributes overall current density profile formation. Neutral beam configuration is optimized by adjusting total current profile and thermal power balance. On-axis and off-axis neutral beams are injected to drive current. Two beams, with a total power of 80MW, are launched: 60 MW to core and 20 MW to the outboard region. Since most plasma heating is provided by alpha heating for the K-DEMO level fusion power, the role of neutral beam heating is mostly for current
The K-DEMO concept with the recent progress of magnet technology is suggested, which leads to the level of fusion demonstration with an ITER-size machine. Operation regime and one-dimensional current density configurations are studied to resolve steady-state operation. An integrated numerical analysis system is used to analyze current density profiles and will be developed as a new system code. Plasma equilibria with high bootstrap current fraction have been used in order to minimize recirculating power and the required current density profile to be driven externally is obtained by substracting bootstrap current profile from the target equilibrium current density profile. Current drive for KDEMO should have low recirculating power but also steady-state properties. Two kinds of transport models are investigated with a little extrapolation from the ITER phase technology. When weak shear calculation with the Weiland transport model is applied as a realistic case with current technology level, it does not sustain a stable pressure distribution due to severe transport loss. The ITER diffusivity model enhances overall transport property, where the steady-state pressure profile is achieved with improved off-axis confinement and the current density profile with high bootstrap fraction is also obtained with relatively sharp pressure gradient. Current drive configuration optimization process is conducted to find advanced steady-state current density profile. Such a highperformance current and pressure profiles are derived and the minimum heating power configuration is presented for an efficient steady-state profile of K-DEMO. Further transport and stability studies on the advanced profile are crucial to demonstrate the advanced current density profile as a K-DEMO steady-state operation scenario. Stability of pressure and safety factor profiles are not guaranteed in this study. MHD stability analyses would be conducted for
Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011
G Model FUSION-8528; No. of Pages 5
ARTICLE IN PRESS J.S. Kang et al. / Fusion Engineering and Design xxx (2016) xxx–xxx
the K-DEMO’s own safety factor distribution by solving equilibrium and stability self-consistently. Various current drive methods other than NB may be considered as well. On-axis current drive could be replaced by fast wave or electron cyclotron wave and offaxis by lower hybrid wave. Optimization process is planned to be improved by mixing various current drive methods to find the best self-consistent external heating configuration considering progress and prospects of current drive technology. Acknowledgments This work was supported by the R&D Program through the National Fusion Research Institute of Korea (NFRI) funded by the Government funds.
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Please cite this article in press as: J.S. Kang, et al., Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.02.011