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Stability analysis of the conductors for CFETR poloidal field coils
Fusion Engineering and Design 95 (2015) 13–19
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Stability analysis of the conductors for CFETR poloidal field coils Xin He a , Jinxing Zheng b,∗ , Hao Zhang a , Xufeng Liu b a b
School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230029, China Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China
h i g h l i g h t s • The stability margin variation rules versus operating conditions were discussed. • The Tcs of PF conductors at different operating conditions were calculated. • The typical distributions of conductor temperature were presented and studied.
a r t i c l e
i n f o
Article history: Received 24 July 2014 Received in revised form 6 February 2015 Accepted 26 March 2015 Available online 11 April 2015 Keywords: Cable-in-conduit conductors Stability Current sharing temperature Poloidal field
a b s t r a c t China Fusion Engineering Testing Reactor (CFETR) is a new tokamak device. The poloidal field (PF) system of CFETR plays an important role in controlling the location and shape of the plasma. The stable operation of the PF system is largely based on the superconductor stability. Therefore, the stability analysis of the PF1, PF4 and DC2 conductors of PF system has been performed. For stability analysis, a mechanical disturbance and an electromagnetic disturbance are applied, respectively. The calculation results of stability margin, current sharing temperature, temperature margin and distribution of conductor temperature are presented and discussed in this paper. The analysis results illustrates that the present design of CFETR PF conductor can satisfy the requirement of safety margin. © 2015 Elsevier B.V. All rights reserved.
1. Introduction China Fusion Engineering Testing Reactor (CFETR) is a new tokamak device to fully bridge the gap between ITER and DEMO [1]. The main design parameters of CFETR compared with those of ITER are shown in Table 1 [2,3]. The CFETR magnet system consists of the toroidal field (TF) system, central solenoid (CS) system and poloidal field (PF) system. Fig. 1 shows the overview structure and geometry of CFETR magnet system. The PF system in CFETR consists of eight coils, namely PF1 through PF6, DC1 and DC2, which control the location and shape of the plasma [4]. The PF coils of CFETR consist of 6–9 double pancakes. Each double pancake is wound in a “two-in-hand” configuration by NbTi cable-in-conduit conductor (CICC). The CICC stability is one of the most important problems related to superconductor behavior and coil protection system design. Therefore, the analysis of stability and quench of the PF conductors is necessary. In this paper, the electric and thermohydraulic
∗ Corresponding author. Tel.: +86 551 5592013; fax: +86 551 5591310. E-mail address: [email protected] (J. Zheng). http://dx.doi.org/10.1016/j.fusengdes.2015.03.048 0920-3796/© 2015 Elsevier B.V. All rights reserved.
simulation code Gandalf is used to evaluate the performance of PF conductors at different working environment [5,6]. Some of the calculation results are presented and the regularities of the results are discussed. 2. Thermohydraulic and stability calculation by Gandalf The sizes of PF coils for CFETR are shown in Table 2. The conductor used in PF coils is a round-in-square CICC as shown in Fig. 2. NbTi strands are cabled as six petals with a multi-stage cable pattern around an open central spiral and are cooled by forced-flow supercritical helium [7]. Copper strands and cores of suitable diameters are incorporated into the cabling layout by adding a central core in the second, third or fourth stages. Schematic diagram for the cable layout of PF conductor is shown in Fig. 3. Therefore, the total amount of copper is adjusted to each coil type in order to provide the necessary quench protection and also give a fully transposed cable layout. The overall cable and spiral are inserted inside a round-in-square jacket made from 316 L stainless steel. Table 3 lists the major parameters of PF conductors and coils. Determining the stability margin and temperature margin of the conductor is the design basis of CICC. For design criteria, the overall
14
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19 Table 1 The physical target parameters of CFETR. Parameter Plasma current Ip (MA) Major radius of plasma R (m) Minor radius of plasma a (m) Central magnetic field Bt (T) Elongation ratio Triangle deformation ı Number of TF coils (N)
CFETR
ITER
8.5/10
15
5.7
6.2
1.6
2.0
4.5/5.0
5.3
1.8
1.70/1.85
0.4
0.33/0.48
16
18
Table 2 The sizes of PF coils for CFETR.
Fig. 1. Overview structure and geometry of CFETR magnet system.
Coils
R (m)
Z (m)
R (m)
Z (m)
Turns
PF1 PF2 PF3 PF4 PF5 PF6 DC1 DC2
3.109 9.150 11.704 11.704 9.150 3.109 5.659 7.840
7.642 6.697 2.743 −2.743 −6.697 −7.642 −7.791 −7.447
1.353 0.834 0.834 0.834 0.834 1.353 0.834 0.834
0.861 0.715 0.715 0.715 0.715 0.861 0.715 0.715
308 168 168 168 168 308 168 168
Note: R and Z are the radial and axial coordinate values of center of the coil cross section, respectively. The origin for R and Z coordinates is the intersection of central axis of CFETR and symmetry axis of D-shaped TF coil annular cross section. R and Z are the radial and axial diameter of the coil, respectively. Turns are the number of turns of coils.
Fig. 2. Schematic diagram for the NbTi CICC used in PF coils.
Fig. 3. Schematic diagram for the cable layout of PF conductor.
stability requirement is that the conductor must not quench during plasma operation, including the electromagnetic disturbances created by a plasma disruption and vertical displacement events and any mechanical heating. It is adequate as long as the stability margin exceeds the expected disturbance with a safety factor of 2. For NbTi strand, the Cu-to-non-Cu ratio lager than 1.0 and the temperature margin must be higher than 1.5 K is also required. The stability margin and temperature margin are mainly affected by the given magnetic field, operating current and operating temperature. The cable patterns of PF1 and PF6 are the same. The cable patterns of PF2, PF3, PF4 and PF5, DC1, DC2 are also the same, respectively. Comparing the electromagnetic parameters of these conductors in Table 3, it can be seen that PF1, PF4 and DC2 are working in the worst environment of the three types of cable patters, respectively. Therefore, the calculation of stability and quench of PF1, PF4 and DC2 are performed. The coolant inlet location is important for conductor stability. For PF coil, the coolant inlet is positioned at the inner-most turn of the double pancake, in the length of the vertical joggle. And the coolant outlets are located at the inter-pancake joint and the intrapancake joint, respectively. The schematic diagram for inlet and outlet location of PF coil is shown in Fig. 4. The schematic diagram
Table 3 Major parameters of PF conductors and coils.
Sc strand type Cable pattern Central spiral (mm) NbTi strand Cu-to-non-Cu ratio Number of sc strands Void fraction (annulus) (%) Cable diameter (mm) Circle-in-square 316 L Jacket (mm2 ) RRR Operating temperature (K) Maximum operating current (kA) Maximum operating magnetic filed (T) Cooling channel length (m) Inlet pressure of He (bar) mass flow rate of He (g/s)
PF1, PF6
PF2, PF3, PF4
PF5, DC1, DC2
NbTi 3sc × 4 × 4 × 5 × 6 10 × 12 1.6 1440 34.3 37.7 53.8x53.8 100 4.5 51, 39 6.91, 5.08 430 6 8
NbTi {[(2sc + 1Cu strand) × 3 × 4 + 1Cu core1)] × 5 + 1Cu core2} × 6 10 × 12 2.3 720 34.2 35.3 51.9x51.9 100 4.5 33, 28, 53 2.69, 2.19, 3.62 405, 530, 530 6 8
NbTi (3sc × 4 × 4 × 4 + 1Cu core3) × 6 10 × 12 2.3 1152 34.1 35.3 51.9x51.9 100 4.5 35, 42, 55 4.56, 4.01, 5.05 405, 500, 690 6 8
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
15
Table 4 Conductor characteristic for stability analysis. Parameter
Unit
Value PF1
Note PF4
DC2
ASC AST AJK AIN ISC AHEB AHEH EPSLON
m2 m2 m2 m2 – m2 m2 –
RRR DHB
– m
100 4.7375e−4
100 5.0430e−4
100 4.9349e−4
DHH PHTC PHTCJ
m m m
12.0e−3 2.7520 1.1844e−2
12.0e−3 1.3760 1.1090e−2
12.0e−3 2.2016 1.1090e−2
PHTJ
m
1.0660e−1
9.9808e−2
9.9808e−2
PERFOR
–
0.15
0.15
0.15
XLENGT PREINI TEMINI MDTINL
m Pa K kg/s
229.27e−6 366.84e−6 1778.16e−6 219.20e−6 1 344.43e−6 113.04e−6 −7e−3
430 6.0e5 4.5 8e−3
90.32e−6 207.73e−6 1714.93e−6 211.60e−6 1 296.19e−6 113.04e−6 −7e−3
144.51e−6 332.37e−6 1714.93e−6 211.60e−6 1 295.48e−6 113.04e−6 −7e−3
530 6.0e5 4.5 8e−3
690 6.0e5 4.5 8e−3
Area of non-copper in sc strand Area of copper in sc strands Area of SS jacket Area of insulation NbTi with bronze, user’s library Area of helium in annulus Area of helium in spiral Total longitudinal strain in sc in operating condition Residual resistivity ratio for stabilizer material 4 × Area of helium in annulus/w. perim annulus Outer diameter of the central spiral W. perim sc strands (applied 5/6) Perimeter used for heat transfer calculation between the strands and the jacket Perimeter used for heat transfer calculation between the bundle helium and the jacket Percentage perforation of the separation perimeter between the bundle helium and the hole helium Total length of the cooling channel Pressure at inlet Temperature at inlet He mass flow at inlet
process described in Gandalf. The PHTC for heat transfer between the strands and helium is considered only for the superconducting strands; the parameter is affected by the ratio 5/6 because of the triplet configuration in the first stage [9]. The Bottura scaling formulae as a function of the operational temperature and magnetic field [10] are used to scale the strand performance: Jc =
C0 ˛ ˇ b (1 − b) (1 − t 1.7 ) B
(1)
Bc2 = Bc20 (1 − t 1.7 )
Fig. 4. Schematic diagram for coolant inlet and outlet location of PF coil.
for coolant circuit is shown in Fig. 5. The boundary conditions for the flow are set for helium pressure, temperature and mass flow rate applied at the inlet of the conductor. The boundary conditions of Gandalf are in constant pressure and temperature, as established from the initial distribution which is routinely calculated [8]. The detailed parameters used for stability analysis by the code Gandalf are presented in Table 4. For conservative purpose, the stabilizer (AST) taken into account is the copper associated with the superconducting strands only. It is also consistent with the joule heating
(2)
b=
B Bc2 (T )
(3)
t=
T Tc0
(4)
where Jc the critical current density, C0 the normalization constant for the critical current density, Bc2 the upper critical field, Bc20 the upper critical field at zero temperature, Tc0 the critical temperature at zero magnetic, ˛, ˇ and the exponential variables. All the parameters for the PF1, PF4 and DC2 NbTi strands are listed in Table 5. 3. Results of calculations and stability analysis 3.1. Stability margin The stability analysis is performed at constant peak magnetic field and constant operating current [11]. For stability analysis, a rectangular energy disturbance over a length L and with a duration t is applied at the middle of the cooling channel length. The Table 5 Scaling parameters for the PF1, PF4 and DC2 NbTi strands.
Fig. 5. Schematic diagram for coolant circuit.
PF1 PF4 DC2
C0 (AT/mm2 )
Bc20 (T)
Tc0 (K)
˛
ˇ
168,512 122,140 113,200
14.61 13.60 13.72
9.03 8.75 8.79
1.000 1.007 1.000
1.540 1.084 0.980
2.100 2.051 1.960
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X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
Fig. 6. Stability margin of PF1 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
stability analysis is performed with the code Gandalf by determining the maximum energy deposition (Q0 ) with given length (L) and duration (t) which can be absorbed without runaway. The stability margin (E) is then derived by Eq. (5): E=
Q0 · L · t (ASC + ACu) · L
(5)
where Q0 ·L·t is the total input energy, (ASC + ACu)·L is the heated volume of superconducting strands. The copper core is not considered in the stability for a conservative analysis. Stability margins and maximum energy depositions of a mechanical disturbance (L = 1 cm, t = 1 ms) and an electromagnetic disturbance (L = 10 m, t = 100 ms) [12,13] at maximum operating magnetic field and maximum operating current of PF1, PF4 and DC2 respectively are shown in Table 6. From Table 6 we can see that the stability margins of conductors of the mechanical disturbance are higher than the stability margins of the electromagnetic disturbance. Under the worst working environment, PF4 conductor has the lowest stability margins of the mechanical disturbance and PF1 conductor has the lowest stability margins of the electromagnetic disturbance in the PF system. Stability margins of PF1, PF4 and DC2 as a function of operating current for different background fields are shown in Figs. 6–8. The trends of stability margins of PF1 and DC2 dependence of operating current and background field are almost the same. Under the mechanical disturbance, the stability margin shows the trend of nearly linear decrease with the increase of operating current and background field. Under the electromagnetic disturbance, at high
Fig. 7. Stability margin of PF4 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
background field (e.g. the background fields of PF1 and DC2 are 6T and 5T, respectively.) the stability margin shows the trend of nearly linear decrease with the increase of operating current; at low background field, the reduction rate of stability margin becomes slower along with the increase of operating current. For PF4, under the mechanical disturbance, the reduction rate of stability margin becomes slower along with the increase of operating current in general. Under the electromagnetic disturbance, the stability margin shows the trend of nearly linear decrease with the increase of operating current, except for at low background field and low operating current. 3.2. Current sharing temperature and temperature margin The current sharing temperature Tcs is a crucial parameter for the stability of the CICC conductor. At Tcs , the operating current gets to the critical current, the superconductor gets to the state of quench, and the current flows into the copper of NbTi strands. The results of Tcs of PF1, PF4 and DC2 at maximum operating magnetic field and maximum operating current are 6.1 K, 7.1 K and 6.7 K, respectively. The temperature margin Tm represents a capacity for heat absorption in the surrounding helium before the strands got quenched. The margin against uncertainties in the strand performance is provided by Tm . Tm can be derived by Eq. (6). Therefore, the Tm of PF1, PF4 and DC2 at maximum operating magnetic field and maximum operating current are 1.6 K, 2.6 K and 2.2 K, respectively. They are all higher than the design criterion of temperature
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
17
Table 6 Stability margins and maximum energy depositions of PF1, PF4 and DC2 conductors. Conductor tape
PF1 PF4 DC2
Mechanical disturbance
Electromagnetic disturbance
Q0 (W/m)
E (mJ/cc)
Q0 (W/m)
E (mJ/cc)
802,553 296,503 1,118,025
1346 995 2344
1164 1102 1370
195 371 287
Fig. 9. The Tcs of PF1 as a function of operating current for different background fields.
Fig. 8. Stability margin of DC2 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
Figs. 12 and 13 show that when energy disturbance happening, the conductor temperature near the disturbance place increases quickly. Then because of the accelerating flow of helium after heating, the transient heat transfer coefficient increases, so the refrigeration is enhanced. In the case of recovery, the conductor temperature decreases quickly and the conductor backs to the superconducting state. In the case of quench, the conductor temperature will remain increasing after a short period of temperature decrease because of multiple effects of joule heat and friction heat. The quench starts in the place where the energy disturbance happens in the middle of conductor, and the quench propagates along the conductor in both helium inlet and outlet directions. The temperature at different positions along the length of conductor is very different. It causes a non-uniform
margin 1.5 K. Therefore, the present design of CFETR PF conductor can satisfy the requirement of safety margin. Tm = Tcs − Top
(6)
where Top the operating temperature. The Tcs of PF1, PF4 and DC2 as a function of operating current for different background fields are shown in Figs. 9–11. Figs. 9–11 show that the Tcs appears the trend of linear decrease with the increase of operating current and background field. From Eq. (6) we can easily know that when the Top is constant, the trend of Tm is the same with Tcs . 3.3. Distribution of conductor temperature Take the PF1 conductor as example, the typical distributions of conductor temperature (Tco ) along the length of conductor of the mechanical disturbance and the electromagnetic disturbance are shown in Figs. 12 and 13 (the minus sign of the horizontal coordinate means the other side of the center of conductor).
Fig. 10. The Tcs of PF4 as a function of operating current for different background fields.
18
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
Fig. 11. The Tcs of DC2 as a function of operating current for different background fields.
heating of the superconducting cable. The superconducting cable may be destroyed because of the emergence of thermomechanical stresses [14]. The emergence and propagation of the quench results in the emergence and rise in active voltage across the part of superconducting cable, which may cause the electrical break down.
Fig. 13. Distribution of PF1 conductor temperature along the length of conductor of the electromagnetic disturbance; (A) recovery, (B) quench. The inserted figure is time history of voltage.
3.4. AC loss and stability analysis of PF4 conductor The stability analysis of PF4 conductor considering the influence of AC loss is performed as an example. AC loss of PF conductor including hysteresis loss and coupling loss, which can be estimated applying the conventional formulas, respectively [15]: PH =
2 d Jc Asc 3 f
PC =
2 0
dB
dB 2 dt
(7)
dt A
(8)
where PH is the hysteresis loss, PC is the coupling loss, df is the equivalent superconducting filament diameter, Jc is the critical current density for the hysteresis loss, Asc is the total cross section of superconducting filament, dB/dt is the changing rate of magnetic field, is the decay time constant of the coupling current, 0 is the permeability of vacuum, A is the total cross section of superconducting filament and total copper. All the parameters for the calculation of hysteresis loss and coupling loss for PF4 conductor are listed in Table 7. For conservative purpose, the value of dB/dt in Table 7 is the maximum changing rate of magnetic field of PF4. Table 7 Parameters for the calculation of PH and PC for PF4 conductor. Fig. 12. Distribution of PF1 conductor temperature along the length of conductor of the mechanical disturbance; (A) recovery, (B) quench. The inserted figure is time history of voltage.
df (m)
Jc (kA/mm2 )
Asc (mm2 )
dB/dt
(ms)
A (mm2 )
8
2.9
90.3
0.41
56.614
515
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
19
electromagnetic disturbance. The variation trend of stability margin along with the change of operating current and background magnetic field is also discussed in detail. Compared with the design criterion of temperature margin, the present design of CFETR PF conductor can satisfy the requirement of safety margin. The results of Tcs show that the Tcs appears the trend of linear decrease with the increase of operating current and background field. From the distributions of conductor temperature along the length of conductor in different situations, it can be concluded that the emergence and propagation of the quench may cause the destruction of superconducting cable because of extremely uneven temperature distribution and also results in the emergence and rise in active voltage, which may cause the electrical break down. And the PF4 conductor is proved operating in superconducting state safely considering the influence of AC loss. Acknowledgments Fig. 14. Distribution of PF4 conductor temperature along the length of conductor.
It can be calculated by Eq. (7) and Eq. (8) that PH equals to 0.1823 W/m, PC equals to 7.80 W/m. Therefore, the AC loss of PF4 conductor is 7.9823 W/m. For stability analysis, the AC loss is applied at the whole length of PF4 conductor as a rectangular energy disturbance. The total AC loss of whole operating time for PF4 conductor is about 41.67 kJ. Therefore, the duration of this energy disturbance should be 9.85 s. To be conservative, the stability analysis is performed at constant peak magnetic field and constant operating current and the duration of energy disturbance extended to 20 s. The distributions of PF4 conductor temperature along the length of conductor is shown in Fig. 14. Fig. 14 shows that the maximum conductor temperature during the duration of energy disturbance is about 5.15 K, which is lower than Tcs . After the duration of energy disturbance the conductor temperature begins to decrease. Therefore, it is proved that the PF4 conductor operates in superconducting state safely considering the influence of AC loss. Fig. 14 also shows that the location of minimum Tm appears at the half of cooling channel length distance away from helium inlet. Considering the influence of AC loss, the maximum conductor temperature of PF4 is 5.15 K. By this time the temperature margin Tm = Tcs − Top = Tcs − Tco = 7.1 K–5.15 K = 1.95 K. Stability margins of the mechanical disturbance (L = 1 cm, t = 1 ms) and the electromagnetic disturbance (L = 10 m, t = 100 ms) become 657 mJ/cc and 282 mJ/cc, respectively. 4. Conclusions The analysis of stability and quench of the PF1, PF4 and DC2 conductors of PF system has been performed. The following main conclusions can be drawn from the calculation results: For the stability margin analysis, the stability margins of conductors of the mechanical disturbance (L = 1 cm, t = 1 ms) are higher than the stability margins (L = 10 m, t = 100 ms) of the
The author would like to express her thanks to all the members of CFETR design team. Besides, the author would like to express her sincere gratitude to CFETR physical design group who provided all the physical target parameters. References [1] Y.T. Song, J.G. Li, Y.X. Wan, B.N. Wan, P. Fu, X. Gao, et al., The accomplishments and next-step plan of EAST in support of fusion, IEEE Trans. Plasma Sci. 42 (2014) 415–420. [2] Y.T. Song, S.T. Wu, J.G. Li, B.N. Wan, Y.X. Wan, P. Fu, et al., Concept design of CFETR tokamak machine, IEEE Trans. Plasma Sci. 42 (2014) 503–509. [3] J.X. Zheng, Y.T. Song, X.F. Liu, J.G. Li, Y.X. Wan, M.Y. Ye, et al., Concept design of hybrid superconducting magnet for CFETR tokamak reactor, in: IEEE 25th Symposium on Fusion Engineering, 2013. [4] Y. Song, P. Bauer, Y. Cheng, A. Devred, F. Rodriguez-Mateos, K. Ding, et al., Design of the ITER TF magnet feeder systems, IEEE Trans. Appl. Supercond. 20 (2010) 1710–1713. [5] Y. Takahashi, K. Yoshida, Y. Nabara, M. Edaya, N. Mitchell, Simulation of quench tests of the central solenoid insert coil in the ITER central solenoid model coil, IEEE Trans. Appl. Supercond. 16 (2006) 783–786. [6] Y. Takahashi, K. Yoshida, Y. Nabara, M. Edaya, D. Bessette, N. Shatil, et al., Stability and quench analysis of toroidal field coils for ITER, IEEE Trans. Appl. Supercond. 17 (2007) 2426–2429. [7] J. Zheng, Y. Song, Concept design of CFETR superconducting magnet system based on different maintenance ports, Fusion Eng. Des. 88 (2013) 2960– 2966. [8] S. Li, Y. Wu, B. Liu, P. Weng, Current sharing temperature test and simulation with GANDALF code for ITER PF2 conductor sample, Plasma Sci. Technol. 13 (2011) 627–630. [9] Y. Shi, Y. Wu, S. Li, B. Liu, F. Long, Performance evaluation and analysis of ITER poloidal field conductors, Fusion Eng. Des. 87 (2012) 1801–1804. [10] L. Bottura, A practical fit for the critical surface of NbTi, IEEE Trans. Appl. Supercond. 10 (2000) 1054–1057. [11] C. Marinucci, Stability analysis of the ITER TF and CS conductors using the code Gandalf, IEEE Trans. Appl. Supercond. 9 (1999) 612–615. ¨ [12] S. Nicollet, D. Bessette, D. Ciazynski, J.L. Duchateau, B. Lacroix, H. Rajainmaki, Stability analysis of the ITER poloidal field coils conductor, Cryogenics 49 (2009) 687–693. [13] L.S. Richard, D. Bessette, R. Zanino, Stability analysis of the ITER PF coils, IEEE Trans. Appl. Supercond. 19 (2009) 1496–1499. [14] J. Fang, Z.M. Chen, S.T. Wu, P.D. Weng, Research of the CICC stability by the numerical code Gandalf, Plasma Sci. Technol. 2 (2000) 383–396. [15] B. Seeber, Handbook of Applied Superconductivity, Institute of Physics Publishing, Bristol/Philadelphia, 1998.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Stability analysis of the conductors for CFETR poloidal field coils Xin He a , Jinxing Zheng b,∗ , Hao Zhang a , Xufeng Liu b a b
School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230029, China Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China
h i g h l i g h t s • The stability margin variation rules versus operating conditions were discussed. • The Tcs of PF conductors at different operating conditions were calculated. • The typical distributions of conductor temperature were presented and studied.
a r t i c l e
i n f o
Article history: Received 24 July 2014 Received in revised form 6 February 2015 Accepted 26 March 2015 Available online 11 April 2015 Keywords: Cable-in-conduit conductors Stability Current sharing temperature Poloidal field
a b s t r a c t China Fusion Engineering Testing Reactor (CFETR) is a new tokamak device. The poloidal field (PF) system of CFETR plays an important role in controlling the location and shape of the plasma. The stable operation of the PF system is largely based on the superconductor stability. Therefore, the stability analysis of the PF1, PF4 and DC2 conductors of PF system has been performed. For stability analysis, a mechanical disturbance and an electromagnetic disturbance are applied, respectively. The calculation results of stability margin, current sharing temperature, temperature margin and distribution of conductor temperature are presented and discussed in this paper. The analysis results illustrates that the present design of CFETR PF conductor can satisfy the requirement of safety margin. © 2015 Elsevier B.V. All rights reserved.
1. Introduction China Fusion Engineering Testing Reactor (CFETR) is a new tokamak device to fully bridge the gap between ITER and DEMO [1]. The main design parameters of CFETR compared with those of ITER are shown in Table 1 [2,3]. The CFETR magnet system consists of the toroidal field (TF) system, central solenoid (CS) system and poloidal field (PF) system. Fig. 1 shows the overview structure and geometry of CFETR magnet system. The PF system in CFETR consists of eight coils, namely PF1 through PF6, DC1 and DC2, which control the location and shape of the plasma [4]. The PF coils of CFETR consist of 6–9 double pancakes. Each double pancake is wound in a “two-in-hand” configuration by NbTi cable-in-conduit conductor (CICC). The CICC stability is one of the most important problems related to superconductor behavior and coil protection system design. Therefore, the analysis of stability and quench of the PF conductors is necessary. In this paper, the electric and thermohydraulic
∗ Corresponding author. Tel.: +86 551 5592013; fax: +86 551 5591310. E-mail address: [email protected] (J. Zheng). http://dx.doi.org/10.1016/j.fusengdes.2015.03.048 0920-3796/© 2015 Elsevier B.V. All rights reserved.
simulation code Gandalf is used to evaluate the performance of PF conductors at different working environment [5,6]. Some of the calculation results are presented and the regularities of the results are discussed. 2. Thermohydraulic and stability calculation by Gandalf The sizes of PF coils for CFETR are shown in Table 2. The conductor used in PF coils is a round-in-square CICC as shown in Fig. 2. NbTi strands are cabled as six petals with a multi-stage cable pattern around an open central spiral and are cooled by forced-flow supercritical helium [7]. Copper strands and cores of suitable diameters are incorporated into the cabling layout by adding a central core in the second, third or fourth stages. Schematic diagram for the cable layout of PF conductor is shown in Fig. 3. Therefore, the total amount of copper is adjusted to each coil type in order to provide the necessary quench protection and also give a fully transposed cable layout. The overall cable and spiral are inserted inside a round-in-square jacket made from 316 L stainless steel. Table 3 lists the major parameters of PF conductors and coils. Determining the stability margin and temperature margin of the conductor is the design basis of CICC. For design criteria, the overall
14
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19 Table 1 The physical target parameters of CFETR. Parameter Plasma current Ip (MA) Major radius of plasma R (m) Minor radius of plasma a (m) Central magnetic field Bt (T) Elongation ratio Triangle deformation ı Number of TF coils (N)
CFETR
ITER
8.5/10
15
5.7
6.2
1.6
2.0
4.5/5.0
5.3
1.8
1.70/1.85
0.4
0.33/0.48
16
18
Table 2 The sizes of PF coils for CFETR.
Fig. 1. Overview structure and geometry of CFETR magnet system.
Coils
R (m)
Z (m)
R (m)
Z (m)
Turns
PF1 PF2 PF3 PF4 PF5 PF6 DC1 DC2
3.109 9.150 11.704 11.704 9.150 3.109 5.659 7.840
7.642 6.697 2.743 −2.743 −6.697 −7.642 −7.791 −7.447
1.353 0.834 0.834 0.834 0.834 1.353 0.834 0.834
0.861 0.715 0.715 0.715 0.715 0.861 0.715 0.715
308 168 168 168 168 308 168 168
Note: R and Z are the radial and axial coordinate values of center of the coil cross section, respectively. The origin for R and Z coordinates is the intersection of central axis of CFETR and symmetry axis of D-shaped TF coil annular cross section. R and Z are the radial and axial diameter of the coil, respectively. Turns are the number of turns of coils.
Fig. 2. Schematic diagram for the NbTi CICC used in PF coils.
Fig. 3. Schematic diagram for the cable layout of PF conductor.
stability requirement is that the conductor must not quench during plasma operation, including the electromagnetic disturbances created by a plasma disruption and vertical displacement events and any mechanical heating. It is adequate as long as the stability margin exceeds the expected disturbance with a safety factor of 2. For NbTi strand, the Cu-to-non-Cu ratio lager than 1.0 and the temperature margin must be higher than 1.5 K is also required. The stability margin and temperature margin are mainly affected by the given magnetic field, operating current and operating temperature. The cable patterns of PF1 and PF6 are the same. The cable patterns of PF2, PF3, PF4 and PF5, DC1, DC2 are also the same, respectively. Comparing the electromagnetic parameters of these conductors in Table 3, it can be seen that PF1, PF4 and DC2 are working in the worst environment of the three types of cable patters, respectively. Therefore, the calculation of stability and quench of PF1, PF4 and DC2 are performed. The coolant inlet location is important for conductor stability. For PF coil, the coolant inlet is positioned at the inner-most turn of the double pancake, in the length of the vertical joggle. And the coolant outlets are located at the inter-pancake joint and the intrapancake joint, respectively. The schematic diagram for inlet and outlet location of PF coil is shown in Fig. 4. The schematic diagram
Table 3 Major parameters of PF conductors and coils.
Sc strand type Cable pattern Central spiral (mm) NbTi strand Cu-to-non-Cu ratio Number of sc strands Void fraction (annulus) (%) Cable diameter (mm) Circle-in-square 316 L Jacket (mm2 ) RRR Operating temperature (K) Maximum operating current (kA) Maximum operating magnetic filed (T) Cooling channel length (m) Inlet pressure of He (bar) mass flow rate of He (g/s)
PF1, PF6
PF2, PF3, PF4
PF5, DC1, DC2
NbTi 3sc × 4 × 4 × 5 × 6 10 × 12 1.6 1440 34.3 37.7 53.8x53.8 100 4.5 51, 39 6.91, 5.08 430 6 8
NbTi {[(2sc + 1Cu strand) × 3 × 4 + 1Cu core1)] × 5 + 1Cu core2} × 6 10 × 12 2.3 720 34.2 35.3 51.9x51.9 100 4.5 33, 28, 53 2.69, 2.19, 3.62 405, 530, 530 6 8
NbTi (3sc × 4 × 4 × 4 + 1Cu core3) × 6 10 × 12 2.3 1152 34.1 35.3 51.9x51.9 100 4.5 35, 42, 55 4.56, 4.01, 5.05 405, 500, 690 6 8
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
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Table 4 Conductor characteristic for stability analysis. Parameter
Unit
Value PF1
Note PF4
DC2
ASC AST AJK AIN ISC AHEB AHEH EPSLON
m2 m2 m2 m2 – m2 m2 –
RRR DHB
– m
100 4.7375e−4
100 5.0430e−4
100 4.9349e−4
DHH PHTC PHTCJ
m m m
12.0e−3 2.7520 1.1844e−2
12.0e−3 1.3760 1.1090e−2
12.0e−3 2.2016 1.1090e−2
PHTJ
m
1.0660e−1
9.9808e−2
9.9808e−2
PERFOR
–
0.15
0.15
0.15
XLENGT PREINI TEMINI MDTINL
m Pa K kg/s
229.27e−6 366.84e−6 1778.16e−6 219.20e−6 1 344.43e−6 113.04e−6 −7e−3
430 6.0e5 4.5 8e−3
90.32e−6 207.73e−6 1714.93e−6 211.60e−6 1 296.19e−6 113.04e−6 −7e−3
144.51e−6 332.37e−6 1714.93e−6 211.60e−6 1 295.48e−6 113.04e−6 −7e−3
530 6.0e5 4.5 8e−3
690 6.0e5 4.5 8e−3
Area of non-copper in sc strand Area of copper in sc strands Area of SS jacket Area of insulation NbTi with bronze, user’s library Area of helium in annulus Area of helium in spiral Total longitudinal strain in sc in operating condition Residual resistivity ratio for stabilizer material 4 × Area of helium in annulus/w. perim annulus Outer diameter of the central spiral W. perim sc strands (applied 5/6) Perimeter used for heat transfer calculation between the strands and the jacket Perimeter used for heat transfer calculation between the bundle helium and the jacket Percentage perforation of the separation perimeter between the bundle helium and the hole helium Total length of the cooling channel Pressure at inlet Temperature at inlet He mass flow at inlet
process described in Gandalf. The PHTC for heat transfer between the strands and helium is considered only for the superconducting strands; the parameter is affected by the ratio 5/6 because of the triplet configuration in the first stage [9]. The Bottura scaling formulae as a function of the operational temperature and magnetic field [10] are used to scale the strand performance: Jc =
C0 ˛ ˇ b (1 − b) (1 − t 1.7 ) B
(1)
Bc2 = Bc20 (1 − t 1.7 )
Fig. 4. Schematic diagram for coolant inlet and outlet location of PF coil.
for coolant circuit is shown in Fig. 5. The boundary conditions for the flow are set for helium pressure, temperature and mass flow rate applied at the inlet of the conductor. The boundary conditions of Gandalf are in constant pressure and temperature, as established from the initial distribution which is routinely calculated [8]. The detailed parameters used for stability analysis by the code Gandalf are presented in Table 4. For conservative purpose, the stabilizer (AST) taken into account is the copper associated with the superconducting strands only. It is also consistent with the joule heating
(2)
b=
B Bc2 (T )
(3)
t=
T Tc0
(4)
where Jc the critical current density, C0 the normalization constant for the critical current density, Bc2 the upper critical field, Bc20 the upper critical field at zero temperature, Tc0 the critical temperature at zero magnetic, ˛, ˇ and the exponential variables. All the parameters for the PF1, PF4 and DC2 NbTi strands are listed in Table 5. 3. Results of calculations and stability analysis 3.1. Stability margin The stability analysis is performed at constant peak magnetic field and constant operating current [11]. For stability analysis, a rectangular energy disturbance over a length L and with a duration t is applied at the middle of the cooling channel length. The Table 5 Scaling parameters for the PF1, PF4 and DC2 NbTi strands.
Fig. 5. Schematic diagram for coolant circuit.
PF1 PF4 DC2
C0 (AT/mm2 )
Bc20 (T)
Tc0 (K)
˛
ˇ
168,512 122,140 113,200
14.61 13.60 13.72
9.03 8.75 8.79
1.000 1.007 1.000
1.540 1.084 0.980
2.100 2.051 1.960
16
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
Fig. 6. Stability margin of PF1 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
stability analysis is performed with the code Gandalf by determining the maximum energy deposition (Q0 ) with given length (L) and duration (t) which can be absorbed without runaway. The stability margin (E) is then derived by Eq. (5): E=
Q0 · L · t (ASC + ACu) · L
(5)
where Q0 ·L·t is the total input energy, (ASC + ACu)·L is the heated volume of superconducting strands. The copper core is not considered in the stability for a conservative analysis. Stability margins and maximum energy depositions of a mechanical disturbance (L = 1 cm, t = 1 ms) and an electromagnetic disturbance (L = 10 m, t = 100 ms) [12,13] at maximum operating magnetic field and maximum operating current of PF1, PF4 and DC2 respectively are shown in Table 6. From Table 6 we can see that the stability margins of conductors of the mechanical disturbance are higher than the stability margins of the electromagnetic disturbance. Under the worst working environment, PF4 conductor has the lowest stability margins of the mechanical disturbance and PF1 conductor has the lowest stability margins of the electromagnetic disturbance in the PF system. Stability margins of PF1, PF4 and DC2 as a function of operating current for different background fields are shown in Figs. 6–8. The trends of stability margins of PF1 and DC2 dependence of operating current and background field are almost the same. Under the mechanical disturbance, the stability margin shows the trend of nearly linear decrease with the increase of operating current and background field. Under the electromagnetic disturbance, at high
Fig. 7. Stability margin of PF4 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
background field (e.g. the background fields of PF1 and DC2 are 6T and 5T, respectively.) the stability margin shows the trend of nearly linear decrease with the increase of operating current; at low background field, the reduction rate of stability margin becomes slower along with the increase of operating current. For PF4, under the mechanical disturbance, the reduction rate of stability margin becomes slower along with the increase of operating current in general. Under the electromagnetic disturbance, the stability margin shows the trend of nearly linear decrease with the increase of operating current, except for at low background field and low operating current. 3.2. Current sharing temperature and temperature margin The current sharing temperature Tcs is a crucial parameter for the stability of the CICC conductor. At Tcs , the operating current gets to the critical current, the superconductor gets to the state of quench, and the current flows into the copper of NbTi strands. The results of Tcs of PF1, PF4 and DC2 at maximum operating magnetic field and maximum operating current are 6.1 K, 7.1 K and 6.7 K, respectively. The temperature margin Tm represents a capacity for heat absorption in the surrounding helium before the strands got quenched. The margin against uncertainties in the strand performance is provided by Tm . Tm can be derived by Eq. (6). Therefore, the Tm of PF1, PF4 and DC2 at maximum operating magnetic field and maximum operating current are 1.6 K, 2.6 K and 2.2 K, respectively. They are all higher than the design criterion of temperature
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
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Table 6 Stability margins and maximum energy depositions of PF1, PF4 and DC2 conductors. Conductor tape
PF1 PF4 DC2
Mechanical disturbance
Electromagnetic disturbance
Q0 (W/m)
E (mJ/cc)
Q0 (W/m)
E (mJ/cc)
802,553 296,503 1,118,025
1346 995 2344
1164 1102 1370
195 371 287
Fig. 9. The Tcs of PF1 as a function of operating current for different background fields.
Fig. 8. Stability margin of DC2 as a function of operating current for different background fields (A) mechanical disturbance, (B) electromagnetic disturbance.
Figs. 12 and 13 show that when energy disturbance happening, the conductor temperature near the disturbance place increases quickly. Then because of the accelerating flow of helium after heating, the transient heat transfer coefficient increases, so the refrigeration is enhanced. In the case of recovery, the conductor temperature decreases quickly and the conductor backs to the superconducting state. In the case of quench, the conductor temperature will remain increasing after a short period of temperature decrease because of multiple effects of joule heat and friction heat. The quench starts in the place where the energy disturbance happens in the middle of conductor, and the quench propagates along the conductor in both helium inlet and outlet directions. The temperature at different positions along the length of conductor is very different. It causes a non-uniform
margin 1.5 K. Therefore, the present design of CFETR PF conductor can satisfy the requirement of safety margin. Tm = Tcs − Top
(6)
where Top the operating temperature. The Tcs of PF1, PF4 and DC2 as a function of operating current for different background fields are shown in Figs. 9–11. Figs. 9–11 show that the Tcs appears the trend of linear decrease with the increase of operating current and background field. From Eq. (6) we can easily know that when the Top is constant, the trend of Tm is the same with Tcs . 3.3. Distribution of conductor temperature Take the PF1 conductor as example, the typical distributions of conductor temperature (Tco ) along the length of conductor of the mechanical disturbance and the electromagnetic disturbance are shown in Figs. 12 and 13 (the minus sign of the horizontal coordinate means the other side of the center of conductor).
Fig. 10. The Tcs of PF4 as a function of operating current for different background fields.
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X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
Fig. 11. The Tcs of DC2 as a function of operating current for different background fields.
heating of the superconducting cable. The superconducting cable may be destroyed because of the emergence of thermomechanical stresses [14]. The emergence and propagation of the quench results in the emergence and rise in active voltage across the part of superconducting cable, which may cause the electrical break down.
Fig. 13. Distribution of PF1 conductor temperature along the length of conductor of the electromagnetic disturbance; (A) recovery, (B) quench. The inserted figure is time history of voltage.
3.4. AC loss and stability analysis of PF4 conductor The stability analysis of PF4 conductor considering the influence of AC loss is performed as an example. AC loss of PF conductor including hysteresis loss and coupling loss, which can be estimated applying the conventional formulas, respectively [15]: PH =
2 d Jc Asc 3 f
PC =
2 0
dB
dB 2 dt
(7)
dt A
(8)
where PH is the hysteresis loss, PC is the coupling loss, df is the equivalent superconducting filament diameter, Jc is the critical current density for the hysteresis loss, Asc is the total cross section of superconducting filament, dB/dt is the changing rate of magnetic field, is the decay time constant of the coupling current, 0 is the permeability of vacuum, A is the total cross section of superconducting filament and total copper. All the parameters for the calculation of hysteresis loss and coupling loss for PF4 conductor are listed in Table 7. For conservative purpose, the value of dB/dt in Table 7 is the maximum changing rate of magnetic field of PF4. Table 7 Parameters for the calculation of PH and PC for PF4 conductor. Fig. 12. Distribution of PF1 conductor temperature along the length of conductor of the mechanical disturbance; (A) recovery, (B) quench. The inserted figure is time history of voltage.
df (m)
Jc (kA/mm2 )
Asc (mm2 )
dB/dt
(ms)
A (mm2 )
8
2.9
90.3
0.41
56.614
515
X. He et al. / Fusion Engineering and Design 95 (2015) 13–19
19
electromagnetic disturbance. The variation trend of stability margin along with the change of operating current and background magnetic field is also discussed in detail. Compared with the design criterion of temperature margin, the present design of CFETR PF conductor can satisfy the requirement of safety margin. The results of Tcs show that the Tcs appears the trend of linear decrease with the increase of operating current and background field. From the distributions of conductor temperature along the length of conductor in different situations, it can be concluded that the emergence and propagation of the quench may cause the destruction of superconducting cable because of extremely uneven temperature distribution and also results in the emergence and rise in active voltage, which may cause the electrical break down. And the PF4 conductor is proved operating in superconducting state safely considering the influence of AC loss. Acknowledgments Fig. 14. Distribution of PF4 conductor temperature along the length of conductor.
It can be calculated by Eq. (7) and Eq. (8) that PH equals to 0.1823 W/m, PC equals to 7.80 W/m. Therefore, the AC loss of PF4 conductor is 7.9823 W/m. For stability analysis, the AC loss is applied at the whole length of PF4 conductor as a rectangular energy disturbance. The total AC loss of whole operating time for PF4 conductor is about 41.67 kJ. Therefore, the duration of this energy disturbance should be 9.85 s. To be conservative, the stability analysis is performed at constant peak magnetic field and constant operating current and the duration of energy disturbance extended to 20 s. The distributions of PF4 conductor temperature along the length of conductor is shown in Fig. 14. Fig. 14 shows that the maximum conductor temperature during the duration of energy disturbance is about 5.15 K, which is lower than Tcs . After the duration of energy disturbance the conductor temperature begins to decrease. Therefore, it is proved that the PF4 conductor operates in superconducting state safely considering the influence of AC loss. Fig. 14 also shows that the location of minimum Tm appears at the half of cooling channel length distance away from helium inlet. Considering the influence of AC loss, the maximum conductor temperature of PF4 is 5.15 K. By this time the temperature margin Tm = Tcs − Top = Tcs − Tco = 7.1 K–5.15 K = 1.95 K. Stability margins of the mechanical disturbance (L = 1 cm, t = 1 ms) and the electromagnetic disturbance (L = 10 m, t = 100 ms) become 657 mJ/cc and 282 mJ/cc, respectively. 4. Conclusions The analysis of stability and quench of the PF1, PF4 and DC2 conductors of PF system has been performed. The following main conclusions can be drawn from the calculation results: For the stability margin analysis, the stability margins of conductors of the mechanical disturbance (L = 1 cm, t = 1 ms) are higher than the stability margins (L = 10 m, t = 100 ms) of the
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