Multifarious Physics Analyses of the Core Plasma Properties in a Helical DEMO Reactor FFHR-d1

1 FTP/P7-34 Multifarious Physics Analyses of the Core Plasma Properties in a Helical DEMO Reactor FFHR-d1 J. Miyazawa 1, M. Yokoyama 1, Y. Suzuki 1, S. Satake 1, R. Seki 1, Y. Masaoka 2, S. Murakami 2, Y. Narushima 1, M. Nunami 1, T. Goto 1, C. Suzuki 1, H. Funaba 1, I. Yamada 1, R. Sakamoto 1, G. Motojima 1, H. Yamada 1, A. Sagara 1, and the FFHR Design Group 1 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan 2 Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan E-mail contact of main author: miyazawa@lhd.nifs.ac.jp Abstract. Physics assessments on the MHD equilibrium and stability, the neoclassical transport, and the alpha particle transport, etc., are being carried out for a helical fusion DEMO reactor named FFHR-d1, using radial profiles extrapolated from LHD. A large Shafranov shift is foreseen in FFHR-d1 due to its high-beta property. This leads to deterioration in the neoclassical transport and alpha particle confinement. Plasma position control using the vertical magnetic field has been examined and shown to be effective for Shafranov shift mitigation. Especially in a high aspect ratio configuration, it is possible to keep the magnetic surfaces similar to those in vacuum with high central beta of 8.5 % by applying a proper vertical magnetic field. As long as the Shafranov shift is mitigated, the neoclassical thermal transport can be kept at a level compatible with the alpha heating power. The alpha particle loss can also be kept at a low level as long as the loss boundary of alpha particles is on the blanket surface and the plasma position control is properly applied. The lost positions of alpha particles are localized around the divertor region that is located behind the blanket in FFHR-d1. 1. Introduction FFHR-d1 is a heliotron type DEMO reactor of which the conceptual design activity has been started since 2010 [1,2]. It is possible to sustain the burning plasma without auxiliary heating (i.e., self-ignition) in FFHR-d1, since there is no need of plasma current drive in heliotron plasmas. The device size is 4 times enlarged from LHD [3], i.e., the major radius of the helical coil center is 15.6 m, the magnetic field strength at the helical coil center is 4.7 T, and the fusion output is ~3 GW [1,2]. One of the distinguished features of FFHR-d1 compared with the former FFHR design series is the robust similarity with LHD. The arrangement of superconducting magnet coils in FFHR-d1 is similar to that of LHD, except a pair of planar poloidal coils omitted to maximize the maintenance ports [4]. This makes it reasonable to assume a similar MHD equilibrium as observed in LHD for FFHR-d1, as long as the beta profiles in these two are similar. In FFHR-d1, radial profiles of density and temperature are determined by multiplying proper enhancement factors on those obtained in LHD, according to the DPE (Direct Profile Extrapolation) method [5]. The enhancement factors are calculated consistently with the gyro-bohm model. Therefore, the global confinement properties as expressed in ISS95 [6] or ISS04 [7] are kept in FFHR-d1. It should be noted that the temperature profile is not necessarily fixed in DPE and various kinds of temperature profiles observed in LHD can be extrapolated to FFHR-d1. This paper discusses the results of detailed physics analyses of the core plasma properties in FFHR-d1. The radial profiles employed are extrapolated from the data obtained in LHD as described in Section 2. Results of physics analyses on the MHD equilibrium and stability, the

2 FTP/P7-34 neoclassical transport, and the alpha particle transport are given in Section 3. Finally, these are summarized in Section 4. 2. Radial Profiles for Detailed Physics Analyses Two sets of radial profiles are used in the detailed physics analyses described in the next section. The first set is named case A, which is shown in FIG. 1. These profiles are extrapolated using the DPE method from the data obtained in the standard configuration of R ax vac = 3.60 m, B 0 = 2.75 T, and γ c = 1.254 in LHD, where R ax vac is the major radius of the magnetic axis in vacuum, B 0 is the magnetic field strength at R ax vac, and γ c = (m a c ) / (l R c ) is the pitch of helical coils (m, l, a c, and R c are the toroidal mode number (= 10), the number of helical coils (= 2), the minor radius (~ 0.9 1.0 m) and the major radius (= 3.9 m) of the helical coils, respectively). The other set is the case B shown in FIG. 2, of which the profiles are extrapolated from the data obtained in the high aspect ratio configuration of R ax vac = 3.60 m, B 0 = 1.50 T, and γ c = 1.20. The averaged plasma aspect ratio, R/a, in vacuum FIG. 1. Radial profiles in the case A of (a) the electron density, (b) the electron temperature, and (c) the plasma beta, (d) the alpha birth profile, and (e) the integrated heating power in FFHR-d1 (closed circles) extrapolated from experimental results of LHD (#96164, t = 6.966 s, R ax vac = 3.60 m, B 0 = 2.75 T, γ c = 1.254, open circles), where enhancement factors for the energy confinement, γ DPE, the density, f n, the temperature, f T, and the plasma beta, f β, are assumed to be 1.29, 2.65, 6.59, and 5.10, respectively. FIG. 2. Radial profiles in the case B of (a) the electron density, (b) the electron temperature, and (c) the plasma beta, (d) the alpha birth profile, and (e) the integrated heating power in FFHR-d1 (closed circles) extrapolated from experimental results of LHD (#109602, t = 3.740 s, R ax vac = 3.60 m, B 0 = 1.50 T, γ c = 1.20, open circles), where enhancement factors for the energy confinement, γ DPE, the density, f n, the temperature, f T, and the plasma beta, f β, are assumed to be 1.14, 12.0, 5.66, and 5.89, respectively.

3 FTP/P7-34 increases from ~5.6 to ~6.4 as γ c is decreased from 1.254 to 1.20. The temperature and density profiles in LHD are measured by Thomson scattering [8]. The density signal of the Thomson scattering is calibrated by the line-density measured by the millimetre wave interferometer [9] that is measuring the same line of sight with the Thomson scattering. In both cases, no auxiliary heating is applied and the conduction power needed to sustain the plasma, P reactor, which is estimated by the gyro-bohm model, is given by the alpha heating power, P α, minus the Bremsstrahlung loss, P B. In other words, the self-ignition condition is satisfied in both cases. The beta profile in the case A is more peaked than that in the case B. As a result, the central beta, β 0, is ~9 % in the case A and ~8 % in the case B. Note that peaked beta profiles are not favourable from the point of view of Shafranov shift mitigation. Furthermore, the high aspect ratio configuration itself is effective for Shafranov shift mitigation [10]. The beta profiles in the standard and the high aspect ratio configurations are compared in FIG. 3. In both cases, the peak position of the beta profile, i.e., the magnetic axis, is moved from the initial position of R ax vac = 3.60 m, due to the Shafranov shift. As seen in the figure, a higher central beta than that in the standard configuration is achieved with a smaller Shafranov shift in the high aspect ratio configuration. 3. Detailed Physics Analyses Using radial profiles shown in FIGs. 1 and 2, detailed physics analyses have been carried out. At first, the MHD equilibrium for these profiles is calculated by HINT2 [11] and VMEC [12]. The MHD stability of these equilibriums is evaluated by TERPSICHORE [13]. Then, the neoclassical transport is calculated by GSRAKE [14] and FORTEC-3D [15]. The alpha particle confinement is estimated by GNET [16] and MORH [17]. 3.1. MHD Equilibrium FIG. 3. Comparison of the beta profiles in the standard configuration (circles) and the high aspect ratio configuration (plusses and crosses). One can use the MHD equilibrium that can fit the radial profiles observed in the experiment, as long as the beta enhancement factor, f β, is equal to one. In the cases shown in FIGs. 1 and 2, f β is 5 6. Therefore, it is necessary to calculate the MHD equilibrium for these cases. As a first step, we tried to reconstruct the MHD equilibrium for the case A by HINT2 [11]. However, it was difficult to obtain the MHD equilibrium with the beta profile shown in FIG. 1(c). As shown in FIG. 4(b), the Shafranov shift is already significant at β 0 ~ 8.5 % and the magnetic surfaces in the edge region become destructed. To resolve this, plasma position control using the vertical magnetic field, B v, is effective. In the LHD type heliotron devices, B v can alter the magnetic axis position in vacuum. In the case of FIG. 4(c), B v identical to that used to form an inward shifted configuration of R ax vac = 14.0 m, which corresponds to R ax vac = 3.50 m in LHD, is applied instead of B v for R ax vac = 14.4 m. Remember that FFHR-d1 is 4 times enlarged from LHD and R ax vac = 14.4 m in FFHR-d1 corresponds to R ax vac = 3.60 m in

FTP/P7-34 4 (a) (a) vacuum vacuum (b) (b) w/o Bv w/o Bv (c) (c) w/ Bv FIG. 4. Magnetic surfaces calculated by the HINT2 code for the case A with (a) β0 = 0 %, Raxvac = 14.4 m (vacuum), (b) β0 ~ 8.5 %, Raxvac = 14.4 m (w/o Bv control), and (c) β0 ~ 10 %, Raxvac = 14.0 m (w/ Bv control). The shape of the beta profile is identical to that shown in Fig. 1(c), while the amplitude is varied. w/ Bv FIG. 5. Magnetic surfaces calculated by the HINT2 code for the case B with (a) β0 = 0 %, Raxvac = 14.4 m (vacuum), (b) β0 ~ 7.5 %, Raxvac = 14.4 m (w/o Bv control), and (c) β0 ~ 8.5 %, Raxvac = 14.0 m (w/ Bv control). The shape of the beta profile is identical to that shown in Fig. 2(c), while the amplitude is varied. LHD. When the plasma position control by Bv is applied, as seen in FIG. 4(c), the destructed magnetic surfaces are reformed. The Shafranov shift is also mitigated by the Bv control, although the Shafranov shift of the magnetic axis is still large. A drastic effect of Bv control is obtained in the case B as shown in FIG. 5. Even in this case, the magnetic surfaces in the edge region become destructed at β0 ~ 7.5 % if Bv control is not applied (FIG. 5(b)). When the Bv control is applied (FIG. 5(c)), however, the magnetic surfaces similar to those in vacuum (FIG. 5(a)) are formed with a high central beta of β0 ~ 8.5 %. The magnetic surfaces in the edge region are reformed and the position of the magnetic axis is effectively pushed back to the initial position of Raxvac ~ 14.4 m. 3.2. MHD Stability In the LHD type heliotron, the inward-shifted configurations of, for example, Raxvac 3.60 m in LHD and Raxvac 14.4 m in FFHR-d1 are characterized by a better neoclassical transport and a worse MHD stability due to the magnetic hill property compared with those of outwardshifted configurations [3,10]. Since the equilibriums used in this study are the inward-shifted configurations, these are expected to be MHD unstable. Especially, the equilibriums shown in FIGs. 4(c) and 5(c) correspond to the strongly inward-shifted configuration of Raxvac = 3.50 m in LHD, where various kinds of MHD instability have been observed. Shown in FIG. 6 is the typical result of 3-D ideal linear MHD stability analysis using TERPSICHORE [13]. The

5 FTP/P7-34 equilibrium analyzed here is the case B with β 0 ~ 8.5 % and B v control (FIG. 5(c)). The positive Mercier index, D I, in the entire region means that the interchange modes can be unstable (FIG. 6(b)). The mode structure composed of m / n = (10 14) / 11 appears as the most unstable mode in the n = 1 mode family, where m and n are the poloidal and toroidal mode number, respectively. These modes are localized around ρ ~ 0.8, where the rational surface of ι / 2π = 1 exists. The consecutive poloidal mode numbers coupled by the toroidal effect show the ballooning-like structure. The low mode number instabilities, e.g., m / n = 1 / 1 or 2 / 1, do not appear as the most unstable mode. Therefore, the high mode number instabilities will become unstable in this case. In LHD, no serious confinement degradation due to the high mode number instabilities has been clearly observed yet. The impact of the high mode number instabilities as shown in FIG. 6 on the MHD stability and the energy confinement property of FFHR-d1 should be carefully considered in the future studies. The core resonant mode of m / n = 2 / 1 does not appear in spite of the large D I. If the rotational transform in the core region decreases below 0.5, then the m / n = 2 / 1 mode will become destabilized. It would be better to take into account the plasma current of, for example, the bootstrap current and/or the neutral-beam driven current, since it can affect the MHD stability by modifying the rotational transform profile. This is also remained for the future studies. In this study, we assume that MHD instability will not be problematic in FFHR-d1, based on the observation in LHD that the plasma can be generated and sustained even in the inward-shifted configurations of R ax vac 3.60 m, which are expected to be Mercier unstable [3,10]. 3.3. Neoclassical Transport FIG. 6. Radial profiles of (a) the rotational transform ι/2π, (b) Mercier index D I, (c) radial deviation ξ S and (d) the potential energy δw. Neoclassical thermal transport is calculated using radial profiles shown in FIGs. 1 and 2, and the MHD equilibriums shown in FIGs. 4 and 5. Radial profiles of integrated total neoclassical flux, Q tot neo = Q i neo + Q e neo, multiplied by the surface area, S, in various cases are shown in FIG. 7, where Q i neo and Q e neo are the neoclassical heat flux transported by ions and electrons, respectively. To calculate Q i neo in the cases with large Shafranov shift, the δf Monte Carlo simulation code FORTEC-3D [15] has been used to take into account the finite drift motion by following the exact guiding-center of ions, while Q i neo in vacuum and Q e neo in all cases are calculated by GSRAKE [14]. In FORTEC-3D, the deuteron plasma is assumed and consideration of deuteron-triton plasma is left for future studies (see Ref. 18 for more details). In the case A without B v control, where the Shafranov shift is large (FIG. 4(b)), the neoclassical heat flow is as large as ~3.5 GW at ρ ~ 0.6. It is reduced to ~2 GW when the B v control is applied. In the case A, however, the neoclassical heat flow cannot be reduced to less than ~1 GW, which is calculated using the vacuum magnetic configuration. This is twice

6 FTP/P7-34 larger than the expected P reactor (= P α P B ) in the case A of ~0.5 GW (see FIG. 1(e)). In the case B with B v control, on the other hand, the neoclassical transport is ~0.4 GW, which is similar to P reactor in the case B (see FIG. 2(e)). Therefore, in terms of energy balance, the case B can be a sustainable option, only if the anomalous transport and the direct loss of alpha particles are negligibly small. Estimation of the anomalous transport is left for the future study. The alpha particle loss is discussed in the next subsection. 3.4. Alpha Particle Confinement The birth and heat deposition profiles of alpha particles calculated by GNET [16] for the case A without B v control are shown in FIG. 8. The energy loss is ~40 % and the particle loss is ~60 % in this case. These results are not affected by the B v control. One of the reasons of this large energy loss can be attributed to the definition of the alpha FIG. 7. Radial profiles of the integrated total neoclassical heat flux. Closed circles, open circles, closed rhombuses, and open squares denote the case A without B v control, the case A with B v control, vacuum (R ax vac = 14.4 m), and the case B with B v control, respectively. particle loss boundary. In GNET, the alpha loss boundary is set at the last-closed-flux-surface (LCFS). However, alpha particles are not practically lost at LCFS. The alpha particles deviated from LCFS can reenter the confinement region. To examine the impact of the definition of loss boundary position, alpha orbit tracing by MORH [17] has been carried out, where the alpha particles loss boundary can be arbitrarily defined by using the magnetic data in the real space. The ratio of confined alpha particles started from various positions with FIG. 8. The birth (broken curve) and heat deposition (thick curve) profiles of alpha particles in FFHR-d1 calculated by GNET, where the MHD equilibrium shown in Fig. 4(b) is used. FIG. 9. The Ratio of confined alpha particles in the case A. Open and closed symbols denote the loss boundary set at LCFS and blanket, while squares and circles denote w/o and w/ B v control, respectively.

7 FTP/P7-34 (a) (b) FIG. 10. Distributions of hitting positions of lost alpha particles on the blanket for the case A, at different toroidal angles of (a) φ = 0 and (b) φ = 27. Four circles in each figure denote the divertor region. Crosses and plusses correspond to without and with B v control, respectively. various pitch angles is summarized in FIG. 9. These are calculated for the case A with and without B v control. It should be noted that the slowing down process is not taken into account in MORH, at this moment. Therefore, the ratio of confined alpha particles shown in FIG. 9 is not necessarily comparable with the deposition to the birth ratio as seen in FIG. 8. When the alpha loss boundary is set at LCFS, the ratio of confined alpha particles is larger than 60 % at ρ < 0.7, in both cases of w/ and w/o B v control. The B v control affects the ratio of confined alpha at ρ > 0.7. However, the number of alpha particles generated in this region is small and this presumably is the reason why no clear difference between w/ and w/o B v control is observed in GNET. When the alpha particles loss boundary is set at the blanket tentatively designed for FFHR-d1 (will be shown in FIG. 10), the ratio of confined alpha particles is improved to > 80 % at ρ < 0.7, even for the case without B v control. Further improvement is obtained when the B v control is applied. In this case, the ratio of confined alpha particles increases to larger than ~85 % at ρ < 0.7. 3.5. Hitting Positions of Alpha Particles To check the hitting positions of alpha particles on in-vessel components, the lost positions of alpha particles calculated by MORH are plotted on the slices of FFHR-d1 at different toroidal angles in FIG. 10. It should be noted that the divertors are placed behind the blanket in FFHRd1, and therefore the divertors are protected from the direct neutron irradiation. This is one of the strong merits of FFHR-d1. According to the MORH results, the majority of lost alpha particles reach the divertor region. A small portion of lost alpha particles started from the edge region of ρ ~ 0.95 will hit the sidewall of the blankets. However, the number of alpha particles generated at ρ ~ 0.95 is small since the temperature in this region is low (see FIGs. 1 and 2). Therefore, we expect that the damage of blanket sidewall will be small. It is necessary to properly design the divertor plates to receive the heat load of lost alpha particles, based on the results obtained here. Note that recalculation of alpha particle orbit is necessary if baffle plates are adopted to increase the neutral pressure in the divertor region.

8 FTP/P7-34 4. Summary The plasma performance in the helical DEMO reactor FFHR-d1 has been analyzed using the radial profiles extrapolated from LHD. Although the large Shafranov shift and resultant destruction of peripheral magnetic surfaces are expected in the high-beta reactor core plasma, it is possible to mitigate the Shafranov shift and restore the magnetic surfaces by selecting a high aspect ratio configuration and applying a proper vertical magnetic field. As long as the Shafranov shift is mitigated, the neoclassical thermal transport can be reduced to less than ~400 MW, which is comparable to the alpha heating power of ~500 MW in FFHR-d1. The energy loss of alpha particles is expected to be less than 20 %, as long as the loss boundary is set on the blanket surface and the proper plasma position control is applied. The lost alpha particles go to the divertor region, which are located behind the blanket in FFHR-d1. These results form the basis for the successive study of the reactor core plasma in FFHR-d1. It is necessary to carry out similar analyses iteratively in close link with engineering design. The MHD equilibrium, the neoclassical transport, and the alpha particle loss obtained in this study can be used as the input parameters for the next step analyses. The MHD stability analysis including the effect of bootstrap current on the MHD equilibrium and evaluation of the anomalous transport will be important as the next step analyses to assure the selfconsistency of the radial profiles in FFHR-d1. References [1] Sagara, A., et al., Fusion Eng. Des. 87 (2012) 594. [2] Goto, T., et al., Plasma Fusion Res. 7 (2012) 2405084. [3] Komori, A., et al., Fusion Sci. Tech. 58 (2010) 1. [4] Miyazawa, J., et al., Plasma Fusion Res. 7 (2012) 2402072. [5] Miyazawa, J., et al., Fusion Sci. Tech. 58 (2010) 29. [6] Stroth, U, et al, Nucl. Fusion 36 (1996) 1063. [7] Yamada, H., et al., Nucl. Fusion 45 (2005) 1684. [8] Yamada, I., et al., Fusion Sci. Tech. 58 (2010) 345. [9] Akiyama, T., et al., Fusion Sci. Tech. 58 (2010) 352. [10] Sakakibara, S., et al., Fusion Sci. Tech. 58 (2010) 176. [11] Suzuki, Y., et al., Nucl. Fusion 46 (2006) L19. [12] Hirshman, S.P., and Whitson, J.C., Phys. Fluids 26 (1983) 3553. [13] Cooper, W.A, Plasma Phys. Control. Fusion 34 (1992) 1011. [14] Beidler, C.D., et al., Plasma Phys. Control. Fusion 37 (1995) 463. [15] Satake, S., et al., Plasma Fusion Res. 3 (2008) S1062. [16] Murakami, S., et al. Nucl. Fusion 46 (2006) S425. [17] Seki, R., Plasma Fusion Res. 5 (2010) 027. [18] Satake, S., et al., 22 nd International Toki Conference (2012).