Vertical stability of ITER plasmas with 3D passive structures and a double-loop control system

Fusion Engineering and Design 74 (2005) 537–542

Vertical stability of ITER plasmas with 3D passive structures and a double-loop control system A. Portone a,∗ , R. Albanese b , R. Fresa c , M. Mattei b , G. Rubinacci d , F. Villone d a

EFDA-CSU, Max Planck Institute for Plasmaphysics, Boltzmannstrasse 2, D-85748 Garching, Germany b Assoc. Euratom-ENEA-CREATE, University Mediterranea RC, Loc. Feo di Vito, I-89060, RC, Italy c DIFA, University della Bastilicata, Contrada Macchia Romana I-85100, Potenza, Italy d Assoc. Euratom-ENEA-CREATE, University Cassino, Via Di Biasio 43, I-03043, Cassino (FR), Italy Available online 2 August 2005

Abstract In this study we derive linear models describing the dynamics of the n = 0 plasma displacements around the main ITER equilibrium configurations. The models derived are consistent with the MHD equilibrium constraint as well as with the 3D geometry of the vacuum vessel and blanket outer triangular support where the main eddy currents flow takes place. Particular emphasis is placed on the analysis of the stability margin, growth time and minimum stabilization voltage. The performances of the present ITER control system (single loop) are compared to those of an upgraded system (double-loop) that is here proposed to improve the stability domain of the ITER plasmas forecast. © 2005 The European Commission. Published by Elsevier B.V. All rights reserved. Keywords: Plasma control; Vertical stabilization; Stability margin

1. Introduction Vertical stabilization of the ITER plasmas will be performed by feeding back the plasma vertical speed to the magnetic control system; this will then react by applying a voltage signal to the four outermost (superconducting) poloidal field coils (PFC) to produce a radial magnetic field [1]. A key element in the design of an efficient plasma stabilization system is the correct modeling of the stabilizing effect of the metallic ∗ Corresponding author. Tel.+49 0 8932994282; fax.+49 0 8932994198 E-mail address: [email protected] (A. Portone).

structures surrounding the plasma (the so called ‘passive stabilization’) and of the coupling of the plasma with the active stabilization coils [2]. The main objective of this work is to analyze the stabilizing effect on the plasma vertical motion of the eddy currents induced in the main ITER metallic structures surrounding the plasma. In particular, fully 3D (solid) models of the vacuum vessel (VV), blanket modules with their outer triangular support (OTS) are derived [3,4]. We proceed by firstly deriving several linear models describing the dynamics of the (n = 0) vertical motion around the most critical (from the controllability standpoint) ITER plasma equilibrium configurations under

0920-3796/$ – see front matter © 2005 The European Commission. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.06.276

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the assumption of axi-symmetric metallic structures. Then the effects of the actual 3D geometry of the vessel ports, OTS, etc. are analyzed in terms of their impact on the plasma stability margin, growth time and minimum stabilization voltage. The performances of the present ITER control system (single loop) are assessed and compared to those of a double-loop control system that is proposed [5] to improve the n = 0 stability domain of the ITER plasmas.

2. ITER modelling In ITER there are six superconducting coils making up the central solenoid (CS) stack and six outer poloidal field coils (PFC) [6]. The two central coils of the CS (CS1U and CS1L) are fed in series, whereas CS3U, CS3L, PF1 coil and PF6 coil are independently fed. A fast (i.e. suitable for plasma vertical stabilisation) 6 kV VS1 amplifier (Fig. 1) feeds the parallel of PF2 in series with a slow (i.e. dedicated to shape control) 1.5 kV amplifier, PF3 in series with a slow 1.5 kV amplifier, PF4 is in series with a slow 1.5 kV amplifier (opposite sign) and PF5 is in series with a slow 1.5 kV amplifier (opposite sign). For the sake of this study it will be also assumed that there is an additional fast 6 kV amplifier (VS2), not presently foreseen in the ITER design [6],

feeding the parallel of CS2U that is in series with a slow 1.5 kV amplifier and CS2L that is in series with a slow 1.5 kV amplifier with opposite sign (Fig. 1). All resistances in the superconducting coils, voltage amplifiers and connections are neglected. The vacuum vessel (VV) is modelled either as a 2D double shell model or as a full 3D solid model. The 2D model consists of two concentric shells (Fig. 2), the inner one made by 57 axi-symmetric conductors carrying uniform current (eight of them simulating the outer triangular support, see below), the outer shell by 50 conductors. To avoid matrices illconditioning the meshed thickness of each shell has been enhanced from the reference design value of 60–150 mm and the equivalent electrical resistivity has been increased to η = 1.9 ␮m respect to the reference value of 0.76 ␮m (316L stainless steel at 150 ◦ C). The 3D model includes, beside the two shells meshed as 60 mm each with η = 0.76 ␮m, 18 upper ports, 18 equatorial ports and 18 lower divertor ports in both the inner and outer shell (Fig. 3) whereas, in the reference design [6] there are only 9 lower divertor ports (instead of 18). The blanket modules outer triangular support (OTS) is a mechanical structure that is electrically continuous in the toroidal direction and attached, and electrically connected, to the inner vessel shell (Fig. 2). It

Fig. 1. The reference vertical stabilisation circuit VS1 connecting coils PF2-PF3-PF4-PF5 circuit (top) and the proposed additional vertical stabilisation circuit VS2 connecting the central solenoid coils CS2U-CS2L (bottom).

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Table 1 ITER plasma equilibrium configurations analyzed

Ip li βp Rp ap κ δ

SOH

SOH

SOH

SOB

SOB

SOB

15.00 0.70 0.10 6.225 1.971 1.867 0.499

15.00 0.85 0.10 6.200 2.000 1.845 0.488

15.00 1.00 0.10 6.200 2.000 1.844 0.479

15.00 0.70 0.65 6.207 1.986 1.864 0.511

15.00 0.85 0.65 6.200 2.000 1.851 0.491

15.00 1.00 0.65 6.200 2.000 1.838 0.473

mula to account for the presence of the holes for the conduits (enhancement factor given by (1 + f/2)/(1 − f), with f fraction of non-conducting material). The main plasma parameters of the equilibrium configurations considered here are reported in Table 1. The axi-symmetric analysis is carried out with CREATE-L [7] and CREATE-NL [8] linear plasma response models derived assuming as input quantities the coil voltages, the internal plasma inductance li and its poloidal beta βp . The 3D analysis is carried out with a combined use of 3D and 2D axi-symmetric codes [9].

3. Main results 3.1. Plasma passive stabilisation analysis

Fig. 2. CREATE-NL 2D mesh. Plasma equilibrium at burn and the axi-symmetric model of the vessel with a detail of the blanket modules outer triangular support. Both OTS and vessel shells have an enhanced thickness of 150 mm instead of 60 mm and an equivalent electrical resistivity ηeq = 2.5η.

has a thickness of 60 mm although in the 2D model the meshed thickness has been increased to 150 mm with η = 1.9 ␮m. The OTS has a 26% cross-sectional area reduction in correspondence of the holes for the in-vessel viewing telescope. Each hole is modeled as being 230 mm wide in the toroidal direction and 18 holes have been assumed (Fig. 3) instead of six as foreseen in the design [6]. The blanket modules (Fig. 3) have six slots on the vessel side, five slots on the plasma side for each module. The equivalent electrical resistivity of each module is assumed to be η = 1.7 ␮m, obtained by enhancing η by a factor of ∼70% given by Clausius-Mossotti for-

In Table 2 are reported the plasma instability growth rate and the stability margin (defined as the eigen-value of the matrix Ms = −L × L0 −1 having the largest real part [11]) for the equilibria in Table 1 with 2D and 3D vessel models as computed by the CREATE-L code.1 These results indicate that the ‘worst plasma’ from the vertical stabilization standpoint is the start of heating equilibrium configuration with li = 1, for which the growth rate of the plasma instability is (see Table 2) between γ = 11.4 s−1 (2D model) and γ = 13.5 s−1 (3D model). As for the effect of the blanket modules, an analysis carried out on the SOH, li = 1 equilibrium shows that the blanket modules have a small stabilizing effect, with a 2–3% reduction in the growth rate and a 6% increase in ms .

1 The growth rate and stability margin computed by the CREATEL and CREATE-NL codes differ less than 5% [4].

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Fig. 3. CARIDDI 3D meshes. Top left: A 10 degrees sector of the VV and OTS (18 upper, equatorial and lower ports). Top right: 1/36 of the inboard blanket modules 1–8. Bottom left: 1/36 of the outboard module 9 (between adjacent upper ports) and modules 13–14 (between adjacent equatorial ports). Bottom right: 1/18 of the remaining outboard modules (10–12, 15–17).

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Table 2 Open loop analysis with axi-symmetric (2D) and 3D model of vessel and OTS (CREATE-L) Equilibrium configuration

2D γ (s−1 )

3D γ (s−1 )

2D ms

3D ms

SOH (li = 0.70, βp = 0.10) SOH (li = 0.85, βp = 0.10) SOH (li = 1.00, βp = 0.10) SOB (li = 0.70, βp = 0.65) SOB (li = 0.85, βp = 0.65) SOB (li = 1.00, βp = 0.65)

7.31 9.18 11.39 5.12 6.59 8.34

8.55 10.80 13.49 5.92 7.62 9.64

0.59 0.51 0.44 0.78 0.66 0.57

0.53 0.44 0.38 0.70 0.59 0.50

Table 3 Maximum controllable initial displacement with single and double loop (CREATE-NL) SOH, li =1

2D axi-symmetric 3D vessel and OTS

Without controller delays and filters

With controller delays and filters

Single loop: VS1 = 6 kV

Double loop: VS1 = VS2 = 6 kV

Single loop: VS1 = 6 kV

Double loop: VS1 = VS2 = 6 kV

38.5 mm 33.3 mm

61.4 mm 52.2 mm

32.3 mm 27.9 mm

51.5 mm 43.7 mm

3.2. Lower bounds on active stabilization voltages

4. Conclusions

To assess the plasma controllability range of the ITER PF system we proceed by assuming that, for the worst-case plasma equilibrium analyzed, i.e. SOH with li = 1, an open loop evolution of the plasma vertical instability takes place with the control action switched off until, at time t0 , the vertical displacement attains a given value δZ0U with velocity γδZ0U . All initial conditions in terms of currents are taken according to the unstable mode. Under these assumptions we evaluate the maximum controllable vertical offset with a 6 kV amplifiers and a single or double control loop. As reported in Table 3, with a 6 kV single loop (VS1) voltage amplifier, the maximum controllable initial displacement is 38.5 mm for the 2D (axi-symmetric) VV and OTS model and 33.3 mm in the 3D counterpart. The corresponding values with 6 kV double loop (VS1 + VS2) are 61.4 mm and 52.2 mm, respectively. The improvement given by the double loop is about 58%. The 3D deterioration of the performance (18%) is clearly related to the corresponding figure for the growth rate, as the plasma response to the control voltage is scarcely modified by the 3D effects. A further deterioration given by time delays and filters is about 19%, leading to a maximum controllable (unstable) offset of 28 mm with a single control loop and 44 mm with a double loop.

The linearized (deformable) plasma response models obtained with CREATE-L and CREATE-NL axisymmetric codes have been coupled to the 3D eddy current CARIDDI code. Among the plasma configurations analyzed, the most critical one is SOH with li = 1 both in terms of growth rate and stability margin (typically γ ∼ 14 s−1 , ms ∼ 0.4). With respect to the axi-symmetric models the 3D effects yield a ∼18% increase in the growth rate and a 14% reduction in ms . This deterioration of stability properties is mostly due to the upper port as the currents in the equatorial port region produce a nearly vertical field and the lower ports are more distant from the plasma centre and are located behind the OTS. The OTS has an important stabilizing effect and its removal would yield a 25% increase in the growth rate and a 14% reduction in the stability margin. The effect of OTS cross-section reduction in correspondence to the telescope is small (∼1% increase in the growth rate; nearly no effects on the stability margin). The contribution to stability of the blanket modules is also small (<3% decrease in the growth rate). As far as the active stabilization system is concerned, the presently foreseen single loop control system with 6 kV voltage saturation leads to a controllable δZ0U ∼ 33 mm at SOH with li = 1. The improvement

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given by the 6 kV double loop on the maximum δZ0U is ∼60% (53 mm).

Acknowledgements This work has been partially supported by MIUR and EFDA. References [1] ITER Final Design Report, Control System Design and Assessment, G 45 FDR 1 01-07-13 R1.0, July 2001. [2] E.A. Lazarus, J.B. Lister, G.H. Neilson, Control of the vertical instability in Tokamaks, Nucl. Fusion 30 (1) (1990) 111. [3] R. Albanese, R. Fresa, G. Rubinacci, S. Ventre, F. Villone, CARIDDI Users’ Guide, draft final report, EFDA study contract 02-699, part 1, April 2004.

[4] R. Albanese, R. Fresa, M. Mattei, G. Rubinacci, F. Villone, Vertical Stabilisation of ITER Plasmas In Presence of a 3D Vessel Structure, draft final report, contract EFDA/03-1108. [5] A. Portone, Controllability of ITER plasmas by a double vertical stabilization scheme, EFDA-CSU Garching internal report, Garching, 4 August 2003. [6] ITER Technical Basis, ITER-EDA Doc. series, no. 24, IAEA, Vienna, 2002. [7] R. Albanese, F. Villone, The linearized CREATE-L plasma response model for the control of current, position and shape in tokamaks, Nucl. Fusion 38 (5) (1998) 723–738. [8] R. Albanese, M. Mattei, G. Calabro’, F. Villone, Unified Treatment of Forward and Inverse Problems in the Numerical Simulation of Tokamak Plasmas, ISEM 2003. Versailles, May 2003. [9] R. Albanese, R. Fresa, G. Rubinacci, F. Villone, Time evolution of Tokamak plasmas in the presence of 3D conducting structures, IEEE Trans. Mag. 36 (4) (2000) 1804–1807. [11] A. Portone, Passive stabilization and stability margin of Tokamak plasmas, ITER JCT internal report no. N 47 IP 8 99-08-31, Naka Joint Work Site (Japan), 31 August 1999.