Magnetic configuration control of ITER plasmas

Fusion Engineering and Design 82 (2007) 1138–1143

Magnetic configuration control of ITER plasmas R. Albanese a , M. Mattei a , A. Portone b,∗ , G. Ambrosino c , G. Artaserse a , F. Crisanti d , G. De Tommasi c , R. Fresa e , F. Sartori f , F. Villone g b

a Assoc. Euratom-ENEA-CREATE, Univ. Mediterranea RC, Loc. Feo di Vito I-89060, RC, Italy EFDA-CSU, Max Planck Institute for Plasmaphysics, Boltzmannstrasse 2, D-85748 Garching, Germany c Assoc. Euratom-ENEA-CREATE, University Napoli Federico II, Via Claudio 21, I-80125 Napoli, Italy d Associazione EURATOM-ENEA sulla Fusione, Frascati, C.P. 65, 00044-Frascati, Italy e DIFA, University della Basilicata, Contrada Macchia Romana I-85100, PZ, Italy f Euratom/UKAEA Fusion Assoc., Culham Science Centre, Abingdon, Oxon OX14 3DB, UK g Assoc. Euratom-ENEA-CREATE, University Cassino, Via Di Biasio 43, I-03043 Cassino (FR), Italy

Received 31 July 2006; received in revised form 21 March 2007; accepted 21 March 2007 Available online 11 May 2007

Abstract The aim of this paper is to present some new tools used to review the capability of the ITER Poloidal Field (PF) system in controlling the broad range of plasma configurations presently forecasted during ITER operation. The attention is focused on the axi-symmetric aspects of plasma magnetic configuration control since they pose the greatest challenges in terms of control power and they have the largest impact on machine capital cost. Some preliminary results obtained during ongoing activities in collaboration between ENEA/CREATE and EFDA are presented. The paper is divided in two main parts devoted, respectively, to the presentation of a procedure for the PF current optimisation during the scenario, and of a software environment for the study of the PF system capabilities using the plasma linearized response. The proposed PF current optimisation procedure is then used to assess Scenario 2 design, also taking into account the presence of axisymmetric eddy currents and possible variations of poloidal beta and internal inductance. The numerical linear model based tool derived from the JET oriented eXtreme Shape Controller (XSC) tools is finally used to obtain results on the strike point sweeping in ITER. © 2007 Elsevier B.V. All rights reserved. Keywords: Magnetic control; ITER; Scenario optimisation; Poloidal field system; Numerical tools for modelling

1. Introduction

∗ Corresponding author. Tel.: +49 89 32994282; fax: +49 89 32994198. E-mail address: [email protected] (A. Portone).

0920-3796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2007.03.043

The time evolution of coil currents in a tokamak, along with the plasma geometrical and physical parameters guaranteeing a sequence of plasma shapes along a pulse, defines a scenario. A scenario is usually constructed from a finite number of plasma equilibria

R. Albanese et al. / Fusion Engineering and Design 82 (2007) 1138–1143

computed by MHD codes, which determine the plasma geometry and current density distribution in force balance with the magnetic field. The solution of the magnetic control problem to drive the plasma through the desired sequence of snapshots is generally approached adopting a feedforward plus feedback strategy. The feedforward control action is generated off-line on the basis of the plasma nominal model, while the feedback control action is designed so as to counteract possible misalignments between the mathematical model and the real system, and to reject external disturbances. In this paper we consider the problem of generating the feedforward control action for the ITER tokamak to drive plasma during ramp up, flat top, and ramp down phases. Also shape transitions during flat top are managed to perform particular plasma “manoeuvres” like changes in triangularity and elongation, rigid displacements, sweeping and wobbling of the plasma separatrix, etc. Two different approaches are presented through the paper to compute current/voltage commands to the PF circuits. The first one is based on the solution of an inverse electromagnetic equilibrium problem. This can be used for arbitrary shape variations but is computationally cumbersome and requires the solution of several nonlinear plasma equilibria [1]. The second approach is based on the plasma linearized model. This kind of approach has been adopted for instance at JET by some of the authors to drive plasma between a starting nominal and a final target shape [2]. In view of ITER design and operations it will also be important to have user friendly tools which help to analyse the PF system with respect to the broad range of plasma configurations required. Two software tools are under development to this aim. • A full nonlinear PF current optimisation code to obtain nominal currents/voltages during ramp up, flat top and ramp down phases. • A linear model based software (SW) environment to compute currents/voltages for shape transitions in the flat top phase, and to provide a valid basis for the closed loop control law design. This is an ITER upgrade of part of the eXtreme Shape Control (XSC) Tools tested at JET during the last three years and being used during C15–C17 experimental campaign.

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2. PF currents/voltages optimization during scenario The proposed procedure is based on the plasma Finite Element electromagnetic modelling implemented in the CREATE-L [3] and CREATE-NL [4] codes. In order to optimize currents/voltages there is the need to find both Fixed and Free boundary equilibrium solutions. In the so called Fixed Boundary equilibrium problem we assign the plasma shape in terms of the boundary curve, the plasma current, poloidal beta βp and internal inductance li , and we find the current density distribution and the flux map inside the plasma region. This calculation is neither dependent on the PF coil currents nor on the boundary flux. On the other hand, in the Free Boundary equilibrium problem, we assign the PF currents, the plasma current, βp and li , and we find the flux map in the integration domain together with the plasma boundary. For air core tokamaks nonlinearities in the equations to be solved are due to the presence of plasma. In facts, if a distribution of filamentary currents is assigned to represent plasma, these equations become linear assuming the form A0 ψ + Afil I fil + APF I PF = 0

(1)

where the A0 matrix is obtained from the discretization of the Shafranov operator with the assignment of the boundary conditions, Afil , and APF account for plasma filamentary currents Ifil and PF circuits currents IPF , respectively. The following procedure is used to optimize currents/voltages during ITER scenarios. A time sequence of equilibrium snapshots in terms of plasma shape, plasma current, βp , li , and boundary flux is fixed. A sequence of Fixed Boundary equilibrium problems is solved; the flux map and the corresponding plasma current density distribution within the plasma region is found for each snapshot. Plasma current distribution is approximated with a vector of filamentary currents. Filaments are located inside the plasma desired boundary and depend on the particular snapshot. In order to compute the PF coil currents to sustain the plasma equilibrium (assuming zero eddy currents),

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due to linearity of (1) a quadratic cost optimization problem is solved for each snapshot. On the basis of the PF currents obtained with the above optimization, a sequence of free boundary equilibria is then calculated. Also the linearized models for each one of the equilibrium conditions is computed. If the results in terms of current and voltages are not satisfactory a trial and error procedure iterating on the optimization weighting matrices is adopted. Moreover since the linearized models computed in correspondence of a snapshots turn out to be independent on the PF equilibrium currents, starting from the second iteration of the trial and error procedure, they can be used to add a cost on voltage commands and to account for eddy currents. The possibility to optimize voltages and to take into account induced currents in the passive structure is offered under the hypothesis that, between snapshots, PF currents, plasma current, βp and li vary linearly, the inductance and resistance matrices can be considered constant in the time interval between two snapshots, the unstable mode is compensated by the action of feedback control. Under these hypotheses the eddy currents and voltages are in facts piecewise affine functions of the PF currents. In real world situations the deviations between the above mentioned piecewise linear behaviours can be considered perturbations to be compensated on line by the closed loop control system.

3. Linear model based procedure: the XSC tools extension to ITER The use of linearized models is of great importance in plasma control. In [3] the procedure adopted to linearize the plasma model response is described approaching to a linear plasma-circuit dynamics in the form ˙ LδI˙ + RδI = δV + LE δw

(2)

δy = CδI + F δw.

(3)

where I is the vector of the currents in the active circuits and the plasma current, w = [βp li ]T the vector of the external disturbances, L and R the inductance and resistance matrices, LE the mutual inductance matrix between disturbance variation and active circuits and plasma currents, y the vector of outputs (gaps, fields,

fluxes, etc.), C and F are the output and disturbance matrices. Linear models were successfully used by the authors for several toroidal machines (TCV [5], FTU [6], ASDEX, ITER, RFX [7], JET [4]). For the JET tokamak a user friendly interface has been created to help the experiment scientific coordinators to design the plasma shapes of interest, and the session leader to verify that the proposed configurations can be safely run on the tokamak [8]. The tool is based on the CREATE-L and CREATENL codes and is now in part available for ITER. At the moment a user friendly interface allows to • run the nonlinear equilibrium codes; • obtain linearized models also in the presence of eddy currents; • calculate the PF currents needed to move plasma from a nominal to a target shape. The SW tool offers a high flexibility on the parameters to be controlled (gaps, strike points, X-point position, elongation, triangularity, etc.) and on the configuration settings (current limits, coils connections and position, gap and strike point definition, etc.).

4. Optimization results on Scenario 2 The Procedure described in Section 3 was tested on ITER Scenario 2, providing results which appears to be congruent with those produced by previous ITER team calculations [9]. Also the presence of axisymmetric eddy currents in the passive structure has been taken into account discretizing passive structure in 107 parts to account for inner shell, outer shell, and triangular support. Fig. 1 shows that, for the 31 snapshots assumed to describe the Scenario 2, there is a satisfactory agreement between EFDA and CREATE calculations. Results obtained in the presence of eddy currents are shown in Fig. 2 with reference to a particular snapshot during the ramp up phase. Fig. 3 shows some results obtained considering a maximum variation of poloidal beta and internal inductance of ±0.1 and ±0.15, respectively. The new time histories of the external flux linked with plasma and of some of the coil currents seem to demonstrate the capa-

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Fig. 1. Comparison between CREATE and EFDA calculations for Scenario 2 (31 snapshots).

bility of the PF system to counteract these variations in nominal conditions.

5. Special equilibrium studies: the sweeping case

Fig. 2. Driving coil currents obtained for snapshot 4 during the ramp-up phase, Ip = 1.5 MA, li = 0.85, betapol = 0.1. EFDA results are labeled as nominal.

The first version of XSC tools for ITER was used to evaluate the performance of the PF system in sweeping the divertor strike points. An example of the XSC tools user interface windows is shown in Fig. 4. The interest in performing this sweeping “manoeuvre” is motivated by the possibility of reducing thermal loads on the divertor. Due to the thermal time constants of the system, a significant benefit would be provided if sweeping is performed at frequency above 1 Hz.

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Fig. 3. Effect of li and betapol variation on the external flux linked with plasma, and on some of the PF coil currents.

Two parameters mainly characterize sweeping: the entity of the separatrix displacement dsw and the sweeping frequency fsw . Limitations on sweeping capabilities are given by currents, voltages and powers. While current is independent on time, voltage depends both on displacement and on sweeping frequency. In our analysis we considered the ITER reference equilibrium (Scenario 2) at Start of Burn, Ip = 15 MA, li = 0.70, βp = 0.65. Fig. 5 shows the optimal PF voltages required to have a 1 cm sweeping fixing all gaps with z > −2m at 1 Hz.

A best achievable performance analysis has also been carried out in the frequency domain. The results are shown in Fig. 6. This frequency diagram was produced in the hypotheses that there is no other shape requirement during sweeping and that there is the possibility to sum the contribution of all the PF coils regardless of phase. The experience has shown that real world situations require an amplification factor of about 5 on voltages with respect to the theoretical ones required by Fig. 6. The diagram provides upper limits with and without eddy currents strongly limiting performance above 1 Hz. At 10 Hz 1 kV on all the PF circuits would have a limitation of 2.4 mm on sweeping in the absence

Fig. 4. Example of interface windows of the ITER XSC tools. Calculation of nominal PF currents to change plasma shape/current.

Fig. 5. Coil voltages required to make a 1 cm strike points sweeping at 1 Hz compared with amplifier limitations.

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this tool is planned to be used extensively for the design of closed loop control laws.

Acknowledgements This work was supported in part by the Italian MIUR, and was performed under the European Fusion Development Agreement. The authors are grateful to D. Campbell, G. Federici, A. Loarte, G. Saibene, G. Strohmayer, A. Tanga, O. Zolotukhin for the helpful discussion.

Fig. 6. Best achievable performance analysis for sweeping (reference equilibrium SOB, Ip = 15 MA, betapol = 0.65, li = 0.85). The strike point displacement upper bound [mm in db] in the presence of 1 kV on each PF circuit is plot vs. frequency [Hz].

of passive structures which is reduced to 0.14 mm in the presence of them.

6. Conclusions Two numerical tools are now available to evaluate the ITER PF system capabilities to obtain the broad range of plasma configurations presently forecasted during operations. A first tool allows to compute optimal PF current driving plasma through ramp up, flat top and ramp down phases of the scenario. This tool has been shown to perform well on Scenario 2 and is now going to be used to study alternative ramp up scenarios with early formation of the X-point and ramp down with limiter plasmas on dome. The second tool is based on linearized models providing a user friendly interface to design and test special equilibria during the flat top. As already done for JET,

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