Error Fields Expected in ITER and their Correction

Transcription

1 1 ITR/P5-9 Error Fields Expected in ITER and their Correction Y. Gribov 1, V. Amoskov, E. Lamzin, N. Maximenkova, J. E. Menard 3, J.-K. Park 3, V. Belyakov, J. Knaster 1, S. Sytchevsky 1 ITER Organization, Route de Vinon sur Verdon, Saint Paul Lez Durance, France D.V. Efremov Scientific Research Institute, St.-Petersburg, Russia 3 Princeton Plasma Physics Laboratory, Princeton, NJ, USA contact of main author: yuri.gribov@iter.org Abstract. The paper summarises the present status in the study of error fields expected in ITER (n = 1 modes) and their correction. Two approaches are used in the study of ITER error fields: analysis of the 3-mode error fields and analysis of the overlap error fields. The error fields expected in ITER from different sources are analyzed. The main contributor to the error fields is misalignments of the ITER coils. The analysis performed has shown that the error field Correction coils are capable to reduce the expected error fields below the present criteria. Capability of the in-vessel ELM control coils to correct error fields is also analyzed. 1. Introduction Non-axisymmetric components of tokamak magnetic field (error fields), caused by asymmetries in the machine design and construction, degrade plasma confinement and can cause a disruption [1]. This paper summarises the present status in the study of error fields expected in ITER (n = 1 modes) and in the analysis of capability of the error fields correction by the Correction coils (CC) and ELM control coils. Section describes criteria used for the error field study. Section 3 describes ITER error field correction system. Assessment of error fields expected from misalignments of the ITER superconducting coils is given in Section 4. Analysis of error fields expected from other sources is given in Section 5. Section 6 draws the conclusions. The studies of the main contributors to the error fields were performed for the latest ITER design (Baseline 010).. Criteria for Error Field Correction Two approaches were used in the error field studies: analysis of the 3-mode error fields [1] and analysis of the overlap error fields []. 3-mode error field criterion Since the earliest phase of the ITER design activity, the 3-mode error field criterion, based on experimental data from a range of tokamaks, has been used to determine the allowable level of error fields (the Locked Mode Threshold for operation with low plasma density) [1, 3-5]: B 5 3 mode 0. ( B1,1 ) ( B,1) 0.8 ( B3,1 ) 5 10 B0. Here B 3-mode is the weighted averaged amplitude of the (1,1), (,1) and (3,1) Fourier modes of the component of magnetic field normal to the q = surface and B 0 = 5.3 T is the toroidal field in the centre of plasma cross section (R =6. m). The definition of the modes amplitude is given in [3-5].

2 ITR/P5-9 Plasma with low β p at the start of current flattop in 155 MA DT inductive scenario ( Plasma 1 ) has been used for the analysis as one of the mostt sensitive to error fields (high plasma current, low density and lack of plasma rotation drivenn by tangential injection of the neutral beams). Overlap error field criteria The algorithm for calculation of the overlap external error field, B over rlap, [, 6] has been derived from analysis performed with thee IPEC code for three fiducial ITERR plasmas: i) Plasmaa 1 - characterised above, ii) Plasmaa - high β p plasma at the state of burn in 155 MA DT inductive scenario, iii) Plasmaa 3 - high β p plasma at the state of burn in 9 MA DT steady-state scenario. The IPEC code calculates those components of the external (to the plasma) error fields which are most efficient at driving the growth of a magnetic island, takingg into account the perturbation to the plasma equilibrium associated with the external fields. For calculation of the overlap errorr field, the normal component of the external error field (n = 1) is calculated on the plasma boundary. The following f criteria on the overlap error fields, B overlap / B 0, were developed for the fiducial plasmas on the basis of experimental results from DIII-D, NSTX and CMOD: B overl lap / B for Plasma 1, for Plasma and a for Plasmaa 3. It should be noted that the criteria for error field correction aree not final and they are studied in the framework of International Tokamak Physics Activity (MHD Stability Topical Group). Moreover other multi-harmonic criteria are being developed at present. p 3. Error Field Correction System Taking into account that at present misalignments of ITER superconducting coils are rather uncertain and criteria for error field correction are still a developing area, ITER hass unique tools for identification of the error fields, for study of how they should be corrected (in dedicated experiments) and for the error fields multi-harmonic correction. c The main actuator for error field correction in ITER is superconducting Correction coils located outside the vacuum vessel (shownn in Figs. 1 and ) [7]. FIG. 1. Error field Correction coils, central solenoid and poloidal field coils. FIG.. Error field Correction coils (blue coils) and ELMM control coils (black coils).

3 3 ITR/P5-9 There are three sets of the coils: Top CC, Side CC, and Bottomm CC. Maximum values of the coil currents are 30 ka turns, 00 ka turns and 30 ka turns, respectively. Each set of the CC consists of 6 saddle coils. Within each set, the toroidallyy opposite coils are connected electrically in anti-seriehas three independent power supplies, which allows a phase adjustment of the to provide suppression of error field modes withh n = 1. Each set of the CC correction field. The primary objective of the in-vessel ELM control coils (shown in Fig. in black) is the control of Edge Localized Modes with h the goal of avoidingg excessive heat loadss on the plasma facing components of the tokamak. However, in combination with the Correction coils, these coils are a unique tool for the control of error fields. The whole coil system, comprising 7 ELM coils (maximum( current 90 ka turns) with 7 independent power suppliess and 18 CCC with 9 independent power supplies, allows a very high flexibility in the production of a range of spectra of non-axisymmetric magnetic fields. 4. Error Fields from Misalignments of TF, CS and PF Coils The main contributor to errorr fields is the manufacturing and assembly errors of the central solenoid (CS), poloidal (PF) and toroidal field (TF) coils, usually considered as positioning errors in the current centrelinee (CCL) of the coils. The baseline set of the coil tolerances [8] is given in Table I. The table specify limitss for 670 independent degrees off freedom (DOF) in position and shape of the CCL of the tokamak main magnetss causing error fields with the toroidal mode number n = 1. Errors in thee CS and PF coil wrapping are defined in Fig. 3. FIG. 3. Error in CS and PF coil wrapping.. FIG. 4. Locations of the reference points ABCDRFG onn the TF coil l current centerline. The TF coil manufacturing and assembly errors come from: 1) winding pack (WP) manufacture, ) WP insertion in the case, and 3) assembling of eighteen TF coils around the vertical axis of the machine. These errorss can be considered separately as follows. 1) The TF coils manufacturing sizes may be checked by indirect methods. A set of seven reference points marked by ABCDEFG (Fig. 4) is used for checking position and shape of the CCL. Shifts in X, Y,, and Z-directions of these pointss (1 DOF per coil) define the WP errors.

4 4 ITR/P5-9 ) On insertion of the winding pack in the case, it may be shifted or tilted as a rigid body (6 DOF per coil). 3) The assembly errors are considered to be in the form of rigid body displacement and/or rotation of TF coil case (6 DOF per coil) around the vertical axis of the machine. TABLE I: BASELINE TOLERANCES ON DIFFERENT DEVIATIONS OF CS, PF AND TF COILS CURRENT CENTRELINES RELATIVE TO THEIR IDEAL POSITION AND SHAPE (n = 1) Type of deviation Tolerance mm CSU3 shift 3 CSU shift 3 CSU1 shift 3 CSL1 shift 3 CSL shift 3 CSL3 shift 3 CSU3 tilt CSU tilt 1.7 CSU1 tilt 1.4 CSL1 tilt 1.1 CSL tilt 0.8 CSL3 tilt 0.5 CS stack shift CS stack tilt 0 CSU3 wrapping 1 CSU wrapping 1 CSU1 wrapping 1 CSL1 wrapping 1 CSL wrapping 1 CSL3 wrapping 1 PF coil shift PF coil tilt 1 PF1 wrapping 1 PF wrapping 1 PF3 wrapping 1 PF4 wrapping 1 PF5 wrapping 1 PF6 wrapping 1 Type of deviation Tolerance mm TFC WP radial shift 0.5 TFC WP side shift 1 TFC WP vertical shift 0.5 TFC WP tilt, around axis Y 0.5 TFC WP tilt, around axis Z TFC WP tilt, around axis X Points A, B, shift along X-axis 1 Points A, B, shift along Y-axis 3 Points A, B, shift along Z-axis 1 Points C, F, shift along X-axis Points C, F, shift along Y-axis 3 Points C, F, shift along Z-axis Points D, E, G, shift along X- axis Points D, E, G, shift along Y- axis 3 Points D, E, G, shift along Z- axis TFC case radial shift TFC case side shift TFC case vertical shift TFC case tilt, around axis Z TFC case tilt, around axis Y 4 TFC case tilt, around axis X 4 Statistical analysis of the expected error fields was performed on the basis of a million Monte Carlo calculations, assuming uniform distribution of the errors within the given tolerances. Assessment of the CC currents required for the error fields correction is based on the Fourier transform of CC correction fields and can be treated as an inverse problem, which in this case is ill-conditioned. The problem is solved by using the regularization procedures. Different set of currents in CC can be obtained using different optimization criteria.

5 5 ITR/P5-9 Two optimization approaches were used in the study. In the first approach, currents in the CC were calculated minimizing their root-mean square norm. The following vector norm was minimized in this approach: 1/ 9 I I i. (1) i 1 In the second approach, currents in the CC were calculated minimizing maximum value of the current among all coils. The following vector norm was minimized in this approach: I max I, () 1 i 9 i The study has shown that, for 1,000,000 statistical events, the "3-mode" error fields, expected from misalignments of the TF, CS, and PF coils for the baseline set of the coil tolerances, is less than B 3-mode /B 0 = with the probability 100% and less than with the probability 99.9%. With the confidence 99.9% the "3-mode" error fields can be reduced to by the currents within 13 ka turns in the Top CC, 60 ka turns in the Side CC, and 164 ka turns in the Bottom CC, if the optimization approach (1) is used. Using the optimization approach (), similar correction can be performed by the currents in all coils within 130 ka turns. However, in this case 130 ka turns will require in all CC. Figs. 5a and 5b illustrate this conclusion. FIG. 5a. Representation of 1,000,000 statistical events (670 DOF) in calculations of 3-mode error fields (horizontal axis) and currents in the Bottom CC required for the error field reduction to calculated using the optimization approach (1) (vertical axis). FIG. 5b. Representation of 1,000,000 statistical events (670 DOF) in calculations of 3-mode error fields (horizontal axis) and currents in the Bottom CC required for the error field reduction to calculated using the optimization approach () (vertical axis). The statistical analysis of the overlap error fields, performed for the three fiducial ITER plasmas, has demonstrated that with the probability 100% the error fields are less than the overlap error field criteria.

6 6 ITR/P Error Fields from other Sources Maximum error fields expected from the TF, CS and PF coils misalignments are shown in the upper row of Table II. TABLE II: ERROR FIELDS (n = 1) EXPECTED IN ITER (IN 10-5 OF THE TOROIDAL MAGNETIC FIELD, 5.3T) Type of analysis 3-mode Overlap Source of error field Plasma 1 Plasma 1 Plasma Plasma 3 misalignments of TF, CS and PF coils (baseline) < 17 < 10 < 4 < joints and busbars of TF, CS and PF coils, 1) 1.0 < 0.8 < 0.41 < 0.15 six test blanket modules, ) irregularity of ferromagnetic inserts (FI), 3) test blanket modules and FI irregularity, ) & 3) scattering in FI magnetic properties, 4) <.0 NBI magnetic field reduction system, 5) 1. rebar in concrete of bioshield, 6) < 1 rebar in concrete of tokamak complex, 7) 0. cryostat and cryostat thermal shield, 8) < 0.04 < 0.03 < 0.03 < 0.0 vacuum vessel thermal shield, 9) < 0.01 < < < scattering in big knuckle magnetic properties, 10) < 0.0 < 0.01 < < misalignments of VS coils (at 40 ka turns), 11) < 4.3 < 5.1 < 6.0 < 7. Locked mode criterion: The table also shows error fields expected from other sources. These are: 1) TF, CS and PF coils joints and busbars (Fig. 6), ) ferromagnetic structures of six test blanket modules (Fig. 7), 3) irregularity of ferromagnetic inserts located between inner and outer shells of the vacuum vessel (for reduction of the toroidal field ripple, Fig. 8), 4) scattering in the values of ferromagnetic inserts steel plate thicknesses (±.5%) and saturated magnetization (±.5%), 5) magnetic field reduction system of the neutral beam injectors (two Heating NBIs and one Diagnostic NBI, Fig. 9), 6) ferromagnetic elements of the bioshield (rebar in concrete), 7) ferromagnetic elements of the tokamak complex other than the bioshield, 8) scattering in weak magnetic permeability of the austenitic steel from which the cryostat and the cryostat thermal shield are made (maximum value of μ = 1.05), 9) scattering in weak magnetic permeability of the austenitic steel from which the vacuum vessel thermal shield are made (maximum value of μ = 1.05, 10) scattering in saturation magnetization of Ni-Al bronze from which the divertor big knuckle is made (μ 0 M S = mt), 11) misalignments of VS in-vessel coils (± cm, at maximum current 40 ka turns). The following comments need to be done on the error fields produced by the VS in-vessel coils due to misalignment of their current centrelines relative to their ideal (axisymmetrical) position. In the statistical analysis, it was assumed maximum value of the coil current (40 ka turns) and deviation of the current centrelines relative to the ideal position (tolerance) +/-0 mm in the horizontal and vertical directions. It should be noted, that due to the VS coils heating they may conduct the maximum current only for a short time (time scale 0. s).

7 7 ITR/P5-9 Maximum allowable value of the coils effective current is only 40 ka turns. Short transient error fields caused by high transient currents in VS coils, if necessary, can be corrected by the ELM control coils. FIG. 6. TF, CS and PF coil joints and busbars. FIG. 7. Magnetic model of six TBMs. FIG. 8. Magnetic model of Ferromagnetic Inserts. FIG. 9. Models of magnetic field reduction system of the neutral beam injectors (upper - Heating NBI, lower - Diagnostic NBI). The following results were obtained using Monte Carlo simulations with 1,000,000 statistical events assuming the current in VS coils 40 ka turns and position tolerance +/-0 mm. 1) With the probability 99.9% the "3-mode" error field is less than of the toroidal magnetic field. Reduction of the error field to about 10-7 with the probability 99.9% requires currents in ELM coils less than 5.3 ka turns. This maximum current is required in the Lower coils. ) With the probability 100% the overlap error field is less than of the toroidal magnetic field for Plasma 1, less than for Plasma, and less than for Plasma 3. Reduction of the error field to about 10-7 with the probability 100% requires currents in ELM coils less than 6.8 kat. This maximum current is required in the Equatorial coils.

8 8 ITR/P Summary Analysis of n = 1 modes of error fields expected in ITER has been performed using two criteria: the 3-mode criterion, used since many years for the ITER error field study [1], and the overlap error field criterion, based on the analysis performed with the IPEC code for three fiducial ITER plasmas []. So far twelve potential sources of error fields have been analyzed. The main contributor to the error fields is the manufacturing and assembly errors of the CS, PF and TF coils. Error fields expected from the coils were calculated using the baseline set of the coil tolerances specifying limits on 670 independent DOF in position and shape of the coils current centrelines causing error fields with the toroidal mode number n = 1. Statistical analysis of the expected error fields was performed on the basis of 1,000,000 Monte Carlo calculations, assuming uniform distribution of the positioning and shaping errors within the given tolerances. The expected error fields can exceed by 3.4 times the 3-mode criterion for the Plasma 1, whereas they should be less than the present overlap criteria for the Plasmas 1, and 3. For the baseline set of the coil tolerances, with the confidence 99.9% the "3-mode" error fields can be reduced to below the criterion by the Correction coils keeping 14% margin in the currents of the Top coils, 33% margin in the Side coils and 95% margin in the Bottom coils, if optimization approach (1) is used. It should be noted, that after the coils manufacturing and installation, the real errors in position and shape of the coils current centrelines can be higher than the baseline set of the coil tolerances. Moreover, the criteria for error field correction are not final and they are studied in the framework of International Tokamak Physics Activity. Other sources of error fields, which have been analyzed so far, produce error fields less that the threshold values according to the both criteria considered. Disclaimer: The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. References [1] HENDER, T.C., et al., Progress in ITER Physics Basis, Chapter 3 MHD stability, operational limits and disruptions, Section.4, Nucl. Fusion 47 (007) 51. [] PARK, J.-K., et al., Error field correction in ITER, Nucl. Fusion 48 (008) [3] AMOSKOV, V, et al., Fourier analysis of 3D error fields in tokamaks, Plasma Devices and Operations 1 (004) 85. [4] AMOSKOV, V, et al., Statistical analysis of expected error fields in tokamaks and their correction, Plasma Devices and Operations 13 (005) 87. [5] KNASTER, J., et al., ITER non-axisymmetric error fields induced by its magnet system, Fusion Engineering and Design 86 (011) [6] PARK, J.-K., et al., Robust correction of 3D error fields in tokamaks including ITER, 3rd IAEA Fusion Energy Conference, Daejon, Korea Rep., October 010, EX- S/P5-1. [7] FOUSSAT, A., et al., From design to development phase of the ITER correction coils, IEEE Transactions on Applied Superconductivity, 1 (011) [8] MITCHELL, N., KNASTER, J., Contributions to Plasma Error Fields from the CS, PF and TF Coils, Private communication, 006, version 1.3.