Alternative equilibrium reconstruction code for the plasma control

Alternative equilibrium reconstruction code for the plasma control of FTU G. Artaserse 1 R. Albanese 2, L. Boncagni 1, D. Carnevale 3 1 Associazione Euratom-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati (RM), Italy 2 Associazione Euratom-ENEA-CREATE sulla Fusione, Via Claudio 21, I-80125 Napoli, Italy 3 Dipartimento di Informatica, Sistemi e Produzione, Università di Roma, Tor Vergata, Via del Politecnico, 00133 Roma, Italy Rehearsal of the contribution to the EPS 2013/05/27 WIP, Frascati G Artaserse 1

Outline q Aims q XCTools description q CREATE-NL main assumptions q Input treatment q Benchmark cases q Flux map: Breakdown/Plasmaless (only T, only V) q Boundary: Plasma run q Open loop simulations q Conclusions q Future work 2013/05/27 WIP, Frascati G Artaserse 2

Aims : - to give to the FTU session leader (Rd. O’s: Responsible of Operation) a tool to easily design desired magnetic configurations with a user friendly interface - to help to identify in a reliable way the location of field null formation during the plasma current breakdown phase - to detect faulty probes, misalignment of probe orientation in the poloidal plane or wrong calibration factors - to have a reliable linearized model of the equilibrium to simulate the plasma quantities of interest - to have a robust plasma control of plasma current, plasma shape and position - to design new control strategies for PF coils currents - to study the plasma-wall interaction due his coupling with EDGE 2 D tool (the equilibrium is given even in EQDSK format) - beware! @ the moment is an off-line (post-pulse) tool 2013/05/27 WIP, Frascati G Artaserse 3

XSCTools: (e. Xtreme Shape Controller Tools) [1/3] q Set of procedures written in Mat. Lab with Graphical User Interface (GUI) q CREATE NL (CNL), CREATE L (CL), CREATE_EGENE (CE) q Linearized model describing the electromagnetic behaviour of plasma surrounded by conducting structures and in presence of ferromagnetic materials q valid in the neighbourhood of an equilibrium point q Used for 2 D axysimmetric modelling q Used for electromagnetic control of current, position, shape q Used with success for operation of JET and design in ITER q Designed to be FLEXIBLE and MACHINE INDEPENDENT 2013/05/27 WIP, Frascati G Artaserse 4

XSCTools: (e. Xtreme Shape Controller Tools) [2/3] … Settings GRID 2 D EQDSK MCF XSCTools CREATE NL CREATE_EGENE PCF linearized form (assuming I=I 0+i, U=U 0+u, W=W 0+w, Y=Y 0+y) L* di/dt + R i = u – LE* dw/dt (L* = ∂ /∂I, LE* = ∂ /∂W) y=Ci+Fw ( C = ∂Y/∂I, F = ∂Y/∂W ) state-space form (assuming x=i, A= (L*)-1 R, B= (L*)-1 , E= (L*)-1 LE*) dx/dt = A x + B u + E dw/dt Model (space state form) y = C Linearized i+Fw ü … EXP DATA EDGE 2 D ü Used for 2 D axysimmetric modelling ü Used for electromagnetic control § current, position, shape ü Used with success for the design&operation of ITER, JET ü MACHINE INDEPENDENT ü Set of procedures written in Mat. Lab with Graphical User Interface (GUI) § CREATE NL (CNL), CREATE L (CL), CREATE_EGENE (CE) Linearized model describing the electromagnetic behaviour of plasma surrounded by conducting structures § valid in the neighbourhood of an equilibrium point Machine Configuration File (MCF): • geometric and electric data of the PF system (region accessible to the plasma, PF coil system geometry, connections and current limits, magnetic diagnostics etc. . ). Program Configuration File (PCF): • users choose what inputs to drive the system, whether plasma is present, what passive structures to consider, what model of a circuit to use, what results he is interested in (geometrical descriptors, magnetic measurements, currents, voltages, etc. . ). 2013/05/27 WIP, Frascati G Artaserse 5

XSCTools: (e. Xtreme Shape Controller Tools) [3/3] CREATE EGENE (CE) How modify an equilibria to design new magnetic configurations linearized backward equilibrium code q change an equilibrium generated by Create-NL q change the plasma shape and current parameters generating a linearized new model corresponding to the new equilibrium in terms of currents to be applied to the reference equilibria Keeping as constrains the flux linked to the plasma and the chosen geometrical descriptors q New equilibria currents within the operational PF saturation limits q Controlled geometrical descriptors must be less than the number of PF independent coil current G(t)=C IPFN(t) GA P 1 2 GAP 17 Controlled Gaps GAP 25 q CREATE EGENE (CE) q Modified boundary Limiter points Vessel CNL boundary G(t) = C IPFN(t) G(t) : geometrical descriptors (gaps, strike points, x-point position, …) IPFN(t): PF coils currents scenario normalized to the plasma current C: space state model matrix (Nout x Nstate) 2013/05/27 WIP, Frascati G Artaserse 6

CNL main assumptions : Problem statement [1/8] Grad-Shafranov eq. topology of problem Plasma region External active coils Passive metallic structures with BC: Homogeneous @ r=0 Regularity conditions @ infinity Hypothesis: H 1 current density inside plasma is modelled with prescribed functions of the poloidal flux and unknown variables and obtained with best fit with are obtained via minimization of a functional related to the difference between the experimental ms and reconstructed measurements mr: Hypothesis: H 2 the eddy currents in the passive structures are negligible H 3: H 3 the currents in the PFCs are known where 2013/05/27 WIP, Frascati G Artaserse 7

CNL main assumptions : Mesh [2/8] q To identify plasma shape the FEM (Finite Element Method) is applied to compute the flux map over the region of interest. q Built a 2 D mesh using the Mat. Lab PDE toolbox with about 30000 first order elements and 15000 nodes q Fine discretization in the region of interest (Vacuum chamber and in the neighborhood of PF coils) Whole domain of interest 2013/05/27 WIP, Frascati G Artaserse 8

CNL main assumptions : Poloidal Field Circuits [3/8] HIA (+) TIA (+) In total there are 4 active PFCs (T, V, H, F) FIA (-) TEA (+) HEA (+) VA (+) FEA (+) T 1 (+) FIB (-) TIB (+) HIB (-) 2013/05/27 WIP, Frascati G Artaserse FEB (+) VB (+) HEB (-) TEB (+) 9

CNL main assumptions : Poloidal Field Circuits [4/8] Transformer circuit (T): Ohmic heating coils used to start the discharge, plasma breakdown voltage up to 40 V and providing most of the flux variation, 5. 1 Vs. This circuit is used in feedback to control the plasma Ip current intensity. Theoretical flux map CNL reconstructed flux map of IT current 2013/05/27 WIP, Frascati G Artaserse XSCTools T circuit schematization Poloidal Coils (T 1, TIA, TIB, TEA, TEB) in series 10

CNL main assumptions : Poloidal Field Circuits [5/8] Vertical circuit (V): Vertical field windings providing the pre-programmed equilibrium field (up to 0. 65 T) and contributing to the flux variation during the rise of the plasma current with 1. 3 Vs. This circuit is not used in feedback, but it is used to control the plasma equilibrium, jx. B= p. Theoretical flux map CNL reconstructed flux map of IV current 2013/05/27 WIP, Frascati G Artaserse XSCTools V circuit schematization Poloidal Coils (VA, VB) in series 11

CNL main assumptions : Poloidal Field Circuits [6/8] Feedback circuit (F): This circuit is used in feedback to control the horizontal plasma current position Rp. Theoretical flux map CNL reconstructed flux map of IF current 2013/05/27 WIP, Frascati G Artaserse XSCTools F circuit schematization Poloidal Coils (FIA, FIB) in HFS region connected in anti-series, while (FEA, FEB) in LFS region connected in series 12

CNL main assumptions : Poloidal Field Circuits [7/8] Horizontal circuit (H): This circuit is used in feedback to control the vertical plasma current position Zp. # of turns? ? Sign? ? No agreement between CNL and theoretical prevision in LFS region Theoretical flux map XSCTools H circuit schematization # of turns? ? , Sign? ? Poloidal Coils (HIA, HEA) in upper part connected in CNL reconstructed flux map of IH current anti-series, while (HIB, HEB) in lower part connected in series 2013/05/27 WIP, Frascati G Artaserse 13

Half turns, 10 instead of 43 Half turns, 22 instead of 43 Double turns, 85 instead of 43 CNL tuning: investigation on H flux map discrepancies [1/2] HIA(+)+HEA(+)+HIB(-)+HEB(-) Test swap sign of HI and HE Test swap sign of HA and HB HIA(+)+HEA(+)+HIB(-)+HEB(-) HIA(-)+HEA(+)+HIB(+)+HEB(-) 2013/05/27 WIP, Frascati HIA(+)+HEA(+)+HIB(-)+HEB(-) Theoretical H flux map HIA(-)+HEA(-)+HIB(+)+HEB(+) G Artaserse 14

CNL tuning: investigation on H flux map discrepancies [2/2] q #3750 (SOLO_H_1 KA) only H circuit amplifier acting Pre-programmed currents #3750@0. 15 s #3750@0. 4 s IT IV IF IH ODIN (%e. eqlplotx 0(0. 2)) ODIN (%e. eqlplotx 0(0. 4)) IP Zoom on IH Pre-programmed currents IH CNL@0. 15 s CNL@0. 4 s L Disagreement between CNL and ODIN snapshots 2013/05/27 WIP, Frascati Which poloidal fields currents are used by ODIN (%e. eqlplotx) as inputs G Artaserse 15

CNL main assumptions: Probes location, Geometrical descriptors [8/8] Pick up coils Saddle loops q SAxx(Pi) = VLxx(Pi+1)-VLxx(Pi) with xx = {01: 16} q SA and BP used both from CNL, ODIN and rt. ODIN for plasma boundary identification q Geometrical descriptors (GAPs: distance of boundary from first wall) used by CNL for plasma shape control 2013/05/27 WIP, Frascati G Artaserse 16

CNL input treatment [1/2] The CNL code inputs must be treated to remove electronic offset and toroidal field effects 2013/05/27 WIP, Frascati G Artaserse 17

CNL input treatment [2/2] The CNL code running need as input the following quantities: q Poloidal Field Coils currents (amplifier currents) IPF, “ 0_SHOT. Zx. M=I’’ from FTU database with electronic offset removed, where x = {T, V, H, F} q Trusted magnetic measurements (used only for plasma run as best fit) with electronic offset and toroidal field effects removed Ø 16 measurements from Oct. #4 Pick up coils (MARTEFE or ODIN channels) ZZZZED. IPL MARTEFE: “MARTEFE. VBww”, where ww = {01: 16} I 20 k. A ODIN: “EQLB 04. Bpyy”, where yy = {01: 16} Ø 16 measurements from Oct. #4 Saddle loops (MARTEFE or ODIN channels) MARTEFE. IPL MARTEFE: “MARTEFE. VSww”, where ww = {01: 16} ODIN: “EQLB 04. SAyy”, where yy = {01: 16} q Other Data Ø Plasma Current , Ipl: “MARTEFE. IPL” computed from compensated magnetic measurements, or “$EQVIPLA” for old shot (before MARTEFE) Ø Plasma centroid coordinates, Rp: “$EQERAX”, Zp: “$EQZAX” forced @0!!, both from equilibria Ø Poloidal beta , βp: “$EQEBETA”, from equilibria Ø Internal inductance , Li: “$EQELI 2”, multiplied by 2 (CNL code need Li instead of Li/2) , from equilibria Ø Toroidal field @ vaccum chamber centre , Btor: “%E. BTOR” 2013/05/27 WIP, Frascati G Artaserse 18

Benchmark case: Breakdown (‘’plasmaless’’) [1/3] q FTU case #36527@-0. 100 s %e. eqlplotx 0 0_SHOT. ZTM=I CNL reconstructed flux and poloidal field map (input 0_Shot cleaned from el. offset ) 0_SHOT. ZVM=I 0_SHOT. ZFM=I 0_SHOT. ZHM=I q Flux and poloidal field map available with CNL code q Plasmaless CNL computation less than 2 min q Compatible with SL modeling needs during exp. session L Discovered discrepancies between CNL and ODIN regarding the location of poloidal field null during breakdown phase 2013/05/27 WIP, Frascati G Artaserse 19

Benchmark case: reconstruction of poloidal field null evolution [2/3] q FTU case #30226@-0. 100 s %e. eqlplotx 0 CNL reconstructed flux map 0_Shot as input pre-programmed currents as input MAXFEA IT IV IF Poloidal field map IH Flux map Using pre-programmed currents as input Which poloidal fields currents are used by ODIN (%e. eqlplotx) as inputs CNL flux map in good agreement with MAXFEA 2013/05/27 WIP, Frascati G Artaserse 20

Benchmark case: Breakdown phase reconstruction [3/3] q Using 0_shot PF currents as CNL input q FTU case #36527, @[-0. 100 -0. 060, -0. 040, -0. 020, 0, +0. 002, +0. 004]s @-0. 100 s @0 s 2013/05/27 WIP, Frascati @-0. 060 s @0. 002 s @-0. 040 s @-0. 020 s @0. 004 s G Artaserse 21

Benchmark case: Plasma run #1[1/6] q FTU case #36527@0. 5 s, (360 k. A, 6 T) Poloidal limiter @0 cm (quiet position, 30 cm far away from first wall), assuming no eddy currents CNL rt. ODIN Equilibria reconstruction time Snapshot of CNL outcome CP ODIN CP 2013/05/27 WIP, Frascati q Maximum reconstruction error (CNL vs rt. ODIN) on plasma boundary less than 1 cm!! q Same contact point (CP) of rt. ODIN and ODIN G Artaserse 22

Benchmark case: Plasma run #1[2/6] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position), assuming no eddy currents q using MARTEFE mag. meas and MARTEFE. IPL as CNL input Faulty probe 2013/05/27 WIP, Frascati q Absolute relative error on pick up coils signals less than 5% q Pick. Up coils: measurements from oct. #4 more reliable than oct. #10? ? q Detect faulty probes q Absolute relative error on saddle loop signals around 30%!!!!! q Revise saddle loop role and treatment in the CNL G Artaserse 23

Benchmark case: Plasma run #1[3/6] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position) CNL vs ODIN Comparison not reliable near the internal vessel q Fair agreement with the ODIN flux map q Bad identification of magnetic axes q Comparison not reliable near internal vessel: due the not wise choice of region of interest to compute ODIN flux map with ftupsi routine CNL contact point 2013/05/27 WIP, Frascati G Artaserse 24

Benchmark case: Plasma run #1[4/6] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position) CNL vs rt. ODIN (MARTEFE) q Fair agreement with the rt. ODIN flux map ONLY in the LFS region q Bad identification of magnetic axes q Bad agreement q Raw discretization of rt. ODIN flux map in future refinement of angle (omega) for a better comparison q rt. ODIN flux map affected by mesh generation (eye) CNL contact point 2013/05/27 WIP, Frascati G Artaserse 25

Benchmark case: Plasma run #2[5/6] q FTU case #36437@0. 5 s, Poloidal limiter inserted of -1 cm CNL rt. ODIN Without knowing poloidal limiter position Knowing poloidal limiter position Beware to the poloidal limiter position!!!! 2013/05/27 WIP, Frascati G Artaserse 26

Benchmark case: Plasma run #3[6/6] Snapshot of CNL outcome q FTU case #33354@1 s, (700 k. A, 7. 2 T) Poloidal limiter @0 cm (quiet position), assuming no eddy currents CP ODIN CP 2013/05/27 WIP, Frascati q Flux map of CNL and ODIN (from ftupsi routine) almost superposed q Same contact point (CP) of ODIN q MARTEFE system not available at that time G Artaserse 27

Benchmark case: Open loop simulation [1/3] FTU CREATE-NL 2013/05/27 WIP, Frascati G Artaserse 28

Benchmark case: Open loop simulation [2/3] FTU case #36527@0. 5 s Plasma run #1 Using the space state model matrices ABCD given by the CNL linearized model of the equilibria Input: Ipl, IT, IV, IH, IF Disturbances: reconstructed Betapol and Li Simulated Outputs: Mag. Meas, Rp, Zp, Elongation, Gaps… Time window simulation [0. 1, 0. 7]s SA 03_04 BP 01_04 BP 10_04 IPL Rp SA 15_04 2013/05/27 WIP, Frascati G Artaserse 29

Benchmark case: Open loop simulation [3/3] Simulation of FTU exp. data, shot #36527, using two different space state models ABCD -#36527@0. 5 (360 k. A, 6 T) Time window simulation [0. 1, 0. 7]s - #33354@1 s (700 k. A, 7. 2 T) BP 01_04 BP 10_04 SA 03_04 SA 15_04 2013/05/27 WIP, Frascati IPL G Artaserse Rp 30

Conclusions: q Create NL code ported to FTU case: to reconstruct magnetic equilibria and provide ‘’reliable’’ linearized model (for the moment neglected eddy currents effect if any) q Comparison of CNL and MAXFEA flux map of dry run shows good agreement q Comparison of CNL and ODIN (or rt. ODIN) flux map of plasma run shows a fair agreement q Comparison of CNL and rt. ODIN boundary shows a reconstruction error less than 1 cm q Reconstructed signals of pick-up coils shows a good agreement with the experimental ones q Preliminary open loop symulation of experimental magnetic measurements shows a good agreement, (using the CNL linearized model in the space state form ABCD drived by PF coils and plasma current) q CNL model capable to reproduce plasma current overshoot in the plasma current ramp-up Future work: q Understand discrepancies beetween CNL and ODIN regarding the location of poloidal field null during breakdown phase --> we need flux map and which are the PF currents in input of ODIN q Plasmaless studies (analize ‘’only T’’ and ‘’only V’’ dry-run): flux maps and open loop simulations q Plasma run comparison with ODIN flux map and boundary q Improve boundary reconstruction (understanding role/modelling in the MCF of saddle loops) q Comparison of plasma flux map computed by MAXFEA code q Integrate CNL linearized model in the FTU plasma current, position and shape control q Study eddy currents effect (if any) to improve dynamic simulations 2013/05/27 WIP, Frascati G Artaserse 31

Draft Abstract EPS 2013: 2013/05/27 WIP, Frascati G Artaserse 32

EXTRA SLIDES 2011/11/06 G Artaserse 33

FTU DAS-FBk flow chart G Artaserse 34

XSCTools data treatment flow chart G Artaserse 35