Fischer, R.

Fuchs, J.

Giannone, L.

Gruber, O.

Lackner, K.

McCarthy, P.

Preuss, R.

Schneider, W.

Schuhbeck, K.

Seidel, U.

English

MPG.PuRe

Self consistency of magnetic probe and flux loop responseto poloidal field currents on ASDEX UpgradeL.Giannone1, R. Fischer1, J.C.Fuchs1, O.Gruber1, K.Lackner1, P.J.McCarthy2,R.Preuss1, W.Schneider1, K.H.Schuhbeck1, U.Seidel1 and the ASDEX Upgrade Team1Max-Planck-Institut für Plasmaphysik,EURATOM-IPP Association, D-85748 Garching, Germany2Department of Physics, University College Cork, Association EURATOM-DCU, Cork, IrelandIntroductionThe reconstruction of magnetic equilibria in ASDEX Upgrade relies on an accurate test ofthe parameters assumed for the position and orientation of the magnetic probes and flux loopsand their calibration factors [1]. The simplest test, carried out in the first shot of the day, is toensure that the integrators are delivering the expected response within an allowed error range tothe flow of currents in individual poloidal field coils. The magnetic probe and flux response tothe individual currents in the poloidal field coils can be written as :MI = b (1)where the terms of the matrix equation are the mutual inductance, Mi j, of the magnetic probeor flux loop with index i for the poloidal field current of index j, I j, and the response of themagnetic probe or flux loop, bi. The coefficient Mi j can be derived from the known position ofthe magnetic probe or flux loop and the coordinates of the poloidal field coil using the Green’sfunction for the magnetic field generated by a current hoop [2]. The poloidal field coils andpassive stabilizing loop, PSL, are simulated as a finite number of filaments, with each filamentcarrying an applicable number of turns.Real time Grad Shafranov solverMagnetic probe and flux loop difference responses to the vacuum field produced by individualcurrents in the poloidal field coils are also calculated with a real time Grad Shafranov solver. Thealgorithm for the solution of Poisson’s equation in cylindrical coordinates using discrete sinetransforms, DST, along the Z axis and a tridiagonal solver [3, 4] has been adapted for solvingthe Grad-Shafranov equation for the poloidal flux, ψ . This algorithm is an alternative to thecommonly used cyclic reduction algorithm [1, 5, 6]. A magnetic equilibrium for discharges withplasma current can be reconstructed in 3.0 ms per iteration on a 33 x 65 grid using 40 magneticprobe and 18 flux loop difference signals. The calculation of six coefficients describing the37th EPS Conference on Plasma Physics P4.122current profile that is the best weighted least squares fit to the measurements closely followsthe documented procedure [1, 6]. Without plasma current, the value of ψ on the spatial gridresulting from the currents in the poloidal field coils is calculated. The magnetic probe and fluxloop difference signals are then calculated using interpolation on the spatial grid.An alternative algorithm for solving the Grad-Shafranov equation has been developed [7].The magnetic probe and flux loop difference response are calculated from the Green’s functionsof the current loops on the grid. The sparseness of the current sources on the grid reducesthe size of the matrix-vector multiplication and a single BLAS subroutine call can perform thecalculation. The final calculation of the Grad-Shafranov equation reduces the operation count bytreating the second solver step in a novel way. By setting the current source to zero in the secondsolver step, the DST can be significantly simplified and accelerated. These improvements reducethe cycle time for magnetic equilibrium reconstruction to 0.7 ms per iteration.Measurements and simulations with poloidal field coil currentsThe currents flowing in the poloidal field coils, each with a flat top of 4 s, are shown inFigure 1. The response of magnetic probes to these current pulses is shown in Figure 2. The 80channels of data are acquired at 5 kHz with a dual quad core Xeon 5365 PCIe system connectedto a PXI chassis [8]. Up until 12 s, the currents in the poloidal field coils are less than 10 A.This period is used to calculate the time dependent drift correction to the signals. The calculatedmagnetic field probe and flux loop differences are shown in Figure 3. A systematic correctionfactor of 1.01 has been applied to the magnitude of the poloidal field current pulse. This isnecessary to force the mean difference of the measured signals to zero. Calibration shots witha current source with an accuracy of 0.1% are planned to improve the calibration procedure.A review of the gain factors of the integrators and the positions of the probes and flux loopsseeking to identify the remaining differences between measured and simulated signals can thenbe carried out. During the current ramp in the poloidal field coil, there is up to 40 kA of currentflowing in the PSL. It is seen in Figure 3, that the measurements and simulations are in betteragreement in the phase of the current ramp when the absolute value of current in the PSL isdecreasing compared to the phase when the absolute value of current in the PSL is increasing.This can be understood as being the result of a change in in the current distribution in thePSL, with surface currents flowing in the poloidal current pulse rise or fall and volume currentsflowing in the poloidal current flat top. The simulations are to be extended by finite elementmodeling of the time dependent behavior of the current distribution in the PSL.The magnetic probe measurements prior to a plasma discharge are shown in Figure 4. Theramp up of toroidal magnetic field starts at -6.5 s. Prior to -4 s, there are no other currents37th EPS Conference on Plasma Physics P4.122Current (kA)50-40-30-20-10010203040Time (s)5010 15 20 25 30 35 40 45IpslunIsponIv1oIv1uICoIoChannelsCurrentFigure 1: Currents in the poloidal field coils and the passive stabilization loop ( Ipslon, Ipslun). Magnetic filed (T)0.15-0.075-0.05-0.02500.0250.050.0750.10.125Time (s)5010 15 20 25 30 35 40 45Bthe14Bthe16Bthe18Bthe20Bthe22Bthe24Bthe26Bthe28Channels 25 - 32Figure 2: Magnetic probe response for current pulses in the poloidal field coils.flowing in the poloidal field coils and the signals are due to misalignment of the magnetic probeswith respect to the toroidal magnetic field. This signal is compensated by subtracting a termproportional to the value of magnetic field. From -4 s to 0 s the currents in the poloidal field coilsin preparation for a tokamak discharge are ramped up. The difference between the measuredand interpolated response from the real time Grad-Shafranov solver is shown in Figure 5. Acalculated and measured magnetic probe signal difference of less than 2 mT in either Figure3 or Figure 5 cannot be achieved even when the simulations in the vacuum field response areimproved by carrying out a 3 point calculation along the 30 cm length of the magnetic probe.Difference (T)0.006-0.006-0.004-0.00200.0020.004Time (s)3826 28 30 32 34 36Bthe14Bthe16Bthe18Bthe20Bthe22Bthe24Bthe26Bthe28CalcDiff 25 - 32Figure 3: Measured and calculated probe response difference for a current pulse.37th EPS Conference on Plasma Physics P4.122 Magnetic filed (T)0.01-0.05-0.04-0.03-0.02-0.010Time (s)0-8 -6 -4 -2Bthe14Bthe16Bthe18Bthe20Bthe22Bthe24Bthe26Bthe28Channels 25 - 32Figure 4: Magnetic probe response for poloidal field currents prior to discharge.Difference (T)0.004-0.002-0.00100.0010.0020.003Time (s)0-8 -6 -4 -2Bthe22Bthe24Bthe26Bthe28Bthe14Bthe16Bthe18Bthe20CalcDiff 25 - 32Figure 5: Measured and calculated probe response difference prior to discharge.ConclusionImprovement of the calibration of the poloidal field current measurements from the present1% to better than 0.1% is needed to significantly reduce the fitting tolerance of magnetic probeand flux loop measurements for magnetic equilibrium reconstruction.References[1] P.J. McCarthy, Physics of Plasmas, 6, 3554 (1999)[2] J.D.Jackson, "Classical Electrodynamics", p142, Wiley, (1999)[3] R.W.Hockney and J.W.Eastwood, "Computer simulation using particles", p208, Taylorand Francis (1988)[4] M.H.Hughes, Comp. Phys. Comm., 2, 157 (1971)[5] K.Lackner, Comp. Phys. Comm., 12, 33 (1976)[6] J.R.Ferron, M.L.Walker, L.L.Lao et. al, Nuc. Fusion 36, 1055 (1998)[7] private communication, Q.Ruan, L.Wenzel and Big Physics Team, National Instruments[8] L.Giannone et. al, Fus. Eng. Design, doi:10.1016/j.fusengdes.2008.12.05937th EPS Conference on Plasma Physics P4.122

Self consistency of magnetic probe and flux loop response to poloidal field currents on ASDEX Upgrade

http://hdl.handle.net/21.11116/0000-0008-B054-2

Self consistency of magnetic probe and flux loop response to poloidal field currents on ASDEX Upgrade

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