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17th IAEA Technical Meeting on Research Using Small Fusion Devices Lisbon, 22 to 24 October 2007

17th IAEA Technical Meeting on Research Using Small Fusion Devices Lisbon, 22 to 24 October 2007 Joint Experiments on the tokamaks CASTOR and T-10. Presented by Guido Van Oost For the CRP “Joint Research Using Small Tokamaks” teams. Department of Applied Physics Ghent University

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17th IAEA Technical Meeting on Research Using Small Fusion Devices Lisbon, 22 to 24 October 2007

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  1. 17th IAEA Technical Meeting on Research Using Small Fusion Devices Lisbon, 22 to 24 October 2007 Joint Experiments on the tokamaks CASTOR and T-10 Presented by Guido Van Oost For the CRP “Joint Research Using Small Tokamaks” teams Department of Applied Physics Ghent University B- 9000 Gent Belgium

  2. G Van Oost1, M Gryaznevich2, E Del Bosco4, A Malaquias6, G Mank6 , M Berta5, 13, J Brotankova3, R Dejarnac3, E Dufkova3, I Ďuran3, M Hron3, P Peleman1, J Sentkerestiova3,J Stöckel3, B Tál5, V Weinzettl3, J Zajac3, S Zoletnik5, V Budaev11, N Kirneva11, G Kirnev11, B Kuteev11, A Melnikov11, M Sokolov11, V Vershkov11, I El Chama Neto15, J Ferreira4, R Gonzales14, C R Gutierrez Tapia18, H Hegazy8, P Khorshid12, A W Kraemer-Flecken16, L I Krupnik19 ,Y Kuznetsov7, A M Marques Fonseca17, A Ovsyannikov9, L Ruchko7, E Sukhov9, A Singh10, V Soldatov16, A Talebitaher12, , G M Vorobjev9 1Dep. of Applied Physics, Ghent Univ., Belgium; 2EURATOM/UKAEA Fusion Association, Culham SC, Abingdon, UK; 3Institute of Plasma Physics, Association EURATOM/IPP, Czech Rep.; 4INPE, São José dos Campos, Brazil; 5KFKI-RMKI, Association EURATOM, Budapest, Hungary; 6IAEA, NAPC Physics Section, Vienna, Austria; 7Institute of Physics, Univ. of São Paulo, Brazil; 8EAEA, Cairo, Egypt; 9Saint Petersburg State Univ., Russia; 10Plasma Physics Lab., Univ. of Saskatchewan, Canada; 11RRC “Kurchatov Institute”, Moscow, Russia; 12Plasma Physics Research Center, Teheran, Iran; 13Széchenyi István Univ., Association EURATOM, Győr, Hungary; 14CICATA-IPN, Mexico; 15Univ. Tuiuti Paraná, Brazil;16Forschungszentrum, Julich, Germany; 17IST, Lisbon, Portugal; 18ININ, Mexico; 19Phys-Tech Inst., Kharkov, Ukraine

  3. OUTLINE • Introduction • Transport barriers and ExB shear • JE1 on CASTOR • JE2 on T-10 • Conclusions

  4. Introduction

  5. Transport barriers: physical mechanisms Possibilities for CRP JE’s

  6. TRANSPORT BARRIERS, ELECTRIC FIELDS, TURBULENCE The understanding and reduction of turbulent transport in magnetic confinement devices is not only an academic task, but also a matter of practical interest, since high confinement is chosen as the regime for ITER and possible future reactors since it reduces size and cost. Generally speaking, turbulence comes in two classes: electrostatic (emphasis) and magnetic turbulence(CASTOR). Over the last decade, step by step new regimes of plasma operation have been identified, whereby turbulence can be externally controlled, which led to better and better confinement.

  7. The physical picture that is generally given is that by spinning up the plasma, it is possible to create flow velocity shear large enough to tear turbulent eddies apart before they can grow, thus reducing electrostatic turbulence. This turbulence stabilization concept has the universality, needed to explain ion transport barriers at different radii seen in limiter-and divertor tokamaks, stellarators, reversed field pinches and mirror machines with a variety of discharge- and heating conditions and edge biasing schemes. Theelectron heat conduction, however, which normally is one to two orders above the collisional lower limit, remained strongly anomalous also in the regime with suppressed electrostatic turbulence. In that case it became the dominant heat loss channel. From this, it is conjectured that magnetic turbulence drives the anomalous electron heat conduction. Experiments at the late Rijnhuizen Tokamak Project (RTP) and the T-10 tokamak which specifically addressed the electron thermal transport properties of the plasma have strongly corroborated this conjecture.

  8. Electron ITB (T-10, TEXTOR) • From previous work [K.A.Razumova et al ,Nuclear Fusion 44 (2004) 1067] we know that e-ITBs are formed when dq/dr is low in the vicinity of rational magnetic surface with low m and n values. • Later, experiments with a rapid plasma current ramp up were performed. In this case, due to (p + li/2)1/Ip2 a rapid change of the magnetic surface densities in the central part of plasma takes place, while current penetration in this region occurs only after t>50ms. Therefore,confinement changes observed in the plasma core are the result of a magnetic surface density change only.

  9. Self-consistent pressure profile ? • Tokamak plasmas have a tendency to self-organization: the plasma pressure profiles obtained in different operational regimes and even in various tokamaks may be represented by a single typical curve, called the self-consistent pressure profile. • About a decade ago local zones with enhanced confinement were discovered in tokamak plasmas. These zones are referred to as Internal Transport Barriers (ITBs) and they can act on the electron and/or ion fluid. • Here the pressure gradients can largely exceed the gradients dictated by profile consistency. So the existence of ITBs seems to be in contradiction with the self-consistent pressure profiles (this is also often referred to as profile resilience or profile stiffness). • Therefore, the interplay between profile consistency and ITBs has been investigated.

  10. Conclusions e-ITB • It is shown that self-consistent profiles exist in tokamak plasmas for the normalized pressure, This profile relates to the lowest level of plasma instabilities, hence to the best confinement. • The radial distribution of plasma transport coefficients is determined by the necessity to maintain the self-consistent pressure profile under different external impacts. • It is shown that the well-known effect of density decrease in the local ECRH heating region (“density pump out”) is connected with p(r)/p(r0) conservation. • Under suitable conditions there may be regions in the tokamak plasma (the ITB regions), where p may be steeper than determined by the self-consistent profile condition. • The only possibility to organize more peaked profile than the self-consistent pressure profile is to form the pronounced ITB in plasmas. • The suggested hypothesis about gaps between turbulent cells in the vicinity of low-order rational surfaces could be the key to all presented experimental results. Razumova et al., PPCF

  11. Although turbulence measurements have been performed on many magnetic confinement devices during the last decades, the additional insight gained from these experiments is relatively limited. • This can be attributed to a number of reasons: • Firstly, only a very coarse spatial resolution was achieved in many measurements of electric fields and turbulence. • Secondly, simultaneous measurements of different fluctuating quantities (temperature, density, electric potential and magnetic field) at the same location, needed for a quantitative estimation of the energy and particle transport due to turbulence were only performed in a very limited number of cases. • Thirdly, theoretical models were often only predicting the global level of turbulence as well as the scaling of this level with varying plasma parameters.

  12. The investigation of the correlations between on the one hand the occurrence of transport barriers and improved confinement in magnetically confined plasmas, and on the other hand electric fields, modified magnetic shear and electrostatic and magnetic turbulent fluctuations necessitates the use of various active means to externally control plasma transport. It also requires to characterize fluctuations of various important plasma parameters inside and outside transport barriers and pedestal regions with high spatial and temporal resolution using advanced diagnostics, and to elucidate the role of turbulence driving and damping mechanisms, including the role of the plasma edge properties. The experimental findings have to be compared with advanced theoretical models and numerical simulations.

  13. Radial electric fields and rotation The radial electric field Er follows from the generalized Ohm’s law rotation driving terms diamagnetic driving term  Er is connected with: • perpendicular heat- and particle transport • perpendicular momentum transport • poloidal flow  Coupling between particle-, heat- and momentum transport!!  Investigation of Er can elucidate plasma transport  Modify Er through: • particle- and energy supply • supply of momentum (e.g. through NBI) • modification of the plasma current profile (poloidal magnetic field) Active Control of Transport

  14. How to modify the edge turbulence (to improve the confinement) Transport coefficients are proportional to the radial size of turbulent structures Radial electric field poloidal rotation Poloidal cross section B is  to the screen Er > 0 Er < 0 • Turbulent structures are torn to several pieces • Size as well as the amplitude is reduced • Transport coefficients become smaller • Transport barrier forms at the shear layer J. Stöckel • Global confinement improves

  15. How does ExB shear suppression work ? • ExB shears enters quadratically into theories: sign irrelevant • Er and Bθ contribute to the shear; Er/RBθ is toroidal angular speed • Shearing rate not constant over flux surface (larger on LFS than on HFS)

  16. Plot of radial electric field Er , toroidal angular speed E /RB , and the EB shearing rate as a function of flux surface label  for a high performance, deuterium VH-mode plasma in DIII-D is proportional to the square root of the toroidal flux inside a given flux surface Although the derivative of Er vanishes near  = 0.5, the EB shearing rate is appreciable across the whole plasma Plasma conditions are 1.2 MA plasma current, 1.6 T toroidal field, 9.8 MW injected deuterium neutral beam power, and 4.7  1019 m-3 line averaged density. Discharge is a double-null divertor.

  17. Improvement and development of diagnostics

  18. MAGNETIC PROBES In the plasma interior magnetic fields can be measured with spectroscopic methods. From magnetic field measurements performed outside the plasma important properties like plasma current, energy content and MHD fluctuations together with their mode structure can be inferred. Such measurements utilize different types of coils. As the discharges became longer, the evaluation of B from its measured time derivative has become increasingly difficult, because the integration needs a precise determination of possible offsets in the preamplifiers. Recently, Hall probes have been used on TEXTOR and CASTOR to measure the absolute value of B directly together with its fluctuations in the boundary plasma of tokamaks. The strongest objection against the use of Hall sensors in the reactor type tokamak is their vulnerability to radiation damage (esp. to the high neutron fluxes). This is presently being investigated.

  19. Joint Experiments on Small Tokamaks: edge plasma studies on CASTOR G. Van Oost1, M.Berta2, 13, J.Brotankova3, R.Dejarnac3, E. Del Bosco4, E.Dufkova3, I.Ďuran3, M. P. Gryaznevich5, M.Hron3, J,Horacek3, A. Malaquias6, G. Mank6, P.Peleman1, J.Sentkerestiova3,J.Stöckel3, V.Weinzettl3, S.Zoletnik2, B. Tál2, J.Ferrera4, A. Fonseca7, H. Hegazy8, Y. Kuznetsov7, A. Ossyannikov9, A. Singh10, M.Sokholov11, A.Talebitaher12 1) Department of Applied Physics, Ghent University, Ghent, Belgium 2) KFKI-RMKI, Association EURATOM, Budapest, Hungary 3) Institute of Plasma Physics, Association EURATOM/IPP.CR 4) INPE, São José dos Campos, Brazil 5) EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, UK 6) IAEA, NAPC Physics Section, Vienna, Austria 7) Institute of Physics, University of São Paulo, Brazil 8) EAEA, Cairo, Egypt 9) Saint Petersburg State University, Russia 10) Plasma Physics Laboratory, University of Saskatchewan, Canada 11) RRC “Kurchatov Institute”, Moscow, Russia 12) Plasma Physics Research Center, Teheran, Iran 13) Széchenyi István University, Association EURATOM, Győr, Hungary

  20. CASTOR tokamak The oldest tokamak in the world Operational till end 2006 1958-1976 Kurchatov Institute as TM 1 1977- 2006 IPP Prague Major radius 40 cm Minor radius 8,5 cm Toroidal magnetic field 0,5-1,5 T Plasma current 5 - 20 kA Pulse length < 50 ms Central electron temperature 100-300eV Central ion temperature 50-100 eV Plasma density 0.5-3.1019 m-3 Energy confinement time <1 ms Edge density/ temperature ~1018 m-3/10-40 eV Research is focused on edge plasma (turbulence, electric fields, ….)

  21. Tokamak COMPASS-D Modern tokamak (operational in Culham Laboratory, UK until 2002)Offered to IPP- ASCR, Prague

  22. Ff VSL Jsat VSL Radial edge turbulence structure Left graph: Radial profiles of floating potential Φf (red circles), and density of ion saturation current Jsat (Jsat=Isat/A, A is 2π x radius x length of the probe). Right graph: Phase velocitiesof fluctuations obtained from Φf (red circles), and Jsat (blue triangles). Horizontal lines in the right panel show velocities calculated from the gradient of Φfl.

  23. Flow measurements with a high temporal resolution - Gundestrup Probe The Gundestrup cauldron (Denmark) Polar diagram of Ion saturation current B Top View Bt, Ip Several (eight) segments with a different orientation w.r.t. magnetic field lines

  24. Mach probe head • “Mach probe”: TEXTOR • main feature: • 16 plates to measure toroidal and poloidal rotation simultaneously at 2 radial positions • ofront pins: • measure n, Vf, E, Er and their fluctuations • min. radius: r=39 cm (R0=214 cm) B f r a q

  25. Radial profiles of (a) the floating potential , (b) the radial electric field , (c) the shear, and (d) the ion saturation current averaged over 4 ms before (open symbols) and during (filled symbols)biasing. The vertical dashed-dotted line marks the position of the LCFS.

  26. Radial profiles of the toroidal velocity and poloidal velocity averaged over 4 ms before (open circles) and during (filled circles)biasing

  27. Fast bolometry • Two arrays of the fast AXUV-based bolometers with 16 and 19 channels were installed in the same poloidal cross-section of CASTOR.The set with unique temporal resolution of 1 µs and spatial resolution of about 1 cm and a very low signal to noise ratio enables the visualization of fine structures in the radiated power profile. This allows to estimate their position and poloidal rotation velocity by using the normalized RMS and cross-correlation techniques, and finally to identify them with turbulent structures in the edge plasma region measured by Langmuir probes.

  28. Fast bolometry on CASTOR: Cross-correlation between the fluctuating part of the signal from one bolometer array and all channels of the second array. Left:before biasing (6 – 9.9ms), periodic structures located from 60mm on LFS to -10mm on HFS and from -15mm to -50mm on HFS, frequency 30kHz, velocity 2.3 km/s. Right: during biasing (10.5 – 14.4ms), biasing voltage +150V, some structures on r = 60mm on LFS and r = -45 on HFS, no periodicity, velocity about 1km/s (on r = 60mm) or 2km/s (on r = 20mm).

  29. Absolute plasma potential, radial electric field and turbulence rotation velocity measurementsin low-density discharges on the T-10 tokamak S.V. Perfilov1, A.V. Melnikov1, L.G. Eliseev1, S.E. Lysenko1, V.A. Mavrin1, R.V. Shurygin1, D.A. Shelukhin1, V.A. Vershkov1, G.N. Tilinin1, S.A. Grashin1, L.I. Krupnik2, A.D. Komarov2, A.S. Kozachek2, A. Kraemer-Flecken3, S.V. Soldatov3, G. Ramos4, C.R.Gutierrez-Tapia5, H. Hegazy6, A. Singh7, J. Zajac8, G. Van Oost9 and M. Gryaznevich10 1 Nuclear Fusion Institute, RRC "Kurchatov Institute", 123182, Moscow, Russia, 2 IPP, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine 3 Institut für Plasmaphysik, Forschungszentrum Jülich, EURATOM Association, Jülich, Germany 4 CICATA, Instituto Politécnico Nacional, Mexico 5 Instituto Nacional de Investigaciones Nucleares, Mexico 6 Egyptor project, Egypt 7 University of Saskatchewan, Canada 8 Institute of Plasma Physics, Prague, Czech Republic 9 Ghent University, Belgium 10 EURATOM-UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire, UK

  30. Rational surfaces play a key role in the establishment of ITBs, as has been observed in stellarators, too[Brakel R et al 2002 Nucl.Fusion 42 903]. • However, this does not exclude a possible supporting role of ExB shear in ITB formation near rational surfaces (interaction between neighbouring cells). Recent work on DIII-D and gyrokinetic simulations [Waltz R.E et al 2006 Phys. Plasmas13 052301 ] hints at possible synergy between ExB shear and effects of rational surfaces. • Large profile corrugations in electron temperature gradients at lowest-order singular surfaces lead to the buildup of a huge zonal flow ExB shear layer which provides a trigger for the low power ITB observed in DIII-D.

  31. The direct experimental study of plasma radial electric fields is the key issue to clarify ExB shear stabilization mechanisms. • The plasma turbulence rotation velocity measurements, compared with ErxBtor drift rotation velocity may explain whether turbulence moves together with the plasma or independently.

  32. HIBP plasma potential and Er profiles in T-10

  33. Experimental set-up – HIBP T-10 (Ro=1.5m, a=0.3m) • Tl+1 beam with energies Eb up to 260 keV. • Measurements in upper outer quadrant of the plasma cross-section. • The sample volume position in plasma in a single discharge can be either fixed or scanned radially with a period of 10 ms, producing a series of profiles during a single shot. Sample volumes look like elliptical disks, approximately 1cm 1.5 cm (radial) 0.5 cm thick. The uncertainty in the sample volume position was up to 2 cm. • HIBP was able to operate in 0.57<ρ<1.0, (depending on Bt ), while Correlation Reflectometry was able to observe whole plasma. At the plasma edge (0.95<ρ<1.2) they both overlapped with Langmuir probes.

  34. Er estimation. 100 B=2.40T, Ipl = 190kA, ne = 1.3x1013cm-3 0 -100 -200 , V -300 j -400 t = 508 - 537 ms -500 t = 580 - 622 ms t = 721 - 765 ms -600 t = 807 - 850 ms U = -2000 #43765 scan 20 21 22 23 24 25 26 27 28 29 30 -300 r, cm -400 , V j -500 ECRH -600 Absolute potential: EC: (21 cm ) = -210V OH: (21 cm ) = -600V Er = -160V/ 7 сm = -23 V/cm Er = -400V/ 6 сm = -67V/cm -700 500 600 700 800 900 t, ms

  35. Er(r) = const 300 200 44260 E=240 t630t680 t730t780 100 t830t880 44278 E=245 t508t536 t609t637 0 t808t836 t906t935 44272 E=250 -100 t508t536 t606t637 t808t836 44274 E=255 -200 t508t536 t609t637 t808t836 t906t935 -300 44276 E=260 t507t536 , V t609t637 -400 j t707t723 -500 -600 -700 -800 -900 -1000 17 18 19 20 21 22 23 24 25 26 27 28 29 30 r, cm B = 2.31 T, Ipl = 185 kA, ne = 1.5x1013 cm-3 Absolute potential: EC: (17.5 cm ) = -680V OH: (17.5 cm ) = -860V Er = -520V/ 9.5 сm  -55 V/cm Er = -650V/ 9.5 сm  -70V/cm

  36. Er(r) depends on ECRH power t = 508 - 537 ms #44253 t = 609 - 650 ms B = 2.33 T, I = 190 kA, ne = 2x1013 cm-3 t = 708 - 751 ms t = 808 - 850 ms , V 19 20 21 22 23 24 25 26 27 28 29 30 r, cm -700 -750 -800 , V j -850 EC -900 -950 500 600 700 800 900 1000 t, ms

  37. Comparison of the ExB rotation velocity by HIBP and turbulence rotation velocity by Correlation Reflectometer

  38. Experimental set-up – Reflectometry and Probes T-10

  39. Comparison of turbulence and ExB rotation Ohmic & ECRH phases of discharge (44392-44415) B = 2.20 T, Ipl = 185 kA, ne = 1.2*1013cm-3 Btor (X) = Btor (XCR) 2/2

  40. Comparison of turbulence and ExB rotation Ohmic & ECRH phases of discharge (44271-44278) B = 2.31T, Ipl = 185 kA, ne = 1.5*1013cm-3 Btor (X) = Btor (XCR) 2/2

  41. Summary T-10 • In the low density OH plasma (B0 = 2.31 T, Ip = 180kA, ne = 1.3 – 1.5 x 1019 m-3) the potential measured at r = 0.17 - 0.28 m was negative. The potential profile exhibits a linear-like function with the lowest absolute value at the deepest point j (0.175) = – 860 V. The slope of the potential profile gives the estimation of the mean radial electric field Er ~ -7.0 kV/m. VEXB = 3.0 km/s • In ECR off-axis heated plasmas (PEC = 0.4 MW)the depth of the potential well becomes significantly smaller, j (0.175)= –680 V, and the electric field decreases to Er ~ -5.5 kV/m. VEXB =2.4 km/s • At the observed plasma conditions in radial range of the HIBP measurements Er ~ constant;the plasma column rotates not as a rigid body due to the B(r) dependence. Typical [EB] ~ 1.25*104rad/s. • Correlation reflectometry shows that the radial dependence of turbulence rotation velocity in consistent with ExB rotation. Both velocities decrease accordingly when ECRH applied. • Within the achieved experimental accuracy turbulence tends to rotate with plasma ExB rotation velocity.

  42. The Characterization of Edge Plasma Intermittency in T-10 and TCABR Tokamaks V.P. Budaev1, S.A. Grashin1, G.S. Kirnev1, B.V. Kuteev1 Yu.K. Kuznetsov2, Z.O. Guimarães‑Filho2, I.C. Nascimento2, I. L. Caldas2, R.M.O. Galvão2,3, M.P. Gryaznevich4, G. Van Oost5 1Nuclear Fusion Institute, RRC Kurchatov Institute, 123182, Kurchatov Sq.1, Moscow, Russia 2Institute of Physics, University of São Paulo, 05508-900, São Paulo, Brazil 3Brazilian Center for Research in Physics, 22290-180, Rio de Janeiro, Brazil 4EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, UK 5Ghent University, Ghent, Belgium

  43. Experimental studies of edge plasma turbulence using Langmuir probes in the T-10 and TCABR tokamaks. In the tokamaks, the plasma turbulence in the scrape-off-layer is characterized by strong intermittency. The analysis of probe signals has shown that the spectra, the correlation functions and the probability density functions (PDF) demonstrate non-trivial power laws with multi-scale properties The PDF of plasma density fluctuations (derived from probe ion saturation current) varies with radius. Direct link to JE 1

  44. Characterization ofIntermittent Bursts at the Edge of the CASTOR Tokamak I. Nanobashvili1,2, P. Devynck3, S. Nanobashvili1, P. Peleman4, J. Stöckel5, G. Van Oost4 1Andronikashvili Institute of Physics, Tbilisi, Georgia 2Kharadze Abastumani Astrophysical Observatory, Tbilisi, Georgia 3Association EURATOM-CEA, CEA/DSM/DRFC Cadarache, Saint Paul Lez Durance, France 4Department of Applied Physics, Ghent University, Ghent, Belgium 5Institute of Plasma Physics, Association EURATOM/IPP.CR, Prague, Czech Republic

  45. Temporal characteristics of density bursts in the scrape-off layer (SOL) of the CASTOR tokamak were investigated. • Intermittent positive bursts of density are observed by means of a radial array of Langmuir probes. • Globally (comparing the closest and furthermost radial positions with respect to the center of the discharge chamber) we observe a radial decrease of average burst rate together with a radial increase of the average burst duration. • Recently, a monotonic radial decrease of average burst rate together with an increase of the average burst duration have been observed in the Tore Supra tokamak , but the decay length is significantly shorter than in CASTOR. This is most probably due to radially elongated turbulent events – streamers which govern the radial transport at the edge of the CASTOR tokamak and which are responsible for the appearance of density bursts.

  46. CONCLUSIONS • These first Joint Experiments have clearly demonstrated that small tokamaks are suitable and important for broad international cooperation, providing the necessary environment and manpower to conduct dedicated joint research programmes. • The contribution of small tokamaks to the mainstream fusion research such as edge turbulence, improved confinement, and diagnostics development can be enhanced through coordinated planning. • The activities under this IAEA Coordinated Research Project are already paying visible dividends both in increased number of publications and improved collaboration between participating tokamak teams. • Another important result of joint experiments is the improvement in understanding and communications between scientists from different countries, creating efficient team work both during experiments and data analysis.

  47. TEXTOR with DED A poloidal region of 120o is covered by the DED coils. • 16 coils wrapped around the HFS of TEXTOR • The coils are parallel to the field lines of the q=3 surface

  48. Operation Modes • Large flexibility due to different configurations: m/n = 3/1, 6/2 & 12/4 • Operation for DC < f < 10kHz; max. coil current: IDED = 15kA in 12/4 configuration • 3/1 Configuration • 4 coils bundled; IDED=3.75kA • Weak radial decay of perturbation field • Influence on the core plasma expected

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