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1 Consorzio RFX, Corso Stati Uniti 4, Padova - Italy 2 University degli Studi di Padova, Via 8 Febbraio, Padova, Italy Real-time plasma boundary reconstruction in RFX-mod tokamak discharges O. Kudlacek 1,2 , R. Cavazzana 1 , C. Finotti 1 , G. Marchiori 1 , L.Marreli 1 ,P. Zanca 1 Introduction- Reversed Field Pinch operated as a tokamak RFP: toroidal device, B P >> B T - high plasma current RFP instabilities: resistive wall modes, tearing modes controlled by a system of saddle coils [1] Resistive wall modes: artificial ideal wall- flux through vessel conserved => no kinks etc… Tearing modes: many TM in RFP, mitigation of B r created by TM => amplitude reduction Tokamak applications: q edge < 2 discharges, sawtooth oscillation control in circular plasma [2,3] Goal of the project: same results in D-shaped plasma, demonstrate extended control possibilities First step: D-shaped discharge design and control RFX-mod active saddle coils. RFX-mod device •Biggest RFP in the world •Location: Padova, Italy •R= 2 m, a= 46 cm, circular vessel shape •I P > 2 MA in RFP regime •192 active saddle control coils •16 PFC => plasma can be shaped •Operated also as a low current tokamak (B T < 0.55 T, I P < 200 kA) RFX-mod device Vacuum magnetic potential estimation •Vacuum magnetic potential that fulfils , analytical solution Model constants: A ks , A kc , B ks , B kc estimated from the magnetic sensors signals via circular harmonics of B P and ψ •Reliable reconstruction: 6-7 harmonics but JUST 8 pick-up coils and 8 flux loops available => 3 harmonics can be estimated, aliasing error •MAXFEA: higher harmonics generated mainly by the PF coils => estimated from PF coils currents in RT 0 2 = Φ ) ( ) sin( ) ( ) cos( 1 0 k ks k ks m k k kc k kc r B r A k r B r A k - = - + + + + Φ = Φ θ θ θ Φ = B Aliasing error removal •Harmonics spectrum of the B P and ψ contains at least 10 non-negligible harmonics •Problem: aliasing corrupts the computation of the first 3 harmonics and generates parasitic sine harmonics •Plasma aliasing low, PFC aliasing removed in RT Aliasing effect at cosine harmonics Aliasing effect at sine harmonics Acknowledgements This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement number 633053 and from Erasmus Mundus International Doctoral College in Fusion Science and Engineering. The views and opinions expressed herein do not necessarily reflect those of European Commission. Plasma boundary calculation •Plasma boundary = contour of the poloidal flux, estimated from the magnetic potential •To estimate the boundary flux, at least one boundary point has to be found- X-point •At X-point: B P and B R = 0 2 equations and 2 unknowns- computationally intensive in cylindrical coordinates and RT => both approximated by a quadratic form •Equation rewritten into Cartesian coordinates, analytical solution X-point •X-point flux computed by integration, a contour found •Difference compared to MAXFEA [4] below 8 mm Comparison of MAXFEA and RT boundary Macroscopic parameters measurement β P , l i , q 95 : important to describe plasma macroscopic properties , x= 0.95 at the plasma edge=> edge plasma currents neglected β P +l i /2 measured first using the following approach [5] ! " # $ % & " β P + l i /2, q 95 are both determined with error lower than 4 % β P measured by diamagnetic loop, not very accurate The time evolution of ! " # $ and q 95 References [1] Martin, P: Lessons from RFP on magnetic feedback control, Fusion Science and Technology, Vol. 59, p. 602-616 [2] Marrelli L., Feedback control of the m=1, n=2 mode in RFX-mod tokamak plasma with qcyl(a) <2, 38th EPS Conference on Plasma Physics [3] Zanca P., Feedback control model of m=2 n=1 resistive wall mode in a circular plasma, Plasma Physics and Controlled Fusion 54 [4] Barabaschi P., The MAXFEA code, Plasma Control Technical Meeting, Naka(Japan), 1993 [5] Swain D.W., Nuclear Fusion, volume 22, No 8 (1982), p. 1015-1030 Conclusions & Outlook •A new method for plasma boundary reconstruction proposed and successfully tested •Error in plasma boundary measurement below 8 mm, β P + l i /2, q 95 with error below 4 % •Applicable for SN, DN, circular and elongated discharge •Future work: H-mode accessibility tests, q 95 < 2 for various plasma shape •Dynamical correction of errors arising from eddy currents during transition phases •Applicability of the method on D-shaped devices- tests ’()∙*+%,- . .) = ) ./ ., , 0 ) 1 . ., = ./ .) )

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Page 1: Real-time plasma boundary reconstruction in RFX-mod ... › sites › default › files › webform › phdevent › 2… · 1Consorzio RFX, Corso Stati Uniti 4, Padova - Italy 2University

1Consorzio RFX, Corso Stati Uniti 4, Padova - Italy2University degli Studi di Padova, Via 8 Febbraio, Padova, Italy

Real-time plasma boundary reconstruction in RFX-mod tokamak discharges

O. Kudlacek1,2, R. Cavazzana1, C. Finotti1, G. Marchiori1, L.Marreli1 ,P. Zanca1

Introduction- Reversed Field Pinch operated as a tokamak•RFP: toroidal device, BP >> BT - high plasma current

•RFP instabilities: resistive wall modes, tearing modes controlled by a system of saddle coils [1]

•Resistive wall modes: artificial ideal wall- flux through vessel conserved => no kinks etc…

•Tearing modes: many TM in RFP, mitigation of Br created by TM => amplitude reduction

•Tokamak applications: qedge< 2 discharges, sawtooth oscillation control in circular plasma [2,3]

•Goal of the project: same results in D-shaped plasma, demonstrate extended control possibilities

•First step: D-shaped discharge design and controlRFX-mod active saddle coils.

RFX-mod device•Biggest RFP in the world

•Location: Padova, Italy

•R= 2 m, a= 46 cm, circular vessel shape

•IP > 2 MA in RFP regime

•192 active saddle control coils

•16 PFC => plasma can be shaped

•Operated also as a low current tokamak

(BT < 0.55 T, IP < 200 kA)

RFX-mod device

Vacuum magnetic potential estimation•Vacuum magnetic potential that fulfils , analytical solution

•Model constants: Aks, Akc, Bks, Bkc estimated from the magnetic sensors signals via circular harmonics of BP and ψ

•Reliable reconstruction: 6-7 harmonics but JUST 8 pick-up coils and 8 flux loops available => 3 harmonics can be estimated, aliasing error

•MAXFEA: higher harmonics generated mainly by the PF coils => estimated from PF coils currents in RT

02=Φ∇ )()sin()()cos(

1

0

k

ks

k

ks

m

k

k

kc

k

kcrBrAkrBrAk

=

−⋅+⋅⋅+⋅+⋅⋅+⋅Φ=Φ ∑ θθθ

Φ∇=B

Aliasing error removal•Harmonics spectrum of the BP and ψ contains at least 10 non-negligible harmonics

•Problem: aliasing corrupts the computation of the first 3 harmonics and generates parasitic sine

harmonics

•Plasma aliasing low, PFC aliasing removed in RT

Aliasing effect at cosine harmonics Aliasing effect at sine harmonics

AcknowledgementsThis project has received funding from the European Union’s Horizon 2020

research and innovation program under grant agreement number 633053 and

from Erasmus Mundus International Doctoral College in Fusion Science and Engineering. The views and opinions expressed herein do not necessarily reflect

those of European Commission.

Plasma boundary calculation•Plasma boundary = contour of the poloidal flux, estimated from the magnetic potential

•To estimate the boundary flux, at least one boundary point has to be found- X-point

•At X-point: BP and BR = 0 �2 equations and 2 unknowns- computationally intensive in

cylindrical coordinates and RT => both approximated by a quadratic form

•Equation rewritten into Cartesian coordinates, analytical solution � X-point

•X-point flux computed by integration, a contour found

•Difference compared to MAXFEA [4] below 8 mm

Comparison of MAXFEA and RT boundary

Macroscopic parameters measurement• βP , li, q95 : important to describe plasma macroscopic properties

•�� ����

���, x= 0.95 at the plasma edge=> edge plasma currents neglected

•βP +li/2 measured first using the following approach [5]

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• !� "#$��

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•βP + li/2, q95 are both determined with error lower than 4 %

•βP measured by diamagnetic loop, not very accurate

The time evolution of !� "#$�

and q95

References[1] Martin, P: Lessons from RFP on magnetic feedback control, Fusion Science and Technology, Vol. 59, p. 602-616

[2] Marrelli L., Feedback control of the m=1, n=2 mode in RFX-mod tokamak plasma with qcyl(a) <2, 38th EPS Conference on Plasma Physics

[3] Zanca P., Feedback control model of m=2 n=1 resistive wall mode in a circular plasma, Plasma Physics and Controlled Fusion 54

[4] Barabaschi P., The MAXFEA code, Plasma Control Technical Meeting, Naka(Japan), 1993

[5] Swain D.W., Nuclear Fusion, volume 22, No 8 (1982), p. 1015-1030

Conclusions & Outlook•A new method for plasma boundary reconstruction proposed and successfully tested

•Error in plasma boundary measurement below 8 mm, βP + li/2, q95 with error below 4 %

•Applicable for SN, DN, circular and elongated discharge

•Future work: H-mode accessibility tests, q95 < 2 for various plasma shape

•Dynamical correction of errors arising from eddy currents during transition phases

•Applicability of the method on D-shaped devices- tests

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