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Perspectives of tearing modes control in RFX-mod. Paolo Zanca Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy. RFX-mod contributions to TMs control (I). Demonstrated the possibility of the feedback control onto TMs

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Perspectives of tearing modes control in RFX-mod

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Perspectives of tearing modes control in rfx mod

Perspectives of

tearing

modes control in RFX-mod

Paolo Zanca

Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy


Rfx mod contributions to tms control i

RFX-mod contributions to TMs control (I)

  • Demonstrated the possibility of the feedback control onto TMs

  • Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands


Rfx mod contributions to tms control i1

RFX-mod contributions to TMs control (I)

  • Demonstrated the possibility of the feedback control onto TMs

  • Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands

  • Not obvious results: phase-flip instability?


Rfx mod contributions to tms control i2

RFX-mod contributions to TMs control (I)

  • Demonstrated the possibility of the feedback control onto TMs

  • Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands

  • Not obvious results: phase-flip instability?

  • No-sign of phase-flip instability; equilibrium condition can be established where CMC induces quasi-uniform rotations of TMs


Rfx mod contributions to tms control ii

RFX-mod contributions to TMs control (II)

  • Wall-unlocking of TMs with CMC

  • In general, the feedback cannot suppress the non-linear tearing modes requested by the dynamo.

  • The feedback keeps at low amplitude the TMs edge radial field

  • Improvement of the magnetic structure: sawtooth of the m=1 n=-7 which produces transient QSH configurations


Cmc optimizations

CMC optimizations

  • Increase the QSH duration → recipes under investigation

  • Which are the possibilities to reduce further the TMs edge radial field? → Model required


Rfxlocking

RFXlocking

  • Semi-analitical approach in cylindrical geometry

  • Newcomb’s equation for global TMs profiles

  • Resonant surface amplitudes imposed from experiments estimates

  • Viscous and electromagnetic torques for phase evolution

  • Radial field diffusion across the shell(s)

  • Feedback equations for the coils current

  • It describes fairly well the RFX-mod phenomenology →L.Piron talk


Perspectives of tearing modes control in rfx mod

General analysis of the TM control


Single shell external coils

Single-shell external coils

Sensors

Vessel

Coils

plasma


Normalized edge radial field

Normalized edge radial field

  • The feedaback action keeps low the normalized edge radial field

  • At best b^senscan be made close but not smaller than the ideal-shell limit


Feedback limit

Feedback limit

Sensors

Vessel

Coils

plasma


Feedback limit1

Feedback limit

Sensors

Vessel

Coils

plasma


Feedback limit2

Feedback limit

Sensors

Vessel

Coils

plasma

br=0 everywhere: impossible


Role of the vessel

Role of the Vessel

  • The stabilizing effect of the vessel is crucial for having low b^sensand moderate power request to the coils

  • The shorterτwthe faster must be the control system (fc=1/Δt) to avoid feedback (high-gain) induced instabilities

  • Optimum range:τw>10ms better τw 100ms


Single shell internal coils

Single-shell Internal coils

Coils

Sensors

Vessel

plasma


Single shell internal coils1

Single-shell Internal coils

Coils

Sensors

Vessel

plasma


Single shell internal coils2

Single-shell Internal coils

  • Continuous-time feedback → solution ωω0 with br(rsens) 0 for large gains

  • Discrete-time feedback : including the latency Δt the high-gain instability may occur

  • The good control region is not accessible for realistic TM amplitudes.

  • For stable gains b^sensis determined by the ideal-shell limit, which is large due to the loose-fitting vessel required by the coils dimension


Perspectives of tearing modes control in rfx mod

RFP design for good TM control

(a personal view)


Premise

Premise

  • The passive stabilization provided by a thick shell does not solve the wall-locking problem

  • In the thick-shell regime wall-locking threshold ~σ1/4

  • Feedback is mandatory to keep TMs rotating


Design in outline

Design in outline

  • In-vessel coils not interesting

  • Single structure (vessel=stabilizing shell) with the coils outside

  • Close-fitting vessel to reduce the ideal-shell limit

  • τw10ms-100ms withΔt10μs-100μs


Perspectives of tearing modes control in rfx mod

RFX-mod perspectives (a personal view)


Rfx mod layout

RFX-mod layout

  • 3ms vacuum-vessel, 100ms copper shell, ~25ms mechanical structures supporting the coils

  • The control limit is mainly provided by the 100ms copper shell


Rfx mod status

RFX-mod status

Gain optimization guided by RFXlocking simulations for the RFX-mod case

m=1 TMs


Optimizations

Optimizations

  • Get closer to the ideal-shell limit (minor optimization)

  • Reduce the ideal-shell limit by hardware modifications (major optimization)


Minor optimizations

Minor optimizations

  • Increase the coils amplifiers bandwidth: maximum current and rensponse time

  • Acquisition of the derivative signal dbr /dt in order to have a better implementation of the derivative control (to compensate the delay of the coils amplifiers)

  • Compensation of the toroidal effects by static decoupler between coils and sensors only partially exploited

  • Compensation of the shell non-homogeneities requires dynamic decoupler (work in progress)


Major optimization

Majoroptimization

  • Approach the shell to the plasma edge possibly simplifying the boundary (removing the present vacuum vessel which is 3cm thick)

  • Moving the τw=100msshell from b=0.5125m to b=0.475m (a=0.459) a factor 3 reduction of the edge radial field is predicted by RFXlocking


Conclusions

Conclusions

  • CMC keeps TMs into rotation

  • Edge radial field: ideal-shell limit found both with the in-vessel and out-vessel coils → br(a)=0 cannot be realized

  • The vessel=shell must be placed close the plasma → coils outside the vessel. Is a close-fitting vessel implementable in a reactor?

  • The feedback helps the vessel to behave close to an ideal shell→ τw cannot be too short


Perspectives of tearing modes control in rfx mod

spare


Perspectives of tearing modes control in rfx mod

Edge radial field control by feedback


Rfxlocking vs experiment

RFXlocking .vs. experiment


Perspectives of tearing modes control in rfx mod

Normalized edge radial field: weak brs dependence


Perspectives of tearing modes control in rfx mod

br(rm,n) vs br(a) experimental


Perspectives of tearing modes control in rfx mod

Locking threshold

The present analysis valid for dw<<rw cannot be extrapolated

to very long tw


Perspectives of tearing modes control in rfx mod

Edge radial field .vs. current time constant


Single mode simulations external coils

Single mode simulations: external coils

a = 0.459m

rw i = 0.475m

c = 0.5815m


Perspectives of tearing modes control in rfx mod

Single-mode analysis: feedback performances dependence on tw


Perspectives of tearing modes control in rfx mod

Single-mode analysis: feedback performances dependence on tw


Perspectives of tearing modes control in rfx mod

Multi-mode analysis: power dependence on tw


Perspectives of tearing modes control in rfx mod

Edge radial field: tw dependence

Data averaged on 0.1s simulation

m=1


Perspectives of tearing modes control in rfx mod

Normalized edge radial field: rwi dependence

m=1


Perspectives of tearing modes control in rfx mod

Normalized edge radial field: no rf dependence

m=1


Perspectives of tearing modes control in rfx mod

Out-vessel coils: signals

4x48 both for coils (c = 0.5815m) and sensors (rwi = 0.475m )


Single shell discrete feedback

Single-shell: discrete feedback

Δt = latency of the system


Perspectives of tearing modes control in rfx mod

External coils: discrete feedback τw=100ms


Perspectives of tearing modes control in rfx mod

External coils: discrete feedback τw=10ms


Perspectives of tearing modes control in rfx mod

External coils: discrete feedback τw=1ms


The in vessel coils

The in-vessel coils


Single mode simulations frequency

Single mode simulations: frequency

τw= 1ms100ms


Single mode simulations i c v c

Single mode simulations: Ic, Vc


Single mode simulations edge b r

Single mode simulations: edge br


Perspectives of tearing modes control in rfx mod

Multi-mode simulations: frequencies

Averages over the second half of the simulation


Perspectives of tearing modes control in rfx mod

Multi-mode simulations: plasma surface distortion


Perspectives of tearing modes control in rfx mod

Multi-mode simulations: no phase-locking

Ideal shell

feedback


Perspectives of tearing modes control in rfx mod

Multi-mode simulations: no phase-locking

Incompatible with


Perspectives of tearing modes control in rfx mod

Internal coils: discrete feedback stable solutions


Perspectives of tearing modes control in rfx mod

Internal coils: discrete feedback stable solutions


The mhd model wi we

The MHD model: Ψwi, Ψwe

Boundary conditions from Newcomb’s solution


The mhd model s

The MHD model: Ψs

From experiment

No-slip condition


The mhd model

The MHD model: Ωθ, ΩΦ


The mhd model t em

The MHD model: δTEM


The mhd model c

The MHD model: Ψc

Further variable: Icm,n


The mhd model i c

The MHD model: Ic

RL equation for the plasma-coils coupled system

Further variable: IREFm,n


The mhd model i ref

The MHD model: IREF

Acquired by the feedback


Why a pure derivative control

Why a pure derivative control?

When |cm,n|>>1, from the RL equation one gets


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