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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

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

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


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 (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)

  • 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

  • Increase the QSH duration → recipes under investigation

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


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


General analysis of the TM control


Single-shell external coils

Sensors

Vessel

Coils

plasma


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

Sensors

Vessel

Coils

plasma


Feedback limit

Sensors

Vessel

Coils

plasma


Feedback limit

Sensors

Vessel

Coils

plasma

br=0 everywhere: impossible


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

Coils

Sensors

Vessel

plasma


Single-shell Internal coils

Coils

Sensors

Vessel

plasma


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


RFP design for good TM control

(a personal view)


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

  • 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


RFX-mod perspectives (a personal view)


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

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

m=1 TMs


Optimizations

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

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


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)


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

  • 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


spare


Edge radial field control by feedback


RFXlocking .vs. experiment


Normalized edge radial field: weak brs dependence


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


Locking threshold

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

to very long tw


Edge radial field .vs. current time constant


Single mode simulations: external coils

a = 0.459m

rw i = 0.475m

c = 0.5815m


Single-mode analysis: feedback performances dependence on tw


Single-mode analysis: feedback performances dependence on tw


Multi-mode analysis: power dependence on tw


Edge radial field: tw dependence

Data averaged on 0.1s simulation

m=1


Normalized edge radial field: rwi dependence

m=1


Normalized edge radial field: no rf dependence

m=1


Out-vessel coils: signals

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


Single-shell: discrete feedback

Δt = latency of the system


External coils: discrete feedback τw=100ms


External coils: discrete feedback τw=10ms


External coils: discrete feedback τw=1ms


The in-vessel coils


Single mode simulations: frequency

τw= 1ms100ms


Single mode simulations: Ic, Vc


Single mode simulations: edge br


Multi-mode simulations: frequencies

Averages over the second half of the simulation


Multi-mode simulations: plasma surface distortion


Multi-mode simulations: no phase-locking

Ideal shell

feedback


Multi-mode simulations: no phase-locking

Incompatible with


Internal coils: discrete feedback stable solutions


Internal coils: discrete feedback stable solutions


The MHD model: Ψwi, Ψwe

Boundary conditions from Newcomb’s solution


The MHD model: Ψs

From experiment

No-slip condition


The MHD model: Ωθ, ΩΦ


The MHD model: δTEM


The MHD model: Ψc

Further variable: Icm,n


The MHD model: Ic

RL equation for the plasma-coils coupled system

Further variable: IREFm,n


The MHD model: IREF

Acquired by the feedback


Why a pure derivative control?

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


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