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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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slide1

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
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
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
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
slide33

Locking threshold

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

to very long tw

single mode simulations external coils
Single mode simulations: external coils

a = 0.459m

rw i = 0.475m

c = 0.5815m

slide39

Edge radial field: tw dependence

Data averaged on 0.1s simulation

m=1

slide42

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

slide51

Multi-mode simulations: frequencies

Averages over the second half of the simulation

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 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