Feedback control of the heating power to access the thermally unstable ignition regime in FFHR

Transcription

1 Feedback control o the heating power to access the thermally unstable ignition regime in FFHR US-Japan Fusion ower lant Studies and Related Advanced technologies with participation rom China and Korea, Feb.6-8,, Kyoto Univ., Uji, Japan Osamu Mitarai (okai Univ., Kumamoto, Japan) Contents:. Motivation.. Concept or eedback control o unstable regime. Calculated results on ignition access. Disturbance eect on control when coninement and impurity change: 5. Feedback control and diagnostic systems or low temperature and high-density ignition 6. Summary

2 . Motivation: While the eedback control algorithm o the heating power has been developed or the thermally stable ignition regime, preprogramming alone has been used or the thermally unstable ignition regime so ar. his has been one o big issue to be solved in the thermally unstable ignition studies in FFHR. By analogy o the thermally stable regime, new eedback control algorithm is discovered. It works successully during ignition access and is robust to various parameter disturbances. FFHR: Machine parameters R=5.7m a=.5m, = GW, η α =.98 <B>=.5 τ α */τ E =,.5MeV NBI, c =6 GHz, n c =.97 m - [] hermally stable regime: α n =.5, α =., γ ISS95 =.9 [] hermally unstable regime: α n =, α =., γ ISS95 =.

3 . Concept or eedback control o unstable regime:.. Feedback control o ueling (published) Stabilized by ID ueling control " (t) = # e D ( ) + $ t de D ( )% e D ( )dt + d int! & dt ' G o(t) nt the integration time, d the derivative time, [Note: (t)= i (t)< ] he error o the usion power e D ( ) = c(- / o ) [] c=+ or the thermally stable, [] c= - or the thermally unstable, n C B SD decreases - ( - ) < Ignition D SD!"#$%&$& - ( - ) > A Constant o line Stabilization mechanism. Cooling by ueling and heating by reducing ueling. rotates to the CCW. > However, eedback method o the heating power is not discovered yet!!

4 .. Concept or eedback control o heating power: [] In the stable ignition regime, the Sudo density limit restricts the operating point to the high-temperature and low-density regime..5 $ #6 {! DLM n() " n() lim [m # NE [W ] $ }B o [ ] ] =! SUDO! pr a R [m] where ( ) NE = + % # b # s he density limit provides the heating power as! DLM n()[m " (* ] [W ] =! #$ % &,* a R [m] ) pr - +*! SUDO.5 '.* B o [ ] ' 6 " ( / " B " S )

5 Eample o eedback control o the heating power in the thermally stable regime n() (m - ) alpha 5.!/a NE NELM RAIO (d) BEAA 5 ime (s) SSD 5 5 () (kev) <"> (m - /s) n() e (m - ) =.GW <!>=.7 % MW Density Limit at the stable ()(kev) Heating power MW, γ ISS =.9 (γ LHD =.) B=.5, n()~.8 m - < n c, ()~7.8 kev, Γ n ~.5 MW/m, <β>~.9 %, Beam penetration length λ/a~.7 E NBI =.5 MeV 5

6 [] Basic principle o proposed eedback control o the heating power: he thermally stable and unstable operation regime has an inverse relationship with respect to -n ais in OCON. Analogy o the density limit provides the temperature limit. As the density limit restricts the operating point to the low-density regime, the temperature limit restricts it to the low temperature regime. OCON 6

7 @ Artiicially posturated temperature limit: (Similar to the density limit)! () " () = %{ NE [W ] # $6 }B o [ ]( LM lim c ' * &' a R [m] )* Here, c and α C are selected by simulations. his temperature limit is rewritten as * #$ + (! " B " S )% & ' "6 ( ) LM ()-! C a R [m] +., c / B o [ ] Finally, the heating power depends on the measured temperature, and alpha, bremsstrahlung power losses #! " () &) C LM a R [m] $ ' % c ( B o [ ] where γ LM is adjusted to reduce with the time + C * 6 + ( ) + B + S )! LM = () lim () ". () lim = c #{ NE [W ]! "6 }B o [ ]& % ( a R [m] $ % '( ) C ( lim and c are dierent) 7

8 . Calculated results on ignition access: c optimization [-] c = 7.7 kev, α C =. ma =6MW γ ISS =., B=.5, α n =, α =. E=.5MeV annbi n()=8. m -, ()=7. kev, <β>=.5 %, div =.MW/m (9, Δ=. ), (nt = s, di = s) Operating temperature is always lower than the temperature limit. -control n() (m - ) alpha !/a ELM RAIO C(d) FB control NE BEAA SSD 6 8 ime (s) () (kev) <"> (m - /s) n() e (m - ) MW at the unstable emperature limit =.GW <!>=.9 % ()(kev) he operating point passes near the saddle point. 8

9 [-] c = 5.5 kev ma =6MW As the temperature limit is lowered, the heating power or ignition access is increased to pass the higher contour map, and the density also increases leading to worse NBI penetration. -control n() (m - ) alpha !/a ELM RAIO C (d) FB control NE BEAA SSD 6 8 ime (s) () (kev) <"> (m - /s) n() e (m - ) MW at the unstable emperature limit =.GW <!>=.9 % ()(kev) 9

10 [-] c = 8.5 kev ma =6MW As the temperature limit is higher, the operating temperature is increased and the operating point stays longer in the low-density regime avorable or NBI heating. But... -control n() (m - ) alpha!/a ELM RAIO C (d) FB control NE BEAA SSD 6 8 ime (s) () (kev) <"> (m - /s) n() e (m - ) MW at the unstable emperature limit =.GW <!>=.9 % ()(kev)

11 . Disturbance eect when coninement actor or impurity change: [-] Coninement degradation during -5s : γ ISS =..5 (-5s) ( c = 7.7 kev, α C =.) Heating power is increased during coninement degradation phase. n() (m - ) alpha "/a ELM C(d) GHH -control FB control NE RAIO SSD 6 8 ime (s) () (kev).6..8.! ISS (m - /s) n() e (m - ) MW at the unstable =.GW <!>=.9 % ()(kev)

12 [-] Coninement increment during -5s γ ISS =..6 (-5s), B=.5, α n =, α =.E=.5MeV annbi ( c = 7.7 kev, α C =.) Heating power is decreased during coninement improvement phase. n() (m - ) alpha "/a ELM C (d) GHH -control FB control NE RAIO SSD 6 8 ime (s) () (kev).6..8.! ISS (m - /s) n() e (m - ) MW at the unstable =.GW <!>=.9 % ()(kev)

13 [ ] Further c optimization Is c =7.7 kev optimum or wide parameter regime? [--] Lower coninement actor γ ISS =.5 ( c =7.7 kev, di = s) proceeds to the inal one smoothly. -control n() (m - ) alpha !/a ELM RAIO C (d) FB control NE GHH SSD 5 5 ime (s) () (kev) " ISS (m - /s) n() e (m - ) MW 8 6 at the unstable =.GW <!>=.9 % ()(kev)

14 [--] Finite dierential time o di =. s (γ ISS =.5, c =7.7 kev) Oscillations on ueling and heating power appear by inite dierential time in ueling control. stops at the highest temperature on = GW line by introducing the dierential time di. -control n() (m - ) alpha!/a ELM RAIO C (d) FB control NE GHH SSD 5 5 ime (s) () (kev) " ISS (m - /s) n() e (m - ). Final operating point 8 =.GW 6 <!>=.9 % MW ()(kev)

15 [--] Lower temperature limit o c =7. kev (γ ISS =.5, di =. s) When the temperature limit is lowered, operating point proceeds to the inal one smoothly even with the inite dierential time. Lower temperature limit drives the operating point to the low temperature regime at the turning point. n() (m - ) alpha!/a ELM RAIO C(d) -control 5 5 ime (s) FB control NE GHH SSD () (kev) " ISS (m - /s) n() e (m - ) MW 8 6 at the unstable =.GW <!>=.9 % ()(kev) 5

16 [-] Impurity disturbances: I impurity content is increased during heating phase, eedback heating power is increased. Sub-ignition [--] Impurity increment to imp =.5 ( c =7.7 kev, di = s) Sub-Ignition is terminated. -control n() (m - ) alpha !/a ELM RAIO C (d) FB control NE Fimp SSD 5 5 ime (s) () (kev) imp (m - /s) n() e (m - ). 8 6 MW =.GW <!>=.9 % ()(kev) 6

17 [--] Lower temperature limit case ( c =7. kev) (impurity increment to imp =.5, di = s) Sub-ignition is maintained or smaller C. Lower temperature limit can keep the operating point on the contour map in the low temperature regime c =7. kev can be used or wide parameters. -control n() (m - ) alpha !/a ELM RAIO C(d) FB control NE Fimp SSD 5 5 ime (s) () (kev) imp (m - /s) n() e (m - ). 8 6 MW 8 6 at the unstable 8 6 =.GW <!>=.9 % ()(kev) 7

18 [-5] Shutdown phase: [-5-] Heating power eedback in all phases. ( c =7. kev, di = s) Feedback control o the heating power is applied during the shutdown phase. -control n() (m - ) alpha "/a ELM C BEAA (d) FB control NE RAIO SSD 5 5 ime (s) () (kev) ! (m - /s) n() e (m - ) at the unstable MW emperature limit =.GW <!>=.9 % ()(kev) 8

19 [-5-] Heating power is shut o ater s. ( c =7. kev, di = s) n() (m - ) alpha "/a Smooth shutdown has been achieved without the heating power and uelling ELM C BEAA (d) -control FB control NE RAIO SSD 5 5 ime (s) () (kev) ! (m - /s) n() e (m - ) Fusion power is slightly changed rom the set value at the unstable MW emperature limit =.GW <!>=.9 % ()(kev) 9

20 5. Feedback control and diagnostic systems or low temperature and high-density ignition emperature measurement is important or eedback control o heating power during high-density ignition access. R, a, B o HNE n LIMI Feedback Controller! DLC () () Neutron n Detector ( reprogram ( # " (set) " )# " * Eternal Heating (NBI,ICRH,ECRH) Fusion power set value o (t) ( ' ID Contol ( ) Bolometer b e R,B t,v ECE Spectrometer s reprogram Fuel ratio set value {n D /(n D +n )} o ' ( ( Deuterium Fueling System S D ritium Fueling System S Intererometer Diamagnetic loop n D /n measurement n <$> dw/dt L!"#$%&

21 6. Summary [] ID ueling control was already developed or the thermally unstable ignition regime. Analogy o the density limit gives us the hint that postulated temperature limit restricts the operating point to the low-temperature regime. he newly discovered control algorithm or the heating power was successully demonstrated or ignition access to the thermally unstable regime in FFHR. [] Lower c tends to increase the heating power and density, and then reduce the penetration ratio o NBI heating. Higher c tends to stop the operating point i the coninement actor is reduced. [] emperature limit actor o c ~7. kev might be suitable or eedback control or wide parameter regimes. Feedback control method o ueling and heating power has been developed or thermally unstable operation.