D- 3 He HA tokamak device for experiments and power generations

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1 D- He HA tokamak device for experiments and power generations US-Japan Fusion Power Plant Studies Contents University of Tokyo, Japan January -, 5 O.Mitarai (Kyushu Tokai University).Motivation.Formalism, control algorithm, and hot ion mode criterion.calculated results 4.Summary and further issues in collaboration with H.Matsuura (Kyushu University), Y.Tomita (NIFS)

2 . Motivation ST has a large potential for D- He fusion. Although the large plasma current required for ignition can be ramped up by the vertical field and heating power even without the central solenoid, the following concerns may appear: []the plasma current itself is very large, []the plasma current changes when the plasma energy changes. []the current hole produced in the initial phase does not shrink due to long resistive decay time, leading to the high energy particle confinement problems, and q min = limitation of the plasma current. Purpose of this Using the central solenoid in the high aspect ratio tokamak, disadvantageous point of ST is removed. Namely, the current hole is removed in the initial low temperature phase, leading to improving the high energy particle confinement, q min limit, and the plasma current Feasibility of D- He HA

3 . Formalism, Control algorithm, and Hot ion mode criterion.. -dimensional particle and power balance equations Deuterium dn D () = ( +α n )S D (t) n D () τ D * [ ] ( +α n ) n D ()n T () σv DT (x) + n D () { σv DDPT (x) + σv DDHEN (x)}+ n D ()n He () σv DHE (x) Helium- dn HE () = ( +α n )S HE (t) + (+ α n ) n () D σv DDHEN (x) n D ()n He () σv DHE (x) n () He * τ HE Tritium dn T () = ( +α n ) n D() σv DDPT (x) n D ()n T () σv DT (x) n T () * τ T Alpha ash dn α () = ( + α n ){ n D ()n T () σv DT (x) + n D ()n He () σv DHE (x)} n α () τ α * Proton ash dn p () = (+ α n ) n D () σv DDPT (x) + n D ()n He () σv DHE (x) n P () * τ P

4 Electron density n e () = n D () + n T () + n He () + n α () + n p () + ( + α n )Zn imp Power balance (T i /T e =.5) dt i () +α = n + α T.5e( f D + f T +/γ i + f He + f α + f P )n e () [{ P EXT /V o + P oh + P DHE + P DDPT + P DDHEN + P DT } { P L + P b + P s }] T i () ( ) f D + f T +/γ i + f He + f α + f P + γ i ( +α n )Zf imp ( ) n e () dn D () + dn T () where T i (x)/t i () = T e (x)/t e () = (-x ) α T n(x)/n() = n α (x)/n α () = (-x ) α n + dn P () + + γ i ( ( + α n )Zf imp ) n e () dn α () + dn He() Tokamak:.9.9 τ IPB (y,) =.56A i I p [MA]n.4 9 [ 9 m.97 ]R o [m]ε κ.78 B.5 to [T]/P.69 HT [MW ] τ AUX = γ HH τ IPB (y,) IPB98(y,) confinement law with τ E = min{τ NA, τ AUX } where the mass factor : 4

5 A i = {n D () + n HE () + n T ()}/{ n D () + n HE () + n T ()}.. Hot ion mode criterion. Energy transfer from ion to electron: ( ) P ie [ W / m ]=.4 5 n e ()[m ]/ f D + 4 f He + α n.5α T A D A He + f p A p + 4 f He4 A He4 + f T ln Λ j A T T i () T e () T e ()[kev].5 Ion power balance P f f i =P ie + P Li Electron power balance P f (-f i )+P ie =P b +(P sw +P sv )+ P Lie where f i is the energy transfer fraction of the fusion power to ion. P f f i >P ie must be satisfied to have ion and electron power balances. The contour map of (P f f i - P ie ) is drawn on the n-t i plane with MW. [] T i /T e =.5, f i =.8, f D =.54,f HE =.8,f T =.5,f p =.,f HE4 =.88, lnλ= T i >9 kev is necessasry 5

6 []Critical ion temperature vs ion energy fraction f i for T i /T e =.5 Higher temperature is required for the hot ion mode..5 5 Ti-critical (ev) Fi 6

7 7

8 Even when the global power balance analysis gives us the answer, it is sometimes rejected by this criterion. [] Improper case: R eff =.9 Fusion power P f =-6 MW(neutron)=6 MW Brems rad. P b =95 MW Synchrotron rad. P s =5+ MW Plasma conduction P L =865 MW n()=.6x m - T i = 8.5 kev, T e = 55.6 kev, T i -T e = 7.9 kev P ie =8 MW 6f i =8 + 6(-f i )+8 = f i > Impossible [] Proper case R eff =.99 Fusion power P f =-6 MW(neutron)=7 MW Brems rad. P b =79 MW Synchrotron rad. P s = = MW Plasma conduction P L =69 MW n()=.8x m - T i =98 kev, T e =65. kev, T i -T e =.7 kev P ie =798 MW 7 f i = (-f i )+788 = For the limit of P Li =, f i >.8 is obtained. This criterion with f i =.8 gives us n() <.x m -, 8

9 T i () > 98 kev for HA D- He fusion reactor. 9

10 .. External heating power: P EXT HL [W] = M HL (t)x 6 P thresh - P oh +P F -P b -P s V o where P thresh [MW] =.84 n.58 [ m - ] B t.8 [T] R. [m] a.8 /A i.4. Fueling Total fueling is controlled by the minimum error between the three signals e DHE ( p f ) = ( P f / P fo ) e DHE (n) = ( n() / n() GW ) e DHE (< β >) = ( <β > / < β > MAX ) { } e DHE (min) = min e DHE (p f ),e DHE (n),e DHE (< β >) S DHE = S DHE e DHE (min) + T INT e DHE (min) + T d de DHE (min) where Integration time: T int = sec, Derivative time: T d =, D- He Fuel ratio is controlled by n S D (t) = D () n D () + n He () + G NDHE e(n D / n He ) + o n S HE (t) = He () n D () + n He () + G NDHE e(n He / n D ) + o n where e(n D / n He ) = D () n D () + n He () o n e(n He / n D ) = He () n D () + n He () o T DHE int T DHE int n D () n D () + n He () n He () n D () + n He () t e(n D / n He ) S (t) DHE t e(n He / n D ) S (t) The fuel ratio: n D : n He = : ~.4 particle confinement time ratio : τ D */τ E = τ HE */τ E = τ T */τ E = τ p */τ E = τ α */τ E = ~ prompt loss of fusion products is to be zero.

11 .5. Plasma circuit equation: Plasma circuit equation: L p di p di + R p (I p I CD I BS ) = M V PV and the vertical field + M Psh di sh + M Pdiv di div + V OH () B VE = B zov I V - B zodiv I div + B zosh I sh () provides the equivalent circuit equation with α div = I div /I p and α sh = I sh /I V, di p L peff = R peff I p M PV + M Psh α sh db VE + V B zov + B zosh α sh OH () where L peff = L p + M Pdiv M PV + M Psh α sh B zov + B zosh α sh B zodiv α div R peff = R p ( f CD f BS ) f BS = I BS / I p = C BS εβ p C BS =.5 α div =.,α sh = Feedback controlled OH by V OH =(-I p /I po ) As the vertical field drives the plasma current, the OH contribution is reduced during the fusion power rise-up phase.

12

13 .6. D- He Tokamak device (5m,.5m) BL (.5m, 6.5m) BT ITER FEAT (4m, m) 6 m m 8 m 6 m 4 m ITER-FEAT Cross section of D- He ST "Thermonuclear Boiler Plant" Final ST D- He HAT Although machine sizes of D- He HAT are slightly larger than the present ITER, it may be constructed with the present technology in spite of the larger plasma parameters. Radial build: R=7.5 m, a=. m, SO =. m, BL =.8 m, SP =. m, BT =. m, OH =.8m (total gap =.4 m) OH coil:r OH =R a - SO - BL - SP - BT - OH / =.7 m B OH =. T, Φ OH = πr OH (B OH )=9.7x(B OH ) = 7 Vs

14 . Calculated results of temporal evolution.. Power generation plant without parameter constraints [] Wall reflection R eff =.95, n/n GW =.8, β max =.7%, T i /T e =.5,τ p * /τ E =, D: He=.46:.54, f ash =5.7%, P f =. GW, Ignition, P n =75 MW, P e = MW [4%] n()=.4x m -, T i ()=99.9 kev, P f f i =4 MW>P ie =5 MW n() (m - ) f ash NE FASH PF PF T T i () (ev) P f BETAP. P n I p P EXT β p τ E (s) Flux(Vs) PNV IP BVFLUX OHFLUX PEXT TAUE (g) BETAA MHLI BV ICD IBS SSDD SSHE β t M HL B v (T) Time (s) TOTFLUX I CD S D.S He (m - /s ) 4

15 [] Worse wall reflection R eff =.9, n/n GW =.65, β max =.9% T i /T e =.5,τ * p /τ E =, D: He=.6:.4, f ash =5.9%,,P f =. GW, Ignition, P n =4MW, P e = MW [4%] n()=.7x m -, T i ()= kev, P f f i =89 MW>P ie =76 MW 5

16 n() (m - ) f ash NE FASH TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT Flux(Vs) β p PNV IP BVFLUX OHFLUX PEXT (h) (g) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX [] Good wall reflection R eff =.99, n/n GW =.85, β max =4.%, T i /T e =.5,τ * p /τ E =, D: He=.4:.58, f ash =5.4%, P f =. GW, Ignition, P n =6MW, P e = MW [4%], I CD S D.S He (m - /s ) 6

17 n()=.46x m -, T i ()= kev, P f f ion =5 MW>P ie =9 MW If a wall reflection is good, the neutron power can be further reduced. n() (m - ) f ash NE FASH (b) TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT β p Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (g) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX.. Possible power generation experiments with parameter constraints : [4] The beta limit: β max =.%, n/n GW =.6, I CD S D.S He (m - /s ) 7

18 R eff =.95, T i /T e =.5,τ p * /τ E =, D: He=.5:.5, f ash =5.5%, P f =.4 GW, Ignition, P n =74MW, P e =877 MW [4%] n()=.x m -, T i ()=98.5 kev, P f f i =887 MW>P ie =79 MW n() (m - ) f ash NE FASH (b) TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT β p Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (h) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX [5] Additional density limit : n/n GW =.5, β max =.%, R eff =.95, T i /T e =.5,τ p * /τ E =, D: He=.5:.48, f ash =5.5%, P f =. I CD S D.S He (m - /s ) 8

19 GW, Ignition, P n =7W, P e =755 MW [4%] n()=.79x m -, T i ()=97 kev, P f f i =64 MW >P ie =58 MW n() (m - ) f ash NE FASH (b) TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT β p Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (g) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX [6] The beta limit : β max =.%, n/n GW =.4, I CD S D.S He (m - /s ) 9

20 R eff =.95, T i /T e =.5,τ * p /τ E =, D: He=.54:.46, f ash =5.9%, P f =.8 GW, Ignition, P n =68MW, P e =6 MW [4%] n()=.59x m -, T i ()=94 kev, P f f i =7 MW>P ie =7 MW n() (m - ) f ash NE FASH (a) (b) TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT β p Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (h) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX I CD S D.S He (m - /s )

21 [7] Additional density limit : n/n GW =., β max =6.8% R eff =.95, T i /T e =.5,τ p * /τ E =, D: He=.6:.4, f ash =6%, P f =.87 GW, Sub-Ignition, P n =47MW, P e = MW [4%], Q E =.7 n()=.86x m -, T i ()=87 kev, P f f ion =78 MW>P ie =696 MW n() (m - ) f ash NE FASH TAUE PF PF T MHLI T i () (ev) P f τ E (s) 5 M HL. BETAP. P n I p P EXT β p Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (g) BETAA BV ICD IBS SSDD SSHE..5.5 β t B v (T) Time (s) TOTFLUX I CD S D.S He (m - /s )

22 [8] Long particle confinement time : τ * p /τ E =, f ash =8.5% R eff =.95, T i /T e =.5,D: He=.58:.4, n/n GW =.6, β max =.8%, P f =.7 GW, Ignition, P n =MW, P e =88 MW [4%] n()=.98x m -, T i ()=95 kev, P f f i =795 MW>P ie =674 MW

23 n() (m - ) f ash NE (a) FASH (b) PF PF T T i () (ev) P f BETAP (c). P n I p P EXT β p τ E (s) Flux(Vs) PNV TAUE (e) IP BVFLUX OHFLUX PEXT (h) (f) (g) (d) BETAA MHLI BV ICD IBS SSDD SSHE β t M HL B v (T) Time (s) TOTFLUX I CD S D.S He (m - /s )

24 [9] He rich operation (Possibly He plasma +D-beam with E> MeV),τ * p /τ E =4, D: He=.:.7, f ash =.67%, H-mode operation,p f =44 MW, P n =.5 W, P EXT = MW, P e =8 MW[4%], Q E =.4,n()=6.x 9 m -, T i ()=7 kev, P f f i =97 MW>P ie =9 MW 4

25 n() (m - ) 4 NE T T i () (ev) f ash FASH TAUE (c) PF PF P f τ E (s) 5 MHLI. M HL BETAP (d). β p BETAA. β t P n I p P EXT Flux(Vs) PNV IP BVFLUX OHFLUX PEXT (g) (e) BV ICD IBS SSDD SSHE.5.5 B v (T) Time (s) TOTFLUX I CD S D.S He (m - /s ) 5

26 .. Parameters of D- He HAT: No Limit Beta limit Density limit Beta limit β % n/n GW.5 β % Major radius: R 7.5 m Minor radius: a. m... Toroidal field: B o T Maximum field: B max. T... Radius B t coil : BT.8m.8m.8m.8m Plasma Current: I p 4 MA Safety factor: Q MHD Internal inductance l i Plasma inductance: L p 7.4 µh Heating power: P EXT -> MW -> ->.6 ->.7 Plasma volume: V m Confinement factor over IPB(y,) scaling : γ HH.... Confinement time: τ E 7. s Ash density fraction: f ash 5.7% Be impurity fraction: f Be % Effective charge: Z eff Particle confinement time ratio: τ α */τ E =τ p */τ E Fuel ratio: n D :n He.46:.54.5:.5.5:.48.54:.46 Fusion product heating efficiency: η α = η p =.. Wall reflectivity: R eff Hole fraction ; f H.... Density profile: α n.... Temperature profile: α T.... Electron density: n().4x m -.87x.8x.8x Greenwald factor n()/n() GW Ion temperature: T i () kev Tmperature ratio: T i ()/T e () Toroidal beta value: <β >.7%... Poloidal beta value: Normalized beta value: <β p > β Fusion power: P f MW 4 78 Neutron power: P n 75 MW Bremsstrahlung loss: P b 958MW Synchrotron radiation loss to the wall: P s 47 MW 89 for energy conv.: P s Plasma conduction loss: P L 48 MW Electric power (η c =4%) P e Average neutron wall loading Γ n.47 MW/m Average heat flux: Γ h.94 MW/m Divertor heat load Γ div.5mw/m P L /(πrx m) Energy multiplication Q F

27 Density limit Worse He rich n/n GW. p/e ratio operation Major radius: R 7.5 m Minor radius: a. m... Toroidal field: B o T Maximum field: B max. T... Radius B t coil : BT.8m.8m.8m.8m Plasma Current: I p 4 MA Safety factor: Q MHD Internal inductance l i Plasma inductance: L p 7.4 µh Heating power: P EXT ->85. MW -> ->.5 -> Plasma volume: V m Confinement factor over IPB(y,) scaling : γ HH.... Confinement time: τ E 5. s Ash density fraction: f ash 6.% Be impurity fraction: f Be % Effective charge: Z eff Particle confinement time ratio: τ α */τ E =τ p */τ E 4 4 Fuel ratio: n D :n He.6:.4.6:.4.58:.4.:.7 Fusion product heating efficiency: η α = η p =.. Wall reflectivity: R eff Hole fraction ; f H.... Density profile: α n.... Temperature profile: α T.... Electron density: n().86x m -.x.98x.6x Greenwald factor n()/n() GW Ion temperature: T i () 87 kev Tmperature ratio: T i ()/T e () Toroidal beta value: Poloidal beta value: <β > <β p > Normalized beta value: β Ν Fusion power: P f 66 MW Neutron power: P n 47 MW Bremsstrahlung loss: P b 45 MW Synchrotron radiation loss to the wall: P s 5 MW for energy conv.: P s Plasma conduction loss: P L 4 MW Electric power (η c =4%) P e MW Average neutron wall loading Γ n. MW/m.8.7. Average heat flux: Γ h.6 MW/m.6.7. Divertor heat load Γ div 7. MW/m P L /(πrx m) Energy multiplication Q E

28 4. Summary and issues [] D- He HA Tokmak device is proposed with R= 7.5 m, a=.m, B to = 5~6.5 T, (5.5 T in Plasma current of ~4MA (7 MA in IPB98y confinement factor γ HH =. (. in Wall Low ash confinement ratio of -->low neutron power of 75 MW Ash confinement time ratio of 4 is Neutron wall loading.4 Heat flux=.87 MW/m (. MW/m Greenwald factor<.8 (.5 in β=. % (.8%) (β=.6 % in DIII-D) A D- He tokamak reactor would be possible within small extension of the present data base. *For reference D- He ST reactor GW power 5.6 m, a=.4m, B to = 4.4 power and vertical field ramp to 9 MA (NSTX <.5 confinement factor γ HH =.5 ~.8 (NSTX flux =.99 MW/m (. MW/m factor=.9 (.5 in DIII-D,ASDEX heating power MW (β=8 % in toroidal field B max =.5 T(Bi-high temperature superconductor B max = T) 8

29 @ash confinement time ratio up to 5 (4 at wall reflection (R ash confinement time ratio down to -->low neutron power of 5 MW, low neutron wall loading of. MW/m. [] Common issues in D- He reactors () A large fraction (8 %) of the fusion power should go to ions to keep the hot ion mode of T i /T e =.5. [] Nuclear elastic scattering (Nakao and Matsuura) may provide 4 %. [] The rest of 4 % should be provided by the stochastic ion heating (D.Gates et al ) as observed in NSTX, NSTX: T i /T e = for V NBI ~ 4V A D- He ST reactor: V α ~.8V A,V p ~ 7.5V A D- He HA tokamak reactor: V α ~.7V A, V p ~ 5.5V A and gyro-stream cyclotron instability as proposed by Cheng. () Divertor heat flux is very large Pebble divertor by Nishikawa Ga Liquid divertor 9

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