The high density ignition in FFHR helical reactor by NBI heating Japan-US Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea February -, at NIFS in Toki, JAPAN Osamu Mitarai Tokai University, Kumamoto, Japan In collaboration with A. Sagara, et al., NIFS, Japan
Contents. Introduction. NBI penetration length 3. -D equations, ignition control algorithm. The stable ignition regime accessed by NBI in FFHRm 5. The high-density ignition regime accessed by NBI in FFHRm 6. The stable ignition regime accessed by NBI in FFHR-C (R=9m,.5m) 7. The high-density ignition regime accessed by NBI in FFHR-C 8. Summary and further challenge
. Introduction A high-density and low temperature operation is advantageous to reduce the divertor heat flux via bremstrahlung radiations and to inject pellets in the FFHRm helical reactor, however [] The first issue: Thermal instability Stabilization of the thermal instability is possible by the PID control based on the fusion power. Solved!! [] The second issues: Heating of the high-density plasma. A very high energy NBI system with 5~6 MeV is required for full penetration into high-density plasmas, which might be impossible to construct. 3
In this work we propose a new operation scenario to use the NBI with the beam energy of ~.5 MeV for both high and low-density operation regimes in FFHR. @ In the thermally stable low density and high temperature operation, as the density is relatively as low as.9x m -3, NBI with ~.5 MeV can be used. @ On the other hand, as the high density inhibits the neutral beam penetration, the new operation scenario is required to access the high-density ignition regime by NBI heating with ~.5 MeV. The density is kept at the low value less than ~x m -3 to ensure the NBI penetration and the operating point passes near the saddle point on POPCON. Above the density, high-density ignition is accessed by alpha heating after turning off NBI using the proposed PID control.
. NBI penetration length The NBI penetration e-folding length is calculated by!(n,t )[m] = % ' & $ # ( n(x)" Yan (n,t )dx* ) # where σ Yan is the cross section for the multi-step ionization for NBI [Yanev]. NBI penetration e-folding length for 5.7 m reactors (a=.5m)! [m] 5 3 E =.5 MeV, " =3 NBI n a E =.5 MeV, " =.5 NBI n E = MeV, " =3 NBI n a/ 6 8 n() [m -3 ] parabolic temperature profile α T =. peaked density profile with α n =3 square root of parabolic α n =.5 Half penetration is possible up to n()=3~x m -3, ensuring NBI heating 5
NBI penetration e-folding length for 9 m reactor (a=.5m) 5! [m] 3 E =. MeV, " =3 NBI n a E =. MeV, " = NBI n a/ 6 8 n() [m -3 ] parabolic temperature profile α T =. peaked density profile with α n =3 parabolic density profile with α n = Half penetration is possible up to n()=3~x m -3. 6
3. -D equations, and ignition control algorithm dn D () dt dn T () dt dn! () dt = ( +! n )S D ( t) " ( +! n )n D ( )n T ( )< #V > DT ( x) " n D ( ) = ( +! n )S T ( t) " ( +! n )n D ( )n T ( )< #V > DT ( x) " n T ( ) = ( +! n )n D ( )n T ( )< "V > DT ( x) # n! ( ) Charge neutrality condition: n e ( ) = n D ( ) + n T ( ) + n! ( ) $! * " 8 f o Combined particle balance equations dn e () dt + $ & = ( + "! 8 f n ) (t)! f + f D T * + f ( " & % * ) O '& # p # " *& n (). - e,- / $ D * $ T * df! dt = ( +! n )n e () f D f T "V DT (x) # f! $ # f! % dn e ()( *! n e () & ' dt ) * 7
Power balance equation d () dt +! = n +! T.5e( f D + f T + / " i + f! )n e () # %& { + P! } $ { P L + P B + P S }' ( $ () ( ) # $ 8 f O + " i $ f! f D + f T + / " i + f! ISS95 scaling %) /* & +, % -. n e () & / dn e () dt ' ( $ % df! () & / dt &(! E [s] = " ISS! ISS95 [s] = " LHD #.6! ISS95 [s] '! ISS95 [s] =.79$..5 )( /3 n9 [ 9 m %3 ]B.83 o [T ]a. [m]r.65 [m] / P.59 HT [MW ] '' ( ( External heating power (in thermally stable regime)! DLM n()[m "3 (* ] [W ] =! #$ % &,* a R [m] ) pr - +*! SUDO.5 '.* B o [T ] ' 6 " ( P / " P B " P S ) External heating power (in thermally unstable regime) Preprogramming now!! 8
Ignition control [] PID fueling control by the fusion power (in thermally stable regime) " (t) = # e DT (P f ) + $ t de DT (P f )% e T DT (P f )dt + T d int! & dt ' G fo(t) The error of the fusion power e DT (P f ) = +(! P f / P f ) nt the integration time, T d the derivative time. [] PID fueling control by the density (in thermally stable regime) (for testing control characteristics) " (t) = # e DT (n) + $ nt! t e DT (n)dt + T d de DT (n) dt % & G fo (t) ' The error of the density: e DT (n) = +(! n e (t) / n set ) [3] PID fueling control by the fusion power (in thermally unstable regime) The error of the fusion power e DT (P f ) =!(! P f / P f ) 9
Machine parameters [] Commercial reactor FFHRm: (Full blanket module) R=5.7m a=.5m, P f =3 GW, η α =.98 <B>=.5T τ α */τ E =,.5MeV NBI Thermally stable regime: α n =.5, α T =., γ ISS =.9.6 Thermally unstable regime: α n =3, α T =., γ ISS =.3.6 [] Experimental helical reactor FFHR-C, close to ARIES-CS. (For testing ignition. Partial blanket and shield: the blanket is only placed on the outboard side and the shield is placed in the inboard side). R=9m a=.5m, P f =. GW, η α =.98 <B>=7.T τ α */τ E =,.MeV NBI Thermally stable regime: α n =., α T =., γ ISS =.9.6 Thermally unstable regime: α n =3, α T =., γ ISS =..6
TABLE I: Plasma parameters at the stable and unstable operating points in FFHRm
. Thermally stable ignition regime accessed by NBI in FFHRm During the access to the thermally stable low density and high temperature operation regime, NBI heating has not any problems due to the relatively low-density. n() (m -3 ) f alpha 5 3.!/a (MW).8.6...8.6.. 5 NE NELMT PF PF PRATIO PEXT (a) (b) (c) (d) T FALPHA BETAA 3 5 Time (s) SSDT 5 5 3 () (kev) P f (GW)..8.6.. 5 9 <"> (m -3 /s) n() e (m -3 ) Heating power MW, γ ISS =.9 (γ LHD =.) n()~.83x m -3, T()~7.8 kev, Γ n ~.5 MW/m. <β>~.9 %, Beam penetration length! / a ~.7. 6 5 3 (e) 8 6 P f =3.GW x <!>=.73 % MW.5 x Sudo density limit Operating point at the stable boundary 5 5 5 ()(kev)
5. The high-density ignition regime accessed by NBI in FFHRm Density control for NBI : The density linearly increases from n()=. x to 3.x m -3 by the density control algorothm. γ ISS =.3, B=.5T, α n =3, α T =. τ E =.3 s, E=.5 MeV TanNBI n()=8.37x m -3, T()=7. kev, <β>=.9 %, P div =.MW/m 9 Δ=. n() (m -3 ) f alpha 8 6..8.6..!/a (MW).8.6.. 5 (a) (b) (d) (c) n-control NE NELMT PF PF PRATIO PEXT PEXTC Pf-control FALPHA T BETAA SSDT 6 8 Time (s) 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary P =3.GW f NBI heating off MW Switching time to the fusion power control <!>=.9 % 5 5 5 ()(kev) 3
Sudden increase in the confinement factor near the saddle point brings the operation into a dangerous situation when the density control is used. After 3 s (which is 5 s before the switching to the fusion power control), the confinement factor is artificially increased by a step manner from.3 to.6. n() (m -3 ) f alpha! ISS 8 6. (MW).8.6...5.5 5 n-control NE NELMT PF PF (b) (c) PEXT PEXTC (d) (a) Pf-control GHH T FALPHA BETAA SSDT 6 8 Time (s) 5 5 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) Fusion power surge to 3.5 GW Unlimited fueling in the Pf-control phase quenches the ignition. n() e (m -3 ). 8 6 (e) 8 6 Operating point at the unstable boundary MW x P f =3.GW <!>=.9 % 5 5 5 ()(kev)
Sudden increase in the confinement factor near the saddle point brings the operation into a dangerous situation when the density control is used. n() (m -3 ) f alpha! ISS 8 6. (MW).8.6...5.5 5 n-control NE NELMT PF PF (b) (c) PEXT PEXTC GHH (d) (a) Pf-control T FALPHA BETAA SSDT 6 8 Time (s) 3 8 6 () (kev) P f (GW)..8.6.. <"> (m -3 /s) Limited fueling < x 9 m -3 /s in the Pf-control phase leads to the excessive fusion power such as ~8 GW. (Thermal runaway) n() e (m -3 ). 8 6 (e) 8 6 Operating point at the unstable boundary MW x P f =3.GW <!>=.9 % 5 5 5 ()(kev) 5
On the other hand, when the confinement factor is suddenly decreased by a step manner from.3 to.3 (3-35s) near the saddle point during the density control, the discharge terminates. n() (m -3 ) f alpha! ISS (MW) 8 6..8.6...5.5 5 n-control NE NELMT PF PF GHH PEXT PEXTC (b) (c) (d) (a) Pf-control FALPHA 6 8 Time (s) T BETAA SSDT 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) safe shutdown. n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary MW P f =3.GW <!>=.9 % 5 5 5 ()(kev) 6
The fusion power control should be employed from the initial phase to avoid this dangerous situation (thermal runaway). γ ISS =.3, B=.5T, α n =3, α T =. E=.5MeV TanNBI n()=8.x m -3, T()=7. kev, <β>=.5 %, P div =.MW/m 9 Δ=. n() (m -3 ) f alpha 8 6!/a (MW) n-control..8.6...8.6.. 5 NE NELMT PF PF (c) (b) PRATIO PEXT PEXTC (a) (d) Pf-control T FALPHA BETAA SSDT 6 8 Time (s) 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) Fusion power is carefully controlled to keep the density at the low around 3 m -3 to ensure the NBI penetration. n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary MW P f =3.GW <!>=.9 % 5 5 5 ()(kev) 7
This unstable control algorithm is robust to the confinement factor disturbance. [] Even when the confinement factor is increased from γ ISS =.3 to.6 during to 6 s, the fusion power is well controlled. γ ISS =.3,.6 (-6s), B=.5T, α =3, α T =. E=.5MeV TanNBI n() (m -3 ) f alpha! ISS (MW) n-control 8 6..8.6...5.5 5 (c) NE NELMT PF PF (b) GHH PEXT PEXTC(d) (a) Pf-control T FALPHA BETAA SSDT 6 8 Time (s) 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) Sudden increase in the confinement factor stable operation. Density increases due to the too much heating power. n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary MW P f =3.GW <!>=.9 % 5 5 5 ()(kev) 8
[] When the confinement factor is decreased by a step manner from.3 to.3 during and 6 s, the fusion power decreases and then the discharge terminates, leading to the safe shutdown. Proper feedback control method of heating power should be developed γ ISS =.3.3 (-5s), B=.5T, α =3, α T =. E=.5MeV TanNBI n-control Pf-control n() (m -3 ) f alpha! ISS (MW) 8 6..8.6...5.5 5 (c) NE NELMT PF PF (b) GHH PEXT PEXTC(d) (a) T FALPHA BETAA SSDT 6 8 Time (s) 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary MW P f =3.GW <!>=.9 % 5 5 5 ()(kev) 9
n() (m -3 ) f alpha E=. MeV NBI can also be used in 5.7 m reactor. γ ISS =.3, B=.5T, α n =3, α T =. E=. MeV TanNBI n()=8.x m -3, T()=7. kev, <β>=.5 %, P div =.MW/m 9 Δ=. n-control Pf-control!/a (MW) 8 6..8.6...8.6.. 5 NE NELMT PF PF (b) PRATIO PEXT PEXTC (a) (c) (d) FALPHA T BETAA SSDT 6 8 Time (s) 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) By careful preprogramming, MeV NBI can be used to access the highdensity operation. n() e (m -3 ). 8 6 (e) 8 6 x Operating point at the unstable boundary MW P f =3.GW <!>=.9 % 5 5 5 ()(kev)
6. The stable ignition regime accessed by NBI in FFHR-C (R=9m,.5m) α n = α T =, γ ISS =.8, τ * α /τ E = P f =. GW P n =.55 MW/m, τ E =.7 s, MeV TanNBI n()=3.56x m -3, T()=3.5 kev <β>=.6 %, P div =5. MW/m (9 Δ=. m), <B>=7 T n() (m -3 ) f alpha!/a (MW) 8 6...8.6.. 5 NE NELMT PF PF PRATIO PEXT (a) (b) (c) (d) T FALPHA BETAA 8 6 Time (s) SSDT 3 () (kev) P f (GW)..8.6.. <"> (m -3 /s) Reaching ignition is possible but the magnetic field of 7 T (the volume averaged ) is needed. MeV NBI is enough for heating for the low density and high temperature operation. n() e (m -3 ). 8 6 (e) 8 6 MW P f =.GW <!>=.5 % Operating point near the stable boundary 5 5 5 ()(kev)
7. The high-density ignition regime accessed by NBI in FFHR-C(R=9m,.5m) α n =3 α T =, γ ISS =., τ α * /τ E = P f =. GW (P n =.55 MW/m ), τ E =.6 s, MeV TanNBI n()=9.3x m -3, T()=7.95 kev <β>=.3 %, P div =. MW/m (9 Δ=. m), <B>=7 T n() (m -3 ) f alpha n-control Pf-control MeV NBI is enough for high- density ignition access. 8 6!/a (MW).5. NE NELMT PF PF (b) (a) T 5 5.5.5.5 FALPHA..8.8 PRATIO.6 (c) BETAA.6.... 5 PEXT (d) SSDT PEXTC 3 5 6 Time (s) 8 () (kev) P f (GW) <"> (m -3 /s) n() e (m -3 ). 8 6 (e) 6 Operating point at the unstable boundary <!>=.3 % x NBI turn off time MW P f =.GW 5 5 5 ()(kev)
8. Summary and further challenge: We have studied how to use NBI heating in FFHR helical reactors. [] From a safe operating point view, the density control should not be used especially near the saddle point on POPCON. It can be used only in the initial phase far from the saddle point. [] Fusion power control is important to stabilize the thermal instability, and it should be used before over-passing the saddle point. It should be also carefully preprogrammed to have a low density for NBI penetration. After over-passing the saddle point on POPCON, NBI heating power can be switched off, leading to ignition by alpha heating power. It is also robust to the parameter changes. But the feedback control of the heating power is desirable. [3] As the NBI energy less than.5 MeV would also bring high-density ignition in the FFHR fusion ignition experimental (FFHR-C) and commercial reactor (FFHRm), the near term NBI technology could be utilized for proposed helical reactors. Further big challenge: To overcome the parameter changes during the ignition access, feedback control of the heating power should be invented. 3