Confinement of Alpha Particles in a Low-Aspect-Ratio Tokamak Reactor - PowerPoint PPT Presentation

The 10 th Spherical Tokamak Workshop STW2004 Confinement of Alpha Particles in a Low-Aspect-Ratio Tokamak Reactor September 29 - October 1, 2004 ＠Kyoto K. TANI, K. TOBITA, S. NISHIO, S. TSUJI-IIO * , H. TSUTSUI*, T. AOKI* Japan Atomic Energy Research Institute, * Tokyo Institute of Technology Contents １． Introduction ２． Ripple-loss processes of suprathermal alpha particles ３． Simulation results on ripple losses of alpha particles ４． Conclusions

Introduction Important features of spherical tokamak (ST) reactors 1. High elongation 、 2. High triangularity 3. Low aspect ratio improvement of level of symmetry line symmetry ⇒ point symmetry 4. Non-inductive plasma current (hollow current profile) no use of center solenoid improvement of plasma performance - negative shear - access to the 2 nd stability region Confinement of alpha particles in an ST reactor is very interesting. Neoclassical confinement (ripple loss), Non-neoclassical confinement (TAE mode etc.) Here we focus our attention only on the neoclassical confinement.

Introduction Objectives - to investigate the confinement of alpha particles in a low-aspect-ratio tokamak by using an orbit-following Monte-Carlo code. Preliminary results indicate that the ripple loss of alpha particles shows a marked reduction in a low-aspect-ratio system . The number of toroidal field (TF) coils is one of the key parameters for the design of tokamak system. The smaller the number of TF coils is, the easier the design of reactor system becomes. Preliminary results also show that i n a tokamak system with a conventional aspect ratio, the reduction of the number of TF coils results in a considerable increase of alpha particle losses. Is there a possibility to reduce the number of TF coils in a low- aspect- ratio tokamak? - to investigate the possibility to design a tokamak system with a low aspect ratio and a low number of TF coils.

Ripple-loss processes of suprathermal alpha particles Neoclassical confinement of α particles ≡ ripple loss of α particles (a) (a) ripple-trapped ripple-trapped Ripple losses orbit orbit α ≤ 1.0 α ≤ 1.0 • ripple-trapped loss B B r/a r/a Z Z 1.0 1.0 ・ collisional trapping banana banana ・ collisionless trapping orbit orbit φ φ in a non-uniform ripple distribution (a) (b) (b) • ripple-enhanced banana B B drift (b) Z Z If the drift exceeds a φ φ critical value, the trajectory becomes stochastic [Goldston, White and Boozer (1981)].

Ripple-loss processes of suprathermal alpha particles • Model MHD equilibrium （ uniform ellipticity κ and triangularity ∆ ） ψ = ψ ρ ( ) [ ] ∆ Z 2 2 2 ρ = 1 + ( R − R ) + ( R − R ) a κ t t 2 a ： minor radius, R ： major radius t κ c = Z Z 1 + ∆ ( R − R ) / a t c ≈ + ∆ − B 1 ( R R ) / a B R t R | α | = 1.0 Hereafter, variables with the superscript ‘c’ denote those in a circular plasma with the r/a same q s (a). 1.0 1) ripple-well parameter 1 B α ≅ ≅ + ∆ − α c R 1 ( R R ) / a t N δ B N ： number of toroidal field coil, δ ： local field ripple Ripple wells are developed in the region | α | α | < 1.0.

Ripple loss processes of suprathermal alpha particles 2) ripple-enhanced banana drift − 3 / 2 ∂ ψ B ∂ ψ * = * ≅ π ρ δ P Z N R Z ＊ φ L ∂ ∂ Z B Z * * c P P 1 φ φ ≅ [ ] 1 / 4 c ψ ψ κ + ∆ − 1 ( R R ) / a a a t ρ * Z ： Z displacement enhanced by ripple, : Larmor radius L 3) critical field ripple for stochastic orbits d ϕ 1 * ≥ b P ϕ ： toroidal angle difference between two banana tips φ ψ b d N  ∆ 1 1    ′ δ ≈ κ + − + ρ + δ c 1 ( R R ) ( q / q )     s t s s s π a 4     1 c δ ≈ （ By Goldston-White-Boozer ） s 3 / 2 ′ π ρ ρ ( N R q / ) q t s L s Banana orbits in the region δ ＞ δ ｓ become stochastic.

Ripple-loss processes of suprathermal alpha particles Summary of dependence of - ripple-well parameter α , - ripple-enhanced banana drift P φ * and - critical field ripple of stochastic orbit δ s on some important system parameters 1) dependence on the elongation κ (Tani et.al in Nucl.Fusion1993) * α ∝ ∝ κ δ ∝ κ independen t , P 1 / , φ s 2) dependence on the aspect ratio A α ∝ * ∝ 3 / 2 δ s ∝ 3 / 2 1 / A , P A , 1 / A φ 3) dependence on the local field ripple δ and the number of TF coils N * 1 / 2 3 / 2 α ∝ δ ) ∝ δ δ s ∝ 1 /( N , P N , 1 / N φ

Simulation results on ripple losses of alpha particles Simulation studies on the ripple loss of alpha particles by using an orbit-following Monte-Carlo code (1) Qualitative investigations of the ripple loss using analytical MHD equilibria into 1-1) the dependence of the aspect-ratio 1-2) the dependence of ripple losses on the number of TF coils (2) Quantitative investigations of the ripple loss using a realistic MHD equilibrium of VECTOR into 2-1) the dependence on the edge field ripple for a hollow and a parabolic plasma current profile 2-2) the dependence on the number of TF coils for a hollow and a parabolic plasma current profile 2-3) the allowable field ripple and the number of TF coils

Simulation results on ripple losses of alpha particles Analytical MHD equilibria Major radius R ｔ = 3.7 ～9.2m Minor radius a = 1.9m Z(m) Toroidal field @R=R t B ｔ = 3.1 T 8.0 TF coils first wall T e ( Ψ ) = T e0 (1- Ψ ) Plasma temperature 6.0 T i ( Ψ ) = T i0 (1- Ψ ) 4.0 T D ( Ψ ) = T T ( Ψ ) = T i ( Ψ ) 2.0 plasma T e0 = T i0 = 35 keV 0.0 ｎ e ( Ψ ) = n e0 (1- Ψ ) 0.3 Plasma density 0.0 5.0 10.0 15.0 R(m) n D ( Ψ ) = n T ( Ψ ) = n i ( Ψ ) n e0 = 2x10 20 m -3 3.0 safety factor q( Ψ ) 1.3 ) ｊ( Ψ ) = ｊ 0 (1- Ψ Plasma current Safety factor q ｓ = 2.56 2.0 κ = 1.55 Elipticity 1.0 ∆ = +0.5 Tiangularity Effective Z Z eff = 1.9 (uniform) 0.0 Charge number of 0.0 0.2 0.4 0.6 0.8 1.0 Z imp = 6.0 (carbon) impurity Ψ N = 4 ～ 18 Number of TF coils

Simulation results on ripple losses of alpha particles Distribution of the field ripple in a system with vertically long TF coils N − 1 − N 1   − R  R a    δ ≅ δ + δ t     o i R + a R     t δ δ , ： field ripples at outer and inner plasma edge o i (R-R t )/a -1.0 -0.5 0.0 0.5 1.0 1.0E+00 The distribution of the field ripple is strongly Field ripple δ (%) 1.0E-01 depends on the aspect ratio. 1.0E-02 A=1.95 1.0E-03 A=2.47 1.0E-04 A=3.79 A=4.84 1.0E-05

Simulation results on ripple losses of alpha particles 100.0 (1) Qualitative investigations of the q a =2.56 ripple loss using analytical δ o =1% Total power loss fraction G t (%) MHD equilibria N=12 1-1) dependence on the aspect ratio A α ∝ 1 / A , * 3 / 2 ∝ P A , φ 10.0 3 / 2 δ s ∝ 1 / A As the aspect ratio is reduced, - the area of ripple-well region , ∼ A 4.3 - the ripple-enhanced banana drift , - the area of stochastic orbit region 1.0 The distribution of the field ripple 1.0 10.0 also strongly depends on A. A The ripple loss shows a very strong dependence on A by the synergy of all of these effects

Simulation results on ripple losses of alpha particles (1) Qualitative investigations of the ripple loss using analytical MHD equilibria 20.0 Total power loss fraction G t (%) 1-2) dependence on the q a =2.56 number of TF coils N δ o =1% 15.0 N=12 α ∝ δ ) 1 /( N , A=4.32 * 1 / 2 ∝ δ P N , 10.0 φ 3 / 2 δ s ∝ 1 / N 5.0 A=2.21 As the number of TF coils is reduced, 0.0 - the area of ripple-well region , 2 6 10 14 18 - the ripple-enhanced banana drift , N - the area of stochastic orbit region Note that the distribution of δ strongly depends on N.

Simulation results on ripple losses of alpha particles Geometry and plasma parameters of VECTOR 6.0 Major radius R ｔ = 3.7m TF coil Minor radius a = 1.9m 4.0 Z(m) first wall Toroidal field B ｔ = 3.1 T T e ( Ψ ) = T e0 (1- Ψ ) 2.0 Plasma temperature T i ( Ψ ) = T i0 (1- Ψ ) plasma 0.0 T D ( Ψ ) = T T ( Ψ ) = T i ( Ψ ) 0.0 2.0 4.0 6.0 8.0 10.0 T e0 = T i0 = 35 keV R(m) ｎ e ( Ψ ) = n e0 (1- Ψ ) 0.3 Plasma density n D ( Ψ ) = n T ( Ψ ) = n i ( Ψ ) 10.0 safety factor q( Ψ ) n e0 = 2x10 20 m -3 9.0 8.0 hollow current Effective Z Z eff = 1.9 (uniform) 7.0 6.0 Charge number of 5.0 Z imp = 6.0 (carbon) impurity 4.0 3.0 Number of TF coils N = 4 ～ 12 2.0 1.0 parabolic current 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Ψ

Simulation results on ripple losses of alpha particles (2) Quantitative investigations of the ripple loss using a realistic MHD equilibrium of VECTOR 2-1) the dependence on the edge field ripple Some axi-symmetric loss has been found in a Total power loss fraction G t (%) 12.0 hollow current plasma. A=1.95 10.0 N=4 Z(m) starting point with v // =0 8.0 5.0 hollow current 4.0 6.0 3.0 4.0 2.0 parabolic current 1.0 2.0 0.0 0.0 -1.0 -2.0 0.0 0.5 1.0 1.5 2.0 2.5 -3.0 δ o (%) -4.0 -5.0 R(m ) 1.0 3.0 5.0