Tutorial Lectures on Stellarator Transport

Tutorial on Stellarator Transport-3 Transport Optimization H.E. Mynick (PPPL) May 12, 2005 -Thanks to: A. Boozer, S. Gerhardt, L.-P. Ku, D. Mikkelsen, M. Redi, G. Rewoldt, D.Spong 1 -Transport Optimization: -Approaches: -Neoclassical: -Quasi-Helical (QH) (HSX) -Quasi-Axisymmetric (QA) (NCSX) -Quasi-Poloidal (QPS) -Quasi-Omnigenous (QO)/ Quasi-Isodynamic (QI) (W7-X, inward- shifted LHD) -Isometric/ Approximately Omnigenous -Pseudo-Symmetric (PS) -Turbulent optimization: -Internal transport barriers via root-jumping -Turbulence modifications from shaping 2 -Particle motion: -Magnetic field: B=∇ψ×∇θ+∇ζ×∇ψ = ∇ψ×∇α (1) t p t p2 with α ≡ θ-ιζ, ψ≡ψ≡B r ≡toroidal flux. p t 0 -Drift eqns: ˆB×∇Vv = v +v = , with V≡µ B+eΦ. (2) D B E MΩc c& ∂ V & − ∂ Vαψ⇒ =∇ψ.v = α , =∇α .v = ψ (3) ppD p De e-Bounce average, using bounce action -1J(ψ,α |µ,E)=(2π) ds Mv(s): (4) p ||∫ ds ds∂ J = ∂ Mv =− ∂ V =−∂ V /Ω ,ψ ,α ψ ,α || ψ ,α ψ ,α b⇒ ∫ ∫ (5) p p p p2π 2πv||ds1/Ω ≡ =∂ Jb E∫with = bounce time/(2π). 2πv|| ∂ J∂ Jc α c c cp ψ− = ∂ H =− ∂ H& α &ψα ψ⇒ = , = , (6) ppe ∂ J e e∂ J eE E2 21with E=H(x, ρ ,µ)= Mρ Ω +V(x, µ) the || ||2Hamiltonian. 3 -Early ideas (assume Φ=0 for simplicity) : -Isodynamic (Palumbo) condition: [Palumbo, Nuovo Cimento X53B, 507 (1968).] -If can create config with B=B(ψ), (7) c& ∂ V &ψ ...