Tutorial Lectures on Stellarator Transport

Tutorial on Stellarator Transport H.E. Mynick (PPPL) April 28, May 12, 2005 1 -Magnetic field Structure: (a) (d) (b) (e) (c)(f) -B-field Model: B(x)=B [1-ε(r)cos θ-δ (r,θ)cosη], (1) 0 h-parameter p≡δ /ε =measure of distance of hstellarator from symmetric limits δ =0, ε=0 h 2 -Neoclassical Transport - Overview: 2~ 1/Eraxiaxihel axi hel Dps DplhelDbn 3 -Radial diffusion: ~ 2νD ≈ F ∆ , with F≡fraction of particles contributing, ~ ν≡ freq of taking step in random walk ∆≡radial step size. -Eg-1: Banana regime, tokamak: 1/2F=F≡ (2ε) =frac of toroidally-trapped particles, t1/2∆=ρ ≡banana width≈ v /(v /qR) ≈qρ/ε , Bt ║bt~ν = ν ≡ toroidal detrapping frequency = ν/(2ε), t with v ≈ ρv/2R = toroidally-induced radial drift Btvelocity. axi 1/2 2 2 2 3/2⇒D ≈ (2ε) ν ρ ≈ ν q ρ /ε bn t bt 4 -Eg-2: Banana regime, straight stellarator: [A.Pytte, A.H. Boozer, Phys. Fluids 24, 88 (1981).] 1/2F=F ≡ (2δ ) =frac of helically-trapped particles, h h 1/2∆=ρ ≡banana width≈v /(v /L ) ≈(q R /r)ρδ , bh Bh ║ h h h~ν = ν ≡ ripple detrapping frequency = ν/(2δ), h with L ≡R/n, v ≈ (ρv/2)(mδ /r) = helically-h Bh hinduced radial drift velocity, q ≡ m/n. h sym 1/2 2 2 2 1/2⇒D ≈ (2δ ) ν ρ ≈ ν(q R/r)ρ δ bn h h bh h h 5 -Ripple-trapped particles: -Well-depth ...