A discussion of tokamak transport through numerical visualization C.S. Chang

Content Visualizatoin of neolcassical orbits - NSTX vs Normal tokamaks - Orbit squeezing and expansion by dE/dr - Polarization drifts by dE/dt Visualization of turbulence transport Nonlinear break-up of streamers by zonal flows, and D(t) Bohm & GyroBohm Zonal Flow generation

If I p =0 (No Bp)

How different are the neoclassical orbits between tokamak and ST? Large variation of B  /B or   . Very different orbital dynamics between R<R o and R>Ro

Passing Orbit in a Tokamak

Passing orbit in NSTX

Banana orbit in a tokamak

Banana Orbit in NSTX (toroidal localization)

Barely trapped orbit in NSTX

ST may contain different neoclassical and instability physics Particles in ST can be more sensitive to toroidal modes (at R>R 0 ). Stronger B-interchange effect at R R 0  stronger shaping effect At outside midplane   : Gyro-Banana diffusion? And others.

Oribt squeezing by Er-shear >0 in NSTX

Orbit expansion by Er-shear <0 in NSTX

Rapid Er development is prohibited by neoclassical polarization current [1+c 2 /V 2 A (1+K)]dE r /dt = -4  J r (driven) dE r /dt is the displacement current. c 2 /V 2 A dE r /dt is classical polarization drift. c 2 /V 2 A K dE r /dt is Neoclassical polarization drift. K  B/B p >>1  Neoclassical polarization effect is much greater. dE r /dt = -4  J r (driven)/ [c 2 /V 2 A K] An analytic formula for K is in progress.

Neoclassical Polarization Drift by dEr/dt <0 in NSTX

Particle diffusion in E-turbulence (Hasegawa-Mima turbulence)

Saturation of Electrostatic Turbulence Turbulence gets energy from  n/n (Drift Waves)  ≈   =k ⊥ v th  / L T ≈k ⊥ T/(eBL T ) n 1 /n= e  1 /T Nonlinear saturation of  1 : Chaotic particle motion at k r V EXB =   V EXB = E/B = k ⊥  1 /B  n 1 /n= e  1 /T = turb / L T

Ion Turbulence Simulation

Nonlinear reduction of turbulence transport 1.Streamers grow in the linear stage (D B ) 2.Streamers saturate, nonlinear stage begins (D B )  V E (2)  * /k r (2) 3.Self-organized zonal flows break up streamers. k r (2)<k r (4) 4.Reduced D B or D GB in nonlinearly steady stage  V E (4)  * /k r (4)<  V E (2)

Bohm or gyro-Bohm? Bohm scaling: D B ≈T/16eB  in small devices? Gyro-Bohm : D GB ≈   T/eB  1/B 2 in large devices?   =  i /a ≈  i /L T  1/B Gyrokinetic ITG Simulation (Z. Lin) Old textbook interpretation D B ≈ Ω  2 is unjustifiable.

Transition rate in Hasegawa-Mima turbulence  0.04 V s /L Exit time in L/V s

The decorrelation rate is often estimated to be the linear growth rate Z. Lin, et al Approximately independent of device Size [at a/  <60?, k  (a)?]. Not much different from Hasegama-Mima  Let’s assume correct.

Bohm or Gyro-Bohm? D  2 : Random walk  = decorrelation time  v/L  = Eddy size    : Natural tendency a * : effective minor radius (significant gradient Large device (a * >>   ):   Small device (a * >    ):  (L   ) 1/2 Streamers:    ,  r  (L   ) 1/2 Large device: D  (v/L)   2  D GB   * D B Small device or streamers: D  (v/L) L    D B H-mode:     by EXB shearing distance  D GB  V E  V dia  V E  V dia (  * ) -1/2 Consistent with Lin

In-between scaling? Lin showed self-similar radial correlation distance   7  i   for a  125  I And found  is different by  2 / [(  2 ) GB (1+50  * ) 2 ] due to  -spread in radius  A transition mechanism due to finite radial spread of turbulence for a>100  I For a < 100  I, device size comes into play  Bohm Z. Lin

EXB Flow Shearing of Streamers by Zonal Flow Sheared E field

Zonal Flow =Poloidal Shear Flow by Wave-beating (and Reynold’s stress) Radial G. Tynant, TTF