A discussion of tokamak transport through numerical visuali

zation

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, a

nd D(t)• Bohm & GyroBohm• Zonal Flow generation

If Ip=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<Ro

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>R0).

• Stronger B-interchange effect at R<R0, weaker at R>R0 stronger shaping effect

• At outside midplane :

Gyro-Banana diffusion?• And others.

Oribt squeezing by Er-shear >0in NSTX

Orbit expansion by Er-shear <0 in NSTX

Rapid Er development is prohibited by neoclassical polarization current

• [1+c2/V2A (1+K)]dEr/dt = -4 Jr(driven)

• dEr/dt is the displacement current.• c2/V2

A dEr/dt is classical polarization drift.• c2/V2

A K dEr/dt is Neoclassical polarization drift.• K B/Bp >>1 Neoclassical polarization effect is

much greater.• dEr/dt = -4 Jr(driven)/ [c2/V2

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⊥vth/ LT≈k⊥T/(eBLT)

• n1/n= e1/T

• Nonlinear saturation of 1:

Chaotic particle motion at krVEXB =

VEXB= E/B = k⊥ 1 /B

n1/n= e1/T = turb/ LT

n1

Ln

n

turb

Ion Turbulence Simulation

Nonlinear reduction of turbulence transport

1. Streamers grow in the linear stage (DB)

2. Streamers saturate, nonlinear stage begins (DB) VE(2)*/kr(2)

3. Self-organized zonal flows break up streamers. kr(2)<kr(4)

4. Reduced DB or DGB in nonlinearly steady stage VE(4)*/kr(4)< VE(2)

Bohm or gyro-Bohm?

•Bohm scaling: DB≈T/16eB in small devices?•Gyro-Bohm : DGB≈T/eB 1/B2 in large devices?

=i/a ≈ i/LT 1/B

Gyrokinetic ITGSimulation (Z. Lin)

Old textbook interpretationDB ≈ Ω 2 is unjustifiable.

Transition rate in Hasegawa-Mima turbulence 0.04 Vs/L

Exit time in L/Vs

The decorrelation rate is often estimated to be the linear growth rate

Z. Lin, et al

Approximately independent of deviceSize [at a/ <60?, k(a)?].

Not much different fromHasegama-Mima Let’s assume correct.

Bohm or Gyro-Bohm?• D2 : 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 DGB *DB

Small device or streamers: D (v/L) L DB

• H-mode: by EXB shearing distance DGB

VEVdia

VEVdia(*)-1/2

Consistent with Lin

In-between scaling?

• Lin showed self-similar radial correlation distance 7i for a 125I

• And found is different by 2

/ [(2)GB (1+50*)2]

due to -spread in radius A transition mechanism du

e to finite radial spread of turbulence for a>100I

• For a < 100I , device size comes into play Bohm

Z. Lin

EXB Flow Shearing of Streamers by Zonal Flow

ShearedE field

Zonal Flow =Poloidal Shear Flow by Wave-beating (and Reynold’s stress)

Radial

G. Tynant, TTF