a discussion of tokamak transport through numerical visualization c.s. chang
TRANSCRIPT
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