1. D. A. Gates, R. B. White NSTX Physics Meeting 1/19/03
Collisional transport in a low aspect ratio tokamak- beyond the drift kinetic formalism
D. A. Gates, R. B. White
NSTX Physics Meeting
1/19/03

2. Outline Motivation Method Inputs Results Benchmarks  surprise
Control System Speedup
Motivation
Method
Inputs
Results
Benchmarks  surprise
Implications

3. Control System Speedup
Characterized system delays
Changed output communication method from VME backplane to FPDP (Front Panel Data Port)
Built New interface module to bridge from FPDP output to (ancient home-made) power supply link
Split the link into four parallel links to avoid communication pileup
Replaced Sky computer FPDP cards to a more recent version (lower latency i/o control)
Rewrote communication software to take advantage of the hardware improvements

4. Measured latency
Measured latency has been reduced to ~1/4 of original value
Some hope for further improvements with existing hardware
Should be sufficient for vertical position control, RWM may need better performance
System used during TF test: measured latency = 1.2ms = tps + tcontrol
< t > = 0.680ms
< t > = 1.39ms
< t > = 2.9ms

5. Motivation
Much recent discussion on whether anomalous ion heating exists in NSTX
Argument rests on whether ci < ci_neo
In spherical tokamak geometry, the toroidal Larmor radius rif ~ rb ~ e1/2riq (banana width)
(See, e.g., Mikkelsen, White, Akers, et al. Phys. Plasmas 4 (1997) 3667
Violates the primary assumption of neoclassical theory
(See, e.g., Hinton and Hazeltine, Rev. Mod. Phys. 48 (1976) Sec IIB)
Neoclassical theory not valid in an ST!
Need full orbit calculation - omniclassical theory
Intuition is ci_omni > ci_neo

6. Method
Compare the diffusivity as calculated by a full orbit code (GYRO) with those calculated by a orbit average code (ORBIT)
ORBIT - solves gyro-averaged Hamiltonian in Boozer coordinates with collisions
GYRO - solves Newton’s equations with Lorentz force on XY grid with collisions

7. NSTX Equilibria Two disparate well characterized equilibria chosen
High current, low field
(1.2MA , 0.3T)
High field, low current
(0.45T , 0.8MA)
Expect larger
change in diffusivity
since |Bf/Bq| smaller

8. Orbits rif ~ 4rb for high current low field case
much larger step size for transport
Banana width = 1.1cm
Full orbit width = 5.2cm

9. Diffusivity calculation
Insert 2000 particles, E = 1.1keV, f(y,q) = d(y), with random initial pitch
Measure diffusivity as slope of RMS deviation from initial flux surface
GYRO
ORBIT
<xN2> = Ncolll2
l = (<v>Dt)/Ncoll 
<xN2> = vlDt (1)
G = [n(r+l) - n(r-l)]v = vldn/dr
G = -D[dn/dr]  D = vl (2)
D = <xN2> /Dt (3)
<xN2> = S(dy/(dy/dr))2

10. Diffusivity profiles High current low field (108989)
Repeat calculation at 10 different radii for each equilibrium using both codes
Plot the ratio of omni - neoclassical diffusion vs. normalized poloidal flux
Omniclassical diffusion is up to ~2.5 times larger than neoclassical
High current low field (108989)
High field low current (108730)

11. Ongoing studies In core of device r* ~ 0.01
Leads to non-conservation of m
Collisionless diffusion exists
Strong dependence of omni - neoclassical ratio on n* when outside banana regime
wb/wc ~ T-1/2

12. Benchmark of collision operators
Different collision operators require comparison
Fix particles in space but allow to diffuse in velocity space
Verify equipartition reached on same timescale
Lorentz collision operator for guiding center code
Random scatter Dv on surface of sphere
with radius v for full orbit code Dv v1
|v1| = |v2| v2

13. Benchmark against high aspect ratio neoclassical theory
But it doesn’t!
Expect that as e  0 and r*  0 that omniclassical  neoclassical
Neoclassical is wrong!
For more see R.B. White Theory seminar Feb. 5

14. Summary
We have demonstrated that neoclassical theory cannot be used to accurately describe the minimum possible collisional transport in a spherical tokamak. Tokamak tools of little use!
We have called the corrected diffusivity “omniclassical” (or all - classical)
Amazingly, the extrapolation of this result to high aspect ratio has uncovered a fundamental flaw with neoclassical theory at high aspect ratio

15. Summary (cont.)
Omniclassical transport is greater than neoclassical at low aspect ratio - strengthening the argument for the existence of an anomalous ion heating mechanism on NSTX