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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. Outline. Control System Speedup Motivation Method Inputs Results Benchmarks surprise Implications. Control System Speedup.
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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
Outline • Control System Speedup • Motivation • Method • Inputs • Results • Benchmarks surprise • Implications
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
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
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) 239 - Sec IIB) • Neoclassical theory not valid in an ST! • Need full orbit calculation - omniclassical theory • Intuition is ci_omni > ci_neo
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
NSTX Equilibria High current, low field (1.2MA , 0.3T) High field, low current (0.45T , 0.8MA) • Two disparate well characterized equilibria chosen Expect larger change in diffusivity since |Bf/Bq| smaller
Full orbit width = 5.2cm Banana width = 1.1cm Orbits • rif ~ 4rb for high current low field case • much larger step size for transport
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
Diffusivity profiles • 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)
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
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
But it doesn’t! Benchmark against high aspect ratio neoclassical theory • Expect that as e 0 and r* 0 that omniclassical neoclassical • Neoclassical is wrong! • For more see R.B. White Theory seminar Feb. 5
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
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