PRELIMINARY RESULTS OF SIMULATION OF A SAWTOOTH CRASH IN CDXU D. D. Schnack and S. E. Kruger Center for Energy and Space Science Science Applications International.

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Presentation transcript:

PRELIMINARY RESULTS OF SIMULATION OF A SAWTOOTH CRASH IN CDXU D. D. Schnack and S. E. Kruger Center for Energy and Space Science Science Applications International Corp. San Diego, CA 92121

CDXU EQUILIBRIUM Computed by TSC R/a = 1.39 B 0 = T I = 58.2 kA I/aB = q 0 = q max =  = 7.8 X  N =  A = 4.5 X sec S = 10 4 Pr = 1

NIMROD GRID 20 X 12 Bi-quartic finite elements n =  t = 5 X sec ~  A Adiabatic pressure Density profile from equilibrium Run with single processor on 2 GHz Linux workstation

LINEAR STABILITY Both n = 1 (~ 1/1) and n = 3 (~ 2/3) linearly unstable

n = 1 EIGENFUNCTION Dominant 1/1 structure (“sawtooth mode”) Higher m harmonics  = 2.39 X 10 5 sec -1  A = 0.11 Poloidal FlowToroidal Current Density

n = 3 EIGENFUNCTION Dominant 2/3 mode Resonant because q 0 = 0.6 < 2/3  = 1.39 X 10 5 sec -1  A = Poloidal Flow Toroidal Current Density

NONLINEAR CALCULATION Modal magnetic energy vs. time

FIELD LINES t = sec

FIELD LINES t = 1.26 X sec

FIELD LINES t = 1.32 X sec

FIELD LINES t = 1.35 X sec

FIELD LINES t = 1.36 X sec

COMMENTS All results are preliminary Linear results converged in  t, not tested in  x Large resistivity and viscosity allow runs to be completed on Linux work station Detailed comparisons with M3D required –Linear stability –Nonlinear time scales –Saturation amplitude? –Stochasticity