Gyrokinetic Turbulence Simulations at High Plasma Beta Moritz J. Pueschel Thanks to F. Jenko and M. Kammerer Ringberg Theory Meeting, Nov. 18, 2008
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The Beta Parameter Definition β β e = 8πn e0t ref B 2 ref Responsible for magnetic field fluctuations: B x = k y A B y = k x A Need high β: bootstrap fraction β reaction rates β 2 Not too high: ballooning threshold magnetic transport
Experimental Results β scaling of normalized confinement time: Widely differing findings, e.g.: JET 2004: no β dependence ASDEX 2007: β JET 2008: β 1.4 However: fixing other parameters difficult need theoretical understanding
Previous Simulations Gyrokinetic: Jenko 2001, Parker 2004, Dannert 2004, Candy 2005 Gyrofluid: Snyder 2001, Scott 2003, Scott 2006 Issue: gyrokinetic codes have trouble reaching the ballooning limit GENE simulations low β: good agreement with Candy 2005 high β: new nonlinear results (Pueschel 2008)
Open Questions What transport levels are to be expected at higher β? What kind of regime transitions will occur? How do subdominant KBMs affect the transport? How do linear and nonlinear KBM thresholds compare? What is the impact of magnetic transport?
Operation Point Motivation Using GENE as both initial value and eigenvalue solver, perform linear and nonlinear simulations in ŝ-α geometry Parameters q 0 = 1.4 ŝ = 0.786 α MHD = 0 ǫ t = 0.18 ω T = 6.89 ω n = 2.22 Cyclone Base Case, hydrogen mass ratio T i = T e
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Linear Beta Scan Linear analysis (data shown here for k y = 0.2): depending on β, one gets dominant ITG, TEM, or KBM Of interest: KBM onset; relevance of linear behavior for turbulent transport?
The KBM Branch GENE eigenvalue mode: KBM stable below β crit, then subdominant, surpasses TEM at β dom crit Critical β values β MHD crit = 1.32% β crit = 1.14% β dom crit = 1.26% Have β MHD crit β crit β dom crit which is relevant nonlinearly?
Linear Mode Transformations KBM can interact with ITG, TEM (Kammerer 2008) marginal stability for β < β crit transformation KBM-TEM no clear definition of β crit Current scenario: marginal stability for some k y, no mode transformations
KBM Critical Beta minimal β crit at k y = 0.2 (corresponds to nonlinear transport peak) equilibrium gradient dependence: only ω Ti significant, β crit increases strongly for low values, exceeds β MHD crit Note: differences not due to β MHD crit 0.6ŝ approximation
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Transport Beta Dependence nonlinear behavior imitates linear growth rate however, linear simulations fail to predict steep decrease of transport with increasing β
TEM transport model Transport model, Jenko (2005): use quasilinear approach to predict transport levels need nonlinear ω Te reference value Current scenario: no reference value qualitative interpretation γ 0.2 χ estimate 0.7 at ω Te = 6.89 likely lower transport levels than γ-based predictions However: does not explain reduction by factor 10
Zonal Flows and Fields Zonal flows Zonal fields Contributing to low transport levels (ω s γ) Effects likely negligible (ŝ ŝ ± s does not change linear physics significantly)
Regime Transitions Nonlinearly, no pure TEM regime: mode interactions at moderate β suppression of transport (Merz 2008) nonlinear KBM onset corresponds to linear β dom crit subdominant KBM does not destroy confinement
Magnetic Transport I Model for electron heat transport along perturbed field lines: Rechester & Rosenbluth 1978, Jenko 2001, Chang 1992 Test particle transport model q e = n e0 χ e ( d T e dz + B x d T e B ref dx + B x dt e0 B ref dx ) Linearly, first term dominates third, second vanishes χ β Nonlinearly, third term dominates first, second χ β 2 χ em e ( ) 1/2 Te = q 0 R ( B x /B ref) 2 m e
Magnetic Transport II Application to the simulation data: measured scalings agree excellently with the model requires scaling factor 1, constant within any turbulence regime
Electromagnetic TEM Simulations Density driven TEM parameters ω Te = 4, ω Ti = 2, ω n = 3 only TEM, KBM; β MHD crit = 2.03% significant shift between βcrit MHD work in progress and β crit
Conclusions & Outlook using GENE for first nonlinear gyrokinetic push up to and beyond the KBM threshold strong decline in transport levels with increasing β nonlinear KBM onset corresponds to linear mode dominance test particle model explains the magnetic transport very well need to understand differences between linear and nonlinear behavior in the moderate-β range TEM turbulence investigation currently underway: β crit significantly higher than β MHD crit