Abstract
Trapped electron mode turbulence is studied by gyrokinetic simulations with the GYRO code and an analytical model including the effect of a poloidally varying electrostatic potential. Its impact on radial transport of highZ trace impurities close to the core is thoroughly investigated, and the dependence of the zeroflux impurity density gradient (peaking factor) on local plasma parameters is presented. Parameters such as iontoelectron temperature ratio, electron temperature gradient, and main species density gradient mainly affect the impurity peaking through their impact on mode characteristics. The poloidal asymmetry, the safety factor, and magnetic shear have the strongest effect on impurity peaking, and it is shown that under certain scenarios where trapped electron modes are dominant, core accumulation of highZ impurities can be avoided. We demonstrate that accounting for the momentum conservation property of the impurityimpurity collision operator can be important for an accurate evaluation of the impurity peaking factor.
This work was funded by the European Communities under Association Contract between EURATOM and Vetenskapsrådet. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Center for High Performance Computing (PDCHPC), and on the HPCFF cluster at the Jülich Supercomputing Center (JSC). The authors would like to thank J. Candy for providing the GYRO code and Ye. O. Kazakov for fruitful discussions.
I. INTRODUCTION
II. STABILITY
III. IMPURITY DENSITY PEAKING
A. Zero flux impurity density gradient
B. Parametric dependences in poloidally symmetric cases
1. Temperature and temperature gradient dependences
2. Density gradient dependence
3. Safety factor dependence
C. Poloidally asymmetric case
D. Collisions
IV. CONCLUSIONS
Key Topics
 Ion temperature gradient mode
 30.0
 Electron temperature gradient mode
 29.0
 Electrostatics
 17.0
 Plasma gyrokinetics
 12.0
 Plasma impurities
 11.0
Figures
Normalized electron energy fluxes as functions of poloidal wavenumber from nonlinear GYRO simulations for Case I (a) and Case II (b).
Normalized electron energy fluxes as functions of poloidal wavenumber from nonlinear GYRO simulations for Case I (a) and Case II (b).
Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of poloidal wavenumber for Case I (a) and Case II (b). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of poloidal wavenumber for Case I (a) and Case II (b). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electronion collision frequency for Case I (a) (note the logarithmic axis) and Case II (b). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electronion collision frequency for Case I (a) (note the logarithmic axis) and Case II (b). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
Linear parallel mode structure of the perturbed potential for Case I (a) and Case II (b). Real part (red solid lines) and imaginary part (blue dashed lines) of ϕ. Real part (orange dashdotted lines) and imaginary part (green dotted lines) of ϕ for the same cases but with parallel ion motion neglected in GYRO. Note that the actual resolution of the simulation covers , by GYRO convention.
Linear parallel mode structure of the perturbed potential for Case I (a) and Case II (b). Real part (red solid lines) and imaginary part (blue dashed lines) of ϕ. Real part (orange dashdotted lines) and imaginary part (green dotted lines) of ϕ for the same cases but with parallel ion motion neglected in GYRO. Note that the actual resolution of the simulation covers , by GYRO convention.
(a), (b) Impurity peaking factor for trace nickel as function of electron temperature gradient for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electron temperature gradient for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of electron temperature gradient for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electron temperature gradient for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of iontoelectron temperature ratio (note that ) for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of iontoelectron temperature ratio for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of iontoelectron temperature ratio (note that ) for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of iontoelectron temperature ratio for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of electron density gradient for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electron density gradient for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of electron density gradient for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of electron density gradient for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of safety factor q for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively, while black hollow squares are results from nonlinear GYRO runs. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of safety factor q for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of safety factor q for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) , orange dashed line the magnetic drifts contribution, and green dasheddotted line the parallel compressibility contribution. Blue dotted line is the peaking factor from Eq. (5) without parallel compressibility effects. Red diamonds and blue dots correspond to GYRO results with and without parallel compressibility effects, respectively, while black hollow squares are results from nonlinear GYRO runs. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and real mode frequency (circle markers, red solid lines) as functions of safety factor q for Case I (c) and Case II (d). Linear growth rate γ (diamond markers, green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of magnetic shear s for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) in the symmetric case, green dasheddotted line corresponds to outin asymmetry, orange dashed line corresponds to updown asymmetry, and black dotted line corresponds to inout asymmetry. Red diamonds correspond to GYRO results. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and realmode frequency (circle markers, red solid lines) as functions of magnetic shear s for Case I (c) and Case II (d). Linear growth rate γ (diamond markers,green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
(a), (b) Impurity peaking factor for trace nickel as function of magnetic shear s for Case I (a) and Case II (b). Red solid line is the peaking factor from Eq. (5) in the symmetric case, green dasheddotted line corresponds to outin asymmetry, orange dashed line corresponds to updown asymmetry, and black dotted line corresponds to inout asymmetry. Red diamonds correspond to GYRO results. (c),(d) Linear growth rate γ (circle markers, blue dashed lines) and realmode frequency (circle markers, red solid lines) as functions of magnetic shear s for Case I (c) and Case II (d). Linear growth rate γ (diamond markers,green dotted lines) and real mode frequency (diamond markers, orange dashdotted lines) for the same cases but with parallel ion motion neglected in GYRO.
Impurity peaking factor for trace nickel as function of electronion collision frequency for Case I (a) and an ITG dominated case (b) (note the logarithmic axis). Red solid line is the peaking factor from Eq. (5) in the symmetric case and black dotted line the corresponding in the inout asymmetric case. Orange dasheddotted line is the peaking factor in the symmetric case from a model that utilize the Lorentz collision operator, and blue dashed line the corresponding in the inout asymmetric case.
Impurity peaking factor for trace nickel as function of electronion collision frequency for Case I (a) and an ITG dominated case (b) (note the logarithmic axis). Red solid line is the peaking factor from Eq. (5) in the symmetric case and black dotted line the corresponding in the inout asymmetric case. Orange dasheddotted line is the peaking factor in the symmetric case from a model that utilize the Lorentz collision operator, and blue dashed line the corresponding in the inout asymmetric case.
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