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Multi-water-bag models of ion temperature gradient instability in cylindrical geometry
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10.1063/1.4804272
/content/aip/journal/pop/20/5/10.1063/1.4804272
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/5/10.1063/1.4804272

Figures

Image of FIG. 1.
FIG. 1.

Equilibrium radial profiles; density and temperature (a); (b); MWB contours (c).

Image of FIG. 2.
FIG. 2.

Growth rate of the most unstable mode in the () spectral plane for the case BIG with .

Image of FIG. 3.
FIG. 3.

Frequency of the most unstable mode in the () spectral plane for the case BIG with .

Image of FIG. 4.
FIG. 4.

Radial envelope of normal mode (13, 7) for the BIG case with ; modulus (a); phase (b).

Image of FIG. 5.
FIG. 5.

Position and width σ of mode envelope modulus in the spectral plane.

Image of FIG. 6.
FIG. 6.

BIG case; parametric scan of peak position ; overlap of growth-rates as function of for modes (, 3), .

Image of FIG. 7.
FIG. 7.

Case BIG; double steps radial profiles; density and temperature (a); (b).

Image of FIG. 8.
FIG. 8.

Double peak study; growth rates maps for each isolated peak equilibrium.

Image of FIG. 9.
FIG. 9.

Double -peaks study; maximum of the isolated growth rates maps (a) and double peak growth rates map (b).

Image of FIG. 10.
FIG. 10.

Double peak study; radial localization of the modes (a); characteristic mode width σ (b).

Image of FIG. 11.
FIG. 11.

SMALL case; normalized growth rates for the multi-water-bag model (mwbN) and continuous Maxwellian model (kin);  = 1 (a),  = 4 (b).

Image of FIG. 12.
FIG. 12.

SMALL case; model comparison of mode envelope geometry; modulus (a); phase (b).

Image of FIG. 13.
FIG. 13.

SMALL case; model comparison; gradients scan over 2400 equilibria (30 × 80); maximum growth rate map for the continuous Maxwellian model and interpolated instability threshold lines for the multi-water-bags models (mwbN) and continuous Maxwellian (kin) (a); distribution of relative errors on growth-rates between the 6-bags MWB model and the continuous Maxwellian model (b).

Image of FIG. 14.
FIG. 14.

SMALL case perturbed by (10, 5); mean density (a) and temperature (b) radial profiles at beginning and end of nonlinear simulation.

Image of FIG. 15.
FIG. 15.

SMALL case perturbed by 239 modes; mean density (a) and temperature (b) radial profiles at beginning and end of simulation.

Image of FIG. 16.
FIG. 16.

SMALL case; time evolution of the mean normalized temperature gradient for single mode perturbation by (10, 5) (a) and 239 modes perturbation (b).

Image of FIG. 17.
FIG. 17.

SMALL case; linear growth rate evolution obtained from the linear code with (0, 0) mode fields extracted from nonlinear simulation data; growth rate of the (10, 5) mode for single mode perturbation by (10, 5) (a); maximum growth rate over (, ) for the single mode perturbation by (10, 5) (b) and the 239 modes perturbation (c).

Image of FIG. 18.
FIG. 18.

SMALL case; time evolution of the normalized mean poloidal velocity for single mode perturbation by (10, 5) (a) and 239 modes perturbation (b).

Image of FIG. 19.
FIG. 19.

SMALL case; filtered power spectra ratios ; 1-mode perturbation by (10, 5) (a); bath of 239 modes (b)—modes for which are binned as “others.”

Image of FIG. 20.
FIG. 20.

SMALL case; electrostatic potential normalized power spectra; single mode perturbation by (10, 5) (a); 239 modes perturbation (b)

Image of FIG. 21.
FIG. 21.

SMALL case perturbed by (6, 3); snapshots of perturbed density (, ) – (, 0)

Image of FIG. 22.
FIG. 22.

SMALL case; comparison of pseudo growth rates of nonlinear and quasilinear potential Fourier modes with linear growth rate; single mode perturbation by (6, 3) (a) and (10, 5) (b).

Image of FIG. 23.
FIG. 23.

SMALL case; comparison of pseudo growth rates of nonlinear and quasilinear potential Fourier modes with linear growth rate; perturbation by 239 modes; results for modes (6, 3) (a) and (10, 5) (b).

Image of FIG. 24.
FIG. 24.

SMALL case; radial norm of electrostatic potential; (a) single mode perturbation by (6, 3); (b) two modes perturbation by (6, 3) and (10, 5); (c) 237 modes perturbation

Image of FIG. 25.
FIG. 25.

SMALL case perturbed by 239 modes; linear growth rate map of initial equilibrium (a) and computed from nonlinear simulation mean fields at (b).

Tables

Generic image for table
Table I.

Reference cases parameters set.

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/content/aip/journal/pop/20/5/10.1063/1.4804272
2013-05-08
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multi-water-bag models of ion temperature gradient instability in cylindrical geometry
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/5/10.1063/1.4804272
10.1063/1.4804272
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