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Discrete particle noise in particle-in-cell simulations of plasma microturbulence
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10.1063/1.2118729
/content/aip/journal/pop/12/12/10.1063/1.2118729
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/12/10.1063/1.2118729
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online). The linear growth rate in units of for Cyclone-base-case-like ETG modes is plotted vs the wave number in the binormal direction, both with (red curve) and without (green curve) magnetically trapped electrons. For comparison, we also plot an estimate of the damping rate, , that would be associated with noise-induced diffusion for (blue curve) or (purple curve).

Image of FIG. 2.
FIG. 2.

(Color online). The coefficient of electron thermal transport from a particle-number and box-size convergence study of Cyclone-base-case-like ETG turbulence without magnetic trapping including runs in a flux-tube cross section of and two particles∕grid cell (blue curve), four particles∕grid cell (green curve), and eight particles∕grid cell (black curve) and in a flux-tube cross section of with 16 particles∕grid cell (red curve).

Image of FIG. 3.
FIG. 3.

(Color online). The ETG fluctuation spectra in the linear phase (, red curve) and at after saturation from the PG3EQ simulation with a cross section of and eight particles∕grid cell (, black curve) corresponding to the black curve in Fig. 2.

Image of FIG. 4.
FIG. 4.

(Color online). The coefficient of electron thermal transport from a particle-number and flux-tube cross-section convergence study of Cyclone-base-case-like ETG turbulence with magnetic trapping , including runs in a flux tube cross section of with 2 particles∕grid cell (green curve), 4 particles∕grid cell (blue curve), and 16 particles∕grid cell (red curve); and in a flux-tube cross section of with 16 particles∕grid cell (black curve).

Image of FIG. 5.
FIG. 5.

(Color online). The ETG fluctuation spectra in the linear phase (, red curve) and 30 linear growth times later at (, black curve). Data from the PG3EQ simulation with a cross section of and 16 particles∕grid cell (corresponding to the black curve in Fig. 4).

Image of FIG. 6.
FIG. 6.

Grey-tone rendering of the potential on the outboard mid-plane at late in the linear phase (top panel) and 30 linear growth times later at (middle panel) show the characteristic ETG streamers. These streamers are absent at very late times, (bottom panel) during the steady-state phase of the simulation. Data from the PG3EQ simulation of the Cyclone-base-case-like ETG turbulence with flux-tube cross section of , magnetic trapping , and 16 particles∕grid cell (black curve of Fig. 4).

Image of FIG. 7.
FIG. 7.

(Color online). (a) The fluctuation spectrum at the outboard midplane averaged over the radial coordinate and the interval is plotted on a semilog scale vs (, black curve), together with the corresponding fully uncorrelated noise estimate (, blue curve) and the self-Debye shield noise estimate (, red curve). The fluctuation spectrum averaged over the radius and the interval (, green curve) and the corresponding self-Debye shielded noise level (, chartreuse curve) are shown for comparison. (b) Fluctuation and noise data for the interval on a linear scale.

Image of FIG. 8.
FIG. 8.

(Color online). (a) The fluctuation spectrum at the outboard midplane averaged over the binormal coordinate and the interval is plotted on a semilog scale vs (, black curve), together with the corresponding fully uncorrelated noise estimate (, blue curve) and the self-Debye shield noise estimate (, red curve). (b) Same data on a linear scale.

Image of FIG. 9.
FIG. 9.

(Color online). The fluctuation energy averaged over the outboard midplane (black curve) is compared with the fluctuation intensity from the fully uncorrelated noise spectrum (blue curve) or self-Debye shielded noise spectrum (red curve).

Image of FIG. 10.
FIG. 10.

(Color online). The fluctuation energy is plotted vs time for a PG3EQ simulation of Cyclone-base-case ITG turbulence (black curve). The red curve shows the fluctuation energy expected from discrete particle noise. The corresponding level of thermal transport from this PG3EQ simulation is shown by the blue curve.

Image of FIG. 11.
FIG. 11.

(Color online). Electron heat flux from the “noise test” of Lin and Bolton. The black curve is from the initial simulation. The remaining five curves correspond to simulations initialized with (red curve), (blue curve), (gold curve), (green curve), (chartreuse curve).

Image of FIG. 12.
FIG. 12.

(Color online). (a) The intensity of the dominant Fourier mode during the linear phase of each run in Fig. 11. The black curve is from the initial simulation (multiplied by ). In the remaining five curves is measured from the time of the restart. For (red curve) and (blue curve) the dominant mode is . For (gold curve), (green curve), and (chartreuse curve) the dominant mode is . (b) The same data replotted to display the weak linear growth of the mode in the restart with (blue curve).

Image of FIG. 13.
FIG. 13.

(Color online). The real frequency (a) and growth rate (b) for the Cyclone-base-case-like ETG turbulence as a function of the magnitude of the diffusion acting on the nonadiabatic part of the electron distribution function for (black curves), (red curves), (blue curves), (green curves), and (chartreuse curves).

Image of FIG. 14.
FIG. 14.

(Color online). Measured maximum linear growth rate (with error bars and connected by the grey line) after restart from the noise test simulations of Sec. IV is compared with from Eq. (15) with (heavy line). The colors of both data points and model are chosen to indicate the corresponding wave number as (black), (red), and (blue).

Image of FIG. 15.
FIG. 15.

(Color online). The value of from Eq. (16) for Cyclone-base-case-like ETG turbulence with magnetic trapping from a PIC simulation in a flux-tube cross section of with 16 particles∕grid cell is displayed both with (red curve) and without (black curve) the contribution of turbulence, toroidal drifts, and magnetic shear to the decorrelation.

Image of FIG. 16.
FIG. 16.

The predicted value of from Eq. (16) is compared with from the noise test described in Sec. IV. The black curves are from the initial simulation (distinguished by large variations) and from Eq. (16) (smooth curve at ). The remaining curves show simulations initialized with (red curves), (blue curves), (gold curves), (green curves), and (chartreuse curves).

Image of FIG. 17.
FIG. 17.

(Color online). (a) The from the noise test described in Sec. IV (larger variation) and the predictions from Eq. (16) (smaller variation), with (black curves), (blue curves), and (red curves). (b) The predicted value of from Eq. (16) (green squares) and the simulation results (red crosses) from all of the random restart tests in Figs. 16 and 17(a) showing that Eq. (16) predicts the observed scaling well as the average squared weight is varied by a factor of 512.

Image of FIG. 18.
FIG. 18.

(Color online). (a) The net linear growth rate vs time for (black curves), (red curves), and (blue curves). The thick (upper) curves use from Eq. (16). The thin (lower) curves show the sensitivity to turbulent decorrelation by setting . (b) The intensity of Fourier modes vs time for (black curve), (red curve), (blue curve), (green curve), and (chartreuse curve).

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/content/aip/journal/pop/12/12/10.1063/1.2118729
2005-12-12
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Discrete particle noise in particle-in-cell simulations of plasma microturbulence
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/12/10.1063/1.2118729
10.1063/1.2118729
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