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Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
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10.1063/1.4794735
Wenbo Tang1,a) and Alex Mahalov1,b)
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Affiliations:
1 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA
Phys. Plasmas 20, 032305 (2013)
/content/aip/journal/pop/20/3/10.1063/1.4794735
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/3/10.1063/1.4794735
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## Figures

FIG. 1.

Initial profiles in dimensional units. (a) Plasma temperature. Black solid curve: ion temperature. Red dashed curve: electron temperature. (b) Ion density. (c)Normalized collision frequency. Black solid curve: ion. Red dashed curve: electron. (d) Reaction parameters. Black solid curve: production rate, coordinate at bottom of figure. Red dashed curve: recombination rate, coordinate at top of figure. Vertical axes are the same in all panels.

FIG. 2.

(a) Current density divergence scaled by . (b) The resulting electrostatic potential. Eight wave periods are shown. y is the vertical coordinate (altitude), and z is the meridional direction.

FIG. 3.

(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = T/4, a quarter wave period.

FIG. 4.

(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = 3 T/4, three quarters of a wave period.

FIG. 5.

Trajectory comparison for initial conditions of plasma parcels released at x = 1 km, z = 19 km and y between 80 and 220 km. The dots denote the end position of trajectories after integration for a wave period. (a) Deterministic. The three red dots denote trajectories started at , and 220 km, respectively. (b) Random case 1 with diagonal diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. (c) Random case 2 with field aligned diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. Note that the z scale is much larger than the x scale, thus the spread is more in z as compared to in x.

FIG. 6.

Statistics of displacements subject to diagonal diffusivity. Row a: first four moments in the x-direction. Row b: first four moments in the z-direction. Row c: first four moments in the y-direction. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.

FIG. 7.

Statistics of displacements subject to field aligned diffusivity. Row a: first four moments in the x-direction. Row b: first four moments in the z-direction. Row c: first four moments in the y-direction. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.

FIG. 8.

Probability density function compared to the mean trajectory. The initial condition is chosen at x = 0 km, y = 43 km, and z = 220 km, where nontrivial skewness and kurtosis are present. (a) Diagonal diffusion. (b) Field aligned diffusion. The blue solid curve is the pdf for x displacement. The black dashed curve is the pdf for z displacement, and the red dash-dotted curve is the pdf for y displacement. The three crosses correspond to the mean value for x, y, and z, respectively. Their vertical coordinates are chosen so the location and the peak density are easily comparable.

FIG. 9.

(a) Deterministic attractors. (b) Stochastic attractors for the diagonal diffusion case. (c) Stochastic attractors for the field-aligned case.

FIG. 10.

Number density of stochastic realization at end of one wave period. (a) The diagonal diffusion case. (b) The field-aligned diffusion case.

/content/aip/journal/pop/20/3/10.1063/1.4794735
2013-03-13
2014-04-19

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