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Electrostatic “bounce” instability in a magnetotail configuration
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Image of FIG. 1.
FIG. 1.

Geometry of the 2D current sheet and notations used in this study. The magnetic field lines are bent curves in the (x, z)-plane with length within a plasma sheet of half thickness L. The curvilinear coordinate, linked to the B-field line, is denoted (ψ, y, ). The considered electrostatic perturbations propagate in the vicinity of a given magnetic surface . The origin of the curvilinear coordinate is at the lower end of the field line. The equatorial plane (x, y) cuts the field line at . The magnetic field at the center of the current sheet is B 0 while its asymptotic value is B 1. The ratio varies typically between 0.01 and 0.3 in the Earth magnetotail.

Image of FIG. 2.
FIG. 2.

Ion term Ai as a function of the normalized perpendicular wavenumber K as given by Eq. (47) . Several values of the stretching parameter are chosen: 0.2 (bottom curve), 0.3 (middle curve), and 0.4 (top curve).

Image of FIG. 3.
FIG. 3.

Imaginary part of electron term Ae as a function of the normalized frequency qr for and various stretching parameters ranging from 0.22 to 0.27. For these values of ε, the imaginary part of the electron term vanishes at a real frequency leading to existence of stable standing electrostatic oscillations of the current sheet. If ε is lower than 1/5, the imaginary part does not vanish for any qr and if ε is higher than, say, 1/3, the real frequency making the imaginary part zero becomes too high to be valid in the simplified frame of the model. The frequency should stay indeed much less than the ion cyclotron frequency, typically of the order of 10.

Image of FIG. 4.
FIG. 4.

Dispersion curves. Top panel: imaginary part of frequency qi versus real frequency qr . Bottom panel: wavenumber K versus qr for various stretching parameters ε and a temperature ratio .

Image of FIG. 5.
FIG. 5.

Real part of the electron term Ae given by Eq. (45) as a function of frequency qr for various stretching parameters ε using the same color code as in Figure 4 . The real part is computed along the dispersion line plotted on top panel of Figure 4 .


Generic image for table
Table I.

Spatial and temporal scales characterizing particle dynamics in the Earth plasma sheet with , L = 3200 km, , and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electrostatic “bounce” instability in a magnetotail configuration