Time-distance plot for Ex for constant background density and uniform beam injection along the x-direction; .
Ex (x) (solid) and ne (x) (dashed) at , zoomed in and arbitrary units on the y-axis for clarity.
Fast-Fourier transform of Ex for constant background density and uniform beam injection. The curves represent the dispersion relation for Langmuir waves, (“horizontal” curve), and the resonance condition for the beam plasma instability, .
Snapshots of the electron distribution function (solid) with respect to energy for constant background density and uniform beam injection. Dotted curves track the initial distribution at t = 0.
As in Fig. 1 but for the weak gradient case.
As in Fig. 3 but for the weak gradient case.
As in Fig. 4 but for the weak gradient case.
As in Fig. 1 but for the strong gradient case.
As in Fig. 3 but for the strong gradient case.
As in Fig. 4 but for the strong gradient case.
Fraction of electrons with energies higher than , as calculated by use of Eq. (2) , over time for constant background density (solid), weak gradient (dotted), strong gradient (dashed).
(a) [E(t)–E(0)]/E(0) for constant background (diamond), weak gradient (cross), strong gradient (asterisk). (b) Kinetic particle energy (solid) and Langmuir wave energy (dotted) for constant background. Langmuir wave energy multiplied by a factor 5 for clarity. (c) As top right but for weak gradient. (d) As top right but for strong gradient.
Localized beam injection with constant background density. (a)Time-distance plot for Ex component. (b) Time-distance plot for background electron density. (c) Ex (k) for (solid, black), (dashed, purple), (dashed-dotted, blue), (dotted, green), (dotted with +, orange), (dotted with *, red). Y-axis in arbitrary units. (d) 2D Fourier transform of Ex (x,t). Note that for clarity in panel (d), the color scheme is inverse to the ones in the upper row.
As Fig. 14 but for the strong gradient case.
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