(a) Graphical representation of IDP for short wavelength ( ) case and long wavelength ( ) case , . (b) Fourier spectrum of these density perturbations in k-space. The vertical dashed line corresponds to the limit , which gives for and divides the perturbations in short and long wavelength regimes.
Schematic diagrams showing some of the steps during formation and evolution of IA pulses for the case of short wavelength IDP.
Spatial and temporal evolution of electrostatic potentials for (Run-2). The upper dark blue bands represent the propagation path ofIA oscillations. The dark red bands correspond to IA pulses propagating opposite to each other. The inset shows Langmuir wave packet with distinct wave structures.
dispersion diagrams during (a) and (b) for , (Run-2). It shows presence of both Langmuir and IA modes. The speed of Langmuir mode (IA mode) estimated from their standard linear dispersion equations (spatial temporal propagation) are shown with upper (lower) slanted dashed lines. The electron plasma frequency is shown with horizontal black dotted line at .
Snapshots of (a) electron and ion densities (b) electric field and (c) electrostatic potential associated with IA soliton for for Run-2. The same parameters are shown in (d)–(f) for . Here, the profiles are associated with the solitary pulse propagating in positive x–direction.
Schematic diagrams illustrate some of the steps during formation and evolution of chains of multiple IA solitons in case of long wavelength IDP.
Spatial and temporal evolution of electrostatic potentials for (Run-7). The upper dark blue bands represent the propagation path of IA oscillations. The red bands correspond to chain of IA pulses propagating opposite to each other. The inset shows Langmuir wave packet with distinct waves. The horizontal dotted lines at and correspond to formation of two unstable IA pulses and initiation of wave breaking, respectively.
dispersion diagrams during (a) , (b) , (c) , and (d) for the simulation Run-7. The dispersion curves show IA mode. The slanted dotted lines represent the average speed of fastest IA soliton in the chain during their stability.
Snapshots of (a) electron and ion densities (b) electric field and (c) electrostatic potential associated with chains of IA solitons for for Run-7. The same parameters are shown in (d)–(f) for . Here, the profiles are associated with the solitons propagating in positive x–direction.
Plots of average amplitude and width as a function of speed for IA solitons established in the simulation system during their stability along with the amplitude and width obtained from nonlinear fluid theory for respective speeds.
Time evolution of electrostatic energy UE and half of kinetic energy of electrons for the long wavelength IDP simulations (a) Run-4, (b) Run-5, (c) Run-6, and (d) Run-7. The profile of electrostatic potential (propagating in positive x–direction) at time close to for respective simulation runs (e) Run-4, , (f) Run-5, (g) Run-6, , and (h) Run-7, .
Time evolution of electrostatic energy UE and half of kinetic energy of electrons for short wavelength IDP simulations (a) Run-1, (b) Run-2, and (c) Run-3.
Simulation parameters for different run.
IA soliton properties during their stability from fluid simulations along with corresponding estimates from nonlinear fluid theory.
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