Solitary phase-space holes in pair plasmas

We present theoretical and computer simulation studies of the formation and dynamics of solitary phase-space holes in pair plasmas, which can be applied to both electron-positron plasmas and to plasmas containing positively and negatively charged macroions or macroparticulates (charged dust grains). We apply our numerical treatment to the parameters used in a recent series of experiments in a pair ion plasma whose constituents are negatively and positively charged fullerene carbon nanotubes. New experiments should be conducted to confirm our theoretical and numerical predictions.

Figure 1

The amplitude $\psi ={\varphi }_{\mathit{max}}$ of the potential for a phase-space hole of negative ions, as a function of the speed $u_0$ of the hole (left panel), with $\beta =-2$ (solid line) and $\beta =-3$ (dashed line), and the amplitude as a function of $\beta$ (right panel), with $u_0=1.0$ (solid line) and $u_0=1.15$ (dashed line). We used $\mathcal{T}=\mathcal{M}=1$ for all cases.

Figure 2

The phase-space hole potential (upper panel), the density of the negatively charged ions (middle panel), and of the positive ions (lower panel) as a function of $\xi$, for $u_0=1$ and $\beta =-2$ (solid lines), for $u_0=1$ and $\beta =-3$ (dashed lines), and for $u_0=1.15$ and $\beta =-2$ (dash-dotted lines). We used $\mathcal{T}=\mathcal{M}=1$ for all cases.

Figure 3

The separatrices between free and trapped negatively charged ions in phase $(\xi ,v)$ space (upper panels) and the separatrices between free and reflected positively charged ions (lower panels), for $u_0=1$ and $\beta =-2$ (left panels), for $u_0=1$ and $\beta =-3$ (middle panels), and for $u_0=1.15$ and $\beta =-2$ (right panels). We used $\mathcal{T}=\mathcal{M}=1$ for all cases.

Figure 4

The particle distribution function for negatively charged ions (upper panels) and for positively charged ions (lower panels) in phase $(\xi ,v)$ space, for $u_0=1$ and $\beta =-2$ (left panels), for $u_0=1$ and $\beta =-3$ (middle panels), and for $u_0=1.15$ and $\beta =-2$ (right panels). We used $\mathcal{T}=\mathcal{M}=1$ for all cases.

Figure 5

The particle distribution function for negatively charged ions (left panels) and for positively charged ions (right panels) in phase $(x,v)$ space for interacting phase-space holes, at different times.