All Figures

$\begin{figure} {\psfrag{V}{$\mathcal{V}$ }\psfrag{O}{$\mbox{\boldmath$\Omega$ }$... ...{{\bf c}}\psfrag{d}{{\bf d}} \epsfig{file=3040f1.eps,width=12cm} } \end{figure}$ Figure 1: Sketch of various models for pair creation (hatched) on the open field lines ${\vec B}$ in the pulsar magnetosphere with level curves of electrostatic potential $\mathcal{V}$ and corresponding electric field ${\vec E}$ : a) axially symmetric vacuum model à la Deutsch (1955); b) RS75, anti-aligned pulsar and infinite ion binding energy; c) Arons (1983); d) Muslimov & Tsygan (1992), general relativistic model. The magnetic moment ${\vec m}$ is oriented along the vertical direction, and the rotation vector is ${\bf\Omega }$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{3040f2.eps}\end{figure}$ Figure 2: The current system I in the axially symmetric case; magnetic field ${\vec B}$ , magnetic moment ${\vec m}$ , rotation vector ${\bf\Omega }$ , null line n, light cylinder lc, critical field line c separating incoming from outgoing current.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3040f3.eps}\end{figure}$ Figure 3: Level curves of the electrostatic potential $\Psi$ on the open field lines in the oblique case; magnetic field ${\vec B}$ , magnetic moment ${\vec m}$ , rotation vector $\mbox{\boldmath$\Omega$ }$ . The plasma circulation is on surfaces of constant $\Psi$ .
Open with DEXTER

In the text

$\begin{figure} \mbox{ \includegraphics[width=4.3cm]{3040f4a.eps}\hskip0.3cm \inc... ...040f4d.eps}\hskip0.3cm \includegraphics[width=4.3cm]{3040f4e.eps} } \end{figure}$ Figure 4: Axially symmetric case: Sketch of the level curves of the electrostatic potential $\Psi$ in the frame corotating with the star on the left, and of the potential V in the lab frame on the right. In the middle are the level curves due to pure corotation with the star. Darker level of grey corresponds to a higher potential value. Hollow arrows mark the corresponding electric field E, with the arrow size being proportional to the field strength. The sum of the potentials on the left equals to the potential on the right. Magnetic field B (thin arrows), magnetic moment m and rotation vector $\Omega$ are displayed.
Open with DEXTER

In the text

$\begin{figure} {\psfrag{delta}{$\Delta n~(n_{\rm GJ})$ }\psfrag{h}{$h$ }\psfrag{... ...$ }\psfrag{0}{$0$ } \epsfig{file=3040f5b.eps,width=0.4\textwidth} } \end{figure}$ Figure 5: Top: model for the hollow beam. The density difference between positrons and electrons is $\Delta n = n_{+} - n_{-} = h~n_{\rm GJ}$ in region II, and zero in regions I and III. At R > R₃, the plasma is assumed to be in solid-body rotation with the star. Bottom: the axial velocity of the beam particles across the beam is taken to be constant.
Open with DEXTER

In the text

$\begin{figure} {\psfrag{delta}{$\Delta n~(n_{\rm GJ})$ }\psfrag{h}{$h$ }\psfrag{... ...3$ }\psfrag{0}{$0$ } \epsfig{file=3040f6.eps,width=0.4\textwidth} } \end{figure}$ Figure 6: Similar to Fig. 5; now, a core component is included. The dimensionless charge difference in Region I is $h_{\rm I}$ .
Open with DEXTER

In the text

$\begin{figure} {\psfrag{bz0}{$\beta^0_z$ }\psfrag{nbz0}{$-\beta^0_z$ }\psfrag{bz... ...p$ }\psfrag{0}{$0$ }\epsfig{file=3040f7.eps, width=0.4\textwidth} } \end{figure}$ Figure 7: Similar to Fig. 5, but now, part of the beam moves in the opposite direction (R_p is defined by Eq. (19)).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3040f8.eps}\end{figure}$ Figure 8: Examples of equilibrium rotational velocity distributions across the beam, where R₁,R₂ are the inner and outer boundary of the beam. See text for the cases and the beam parameters.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{3040f9.eps}\end{figure}$ Figure 9: Equipotential for annular beam with Q = 0, R₁ = 0.5, R₂ = 0.6 and l = 5 at t = 0. Black areas denote negatively valued $\tilde{V}$ , and white the positive values.
Open with DEXTER

In the text

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f10a.eps}\hskip1.7c... ...10e.eps}\hskip1.7cm \includegraphics[width=5.6cm]{3040f10f.eps}\\ } \end{figure}$ Figure 10: Left: unstable diocotron modes in the parameter space of R₁/R₃ (along the horizontal axis) and R₂/R₃(along the vertical axis). In levels of grey is plotted $l_{\rm max}$ , which is the azimuthal wave number l for which the combination of R₁/R₃ and R₂/R₃ results in the largest growth rate (Eq. (35)). The parameter $Q = \beta _z^{02} f/h$ is found above each graph. Right: maximum growth rates $\tilde{\Gamma}/h$ (triangles) and pattern velocities $\tilde{\omega}_{\rm pat}/h$ (squares) as functions of $l_{\rm max}$ .
Open with DEXTER

In the text

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f11a.eps}\hskip1.7c... ...11e.eps}\hskip1.7cm \includegraphics[width=5.6cm]{3040f11f.eps}\\ } \end{figure}$ Figure 11: The same as in Fig. 10, but now including a charge-separated core in Region I (see Eq. (25) and Fig. 6). The corresponding value of $\tilde{h}_{\rm I}$ is specified above each graph, and $Q_{\rm II}=0.4$ in all graphs. The growth rate and the pattern speed are displayed as squares and triangles, respectively.
Open with DEXTER

In the text

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f12a.eps}\hskip2cm ... ...040f12c.eps}\hskip2cm \includegraphics[width=5.6cm]{3040f12d.eps} } \end{figure}$ Figure 12: The same as in the left column of Fig. 10, but now including a return current (see Eq. (26) and Fig. 7). Above each graph are seen the corresponding parameters Q and p, the latter defining R_p, i.e. the radius where the axial velocity of the beam particles changes sign (see Eq. (19)).
Open with DEXTER

In the text

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f13a.eps}\hskip2cm ... ...040f13c.eps}\hskip2cm \includegraphics[width=5.6cm]{3040f13d.eps} } \end{figure}$ Figure 13: Maximum growth rate (squares) and pattern velocities (triangles) corresponding to the case in Fig. 12.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{3040f14.eps}\end{figure}$ Figure 14: Growth rates as functions of Q, for different values of azimuthal mode number l (indicated in the plot), for a hollow beam with R₁/R₃ = 0.65 and R₂/R₃ = 0.92.
Open with DEXTER

In the text

$\begin{figure} \mbox{ \includegraphics[width=5.4cm]{3040f15a.eps}\hskip1.7cm \in... ...0f15c.eps}\hskip1.7cm \includegraphics[width=5.4cm]{3040f15d.eps} } \end{figure}$ Figure 15: Similar to Fig. 14, but now for different combinations of the inner and outer radii of the beam. Top: R₁/R₃ = 0.6 ( left) and R₁/R₃ = 0.8 ( right). Bottom: R₂/R₃ = 0.86 ( left) and R₂/R₃ = 0.93 ( right).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3040f16.eps}\end{figure}$ Figure 16: Domain of instability for l=13 as applied to PSR B0826-10. The three regions denote different intervals of $\tilde{\omega}_{\rm pat}/h$ (see legend).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{3040f2.eps}\end{figure}$	Figure 2: The current system I in the axially symmetric case; magnetic field ${\vec B}$ , magnetic moment ${\vec m}$ , rotation vector ${\bf\Omega }$ , null line n, light cylinder lc, critical field line c separating incoming from outgoing current.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3040f3.eps}\end{figure}$	Figure 3: Level curves of the electrostatic potential $\Psi$ on the open field lines in the oblique case; magnetic field ${\vec B}$ , magnetic moment ${\vec m}$ , rotation vector $\mbox{\boldmath$\Omega$ }$ . The plasma circulation is on surfaces of constant $\Psi$ .
Open with DEXTER

$\begin{figure} {\psfrag{delta}{$\Delta n~(n_{\rm GJ})$ }\psfrag{h}{$h$ }\psfrag{... ...$ }\psfrag{0}{$0$ } \epsfig{file=3040f5b.eps,width=0.4\textwidth} } \end{figure}$	Figure 5: Top: model for the hollow beam. The density difference between positrons and electrons is $\Delta n = n_{+} - n_{-} = h~n_{\rm GJ}$ in region II, and zero in regions I and III. At R > R₃, the plasma is assumed to be in solid-body rotation with the star. Bottom: the axial velocity of the beam particles across the beam is taken to be constant.
Open with DEXTER

$\begin{figure} {\psfrag{delta}{$\Delta n~(n_{\rm GJ})$ }\psfrag{h}{$h$ }\psfrag{... ...3$ }\psfrag{0}{$0$ } \epsfig{file=3040f6.eps,width=0.4\textwidth} } \end{figure}$	Figure 6: Similar to Fig. 5; now, a core component is included. The dimensionless charge difference in Region I is $h_{\rm I}$ .
Open with DEXTER

$\begin{figure} {\psfrag{bz0}{$\beta^0_z$ }\psfrag{nbz0}{$-\beta^0_z$ }\psfrag{bz... ...p$ }\psfrag{0}{$0$ }\epsfig{file=3040f7.eps, width=0.4\textwidth} } \end{figure}$	Figure 7: Similar to Fig. 5, but now, part of the beam moves in the opposite direction (R_p is defined by Eq. (19)).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3040f8.eps}\end{figure}$	Figure 8: Examples of equilibrium rotational velocity distributions across the beam, where R₁,R₂ are the inner and outer boundary of the beam. See text for the cases and the beam parameters.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{3040f9.eps}\end{figure}$	Figure 9: Equipotential for annular beam with Q = 0, R₁ = 0.5, R₂ = 0.6 and l = 5 at t = 0. Black areas denote negatively valued $\tilde{V}$ , and white the positive values.
Open with DEXTER

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f11a.eps}\hskip1.7c... ...11e.eps}\hskip1.7cm \includegraphics[width=5.6cm]{3040f11f.eps}\\ } \end{figure}$	Figure 11: The same as in Fig. 10, but now including a charge-separated core in Region I (see Eq. (25) and Fig. 6). The corresponding value of $\tilde{h}_{\rm I}$ is specified above each graph, and $Q_{\rm II}=0.4$ in all graphs. The growth rate and the pattern speed are displayed as squares and triangles, respectively.
Open with DEXTER

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f12a.eps}\hskip2cm ... ...040f12c.eps}\hskip2cm \includegraphics[width=5.6cm]{3040f12d.eps} } \end{figure}$	Figure 12: The same as in the left column of Fig. 10, but now including a return current (see Eq. (26) and Fig. 7). Above each graph are seen the corresponding parameters Q and p, the latter defining R_p, i.e. the radius where the axial velocity of the beam particles changes sign (see Eq. (19)).
Open with DEXTER

$\begin{figure} \mbox{% \par\includegraphics[width=5.6cm]{3040f13a.eps}\hskip2cm ... ...040f13c.eps}\hskip2cm \includegraphics[width=5.6cm]{3040f13d.eps} } \end{figure}$	Figure 13: Maximum growth rate (squares) and pattern velocities (triangles) corresponding to the case in Fig. 12.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{3040f14.eps}\end{figure}$	Figure 14: Growth rates as functions of Q, for different values of azimuthal mode number l (indicated in the plot), for a hollow beam with R₁/R₃ = 0.65 and R₂/R₃ = 0.92.
Open with DEXTER

$\begin{figure} \mbox{ \includegraphics[width=5.4cm]{3040f15a.eps}\hskip1.7cm \in... ...0f15c.eps}\hskip1.7cm \includegraphics[width=5.4cm]{3040f15d.eps} } \end{figure}$	Figure 15: Similar to Fig. 14, but now for different combinations of the inner and outer radii of the beam. Top: R₁/R₃ = 0.6 ( left) and R₁/R₃ = 0.8 ( right). Bottom: R₂/R₃ = 0.86 ( left) and R₂/R₃ = 0.93 ( right).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3040f16.eps}\end{figure}$	Figure 16: Domain of instability for l=13 as applied to PSR B0826-10. The three regions denote different intervals of $\tilde{\omega}_{\rm pat}/h$ (see legend).
Open with DEXTER