(Color online) Schematic illustration of the channeling concept for fast ignition.
(Color online) Schematic of the focal region where the scattering of electrons is observed (a) with and (b) without the electrostatic field.
(Color online) (a)-(c) Simulation results calculated for the Gaussian beam specified by Eqs. (1a)–(1c), including small longitudinal fields E z and B z . (d)-(f) Simulation results without E z and B z . The laser intensity is I = 1021 W cm−2 with Δτ = 0.2 ps. (a) and (d) show the ejection angles θ of the electrons as a function of the final relativistic factor γ for 7000 electrons with different starting positions. The solid curves (red) correspond to the theoretical function for θ in a plane-wave field, Eq. (6). The normalized final electron momentum components, vs and vs , are shown in (b), (e) and (c), (f), respectively. The solid lines (red) correspond to the parabolic relationship Eq. (5). The lightly shaded (blue) area near the origin in (b) represents electrons whose initial positions are outside of the beam radius w. The empty portions shown in (b) and (e) are found to be filled in by extending the range of electron initial positions.
(Color online) Kinetic energy and angular distributions of the electrons for a 10-ps laser pulse at an intensity of I = 1021 W cm−2. The solid curves (red) correspond to the theoretical function for θ, Eq. (6). The light shaded (blue) regions near the vertical axis represent electrons whose initial positions are outside of the beam radius w. In (a), the electrons begin to respond to the field when the head of the laser pulse overtakes them. In (b), the same laser field is switched on instantaneously at t 0 = z 0/c, so that the electrons start when the highest fields arrive at their initial locations.
Simulation region. The center of cell (i, j) has coordinates (r i , z j ).
(Color online) Initial particle configurations. The particles are located uniformly (but randomly) in all three spatial dimensions inside the focal region (0 < r < 15 μm and |z| < z R ≈ 3.142 × 10−2 cm). (a) Projection of the electrons onto the x − y plane. (b) Projection of the electrons onto the r − z plane, with the thin lines indicating the numerical grid. In (b), the solid curve (red) represents the beam radius w at longitudinal position z.
(Color online) Snapshots of (a) the normalized electron number density δn e = (n e − n i0)/n i0 relative to the ion background number density n i0 and (b) the radial electrostatic field E r at t = −0.144 ps for a 0.2-ps laser pulse at an intensity of I = 1021 W cm−2.
(Color online) Comparison of simulation runs for a laser intensity of I = 1021 W cm−2 with Δτ = 10 ps, with and without the radial electrostatic field E r . (a)-(c) Electrostatic field included; (d)-(f) no electrostatic field. The angular and energy spectra of the longitudinally escaping electrons are shown in (a), (d) and (b), (e), respectively. For the case with the radial electrostatic field E r , an electron beam is observed from the simulation system in the laser direction with a small number of backward-scattered electrons. (c) and (f) show the ejection angles θ (with respect to the laser propagation direction) of the electrons as a function of the final relativistic factor γ. The solid curves in (c) and (f) correspond to the theoretical function for θ, Eq. (6). The third column ((g) to (i)) matches the first column, except that the initial particle positions are extended from r max = 15 μm to r max = 22.5 μm to illustrate convergence. In the top two rows, the darker shaded (red) bars indicate electrons whose initial positions are outside of the beam radius w.
Quantitative comparison of two simulations at a number of laser intensities where one simulation includes electrostatic effects and the other does not.
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