Spatial distribution of the electric field (a) and temporal variation of the electron density at two fixed positions () (b), during the expansion of a Gaussian 1D plasma in vacuum (see text for details). Note that in (a), only half of the problem is shown.
(a) One-dimensional electron position (and velocity, insert) as a function of time, for and ; the final rectilinear trajectory corresponds to a velocity (in arbitrary units). (b) Two-dimensional electron trajectories for two different initial positions (blue and red lines, the starting position is denoted with a filled circle) and for in the x direction and in the y direction. Black broken lines represent iso-density contours, assuming the same speed of sound in the two directions.
Electron trajectories for particles starting at rest, for the same simulation as in Fig. 1. Note that the symmetry condition at x = 0 has the effect of reflecting the particles at the boundary.
(a) Proton trajectories from the expansion of a Gaussian proton plasma, obtained from Eq. (15). Blue, red, and green lines correspond to particles of increasing energy and black lines are iso-energy contours (ellipsoids). Parameters: m, m m. The blue and red trajectories are used in (b) to plot the asymptotic angle of divergence as a function of the initial radial position of the particle. The inset in (b) shows traces of the same protons, if an RCF were positioned at a distance m from the origin.
Proton trajectories after 60 ps, from the expansion of a flat foil in vacuum, with initial temperature keV and for a thickness (a) m and (b) m. Broken lines denote the initial position of the foils, black and red trajectories originate from different positions in x (see text for details).
Proton trajectories from the expansion of a Gaussian proton plasma, obtained from Eq. (22) in cylindrical geometry. Blue and red lines correspond to particles of increasing energy. Parameters: m, ms m, and ms− 1.
Proton trajectories resulting from the expansion of a partial, hollow hemisphere with radius of curvature of m, thickness of m and (a) keV and (b) keV. Test protons in (a) and (b) are initialized at the same positions, at a distance of m (black lines) and m (red lines) on the right of the central arc passing through m. Note that the higher electron temperature in (b) results in a larger focal spot.
Snapshots of the spatial distribution of the protons at different times (in red, units are in ps) for different energies ( MeV and MeV). The target is a partial hollow hemisphere with radius of curvature m, the hot electrons are excited at the target front side for 500 fs, with either temperature keV and m (cases a and b) or MeV and m (cases c and d).
D 50 diameter (see text for details) vs. longitudinal direction for different energy ranges (blue: 3-5 MeV, red: 10-12 MeV, and green: 15-20 MeV) and different target and heating conditions (in terms of FWHM, duration and temperature of the hot electrons): (a) m, m, and fs - corresponding to cases a and b in Fig. 8; (b) m, m, and fs - corresponding to cases c and d in Fig. 8; (c) m, m, and fs; (d) m, m, and fs. For cases a, c, and d, the hot electron temperature keV and for case b, MeV.
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