Abstract
This work investigates the capability of ultraintense lasers with irradiance from 10^{18} to 10^{21} W cm^{−2} to produce highly energetic electron beams from a Gaussian focus in a lowdensity plasma. A simple particle simulation code including a physical model of collective electrostaticeffects in relativistic plasmas has been developed. Without electrostatic fields, free electrons escape from the Gaussian focal region of a 10ps petawatt laser pulse very quickly, well before the laser field reaches its maximum amplitude. However, it has been demonstrated that the electrostatic field generated by the electron flow is able to strongly modify the range and direction of the lasergenerated MeV electrons by allowing trapped electrons to experience much higher laserintensity peaks along their trajectories. This modeling predicts some collimation but not enough to meet the requirements of fast ignition.
I. INTRODUCTION
II. ELECTRON MOTION WITH NO SPACECHARGE EFFECT
A. Gaussian laser field in a focus
B. Kinetic energy and angular distributions of ponderomotively driven electrons
III. CYLINDRICAL MODEL OF COLLECTIVE ELECTROSTATICEFFECTS
A. Numerical procedures
B. Initial particle configuration
C. Results including a radial electrostatic field
IV. CONCLUSIONS
Key Topics
 Electrostatics
 46.0
 Electron beams
 15.0
 Fast ignition
 11.0
 Particleincell method
 11.0
 Space charge effects
 11.0
Figures
(Color online) Schematic illustration of the channeling concept for fast ignition.
(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) 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 = 10^{21} 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 planewave 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) (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 = 10^{21} 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 planewave 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 10ps laser pulse at an intensity of I = 10^{21} 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.
(Color online) Kinetic energy and angular distributions of the electrons for a 10ps laser pulse at an intensity of I = 10^{21} 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 }).
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) 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 0.2ps laser pulse at an intensity of I = 10^{21} W cm^{−2}.
(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 0.2ps laser pulse at an intensity of I = 10^{21} W cm^{−2}.
(Color online) Comparison of simulation runs for a laser intensity of I = 10^{21} 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 backwardscattered 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.
(Color online) Comparison of simulation runs for a laser intensity of I = 10^{21} 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 backwardscattered 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.
Tables
Quantitative comparison of two simulations at a number of laser intensities where one simulation includes electrostatic effects and the other does not.
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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