High Power Laser Science and Engineering, Volume. 10, Issue 6, 06000e45(2022)
Electron pulse train accelerated by a linearly polarized Laguerre–Gaussian laser beam On the Cover
Figures & Tables(9)
Fig. 1. Electric and magnetic field components of an LP-LG laser beam before it encounters the plasma. Panels (a) and (d) show 
; panels (b) and (e) show 
; panels (c) and (f) show 
. The left-hand column ((a)–(c)) shows the field structure in the 
-plane at 
. The right-hand column ((d)–(f)) shows the field structure in the 
-plane at the 
-position indicated with the dashed line in panels (a)–(c). All the snapshots are taken at 
fs from the simulation with parameters listed in Table
Fig. 2. Structure of electron bunches shortly after laser reflection off the plasma (
fs). (a) Electron density on a log-scale, with the color representing 
. The blue, red and green contours denote 
, 
and 
, respectively. The dashed rectangle marks the third bunch, whose additional details are provided in the remaining panels. (b) Electron areal density 
in the third bunch. (c) Cell-averaged electron divergence angle 
in the third bunch. (d), (e) 3D rendering of the electron density in the third bunch using different viewpoints.
Fig. 3. (a) Areal density of the electrons in the third bunch at time 
fs. (b) Three groups of electrons (blue, green and red markers) selected from the third bunch at 
fs for tracking. The electrons in each group are selected randomly. (c) Transverse positions of the three groups of electrons from (b) at 
fs. (d)–(f) Trajectories of the three groups of electrons in the transverse plane over the duration of the simulation. The line color shows electron energy. The markers show the electron locations at 
fs. (g)–(i) Time evolution of the longitudinal position for the same three groups of electrons, with (g) showing ‘blue’ electrons, (h) showing ‘green’ electrons and (i) showing ‘red’ electrons. The line color shows electron energy.
Fig. 4. Electric and magnetic fields after reflection of the LP-LG laser beam off the plasma. (a) Longitudinal profiles of the transverse electric field 
(red curve) and longitudinal magnetic field 
(blue line) at 
fs. Here, 
is plotted along the axis of the beam (
, 
), whereas 
is plotted at an off-axis location (
, 
) where its amplitude has the highest value. (b) Frequency spectra of 
(red line) and 
(blue line) from panel (a).
Fig. 5. Result of the long-term electron acceleration in the reflected LP-LG laser beam close to the beam axis. (a) Electron energy distribution as a function of 
at 
fs for electrons with 
. The inset shows the third bunch that is marked with the dashed rectangle in the main plot. (b) Time evolution of the electron distribution over the divergence angle 
in the third bunch (
). (c) Time evolution of the electron energy spectrum in the third bunch. The black dashed curve is the prediction obtained from 
. The start time of the acceleration is used as an adjustable parameter. (d) Electron energy versus the divergence angle in the third bunch shown in the inset of panel (a).
Fig. 6. (a) Areal density 
and (b) cell-averaged divergence angle 
in the cross-section of the third bunch at 
fs and 
. (c)–(e) Snapshots of the longitudinal electric field 
in the cross-section of the laser beam at 
, 
fs (c), 
, 
fs (d) and 
, 
fs (e). Here, 
is calculated using the analytical expression 
is the amplitude of 
at 
, 
.
Table 1. 3D PIC simulation parameters. Here,
m
is the critical density corresponding to the laser wavelength 
. The initial temperatures for electrons and ions are set to zero.View tableView in ArticleTable 1. 3D PIC simulation parameters. Here,
m is the critical density corresponding to the laser wavelength . The initial temperatures for electrons and ions are set to zero.Parameters for linearly polarized Laguerre–Gaussian laser Peak power (period averaged) 0.6 PW Radial and twist index $p = 0,\ l = -1$ Wavelength ${\lambda}_0 = 0.8\ \unicode{x3bc} \mathrm{m}$ Pulse duration ( ${\sin}^2$ ${\tau}_{\textrm{g}} = 20$ Focal spot size ( $1/\mathrm{e}$ ${w}_0=3\ \unicode{x3bc} \mathrm{m}$ Location of the focal plane $x = 0\ \unicode{x3bc}$ Laser propagation direction $-x$ Polarization direction $y$ Other simulation parameters Position of the foil and the pre-plasma $-1.0\kern0.24em \mathrm{to}-0.3\ \unicode{x3bc} \mathrm{m}$ $-0.3$ $\unicode{x3bc} \mathrm{m}$ Density distribution of pre-plasma ${n}_{\textrm{e}} = 180.0{n}_{\textrm{c}}\exp \left[-20\left(x+0.3\ \unicode{x3bc} \mathrm{m}\right)/{\lambda}_0\right]$ Electron and ion (C ${}^{6+}$ ${n}_{\textrm{e}} = 180.0{n}_{\textrm{c}}$ ${n}_{\textrm{i}} = 30.0{n}_{\textrm{c}}$ Gradient length $L = {\lambda}_0$ Simulation box ( $x\times y\times z$ 10 $\unicode{x3bc} \mathrm{m}$ $\times$ $\unicode{x3bc} \mathrm{m}\times 20\ \unicode{x3bc} \mathrm{m}$ Cell number ( $x\times y\times z$ 800 cells $\times$ $\times$ Macroparticles per cell for electrons 100 at $r<$ $\unicode{x3bc} \mathrm{m}$ $r\ge 2.5\ \unicode{x3bc} \mathrm{m}$ Macroparticles per cell for C ${}^{6+}$ 12 Order of electromagnetic field solver 4
Table 2. Parameters used for the four simulations depicted in
Figure 7 .View tableView in ArticleTable 2. Parameters used for the four simulations depicted in
Figure 7 .Sim. No. Cell size Cell number Macro-particles per cell Order of electromagnetic (window size is the same) e ( $r<2.5\;\unicode{x3bc} \mathrm{m}$ $r>2.5\;\unicode{x3bc} \mathrm{m}$ ${}^{6+}$ field solver #1 1/40 $\unicode{x3bc} \mathrm{m}$ $400\times 800\times 800$ 200, 36, 24 2 #2 1/40 $\unicode{x3bc} \mathrm{m}$ $400\times 800\times 800$ 400, 72, 48 4 #3 1/50 $\unicode{x3bc} \mathrm{m}$ $500\times 1000\times 1000$ 200, 36, 24 4 #4 1/80 $\unicode{x3bc} \mathrm{m}$ $800\times 1600\times 1600$ 100, 18, 12 4
Table 3. Parameters of all five electron bunches at
= 261 fs.View tableView in ArticleTable 3. Parameters of all five electron bunches at
= 261 fs.#1 #2 #3 #4 #5 ${\varepsilon}_{\textrm{e}}$ $\Delta {\varepsilon}_{\textrm{e}}/{\varepsilon}_{\textrm{e}}$ 0.02–0.1 0.02–0.28 0.29 (10%) 0.22 (6%) 0.1 (15%) ${\tilde{\varepsilon}}_{\textrm{rms}, yz}\ [\unicode{x3bc}$ 0.95 0.88 1.5 0.64 0.92 $W$ 0.06 1.5 2.2 1.3 0.06 $Q$ 1.4 8 9 6.8 0.7 $\Delta t$ 300 360 270 260 540
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Yin Shi, David R. Blackman, Ping Zhu, Alexey Arefiev. Electron pulse train accelerated by a linearly polarized Laguerre–Gaussian laser beam[J]. High Power Laser Science and Engineering, 2022, 10(6): 06000e45
Paper Information
Category: Research Articles
Received: Jun. 15, 2022
Accepted: Nov. 3, 2022
Published Online: Dec. 27, 2022
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