Energetic electron-bunch generation in a phase-locked longitudinal laser electric field

Energetic electron acceleration processes in a plasma hollow tube irradiated by an ultraintense laser pulse are investigated. It is found that the longitudinal component of the laser field is much enhanced when a linear polarized Gaussian laser pulse propagates through the plasma tube. This longitudinal field is of $\pi /2$ phase shift relative to the transverse electric field and has a $\pi$ phase interval between its upper and lower parts. The electrons in the plasma tube are first pulled out by the transverse electric field and then trapped by the longitudinal electric field. The trapped electrons can further be accelerated to higher energy in the presence of the longitudinal electric field. This acceleration mechanism is clearly illustrated by both particle-in-cell simulations and single particle modelings.

Figure 1

Target configuration in simulations. A short pulse laser irradiates and injects into a hollow tube.

Figure 2

Both longitudinal (red or light gray) and transverse (blue or dark gray) laser electric fields in the plasma tube. (a) The profile of both fields at the upper tube edge. (b) The longitudinal electric field $E_x$, and (c) the transverse electric field $E_y$ in units of $\mathrm{V}/\mathrm{m}$. (d) The electron number density in log scale with unit of ${\mathrm{m}}^{-3}$.

Figure 3

The trajectories of energy gain in both parallel and perpendicular directions for traced energetic electrons.

Figure 4

Acceleration processes for traced electrons. These electrons are divided into two groups (see context for details). Group A (a)–(c) for electrons which mainly obtain energy in the parallel direction, where the longitudinal electric field dominates. Group B (d)–(f) for electrons which mainly obtain energy in the perpendicular direction, where the ponderomotive force dominates. Subplots (a) and (d) for electron trajectories, (b) and (e) for total energy, (c) and (f) for energy gain source, respectively.

Figure 5

(a) Statistic of energetic electron (with energy greater than $20\mathrm{MeV}$) numbers for electrons mainly obtained energy from the longitudinal electric field (${\epsilon }_{\parallel }>{\epsilon }_{\perp }$) or the transverse electric field (${\epsilon }_{\parallel }<{\epsilon }_{\perp }$), normalized by the final total energetic electron numbers. (b) Electron maximum energy varying with time. (c) Electron energy spectrum and (d) electron divergence angle for electrons in the tube at time $t=42{\mathrm{T}}_0$ when the acceleration is saturated.

Figure 6

Numerical results for single particle model, where a combined planar laser field of $E_y=2\times {10}^{13}\mathrm{V}/\mathrm{m}$ and $\pi /2$ phase shifted $|E_x|=0.1|E_y|$ is supposed. (a) The laser electric fields and definitions of points. (b, c) Electron motion in $E_x=0$ case as a contrast. (d, e) Electron motion with initial phase at point A (E). (f, g) Electron motion with initial phase at point D. The relations between fields and electron trajectories are shown in (b), (d), and (f). The field shown in (b) is $E_y$, in (d) and (f) are $E_x$. Panels (c), (e), and (g) show the electron energy gain.

Figure 7

Electron number density in log scale with unit of ${\mathrm{m}}^{-3}$, and energy spectrum for electrons in the tube at time $t=42{\mathrm{T}}_0$. (a, b) Tube with inner diameter of $d_0=3\mu \mathrm{m}$ and (c, d) tube with inner diameter of $d_0=5\mu \mathrm{m}$.

Figure 8

Comparison of electron energy spectrums for tubes with diameters near $d_0=4\mu \mathrm{m}$ at time $t=42{\mathrm{T}}_0$.