Generation of Terawatt Attosecond Pulses from Relativistic Transition Radiation

When a femtosecond duration and hundreds of kiloampere peak current electron beam traverses the vacuum and high-density plasma interface, a new process, that we call relativistic transition radiation (RTR), generates an intense $\sim 100$ as pulse containing $\sim 1$ terawatt power of coherent vacuum ultraviolet (VUV) radiation accompanied by several smaller femtosecond duration satellite pulses. This pulse inherits the radial polarization of the incident beam field and has a ring intensity distribution. This RTR is emitted when the beam density is comparable to the plasma density and the spot size much larger than the plasma skin depth. Physically, it arises from the return current or backward relativistic motion of electrons starting just inside the plasma that Doppler up shifts the emitted photons. The number of RTR pulses is determined by the number of groups of plasma electrons that originate at different depths within the first plasma wake period and emit coherently before phase mixing.

Figure 1

Relativistic transition radiation when an electron beam propagates through a plasma. (a) The charge density isosurfaces of the beam (blue, yellow, and green) and the plasma (gray) at $t=0\mathrm{fs}$. The beam center is $z=-1.5\mu \mathrm{m}$. (b) The charge density isosurface of the plasma electrons at $t=10\mathrm{fs}$. (c) The isosurfaces of the radiated transverse electric field $E_{\perp }$ (green and blue) and the axial current $j_z$ (red and yellow represent forward current density while cyan represents the backward current density) at $t=26.7\mathrm{fs}$. Red times are relative to the time when the middle of the beam hits the surface.

Figure 2

Attosecond radiation pulse. (a) The recorded electric field when $n_p=n_{b0}$ (blue curve) and $1000n_{b0}$ (red curve). Normalized intensity profile of the radiation (pulse 2) is shown in the inset. (b) The distribution of the transverse electrical field in the $x–y$ plane at $t=27.1\mathrm{fs}$ and $z=-1.5\mu \mathrm{m}$. The gray arrows indicate the direction of the field. The solid blue line shows the field amplitude at $y=0\mu \mathrm{m}$ and the dashed red line is for magnitude of the incident Coulomb field. (c) The spectrum of the radiation when $n_p=n_{b0}$ (blue line), $1000n_{b0}$ (red line), the fitted scaling law (yellow line), and the pulse 2 when $n_p=n_{b0}$ (purple line).

Figure 3

The motion of plasma electrons. (a) The $x–z$ plane distribution of the longitudinal ($j_z$) and transverse ($j_x$) current densities at four different times ($t$). The radiation generated at these times will arrive at the recorded position at $t_{\mathrm{rad}}$. The dashed lines indicate the two boundaries of the target. The field distribution of the attosecond pulse (gray) is also shown in the last $j_x$ plot. (b) The initial positions of the electrons in three groups indicated by crosses, dots, and triangles originating at different locations within the target determine the source of the current densities that radiates the zeroth, first, and second electromagnetic pulse. The positions of each group of electrons when they coalesce into a high-density current sheath are shown as white dots in the corresponding $j_x$ plots of (a). Also shown are sample trajectories of three of these electrons (see also Movies M4–M6 in Supplemental Material [30]). (c) The evolution of $p_z$ for the electrons in return currents. The solid lines represent two sample electrons and the black dashed line shows the ${\gamma }_z$ of one sample from return current 2.

Figure 4

(a) The isosurface of the radiation intensity (yellow, $E^2=50(m^2{c}^2{\omega }_p^2/e^2)$; green, $E^2=30m^2{c}^2{\omega }_p^2/e^2$) and its projections in each plane when the beam propagates along the $z$ direction and the target is oblique in the $z–x$ plane with angle $\theta =5.7°$. (b) The duration, peak electric field of the attosecond pulse, and the maximum backward momentum of the electrons when scanning the current of the normally incident beam.