Laser-Driven Coherent Betatron Oscillation in a Laser-Wakefield Cavity

The origin of beam disparity in emittance and betatron oscillation orbits, in and out of the polarization plane of the drive laser of laser-plasma accelerators, is explained in terms of betatron oscillations driven by the laser field. As trapped electrons accelerate, they move forward and interact with the laser pulse. For the bubble regime, a simple model is presented to describe this interaction in terms of a harmonic oscillator with a driving force from the laser and a restoring force from the plasma wake field. The resulting beam oscillations in the polarization plane, with period approximately the wavelength of the driving laser, increase emittance in that plane and cause microbunching of the beam. These effects are observed directly in 3D particle-in-cell simulations.

Figure 1

Electron density distribution at $t=6.2\mathrm{ps}$ from 3D PIC simulations showing the structure of the bubble and the accelerated beam. The sinusoid structure of the beam is a result of the laser-driven coherent betatron oscillation. Note that the laser propagates in the $x$ direction, and it is linearly polarized in the $z$ direction. $\zeta$ denotes the distance from the base of the bubble along $x$. The volumes of the injected electrons are indicated by electron isodensity surfaces of $6.2\times {10}^{19}1/{\mathrm{cm}}^3$ and the volumes of the shell of the bubble by isodensity surfaces of $1.86\times {10}^{20}1/{\mathrm{cm}}^3$.

Figure 2

Time-evolution (a) of the period $\lambda$ of the beam structure and (b) that of the maximum beam amplitude ($z_{\max }$) for laser wavelengths of ${\lambda }_L=820$ and 300 nm in 2D PIC simulations for similar conditions as in Fig. 1. The beam structure, $z(x)$ has been defined by density-weighted $z$ averages at every $x$, at each given time-point. The predominant peak in the Fourier transform of $z(x)$ determines $\lambda$. Error bars of $z_{\max }$ are visual estimates of the half-width of the beam. Error bars of the period, $\lambda$, are calculated from the FWHMs of the peaks of the Fourier tranforms of $z(x)$.

Figure 3

Distribution of electrons from the PIC simulation (a) and from test electrons (b) in the $xz$ plane and (a) that of the $B_y$ field (along the $x$ axis, scaled by $3\times {10}^{-4}\mu \mathrm{m}/\mathrm{T}$), at $t=6.2\mathrm{ps}$, $\zeta$ is the distance from the base of the bubble. Note that the electrons move in phase with the $B$ field of the laser. Trajectories of some of the highest energy electrons (c) and a test-electron one (d) show similar amplitudes and periodicity along $\xi =x-V_{p}t$, with $V_p=0.9985c$.

Figure 4

Microbunching of the beam at 4 mm propagation after leaving the plasma.