Pulse evolution and plasma-wave phase velocity in channel-guided laser-plasma accelerators

The self-consistent laser evolution of an intense, short-pulse laser exciting a plasma wave and propagating in a preformed plasma channel is investigated, including the effects of pulse steepening and energy depletion. In the weakly relativistic laser intensity regime, analytical expressions for the laser energy depletion, pulse self-steepening rate, laser intensity centroid velocity, and phase velocity of the plasma wave are derived and validated numerically.

Figure 1

Initial energy depletion rate, ${\eta }_{\mathcal{E}}$, as a function of the laser spot, $w_0$, for different values of the normalized laser strength, $a_0=0.1$ (red circles), $a_0=0.2$ (green dots), and $a_0=0.5$ (blue circles). The longitudinal laser profile is Gaussian with $L=2$, and $k_0/k_p=20$. The black dotted lines are the theoretical predictions Eq. (17).

Figure 2

Initial energy depletion rate, ${\eta }_{\mathcal{Q}}$, as a function of the laser spot, $w_0$, for different values of the normalized laser strength, $a_0=0.1$ (red circles), $a_0=0.2$ (green dots), and $a_0=0.5$ (blue circles). The longitudinal laser profile is Gaussian with $L=2$, and $k_0/k_p=20$. The black dotted lines are the theoretical predictions Eq. (21).

Figure 3

Lorenz factor of the initial intensity transport velocity, ${\gamma }_{i,0}$, as a function of the laser spot, $w_0$, for different values of the normalized laser strength, $a_0=0.1$ (red circles), $a_0=0.2$ (green dots), $a_0=0.5$ (blue circles), and $a_0=0.8$ (purple dots). The longitudinal laser profile is Gaussian with $L=2$, and $k_0/k_p=20$. The black dotted lines are the theoretical predictions Eq. (29).

Figure 4

Lorenz factor of the initial wake velocity, ${\gamma }_{p,0}$, as a function of the laser spot, $w_0$, for different values of the normalized laser strength, namely $a_0=0.1$ (red circles), $a_0=0.2$ (green dots), and $a_0=0.5$ (blue circles). The longitudinal laser profile is Gaussian with $L=2$, and $k_0/k_p=20$. The black dotted lines are the theoretical predictions Eq. (42).

Figure 5

Evolution of the wake phase velocity, ${\gamma }_p\left(s\right)$ (black solid line), and normalized-intensity-weighted laser radius $\overline{w}\left(s\right)$ (black dashed line), for a Gaussian laser driver with $a_0=0.5, w_0=4$, and $f\left(\zeta \right)=exp(-{\zeta }^2/L^2)$ with $L=2$. The laser is linearly matched in a parabolic plasma channel, and $k_0/k_p=20$. The two insets show snapshots of the laser envelope for two propagation distances: (i) $s=0$ and (ii) $s=252$, illustrating the compression of the laser driver in the region towards the back of the pulse. The red solid line and the red dashed line show, respectively, the evolution of the wake phase velocity and laser radius for a “supermatched” driver.

Figure 6

Normalized laser intensity field $|\widehat{a}(x,y=0,\zeta )|$ for a “supermatched” laser pulse driver in a parabolic plasma channel. The form of the laser envelope is given in Eq. (A2), with $a_0=1$, and where we choose $f\left(\zeta \right)=exp(-{\zeta }^2/L^2)$, with $L=2$. The function $g(\zeta ,r)$ is the solution of Eq. (A7) with $q=0$ and $R=5$.