Resonant Excitation of Surface Plasmon for Wakefield Acceleration by Beating GW Lasers on Smooth Cylindrical Surface

Abstract

We present a theoretical and numerical study of resonant surface-plasmon (SP) excitation driven by the beating of two co-propagating laser pulses on a smooth cylindrical plasma-vacuum interface. Analytical expressions for the SP dispersion relation, field amplitude, geometric coupling factor, and resonance conditions are derived and validated by fully three-dimensional particle-in-cell simulations. We reveal that curvature-induced geometric effects can substantially modify the SP dispersion and enable resonant matching by laser beat waves. This is inaccessible in planar geometries or with a single laser. Under matched resonance conditions, a high-amplitude SP-based wakefield can be generated by a few gigawatt lasers, placing this mechanism within reach of state-of-the-art fibre lasers. It therefore opens a route toward portable laser-driven plasma wakefield accelerators.

Figures (5)

• Figure 1: PIC results after two laser pulses co-propagating $40~\mu m$ inside a solid microtube: (a) electron density (grey) and beating laser field $E_y$ (blue-red) in $xz$ plane. (b) Acceleration field $E_z$ in $xz$ plane. (c) Energy spectrum of the electron beam accelerated. (d) radial phase space ($r, u_r$) of the accelerated electron beam. The vacuum and plasma regimes are on the left and right, respectively. (e) and (f) show the transverse (indicated by green dashed line in (b)) and longitudinal line plots of on-axis ($x=0~\mu m$) $E_z$. Black solid lines are from PIC, and orange dashed lines are from analytical calculation with $\varrho=1.05$. (g) Energy spectrum of the electron beam accelerated inside the vacuum channel.
• Figure 2: Phase velocity $v_{\rm ph}$ of SP on planar and cylindrical surfaces of different plasma density, calculated with $a=1.0~\mu m$ by Eq. \ref{['eq:disper_relation']}.
• Figure 3: Resonant condition between matched plasma density $n_e$ and second laser wavelength $\lambda_2$, where $\lambda_1=0.8~\mu m$, $a=1.5~\mu m$ and $\gamma_0=1.0$, calculated by Eq. \ref{['eq:light_resonance']}.
• Figure 4: Radial distribution of longitudinal component of electric field $E_z^{\rm wake}$ for different values of detuning rate $\varrho$ defined by $\varrho=(\Delta \omega - \alpha \Delta k)/(\omega_{sp} - \alpha k_{sp})-1$. Here, $\nu=0$. The light blue regions indicate the plasma wall.
• Figure 5: (a) $G_{\rm SP}$ as a function of plasma density $n_e$ from theory (normalised, blue solid) and PICs (red-dot). (b) Amplitude of on-axis acceleration field $E_{\rm z, max}^{\rm wake}$ as a function of $a_0^2$ from theory (blue solid) and PICs (red-dot). Here, $a_{0,1}=a_{0,2}=a_0$. The other parameters are $\lambda_1=0.8~\mu m$, $\lambda_2=0.6~\mu m$, $a=1.0~\mu m$ and $w_0=2.0~\mu m$. In (a), and $a_{0}=0.6$, corresponding to laser peak powers $P_{\rm 1, peak}=48~GW$ and $P_{\rm 2, peak}=80~GW$, respectively. In (b), $n_e=6\times 10^{20}~cm^{-3}$, close to the resonant density. The PIC results are obtained after the laser pulses co-propagate $40~\mu m$ inside a microtube.