Subfemtosecond Wakefield Injector and Accelerator Based on an Undulating Plasma Bubble Controlled by a Laser Phase

We demonstrate that a long-propagating plasma bubble executing undulatory motion can be produced in the wake of two copropagating laser pulses: a near-single-cycle injector and a multicycle driver. When the undulation amplitude exceeds the analytically derived threshold, highly localized injections of plasma electrons into the bubble are followed by their long-distance acceleration. While the locations of the injection regions are controlled by the carrier-envelope phase (CEP) of the injector pulse, the monoenergetic spectrum of the accelerated subfemtosecond high-charge electron bunches is shown to be nearly CEP independent.

Figure 1

Schematic of a laser-wakefield accelerator with PUB injection. A transversely undulating plasma bubble driven by the combination of a near-single-cycle injector pulse (orange) and a multicycle driver pulse (light blue) periodically traps electrons from the ambient plasma. Time-dependent injector CEP controls bubble centroid displacement from the propagation axis (dashed line), determining which electrons are injected into (red line) or pass through (blue line) the bubble.

Figure 2

(a)–(c) Test particle trapping by an undulating bubble and (d) bubble asymmetry by an NSC pulse. (a) Trapped (red, ${\varphi }_{\mathrm{CEP}}=\pi /2$) and passing (blue, ${\varphi }_{\mathrm{CEP}}=\pi$) trajectories for $0<t<200$. Bubble boundaries (black lines), unperturbed (solid) and maximally displaced (dashed). (b)–(c) Particle swarm at $t=200$ from a range of initial conditions $(x_0,y_0,z_0)$ color coded by $x_0$. Trapped electrons are plotted in the $(x_0,z_0)$ plane (b) and inside the bubble (c). Red line in (b), density of injected electrons vs their initial position. Black line in (c), longitudinal density. PUB parameters, $k_{p}R=5$, $z_{\mathrm{u}}/R=0.28$, $T_{\mathrm{CEP}}=35/{\omega }_p$, ${\gamma }_b=5$. (d) Normalized plasma flow asymmetry $\delta z_{\mathrm{ex}}$ (color coded) after passing through the injector pulse and nonoscillating bubble vs NSC wavelength ${\lambda }_{\mathrm{inj}}$ and pulse cycles $T={\sigma }_x/{\lambda }_{\mathrm{inj}}$.

Figure 3

Evolution of the injector-driver pulses and transverse plasma wakes. (a)–(b) Grayscale, plasma density in the $x–z$ plane around the bubble. Red (blue) lines, on-axis normalized electric fields of the injector (driver) pulses at (a) $x_1=0.08\mathrm{mm}$ and (b) $x_2=0.2\mathrm{mm}$. (c)–(d) On-axis transverse wakes at $\zeta \equiv (x-ct)/\lambda =9$ [green stars in (a)–(b)]. (c) CEP dependence of $W_{\perp }$ for ${\lambda }_{\mathrm{inj}}=2.4\mu \mathrm{m}$ injector pulse, ${\varphi }_{\mathrm{CEP}}=0$ (black solid line) and ${\varphi }_{\mathrm{CEP}}=\pi /2$ (black dashed line). (d) Dependence of $W_{\perp }$ on the injector pulse wavelength, ${\lambda }_{\mathrm{inj}}=2.4\mu \mathrm{m}$ (black solid line) and ${\lambda }_{\mathrm{inj}}^{(2)}=1.2\mu \mathrm{m}$ (black dashed line); ${\varphi }_{\mathrm{CEP}}=\pi$ for both wavelengths. Red (blue) dotted-dashed lines, propagation distances $x_1$ ($x_2$). All fields scaled to $E_0=e/mc{\omega }_{\mathrm{dr}}$. Plasma density, $n_p=4.4\times {10}^{18}{\mathrm{cm}}^3$; laser parameters, see Table 1. Simulations, 3D PIC VLPL.

Figure 4

PUB-based injection/acceleration. (a) Grayscale, density cross section at $x=0.32\mathrm{mm}$. (b) Electron injection rate (solid line) and injected electrons’ initial transverse positions (blue dots) as a function of propagation distance. (c)–(d) Injected electrons’ energy spectra (c) and current (d) at $x=1.5\mathrm{mm}$ for Injector 1 (blue line) and Injector 2 (red line). Star and square in (b)–(d): the corresponding injection times (b), energy spectra (c), and positions inside the bubble (d). Inset in (c): high-energy spectral peaks at ${\varphi }_{\mathrm{CEP}}=0$ (solid line) and ${\varphi }_{\mathrm{CEP}}=\pi /2$ (dashed line). Laser parameters, see Table 1. Simulations, 3D PIC VLPL.