Plasma Undulator Based on Laser Excitation of Wakefields in a Plasma Channel

An undulator is proposed based on the plasma wakefields excited by a laser pulse in a plasma channel. Generation of the undulator fields is achieved by inducing centroid oscillations of the laser pulse in the channel. The period of such an undulator is proportional to the Rayleigh length of the laser pulse and can be submillimeter, while preserving high undulator strength. The electron trajectories in the undulator are examined, expressions for the undulator strength are presented, and the spontaneous radiation is calculated. Multimode and multicolor laser pulses are considered for greater tunability of the undulator period and strength.

Figure 1

Schematic of the plasma undulator.

Figure 2

Undulator strength $a_u$ given by Eq. (11) versus undulator period ${\lambda }_u$ for several values of laser amplitude, wavelength, and centroid displacement: (a) $a_0=0.28$, ${\lambda }_L=1\mu \mathrm{m}$, and $x_{\text{ci}}/w_0=0.2$; (b) $a_0=0.28$, ${\lambda }_L=1\mu \mathrm{m}$, and $x_{\text{ci}}/w_0=0.3$; (c) $a_0=0.5$, ${\lambda }_L=10\mu \mathrm{m}$, and $x_{\text{ci}}/w_0=0.4$; and (d) $a_0=0.5$, ${\lambda }_L=1\mu \mathrm{m}$, and $x_{\text{ci}}/w_0=0.2$.

Figure 3

Normalized radiation spectrum generated by a beam with ${ϵ}_n=0.1\mu \mathrm{m}$ and ${\sigma }_{\gamma }/{\gamma }_0=0.01$, in a plasma undulator with $a_u=1.01$ and $N_u=30$. Harmonics, Eq. (12), are shown with white dashed curves. The spectrum for $\theta =0$ (arb. units) is shown with white solid line. Peaks corresponding to betatron radiation, fundamental, and third harmonics of the undulator radiation are annotated with white arrows.

Figure 4

On-axis spectrum showing the fundamental undulator radiation for several emittance values: ${ϵ}_n=0.1\mu \mathrm{m}$ (blue curve), ${ϵ}_n=0.025\mu \mathrm{m}$ (red curve), ideal pointlike electron beam with zero emittance and no energy spread [from numerical calculations (green curve) and from theory (dashed black curve)], and ${ϵ}_n=0.1\mu \mathrm{m}$ with exponential term in the wakefield included (magenta curve). All beams except the ideal pointlike electron beam case have an energy spread ${\sigma }_{\gamma }/{\gamma }_0=1\%$.