Flexible x-ray source with tunable polarization and orbital angular momentum from Hermite-Gaussian laser modes driven plasma channel wakefield

A plasma channel undulator/wiggler may be created through the plasma wakefield excited by the beating of several Hermite-Gaussian laser modes propagating in a parabolic plasma channel. Control over both the betatron and undulator forces is conveniently achieved by tuning the amplitude ratios, colors, and order numbers of the modes. A special structure of the undulator/wiggler field without the focusing force near the propagation axis is generated inside the plasma wakefield by matching the strengths of the fundamental and first-order Hermite-Gaussian modes. The electron beam only experiences forced undulator oscillations in such a field, which significantly improves the quality of the emitted radiation. Since the value of the undulator strength parameter could be in a wide range, less or larger than unity, it is capable of generating narrow bandwidth x-ray, as well as the synchrotronlike high-energy $\mathrm{x}/\gamma$-ray, radiation by harmonics. Additionally, controlling the relative phases between the laser modes allows for polarization control of the plasma undulator. High-order harmonics produced from a circularly polarized plasma undulator clearly show the vortex nature and carry well-defined orbital angular momentum.

Figure 1

Integrated transverse intensity profile of laser pulse as a function of propagation distance $Z^{\prime }/{\lambda }_L$ for (a) a fundamental mode plus a first-order Hermite-Gaussian mode; (b) a fundamental mode plus a third-order Hermite-Gaussian mode; (c) a fundamental mode plus two first-order Hermite-Gaussian modes.

Figure 2

(a), (b) Projection of the transverse wakefield $E_x$, generated by two different modes without and with the condition (12), as a function of time $\tau$ on $\widehat{x}\widehat{z}$ plane. The dashed white lines show the trajectories of an electron in the wakefield; (c), (d), (e), (f) Slices of the transverse wakefield $E_r$, generated by two different modes with the condition (12), on $\widehat{x}\widehat{y}$ plane at four different propagation positions, $\tau =2269$, 2432, 2512, 2592, respectively; (g), (h), (i), (j) Slices of transverse wakefield $E_r$, generated by three different modes with the condition (12), at four different propagation positions, $\tau =2045$, 2432, 2816, 3200, respectively.

Figure 3

Betatron oscillation frequency of an injected electron in Eq. (13), introduced by the inaccuracy of laser strength, $a_1$.

Figure 4

The normalized momentum $u_x$ in $\widehat{x}$ direction. Red dashed line: analytical result from Eq. (18); Blue solid lines: numerical results obtained for an electron beam by solving the transverse momentum equation with the electric field in Eq. (7).

Figure 5

Variation of the undulator strength with different laser pulse strength: read solid line with $a_1=0.6$; blue solid line with $a_1=0.3$. The parameters are chosen as: plasma density $10^{18}{\mathrm{cm}}^{-3}$, wavelength of the laser pulse ${\lambda }_L=1\mu \mathrm{m}$ and laser spot size $r_m=1.14$, gamma factor of the injected electron ${\gamma }_0=1000$.

Figure 6

Radiation spectrum from plasma-based undulator/wiggler with (a) $a_u\simeq 0.62$ and (b) $a_u\simeq 16$. Dashed white line is the theoretical on-axis solution and solid cyan lines in both plots are for the numerical on-axis radiation with ${\gamma }_0\theta =0$.

Figure 7

(a)-(c) show the intensity and transverse vector field (white arrows, ${\overrightarrow{I}}_{\perp }=I_{n+}{\widehat{e}}_{+}+I_{n-}{\widehat{e}}_{-}$) of radiation for the fundamental ($n=0$), second ($n=1$), and third ($n=2$) harmonics, respectively in Eq. (24) and (25), viewed along $z$-axis; (d)-(f) show the corresponding rotation components.