Three-dimensional time and frequency-domain theory of femtosecond x-ray pulse generation through Thomson scattering

The generation of high intensity, ultrashort x-ray pulses enables exciting new experimental capabilities, such as femtosecond pump-probe experiments used to temporally resolve material structural dynamics on atomic time scales. Thomson backscattering of a high intensity laser pulse with a bright relativistic electron bunch is a promising method for producing such high-brightness x-ray pulses in the 10–100 keV range within a compact facility. While a variety of methods for producing subpicosecond x-ray bursts by Thomson scattering exist, including compression of the electron bunch to subpicosecond bunch lengths and/or colliding a subpicosecond laser pulse in a side-on geometry to minimize the interaction time, a promising alternative approach to achieving this goal while maintaining ultrahigh brightness is the production of a time-correlated (or chirped) x-ray pulse in conjunction with pulse slicing or compression. We present the results of a complete analysis of this process using a recently developed 3D time and frequency-domain code for analyzing the spatial, temporal, and spectral properties an x-ray beam produced by relativistic Thomson scattering. Based on the relativistic differential cross section, this code has the capability to calculate time and space dependent spectra of the x-ray photons produced from linear Thomson scattering for both bandwidth-limited and chirped incident laser pulses. Spectral broadening of the scattered x-ray pulse resulting from the incident laser bandwidth, laser focus, and the transverse and longitudinal phase space of the electron beam were examined. Simulations of chirped x-ray pulse production using both a chirped electron beam and a chirped laser pulse are presented. Required electron beam and laser parameters are summarized by investigating the effects of beam emittance, energy spread, and laser bandwidth on the scattered x-ray spectrum. It is shown that sufficient temporal correlation in the scattered x-ray spectrum to produce sub-100 fs temporal slice resolution can be produced from state-of-the-art, high-brightness electron beams without the need to perform longitudinal compression on the electron bunch.

Figure 1

Thomson interaction geometry in the electron rest frame.

Figure 2

(a) Illustration of laser incident direction and polarization. $\mathit{\alpha }$ is the direction of the polarization vector of the laser, where ${\varphi }_p$ represents the rotation angle of $\mathit{\alpha }$ about the $z_L$ axis. (b) Illustration of the electron incident direction. The electron beam is incident along the $z$ axis, but the direction of each electron deviated by the angles specified by ${\xi }_{xe}$ and ${\xi }_{ye}$.

Figure 3

Scattered photon density vs scattering angle ($\theta$) from the $z$ axis in the $x\mathrm{\text{−}}z$ plane (solid line) and the $y\mathrm{\text{−}}z$ plane (dotted line) for the case of an electron at rest and an $x$ polarized photon incident along the negative $z$ axis.

Figure 4

Scattered photon density vs scattering angle ($\theta$) from the $z$ axis in the $x\mathrm{\text{−}}z$ plane (solid line) and the $y\mathrm{\text{−}}z$ plane (dotted line) for the case of a relativistic electron ($\gamma =2$) traveling along the $z$ axis and an $x$ polarized photon incident along the negative $z$ axis.

Figure 5

Scattered energy density vs scattering angle ($\theta$) from the $z$ axis in the $x\mathrm{\text{−}}z$ plane (solid line) and the $y\mathrm{\text{−}}z$ plane (dotted line) for the case of a relativistic electron ($\gamma =2$) traveling in along the $z$ axis and an $x$ polarized photon incident in the negative $z$ direction.

Figure 6

Scattered photon density from a relativistic electron ($\gamma =5$) in the $x\mathrm{\text{−}}z$ plane produced by an $x$ polarized photon for the case of head-on interaction (solid line) and a side-on interaction (dotted line).

Figure 7

On-axis x-ray spectrum produced by a $\gamma =100$ electron colliding head on with an 800 nm laser pulse with a bandwidth corresponding to a 0.5 ps $1/e^2$ pulse width for the case of a plane wave (dots), $20\mu \mathrm{m}$ laser focus (dark blue line), $10\mu \mathrm{m}$ laser focus (green line), and $5\mu \mathrm{m}$ laser focus (light blue line).

Figure 8

On-axis x-ray spectrum produced by a $\gamma =100$ electron colliding side on with an 800 nm laser pulse with a bandwidth corresponding to a 0.5 ps $1/e^2$ pulse width for the case of a plane wave (dots), $200\mu \mathrm{m}$ laser focus (dark blue line), $100\mu \mathrm{m}$ laser focus (green line), and $50\mu \mathrm{m}$ laser focus (light blue line).

Figure 9

On-axis x-ray spectrum resulting from a head-on collision of a 50 MeV electron beam with an 800 nm laser pulse for the case of an rms normalized emittance of 1 mm mrad (line) and 2 mm mrad (dots).

Figure 10

False color plot of the spectral density of scattered x rays in the $y\mathrm{\text{−}}z$ plane resulting from the head-on collision of a 50 MeV electron bunch with ${\epsilon }_{nx}=1\mathrm{mm}\mathrm{mrad}$ focused to an rms spot size of $20\mu \mathrm{m}$ with an 800 nm, 0.5 ps bandwidth laser pulse polarized in the $x$ direction.

Figure 11

Longitudinal phase space of a chirped x-ray pulse.

Figure 12

Methods for chirped x-ray pulse production.

Figure 13

Simulated transverse and longitudinal phase space of the electron beam at the interaction point.

Figure 14

Simulated on-axis x-ray spectrum of the chirped Thomson scattered x rays before (top panel), and after (bottom panel) spectral filtering.

Figure 15

Simulation of pulse slicing by Bragg reflection showing the spatially averaged intensity vs time for the case of radial collimation widths of 0.1 mrad (left panel), 0.25 mrad (middle panel), and 0.5 mrad (right panel), corresponding to FWHM pulse durations of 70, 80, and 100 fs, respectively, and total photon counts of 19, 113, and 420.

Figure 16

Simulated on-axis x-ray spectrum for the chirped Thomson scattered x rays produced by colliding a chirped laser pulse side on with an unchirped electron bunch, before (top panel) and after (bottom panel) spectral filtering.