Laser pulsing in linear Compton scattering

Previous work on calculating energy spectra from Compton scattering events has either neglected considering the pulsed structure of the incident laser beam, or has calculated these effects in an approximate way subject to criticism. In this paper, this problem has been reconsidered within a linear plane wave model for the incident laser beam. By performing the proper Lorentz transformation of the Klein-Nishina scattering cross section, a spectrum calculation can be created which allows the electron beam energy spread and emittance effects on the spectrum to be accurately calculated, essentially by summing over the emission of each individual electron. Such an approach has the obvious advantage that it is easily integrated with a particle distribution generated by particle tracking, allowing precise calculations of spectra for realistic particle distributions “in collision.” The method is used to predict the energy spectrum of radiation passing through an aperture for the proposed Old Dominion University inverse Compton source. Many of the results allow easy scaling estimates to be made of the expected spectrum.

Figure 1

The number density of the energy spectrum of a Compton gamma-ray beam produced by the head-on collision of a 466 MeV electron with a 789 nm laser beam, as in Fig. 2 in Ref. [7]. A collimation aperture with radius $R$ of 50 mm is placed a distance $L$ of 60 m downstream from the collision point (${\theta }_a={\tan }^{-1}(R/L)$). Here a Gaussian laser pulse with $\sigma =50$ is used, while the laser in Ref. [7] is CW.

Figure 2

The number density of the energy spectrum of a Compton gamma-ray beam produced by the head-on collision of a 500 MeV electron with a 800 nm pulsed laser beam, for different radii $R$ of the collimation point (in mm), as in Fig. 3 in Ref. [7]. The aperture is 60 m downstream from the collision point. The horizontal emittance and energy spread of the electron beam are held constant at 0.05 nm rad and $2\times {10}^{-3}$, respectively. Here a Gaussian laser pulse with $\sigma =50$ is used, while the laser in Ref. [7] is CW. Each curve is generated by averaging 400 electrons sampling the prescribed distribution. Left panel: Spectra scaled to their respective peak values (compare with Fig. 3(b) of Ref. [7]). Right panel: Spectra in physical units.

Figure 3

The number density of the energy spectrum of a Compton gamma-ray beam produced by the head-on collision of a 500 MeV electron with a 800 nm pulsed laser beam, for different horizontal emittances ${\epsilon }_x$ as in Fig. 4(a) in Ref. [7]. The laser is collimated by an aperture with radius of 16 mm, placed 60 m downstream from the collision point. The relative energy spread of the electron beam ${\sigma }_E$ is held constant at $2\times {10}^{-3}$. Here a Gaussian laser pulse with $\sigma =50$ is used, while the laser in Ref. [7] is CW. Each curve is generated by averaging 400 electrons sampling the prescribed distribution. Left panel: Spectra scaled to their respective peak values (compare with Fig. 4(a) of Ref. [7]). Right panel: Spectra in physical units.

Figure 4

The number density of the energy spectrum of a Compton gamma-ray beam produced by the head-on collision of a 500 MeV electron with a 800 nm pulsed laser beam, for different relative energy spread of the electron beam ${\sigma }_E$ as in Fig. 4(b) in Ref. [7]. The laser is collimated by an aperture with radius of 16 mm, placed 60 m downstream from the collision point. The horizontal emittance ${ϵ}_x$ is held constant at 0.05 nm rad. Here a Gaussian laser pulse with $\sigma =50$ is used, while the laser in Ref. [7] is CW. Each curve is generated by averaging 400 electrons sampling the prescribed distribution. Left panel: Spectra scaled to their respective peak values (compare with Fig. 4(b) of Ref. [7]). Right panel: Spectra in physical units.

Figure 5

Relationship between the energy spread of the two colliding beams—${\sigma }_{E_e}/E_e$ for the electron beam and ${\sigma }_{E_p}/E_p$ for the incident photon beam—and the energy spread of the scattered radiation ${\sigma }_{E^{\prime }}/E^{\prime }$: analytically predicted from Eq. (47) (red curves) and computed with our code (blue crosses). The parameters of the simulation are 500 MeV electron beam energy with a 800 nm pulsed laser beam, the horizontal emittance ${ϵ}_x=0$. The laser is collimated by an aperture with radius of 16 mm, placed 60 m downstream from the collision point. Each blue point is generated by averaging 1000 electrons sampling the prescribed distribution. Top left: Energy spread of the electron beam is varied; Gaussian laser pulse width is fixed at $\sigma =50$, and aperture at 16 mm, placed 60 m downstream from the collision point. Top right: Energy spread of the laser beam is varied by changing its width in physical space; electron beam energy spread is held constant at ${\sigma }_{E_e}/E_e=0$ and aperture at 16 mm, placed 60 m downstream from the collision point. Bottom: Radius of the aperture $R$ is varied; electron beam energy spread is held constant at ${\sigma }_{E_e}/E_e=0$, photon beam at $\sigma =50$.

Figure 6

Same as Fig. 1, only with varying width of the laser pulse $\sigma$.

Figure 7

Frequency shift between the spectra of Compton and Thomson scattering of a single electron with $E_b=300\mathrm{MeV}$, with a laser pulse with $a_0=0.01$, $\lambda =800\mathrm{nm}$, $s=20.3$, captured by aperture of $A=1/10\gamma$.

Figure 8

Spectra—in both the Compton and Thomson regimes—for the ELI project, with parameters given in Table 3. A total of 10 000 particles were used in generating this spectrum.

Figure 9

A cross section picture of the SRF gun (left) and the SRF double-spoke accelerating cavity (right).

Figure 10

The transverse spot size of the beam as it is focused down into a small spot size.

Figure 11

The beam spot (upper left), longitudinal phase space (upper right), horizontal phase space (lower left), and vertical phase space (lower right) of the electron bunch at the collision point.

Figure 12

Number spectra for the Old Dominion University Compton source with 10 pC electron bunch charge. Left: For apertures $1/40\gamma$, $1/20\gamma$, and $3/20\gamma$, 4,000 particles were used in generating each curve. For aperture $1/10\gamma$, 48 756 particles were used in generating the plot. Right: The same as the panel on the left, except on the log scale.