Combining harmonic generation and laser chirping to achieve high spectral density in Compton sources

Recently various laser-chirping schemes have been investigated with the goal of reducing or eliminating ponderomotive line broadening in Compton or Thomson scattering occurring at high laser intensities. As a next level of detail in the spectrum calculations, we have calculated the line smoothing and broadening expected due to incident beam energy spread within a one-dimensional plane wave model for the incident laser pulse, both for compensated (chirped) and unchirped cases. The scattered compensated distributions are treatable analytically within three models for the envelope of the incident laser pulses: Gaussian, Lorentzian, or hyperbolic secant. We use the new results to demonstrate that the laser chirping in Compton sources at high laser intensities: (i) enables the use of higher order harmonics, thereby reducing the required electron beam energies; and (ii) increases the photon yield in a small frequency band beyond that possible with the fundamental without chirping. This combination of chirping and higher harmonics can lead to substantial savings in the design, construction and operational costs of the new Compton sources. This is of particular importance to the widely popular laser-plasma accelerator based Compton sources, as the improvement in their beam quality enters the regime where chirping is most effective.

Figure 1

Integration of a single scale-free spectrum ${\tilde{D}}_x$ and an electron beam with a 34% energy spread versus the approximation from Eq. (13a) (red line). The inset shows the absolute difference $ϵ$ between the two results. Spectra are computed from scattering a FM Gaussian laser pulse with $\lambda =800\mathrm{nm}$, $a_0=0.587$ off a Gaussian electron beam with $Q=100\mathrm{pC}$ and $E_{\mathrm{beam}}=51.1\mathrm{MeV}$.

Figure 2

Single-electron scattering approximation in Eq. (10) against the exact solution of TDHK2014. Spectra are computed from scattering a FM Gaussian laser pulse with $\lambda =800\mathrm{nm}$, $a_0=0.587$ off a Gaussian electron beam with $Q=100\mathrm{pC}$ and $E_{\mathrm{beam}}=51.1\mathrm{MeV}$.

Figure 3

Backscattered radiation of a laser pulse with $\lambda =1\mu \mathrm{m}$, $a_0=0.707$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, $E_{\mathrm{beam}}=163\mathrm{MeV}$, and 1% FWHM energy spread: FM (red), non-FM (green), and the single electron FM case (normalized to FM) (blue). Top: Gaussian pulse. Middle: Lorentzian pulse. Bottom: Hyperbolic secant pulse.

Figure 4

Maximum amplitude as a function of the energy spread for a laser pulse with $\lambda =1\mu \mathrm{m}$, $a_0=0.707$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, $E_{\mathrm{beam}}=163\mathrm{MeV}$ without FM (blue dots) and with FM (red dots), along with the theoretical limit for the FM monochromatic (${\sigma }_E=0$) beam from Eq. (13a) (solid black line), computed by scale-free integration. Top: Gaussian laser pulse. Middle: Lorentzian laser pulse. Bottom: Hyperbolic secant laser pulse.

Figure 5

Ratio of the maximum photon yield between the FM and non-FM laser pulse as a function of the intensity (and the amplitude of the normalized vector potential $a_0$) for a Gaussian laser pulse with $\lambda =1\mu \mathrm{m}$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, $E_{\mathrm{beam}}=163\mathrm{MeV}$ and 0.1% FWHM energy spread (red dots), 1% (blue) and 10% (green). The leftmost set of points ($a_0=0.27$ or $I={10}^{17}\mathrm{W}/{\mathrm{cm}}^2$) corresponds to the current upper limit of operation of the laser-plasma accelerators [16].

Figure 6

Backscattered radiation of a laser pulse with $\lambda =1\mu \mathrm{m}$, $a_0=1.6$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, 0.1% FWHM energy spread: first harmonic from the collision of the non-FM Gaussian pulse and the 282 MeV electron beam (blue); third harmonic from the collision of the FM Gaussian pulse the 163 MeV electron beam (red).

Figure 7

Ratio of the maximum photon yield between the FM third harmonic from $E_{\mathrm{beam}}=163\mathrm{MeV}$ and the non-FM first harmonic from $E_{\mathrm{beam}}=282\mathrm{MeV}$ as a function of the intensity (and the amplitude of the normalized vector potential $a_0$) for a Gaussian laser pulse with $\lambda =1\mu \mathrm{m}$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, and 0.1% FWHM energy spread (red dots), 1% (blue) and 10% (green). The leftmost set of points ($a_0=0.27$ or $I={10}^{17}\mathrm{W}/{\mathrm{cm}}^2$) corresponds to the current upper limit of operation of the laser-plasma accelerators [16].

Figure 8

Ratio of the maximum photon yield between the FM fifth harmonic from $E_{\mathrm{beam}}=126\mathrm{MeV}$ and the non-FM first harmonic from $E_{\mathrm{beam}}=282\mathrm{MeV}$ as a function of the intensity (and the amplitude of the normalized vector potential $a_0$) for a Gaussian laser pulse with $\lambda =1\mu \mathrm{m}$ off a Gaussian electron beam with $Q=100\mathrm{pC}$, and 0.1% FWHM energy spread (red dots), 1% (blue) and 10% (green).

Figure 9

Backscattered radiation of a non-FM Gaussian laser pulse off a Gaussian electron beam with $E_{\mathrm{beam}}=282\mathrm{MeV}$ (blue) and a FM Gaussian laser pulse off a Gaussian electron beam with $E_{\mathrm{beam}}=126\mathrm{MeV}$ (red). $\lambda =1\mu \mathrm{m}$, $Q=100\mathrm{pC}$, and 0.1% FWHM energy spread.