Narrowband inverse Compton scattering x-ray sources at high laser intensities

D. Seipt, S. G. Rykovanov, A. Surzhykov, and S. Fritzsche

Phys. Rev. A 91, 033402 – Published 9 March 2015

Abstract

Narrowband x- and $γ$ -ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow one to operate narrowband Compton sources in the high-intensity regime. In this paper we therefore present the theory of nonlinear Compton scattering in a frequency-modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitively this compensation depends on the electron-beam energy spread and emittance, as well as the laser focusing.

Received 8 December 2014

DOI:https://doi.org/10.1103/PhysRevA.91.033402

Authors & Affiliations

D. Seipt^1,*, S. G. Rykovanov¹, A. Surzhykov¹, and S. Fritzsche^1,2

¹Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena, Germany
²Universität Jena, Institut für Theoretische Physik, 07743 Jena, Germany

^*d.seipt@gsi.de

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Vol. 91, Iss. 3 — March 2015

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Images

Figure 1
Compensated energy and angular differential emission probability for nonlinear Compton scattering $d N / d Ω d ω^{'}$ [Eq. (17)] as a function of the normalized scattering angle $γ ϑ$ and normalized frequency of the scattered photons $y = ω^{'} / 4 γ^{2} ω_{0}$ . We consider a high-intensity laser pulse with $a_{0} = 2$ , frequency $ω_{0} = 1.55 e V$ and a Gaussian pulse duration of $Δ = 13 f s$ that collides head-on with an electron beam with an energy of $51 M e V$ . The spectrum is observed perpendicular to the linear laser polarization. The uncompensated nonlinear CS spectrum in (a) shows the typical signature of ponderomotive broadening with very broad spectral lines with a series of subpeaks. In contrast, the compensated spectra in (b)–(d) are much narrower, with the lowest spectral width and the largest peak height occurring at the scattering angle that equals the optimization angle $ϑ_{0}$ , which is marked with an arrow in each panel: (b) $ϑ_{0} = 1 / γ$ , (c) $ϑ_{0} = 0.5 / γ$ , and (d) $ϑ_{0} = 0$ .
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Figure 2
Detail of the frequency spectrum of the fundamental line $(ℓ = 1)$ for compensated nonlinear CS at fixed scattering angles (a) $ϑ = 0$ and (b) $ϑ = 1 / γ$ . The calculation is for the head-on scattering of a linearly polarized laser with pulse duration $Δ = 21 f s$ and $a_{0} = 1$ on an electron beam with initial energy $51 G e V$ . The optimally compensated fundamental lines (black solid curves) for $ϑ = ϑ_{0}$ are much narrower as compared to the uncompensated spectra (red curves) and partially compensated spectra (blue and green dashed curves, respectively), where the optimization angle $ϑ_{0}$ does not coincide with the scattering angle $ϑ$ .
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Figure 3
The normalized frequency $y$ of the largest peak of the compensated fundamental line depends much more weakly on the normalized scattering angle $γ ϑ$ for increasing values of $a_{0}$ , e.g., for (a) $a_{0} = 1$ and (b) $a_{0} = 2$ , and follows the modified angular dependence of the normalized photon frequency (dashed curve) that is given by Eq. (36). The radiation becomes more monochromatic over a larger angular region, as compared to the case of a linear CS, whose frequency-angular correlation is depicted by the dotted curve. Thus, a high laser intensity $a_{0} ≳ 1$ helps to reduce the spectral bandwidth of the compensated nonlinear CS x-ray source when the scattered radiation is collected over a finite collimation angle, e.g., $γ ϑ_{c} = 0.5$ (c).
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Figure 4
Simulated energy and angular radiation spectrum of a realistic electron beam interacting with a focused laser pulse with peak intensity $a_{0} = 2.83$ . The white dashed curve shows the angular dependence of the radiation's energy according to Eq. (36). The solid green line depicts the on-axis line out of the radiation spectrum.
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Figure 5
Comparison of the functional dependence of the optimal frequency modulation $ω (x^{+})$ as a solution of the differential equation for various values of $a_{0}$ for (30) for (a) asymptotic initial conditions and (b) peak initial conditions.
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