Nonlinear inverse Compton scattering

Inverse Compton scattering (ICS) is an attractive pulsed radiation sources in the X- to gamma-ray spectral regions with photon energy of 4γhνL, where γ is the electron beam Lorenz factor and hνL is the incident laser’s photon energy. This blue shifting is owed to a relativistic Doppler effect. At the BNL Accelerator Test Facility, use of TW class relativistically-intense, long wavelength, CO2 laser of peak normalized vector potential aL~1 with 50-70 MeV electron beams enables investigation of nonlinear effects associated with the relativistic figure-8 motion due to the significance of v×B term in the Lorentz force under the strong laser fields (Figure 1).

Rigorous studies on the multi-photon process of 2nd , and 3rd harmonic generation [1], based on the spectral study using a K-edge [2] and single shot diffraction from Si crystals in the linear regime [3] has been conducted. As a clarification of the existence of the phenomena, observation of the double differential spectrum of nonlinear ICS using a Si-Mo multilayer curved grating [4] has been successfully done as follows.

The curved grating consists of 45 identical layers of Si/Mo with d ≈ 3-4 nm having curvature of 2.5 m. Dispersion of ICS X-ray at energy of >5 keV is observed on the KBr coated MCP screen through two Be vacuum windows of 250 μm and ~1 m air path. In the experiment, TW CO2 laser with stable, solid state seed system having a wavelength of 9.25 μm is collided by a 61 MeV, 300 pC, ~3 ps electron beam to give a Compton edge of 7.6 keV, corresponding to the Bragg angle of ~25 mrad.

Figure 3 shows the observed double differential spectrum (∂^2 I)/h∂ν∂x ∂ for an approximate total energy of the laser 1.5 J (left) and 3.0 J (right), respectively. For the 1.5 J case, a relatively narrow band linear ICS spectrum has been verified. Note that the crescent shape of the double differential spectrum nicely represents off-axis relativistic red-shifting according to the undulator equation hvX-ray ≈ 4γ2hvL /(1+γ2θ2). In the 3.0 J cases, the estimated photon number generated at I.P. is estimated to be approaching ~109.

As a consequence of higher laser field, the mass-shift effect due to the nonlinear motion under laser illumination is observed as broader width of photon energy spectrum for the 3.0J case. These experimental results contribute to the understanding of the intense monochromatic ICS X-rays or high order harmonic production, as well as strong field physics itself.

Figure 4. (left) Calibrated ICS DDS data through 2X 250 mm Be window and 65cm air path, 3 J laser energy case, using bent crystal system. (right) Analysis of angularly resolved energy distribution of ICS X-rays from measurement. For a given , high energy and low energy edges (15% integrated intensity) are shown. Predictions of the Lenard-Wiechert potential numerical calculation generated on the observation screen emitted from the moving electron beam is shown in color map.

In fact, the figure of 8 motion induces harmonic radiation of Compton X-ray. These can be observed as a unique radiation pattern as shown in Fig. 5 through high energy metal spectral filters.

Figure 5. Observed ICS 2nd and 3rd harmonics at MCP with the laser parameter 0.5 < aL < 0.7 with: (a) narrow-band transmission through 20 µm Au foil giving the characteristic shape of the ICS 2nd harmonic; (b) transmission through 250 µm Al foil showing the superposition of 2nd and 3rd harmonics; and (c) 1000 µm Al foil effectively transmitting only 3rd and higher harmonics. Contrast has adjusted for the rendered color MCP image. Line-out profiles correspond to the line y = 0, giving the normalized intensity distributions measured.

In other words, counter collision of an electron beam and circularly polarized laser should induce a photon having Orbital Angular Momentum which has a ring, or donuts, shape radiation distribution due to the significant Helical election motion.

OAM light at photon energy of X-ray to Gamma Ray regime has a special interest for future optical probe of angular momentum in Nuclear Photonics community suggested by our Japanese collaborators [5].

As a feasibility study for actual application, high duty cycle inverse Compton scattering X-ray source recirculated ICS [6] was investigated together with advanced accelerator schemes such as demonstration of an inverse free electron laser acceleration-driven Compton scattering X-ray source [7], or cryo-cooled high gradient copper linac in the same context of Ultra Compact Free Electron Laser development. Hard X-ray generation at up to 100 keV range using an infrared, shorter wavelength laser, are under active examination for medical and material research the of which are included in the on going construction project of the MITHRA Lab [8].

Meanwhile, as an further extension of strong field physics owing to the upgraded 5 TW CO2 laser in BNL, experiments on demonstration of relativistic nonlinear motion induced by inverse Compton scattering using two laser wavelengths are being conducted utilizing YAG laser and a CO2 laser [9] at scattered photon energy of 87 keV.

  1. Y. Sakai et.al., Observation of redshifting and harmonic radiation in inverse Compton scattering, Phys. Rev. ST Accel. Beams 18, 060702 (2015), https://doi.org/10.1103/PhysRevSTAB.18.060702
  2. O. Williams et al., Characterization resultsof the BNL ATF Compton X-ray source using K-edge absorbing foils, Nucl. Instrum. Meth. A 608, S18 (2009) https://doi.org/10.1016/j.nima.2009.05.166
  3. F. H. O'Shea et al., Single shot diffraction of picosecond 8.7-keV x-ray pulses, Phys. Rev. ST Accel. Beams 15, 020702 (2012) https://doi.org/10.1103/PhysRevSTAB.15.020702
  4. Y Sakai et al, Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime, Physical Review Accelerators and Beams 20 (6), 060701 (2017) https://doi.org/10.1103/PhysRevAccelBeams.20.060701
  5. Yoshitaka Taira, Takehito Hayakawa & Masahiro Katoh, Gamma-ray vortices from nonlinear inverse Thomson scattering of circularly polarized light, Scientific Reports volume 7, Article number: 5018 (2017) https://doi.org/10.1038/s41598-017-05187-2
  6. A Ovodenko, High duty cycle inverse Compton scattering X-ray source Applied Physics Letters 109 (25), 253504 (2016) https://doi.org/10.1063/1.4972344
  7. I Gadjev, N Sudar, M Babzien, J Duris, P Hoang, M Fedurin, K Kusche, ... An inverse free electron laser acceleration-driven Compton scattering X-ray source, Scientific reports 9 (1), 1-10 (2019) https://doi.org/10.1038/s41598-018-36423-y
  8. Y. Sakai et. al., “INTRODUCTION OF WESTWOOD LINEAR ACCELERATOR TEST FACILITY IN UNIVERSITY OF CALIFORNIA LOS ANGELE”, 132th Int. Particle Acc. Conf. IPAC2021--TUPOPT03 WEPAB056 (2022) https://accelconf.web.cern.ch/ipac2022/papers/tupopt035.pdf
  9. Y Sakai, Harmonic radiation of a relativistic nonlinear inverse Compton scattering using two laser wavelengths, Physical Review Special Topics-Accelerators and Beams 14 (12), 120702 (2011) https://doi.org/10.1103/PhysRevSTAB.14.120702
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