Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to $\gamma$ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray $K$-edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.

Figure 1

Schematic layout of bent multilayer spectrometer used to obtain double differential ICS spectrum in BNL ATF experiments.

Figure 2

Results of calibration tests of spectrometer at BNL NSLS-I X15A (in blue), measured dispersion (photon energy vs radiation angle $x$), displaying a resolution at 7.5 keV central energy of 0.26 keV (rms), as illustrated by Gaussian fit to peak (in red).

Figure 3

(a) ICS photon distribution for 1.5 J laser interaction ($a_L=0.7$), after passage through bent crystal, showing both undiffracted (vertically oriented bright red spot) and diffracted (dispersed) component; (b) higher laser energy case, with 3.0 J and $a_0=1$. Note the curved shape of the diffracted double differential spectrum in both images, as well as the enhanced width due to nonlinear redshifting in the higher laser energy case.

Figure 4

(left) Calibrated ICS DDS data through $2\times 250\mu \mathrm{m}$ Be windows and 65 cm air path, 3 J laser energy case, using bent crystal system, from Fig. 3. (right) Analysis of angularly resolved energy distribution of ICS x-rays from measurement. For a given ${\theta }_y$, high energy and low energy edges (15% integrated intensity) are shown. Predictions of the Liénard-Wiechert calculated spectral intensity are displayed with a color map.

Figure 5

(a) ICS spectrum considering only a longitudinal field variation (maximum photon energy $h{\nu }_{\max }=8.7\mathrm{keV}$, $a_0=1$, maximum redshift 2.9 keV) from probability model (red dashed). Also shown, the ICS spectrum as calculated by the L-W model, which displays self-interference derived oscillations in this spectral intensity. (b) The prediction of the probability model when the transverse field variations are dominant ($\kappa =0$ limit, with $h{\nu }_{\max }=8.7\mathrm{keV}$, $a_0=1$), showing the peak in spectrum at minimum redshift.

Figure 6

ICS spectrum with maximum photon energy $h{\nu }_{\max }=8.7\mathrm{keV}$, $a_0=1$ (maximum redshift 2.9 keV) from probability model convolution of Eq. (6), for varying ratios of laser to electron beam size: $\kappa =0$, 0.25, 0.5, 1, 2, and 4.

Figure 7

(a) Observed near-axis radiation spectrum extracted from DDS image in Fig. 3 (blue dashed line). Also shown, predictions of probability model assuming $U_b=65\mathrm{MeV}$, ${\kappa }^{0.5}=0.75$, $a_0=1$ (red solid line, with predications smoothed to reflect determined Gaussian resolution, per Fig. 2). (b) Simulated spectrum from the L-W calculation with the same parameters, showing self-interference effects (blue dashed line). Also shown, the L-W spectrum smoothed for experimental resolution (red line).

Figure 8

Spectral shape of near-axis multiple-shot radiation, for experimental conditions near to those of Fig. 7.

Figure 9

Theoretically predicted locations of the spectral maximum as a function of $\kappa$ (solid red line). Also shown, the experimentally observed location of the maximum at 8.1 keV, placed to intercept the theoretical prediction (red line) at ${\kappa }^{0.5}\sim 0.82$. Also shown are the upper and lower limits (double lines) on the energy of maximum spectral intensity obtained from the system spectral resolution, $0.70<{\kappa }^{0.5}<0.92$, and the value from electron and laser beam measurements, ${\kappa }^{0.5}=0.75$.