Deducing the Electron-Beam Diameter in a Laser-Plasma Accelerator Using X-Ray Betatron Radiation

We investigate the properties of a laser-plasma electron accelerator as a bright source of keV x-ray radiation. During the interaction, the electrons undergo betatron oscillations and from the carefully measured x-ray spectrum the oscillation amplitude of the electrons can be deduced which decreases with increasing electron energies. From the oscillation amplitude and the independently measured x-ray source size of $(1.8\pm 0.3)\mu \mathrm{m}$ we are able to estimate the electron bunch diameter to be $(1.6\pm 0.3)\mu \mathrm{m}$.

Figure 1

Three representative electron spectra with peaked features at (a) 67, (b) 79, and (c) 114 MeV. On the left we show raw data from the scintillator screen of the spectrometer and on the right the corresponding energy spectra together with the calculated energy spread.

Figure 2

Normalized x-ray spectra in a range limited by the transmission of a 0.35 mm mylar filter for low photon energy and the reduced detection efficiency of the CCD for high photon energy. The black curve corresponds to the background, the green curve represents the sum of background and betatron radiation. Additionally, we show the transmission curve of a 0.35 mm thick mylar foil in front of the detector (dashed line). The red curve corresponds to the theoretically predicted spectrum convolved with the filter transmission and the CCD response for a betatron amplitude of $r_b=(0.9\pm 0.3)\mu \mathrm{m}$.

Figure 3

(a) Experimentally measured betatron oscillation amplitude $r_b$ as a function of the electron’s $\gamma$ factor. The dashed line is to guide the eye. The arrow indicates the data set mentioned in the text which was used for further evaluation. (b) 3D PIC simulation results showing the number of emitted photons per time interval (blue crosses), the peak-electron energy (green squares) and the relative width of the monoenergetic peak at the end of the electron spectrum (red circles) as a function of time in laser periods. As long as the electron bunch has a narrow energy spread at the maximum electron energy (only plotted above 50 MeV), i.e., before deceleration sets in (for $1250<t<1700$) the largest total number of photons is emitted.

Figure 4

(a) Single-shot x-ray beam profile measured 1.6 m behind the gas jet. The right part of the beam is blocked to measure the background. The horizontal and vertical line-outs of the x-ray beam profile are fitted by a Gaussian distribution (red dashed curve) with an emission cone of 10 mrad. (b) Single-shot shadow image of thin tungsten wires having thicknesses between 10 and $40\mu \mathrm{m}$ (upper image). Shadow of a $10\mu \mathrm{m}$ wire only (lower image). The thinnest wire is still clearly visible indicating an x-ray source size smaller than the wire diameter.

Figure 5

Measured (squares) and simulated (green) intensity distribution of a wire shadow on a detector using Fresnel diffraction for a radiation source with a broadband betatron spectrum ($E_m=6\mathrm{keV}$) and a Gaussian shape for a source size of $\sigma =(1.8\pm 0.3)\mu \mathrm{m}$. The gray area represents the error band of $(\pm 0.3)\mu \mathrm{m}$.