Energy and energy spread measurements of an electron beam by Compton scattering method

A gamma-ray beam produced by Compton scattering of a laser beam with an electron beam can be used to measure the electron beam parameters. In several published works, a simple fitting model has been applied to determine the electron beam energy and energy spread without considering the gamma beam collimation and electron beam emittance effects. This fitting model is rederived in this work, and the underlying assumptions and resultant limitations are discussed. To overcome these limitations, a new fitting model is proposed, which takes into account the collimation and emittance effects. Using the new model and a gamma-ray beam produced at the high intensity $\gamma$-ray sources facility at Duke University, we have successfully determined the electron beam energy with a relative uncertainty of about $3\times {10}^{-5}$ around 460 MeV as well as the electron beam energy spread. We also experimentally demonstrated for the first time that a small relative energy change (about $4\times {10}^{-5}$) of the electron beam by varying the storage ring dipole field can be directly detected using the Compton scattering technique.

Figure 1

Diagram of Compton scattering process. The vectors $\overrightarrow{p}$ and $\overrightarrow{k}$ represent the momenta of the electron and photon before the scattering, respectively. The vectors ${\overrightarrow{p}}^{\prime }$ and ${\overrightarrow{k}}^{\prime }$ represent the momenta of the electron and photon after the scattering, respectively. ${\theta }_i$ is the angle between $\overrightarrow{p}$ and $\overrightarrow{k}$, ${\theta }_p$ the angle between $\overrightarrow{k}$ and ${\overrightarrow{k}}^{\prime }$, and ${\theta }_f$ the angle between $\overrightarrow{p}$ and ${\overrightarrow{k}}^{\prime }$.

Figure 2

The energy spectrum of a Compton gamma-ray beam produced by the head-on collision of a 466 MeV pointlike electron beam with a 789 nm pointlike laser beam. A collimation aperture with radius of 50 mm is placed 60 m downstream from the collision point. The low energy edge $E_{\gamma }^L$ is determined by the collimation acceptance, while the high energy edge $E_{\gamma }^H$ is determined by the electron and laser photon energy. The slope of the spectrum at the high energy edge is denoted as $a_4$.

Figure 3

Calculated energy spectra of gamma beams produced by Compton scattering of a 800 nm laser beam with a 500 MeV electron beam for different radii of the collimation aperture. The aperture is placed 60 m downstream from the collision point, and its radius $R$ is varied from 14 to 4 mm. $\alpha$ is defined in Eq. (17). The horizontal emittance and energy spread of the electron beam are fixed at 0.05 nm rad and $2\times {10}^{-3}$, respectively. (a) Spectra are normalized to the intensities of incident electron and laser beams. (b) Spectra are scaled to their respective peak values.

Figure 4

Calculated energy spectra of gamma beams produced by Compton scattering of a 800 nm laser beam with a 500 MeV electron beam for different horizontal emittances ${\epsilon }_x$ and energy spread ${\sigma }_{E_e}$ of the electron beam. The gamma beam is collimated by an aperture with radius of 16 mm which is placed 60 m downstream from the collision point. The spectra are scaled to their respective peak values. (a) The horizontal emittance ${\epsilon }_x$ of the electron beam is varied from 0.5 to 500 nm rad, while the relative energy spread is fixed at $2\times {10}^{-3}$. (b) The relative energy spread ${\sigma }_{E_e}/E_e$ is varied from $5\times {10}^{-4}$ to $8\times {10}^{-3}$, while the horizontal emittance ${\epsilon }_x$ is fixed at 0.05 nm rad.

Figure 5

Calculated energy spectra of gamma beams produced by Compton scattering of a 800 nm laser beam with a 500 MeV electron beam for different alignment offsets of the collimator. The collimator with an aperture radius of 16 mm is placed 60 m downstream from the collision point. The electron beam energy spread and horizontal emittance are fixed to $2\times {10}^{-3}$ and 10 nm rad, respectively. The spectra are scaled to their respective peak values.

Figure 6

The fit electron beam energy as a function of the relative collimation factor $\alpha$. Both Eq. (16) and Eq. (12) are used for the determination of the electron beam energy. The error bars represent fitting errors. The horizontal line represents the actual energy value of the electron beam used in producing simulated gamma beam spectra.

Figure 7

Schematic of the $\mathrm{HI}\gamma \mathrm{S}$ beam production and measurement at Duke University.

Figure 8

A typical $\mathrm{HI}\gamma \mathrm{S}$ beam spectrum measured by a large volume 123% efficiency HPGe detector. The radiation sources of ${}^{226}\mathrm{Ra}$ and ${}^{60}\mathrm{Co}$ as well as the nature background from ${}^{40}\mathrm{K}$ are used in the real time for the detector energy calibration.

Figure 9

The calibration curve of the HPGe detector. The straight line is a linear fit of the peak energies of the calibration sources.

Figure 10

High energy edges of the measured $\mathrm{HI}\gamma \mathrm{S}$ beam spectra for different storage ring set energy which is increased from 461.06 to 461.14 MeV with increments of 0.02 MeV per step. The inset is the magnified plot around the gamma-ray energy of 5.005 MeV.

Figure 11

An illustration of the fitting on the high energy edge of the measured gamma beam spectrum. The least squares method is used to fit Eq. (16). The goodness of fit is given by the reduced ${\chi }^2$. The fit electron beam energy $E_e$ and relative energy spread ${\sigma }_{E_e}^{\prime }/E_e$ as well as the fitting errors associated with them are also shown in the plot.

Figure 12

Electron beam energy determined by Eq. (16) as a function of the set energy of the storage ring. The set energy has been corrected according to the digital-to-analog converter value which controls a power supply of dipole magnets. The vertical error bars only represent the statistical errors of the electron beam energy measurement, excluding the systematic errors. The straight line is the linear fit of the determined electron beam energies. The slope of the fit line as well as the fitting error associated with it are also shown in the plot.