Introduction

Gamma rays, which are high-energy photons, possess the inherent advantage of relative insensitivity to strong nuclear forces during nuclear reactions. This characteristic enables a variety of high-precision experiments, such as polarization measurements, studies of weak interaction processes, and investigations into fundamental physics issues such as isospin non-conservation [1, 2].

Polarization is a key characteristic of gamma photons, representing a fundamental quantum degree of freedom analogous to properties such as spin and isospin. For linearly polarized gamma beams, the polarization direction provides essential information by revealing the dependence of the differential scattering cross-section on the relative azimuthal angle between the polarization vector and the production plane. The use of linearly polarized beams significantly simplifies the experimental design by providing an additional observable, enabling effective discrimination between competing transition mechanisms. Circularly polarized gamma photons possess a definite helicity (±1), corresponding to the projection of the photon’s spin angular momentum onto its momentum direction. This well-defined helicity provides unique experimental capabilities. When combined with longitudinally polarized target particles, the helicities of both the beam and target can be employed to prepare an initial state with a precisely defined total angular momentum projection. This control significantly enhanced the precision and information content of the experimental measurements.

There are two main methods for generating polarized gamma beams using accelerators: bremsstrahlung and Laser Compton Scattering (LCS). In the 1950s and the 1960s, several polarized bremsstrahlung gamma beams with photon energies of 10–20 MeV were produced to study the giant electric-dipole resonance in nuclei [3, 4]. Higher-energy bremsstrahlung gamma beams of approximately 350 MeV were also developed to measure the cross sections for pion photoproduction in the 1960s [5]. The first linearly polarized gamma beams, with a polarization degree of the order of 30%–50%, were produced by exploiting the natural polarization of bremsstrahlung when the photons were collimated at a small solid angle away from the direction of the primary electrons [6, 7]. The first polarized LCS gamma beam was achieved in 1987 at the Adone storage ring in Frascati with a laser-electron head on collision, known as the Laser Compton Back Scattering (LCBS) [8]. Gamma beams produced by the LCBS method offer nearly 100% Degree Of Polarization (DOP), combined with advantages such as a small divergence angle, narrow energy bandwidth, and high spectral brightness. Following the early successes at Adone, several polarized gamma beam facilities using this method have been established at several other storage rings, such as ROKK-1M at the Novosibirsk Laboratory in Russia [9], GRAAL at ESRF in France [10], and LEGS at NSRF in the United States [11]. Several gamma LCBS-polarized gamma beams are currently in operation for users. HIγS in the United States can produce 1–100 MeV polarized gamma beams, allowing it to carry out a set of high-precision Nuclear Resonance Fluorescence(NRF) experiments [12]. Meanwhile, GeV-polarized gamma beams are produced at LEPS and LEPS2 at SPring-8 in Japan, contributing to the understanding of nucleon resonance [13, 14].

The Laser Compton Slant Scattering (LCSS) technique offers an alternative method for generating polarized gamma rays. Unlike head-on collisions, LCSS produces photons via Compton scattering between a laser and an electron beam at a collision angle smaller than 180° relative to the electron beam direction. The corresponding incident angles are referred to as slanting incident angles in this paper. The feasibility of the LCSS was first demonstrated in 1996 [15]. More recently, MeV-range polarized gamma beams with high polarization purity and brilliance have been successfully produced via LCSS at 90° incident angles at the UVSOR-III electron storage ring [16-19].

The polarization properties of LCS gamma rays have been theoretically discussed by several research groups. A theoretical analysis of LCBS-polarized gamma-ray properties was performed in HIγS [20], where the integral values of polarization-related variables were provided by an MCCMPT simulation code within the QED framework. Ref.[21] has analyzed the polarization of LCBS X/gamma rays produced in SPARC-LAB device and ELI-NP facility in both classical and quantum schemes. The classical electrodynamics treatment of the photon polarization transfer during the LCSS process in the X-ray Thomson energy region is given in Ref. [22-27]. In UVSOR-III, the polarization properties of LCSS MeV gamma rays generated between a 750 MeV electron beam and an 800 nm polarized laser at a certain slant incident angle of 90° were calculated using the Lienard-Wiechert potentials [17, 18].

The Shanghai Laser Electron Gamma Source (SLEGS) is a new MeV LCSS gamma-ray facility. By adjusting the slant incident angle, in a range from 20° to 160°, between the polarized 10.64 μm CO₂ laser and the 3.5 GeV electron beams in the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF) [28, 29], SLEGS produces polarized gamma rays ranging from 0.66 to 21.1 MeV [30-38]. In contrast to the UVSOR-III gamma rays produced via LCSS at a 90° incident angle, SLEGS is a new class of tunable gamma rays generated using the LCSS process over a wide range of continuously tunable incident angles. The polarization of gamma rays is one of the properties that SLEGS users are most concerned with.

To analyze the polarization properties of the LCSS gamma rays in SLEGS and provide a more explicit representation of the LCSS process, we developed a simulation code based on the QED framework. Using the simulation codes, the polarization properties of the LCSS gamma beam generated by SLEGS, including the spatial and polarization distributions with linearly/circularly polarized lasers, were obtained over a wide range of incident angles. To confirm the reliability of the simulation, the spatial distributions of LCSS gamma rays with a linearly polarized CO₂ laser were measured and compared with the simulation results.

The remainder of this paper is organized as follows: Section 2 presents the theoretical framework for the LCSS process. Section 3 introduces the LCSS setup used in this study. Section 4 presents the simulation results. Section 5 provides a comparative analysis of the simulated and measured results of the proposed model. Finally, Section 6 provides a summary of the study.

Polarization Theory of LCSS mode

2.1

Differential scattering cross sections and gamma ray distribution

The geometry of the LCSS process at the interaction point (IP) in the laboratory frame is illustrated in Fig. 1. The incident electron with momentum p moves along the z-direction. The incident laser photon with momentum k propagates along the direction defined by the angles and . After slant scattering, the scattered photon possesses a momentum k′ directed along the angles and .

Fig. 1Full-screen View

The scattering process of relativistic electrons and laser photons in the laboratory system. and is the azimuthal angle of the incident laser photon, and is the azimuthal angle of the scattered photon, is the angle between the incident laser beam stream and the outgoing gamma beam stream

According to classical electrodynamics and quantum electrodynamics (QED) [39] the scattering process of electrons and photons can be given by (1)where p and k are the four-momenta of the incident electron and photon, respectively, and p′ and k′ are the four-momenta of the scattered electron and photon, respectively. Considering the conservation of momentum and some simple transformations, the energy of the scattered photon E_g can be written as (2)where E_p and E_e are the energies of the incident laser photon and electron, respectively. The relationship between these angles is illustrated in Fig. 1. And is calculated by the formula (3)According to the conclusion in QED, the differential cross section of unpolarized electrons scattering with linearly polarized photons is given as [40] (4)where r_e represents the classical electron radius, P_t is the degree of linear polarization of the incident laser, is the rotation angle of the polarization direction, and mc² is the electron rest mass energy. X and Y are Lorentz invariants, calculated by the formula (5)where s and u are Mandelstam variables calculated by the formula [39] (6)Considering that the phase space of the electron pulse and the intensity distribution of the laser beam have an effect on the distribution of gamma ray beam, the calculation formulas are introduced as follows (7) (8)where the formula for is (9)Here c is the speed of light, p is the electron momentum, is the electron center momentum, and are the angular divergence of the electron in the x and y-direction, are the Twiss parameters of the electron, and are the momentum spread of the electron beam; and k is the wavevector of the laser photon, is the center wavevector of the laser photon, and are the Rayleigh range, energy diffusion, and beam length of the laser beam, respectively.

LCSS setup at SLEGS

The SLEGS was approved in 2016 as one of the 16 beamlines in the Phase II project of the SSRF [41, 42]. The beamline passed the commissioning test in 2021 and was opened to users at the end of 2022 [43]. A schematic representation of the SLEGS is shown in Fig. 2.

Fig. 2Full-screen View

(Color online) Schematic diagram of the SLEGS LCSS mode. (a) Intersection of laser with electron bunch, (b) Configuration of GSM. The gamma beam enters the dark box through the front aluminum window and hits the LYSO crystal of Φ76 mm×2 mm vertically. The camera was mounted at the top of the dark box, perpendicular to the beam direction. To acquire fluorescence from the LYSO crystal, a mirror was inserted into the beam path back to the target at 45° with respect to the beam direction. The inner surface of the dark box has been anodized to prevent fluorescent reflection

The CO₂ laser was 100% linearly polarized and operated in a gated CW mode with an output power range of 0.1–137 W. A 632.8 nm visible He-Ne laser was coaxial to act as a reference beam to align the invisible CO₂ laser. The laser beam then propagates through a laser transport system [44], including a set of plane mirrors and a pair of off-axis parabolic mirrors, to the IP for the LCSS process. A position feedback system consisting of a CCD camera and piezoelectric ceramic driver system was installed at the end of the path. This effectively suppresses the drift and jitter of the laser pointing direction. The total length of the laser transportation path was approximately 25 m.

A rotatable optical system was installed at the center of the C03 section of the SSRF storage ring to introduce the laser into the IP [30]. A 3D structural diagram is shown in Fig. 2. The CO₂ laser beam is vertically injected along the rotation axis through m₄, guided through m₃, m₂ and m₁, and horizontally led to the IP to collide with the electron beam in an angular range of 20°-160°. After passing through the IP, the laser beam was guided through m₀ to a water-cooled laser-beam dump. The parameters of the CO₂ laser and electrons at the IP are listed in Tables 1 and 2.

It can be deduced through geometry that the rotation of the mirror group from the m₃ to the m₁ mirror along the axis leads to the rotation of the laser spot at the IP, which consequently results in the rotation of the polarization direction. The alteration in the direction of polarization was equivalent to the change in the slanting incident angle of the laser.

The gamma beam generated by the LCSS process travels approximately 42 m and passes through multiple collimators before arriving at the experimental station for imaging. A Gamma Spot Monitor (GSM) [45] was used to measure the gamma spot. It consists of a LYSO crystal to generate fluorescence, an optical transmission path, a camera to collect fluorescence, and a data acquisition system. The structure of the GSM is illustrated in Fig. 2(b). The contrast resolution was better than 14%. The spatial resolution of the imaging system was characterized by the modulation transfer function (MTF), which was 6.4 lp/mm.

Simulation results

4.1

Energy distribution

The LCSS energy distribution at IP simulated in three typical slant incident angles of 60°, 90° and 120° is shown in Fig. 3. The results show that as the slant incident angle increases, the gamma-ray spectrum shifts regularly towards higher energies, illustrating the angular dependence of the gamma-ray energy in the LCSS mode.

Fig. 3Full-screen View

(Color online) Simulated gamma-ray energy distributions produced in LCSS mode at the slant incident angles, , 60°, 90° and 120° (normalized)

4.2

Spatial and polarization distribution with linearly polarized laser

Here, we assume that the incident CO₂ laser is fully linearly polarized (100%), with its polarization azimuth oriented horizontally or vertically. It should be noted that in the LCSS process, the azimuthal angle is defined relative to the axis of the laboratory coordinate system.

First, the effects of the shapes of the electron beam and laser, as well as the momentum distribution of the electron beam on the spatial distribution of the LCSS gamma ray, were analyzed. By using Eq. (7) and Eq. (8), calculations of the ideal condition versus the condition including the above-mentioned distribution in the phase space of electron and laser have been carried out in the 180° laser Compton back scattering process. Figure 4 shows the spatial distribution of the simulated gamma rays at the GSM position. The calculation was performed with a 100% linearly polarized incident laser with associated Stokes coefficients equal to 1 and -1, respectively. This shows that the spatial intensity distribution of linearly polarized gamma rays varies with the polarization angle and is azimuthally “symmetric". Figure 5 shows the intensity profiles of the cross-sections taken along the short and long axes, passing through the center of the light spot. From Figs. 4 and 5, the diffusion due to the phase space distribution is not significant compared to the ideal condition. The specific numerical values are summarized in Table 3.

Fig. 4Full-screen View

(Color online) Simulation of fully linearly polarized gamma ray beam spatial distribution. (a) and (c) are horizontally polarized gamma-ray beam spots, (b) and (d) are vertically polarized gamma-ray beam spots. (a) and (b) show the simulation results without considering the phase space of the electron pulse and the intensity distribution of the laser. While (c) and (d) show the simulation results considering the phase space of the electron pulse and the intensity distribution of the laser. The white dashed circle represents the position of the beam spot corresponding to when the scattering angle reaches ,where is the Lorentz factor of the electron beam. The intensities shown in the figures are all relative intensities normalized to 1

Fig. 5Full-screen View

(Color online) Simulation of intensity profiles of cross-sections taken along the short and long axes passing through the gamma ray spot center. The fully ideal case (cyan line) and the cases with laser polarization directions of 90° (red line) and 180° (purple line) after adding the electron position and momentum information. Where (a) is the slice at the short axis of the calculated spot and (b) is the slice at the long axis of the calculated spot

Table 3Full-screen View

Simulation result of spatial distribution with a linearly polarized laser in LCBS

Laser polarization direction Electron phase space distribution	Arbitrary Unconsidered	Horizontal Considered	Vertical Considered
FWHM along short axis (mm)	4.0	4.3	4.0
FWHM along long axis (mm)	7.6	7.8	7.8

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Considering that the electronic phase space and laser intensity distribution do not significantly affect the intensity distribution of the gamma spot, the ideal model was employed to simulate the spatial distribution of polarization. The spatial distribution and polarization distribution in three typical slant incident angles of 60°, 90° and 120° on GSM are systematically simulated and shown in Fig. 6. The three incident angles are 60° (a1-a4), 90° (b1-b4), and 120° (c1-c4). For each angle, the subpanels correspond to the 3D surface plot of the gamma-ray intensity, its 2D pseudocolor representation, and the distributions of the Stokes parameters and .

Fig. 6Full-screen View

(Color online) Simulations for LCSS of a Gaussian CO₂ 10640 nm laser beam with 100% linear polarization on realistic 3.5 GeV electron beam in three typical slant incident angles 60°, 90°, and 120°. (a1), (b1), (c1) three-dimensional intensity gamma beam distribution in the three typical slant incident angles; (a2), (b2), (c2) two-dimensional intensity gamma beam distribution in the three typical slant incident angles; (a3), (b3), (c3) the distributions of the Stokes covariates ; (a4), (b4), (c4) the distributions of the Stokes covariates . All simulation results were calculated in the laboratory frame, and the imaginary position was placed 42 m downstream of the IP

The three-dimensional intensity distribution (Fig. 6a1, b1, c1) and intensity distribution (Fig. 6a2, b2, c2) show that the azimuthally asymmetric linearly polarized gamma ray spots rotate with the slant incident angle. The distributions of the Stokes covariates and for different slant incident angles (Fig. 6a3, b3, c3) suggest that the gamma-ray’s angle of linearly polarization changes with the slant incident angle. The DOP of scattered gamma ray is jointly determined by and , the value is in the ideal condition. From the distributions of the Stokes covariates and (Fig. 6a3, a4, b3, b4, c3, c4), the present simulation shows that the DOP remains almost 1 within the scattering angle of , where is the Lorentz factor. This suggests that the DOP is completely transferred from the incident CO₂ laser photon to the scattered gamma ray and does not show significant changes with different slant incident angles. This result is also consistent with the prediction of Filipescu’s simulation in Ref. [46]. If this conclusion is confirmed experimentally, it implies that highly polarized gamma rays can be produced based on the LCSS process using an incident laser with a high DOP at any slant incident angle.

4.3

Spatial and polarization distribution with circularly polarized laser

To compare with the linearly polarized scenario, a fully circularly polarized CO₂ laser was used in the analysis. Because the SLEGS LCSS process changes the direction of the incident laser polarization in a manner similar to the effect of a 1/2 wave plate, the polarization direction of the scattered gamma rays from the LCSS would not change if a circularly polarized laser was injected at different slant incident angles. The spatial distribution and polarization distribution in a typical slant incident angles of 90° on GSM was simulated and shown in Fig. 7.

Fig. 7Full-screen View

Simulations for LCSS of a Gaussian CO₂ 10640 nm laser beam with 100% circularly polarization on realistic 3.5 GeV electron beam in a typical slant incident angles 90°. (a) the relative intensity gamma beam distribution. (b), (c) and (d) are the distributions of the Stokes covariates , , and , respectively. All simulation results were calculated in the laboratory frame, and the imaginary position was placed 42 m downstream of the IP. The circle formed by the white dotted line is the position, where is the Lorentz factor of the 3.5 GeV electron

The simulation results indicate that the circularly polarized photons undergo a flip in their helicity following slant Compton scattering with unpolarized electrons, for instance, changing from a left-handed circularly polarized laser to a right-handed circularly polarized gamma ray. In the case of a linearly polarized laser, which can be viewed as a superposition of left- and right-handed circularly polarized components, this phenomenon remains concealed.

It is worth noting that as the radius of the beam spot increases, the DOP of circular polarization gradually decreases to 0, takes on the characteristics of linear polarization, and acquires the characteristics of “azimuthal polarization” at the radius corresponding to the critical scattering angle , and then returns to circular polarization if the radius continues to increase beyond the critical scattering angle.

Experiment

Recently, we conducted a test run of the spatial distribution measurement of LCSS gamma rays with a linearly polarized CO₂ laser at SLEGS. The electron beam current was 200 mA, and the CO₂ laser power was approximately 10 W. The incident CO₂ laser was approximately 100% linearly polarized. The aperture of the double collimator system was set to 20 mm and 40 mm for the upstream coarse collimator and downstream fine collimator, respectively, to ensure that the scattered gamma ray beam was not blocked. The spatial distribution were measured at three slant incident angles of 60°, 90° and 120° with the GSM [45]. The background gamma rays were measured by turning off the laser and subtracting them from the images recorded of the total radiation distribution.

Figure 8 shows the measured spatial distributions of the scattered gamma rays in the 2D and 3D frames. Comparing the Figs. 8 and 6, the measured polarization shape and size of the scattered gamma spatial distribution are in general agreement with the simulations, which basically ensures the reliability of the simulation results. A tilt was observed between the measured direction of the gamma beam spot and the simulation results. This discrepancy was attributed to the rotation of the polarization angle in the initial laser optical path setup. The deviation remained consistent across all incident angles, and this stable offset supported this interpretation.

Fig. 8Full-screen View

(Color online) Measured GSM gamma ray image for a 100% linearly polarized CO₂ 10640 nm laser beam slant scattered on realistic 3.5 GeV electron beam in three angles 60°, 90°, and 120°. (a1, b1, c1) Three-dimensional intensity gamma beam distribution at the three slant incident angles; (a2, b2, c2) Two-dimensional intensity gamma beam distribution at the three slant incident angles

A further comparison between Fig. 8 and Fig. 6 shows that the size of the measured spatial distributions of scattered gamma rays is larger than that of the simulated ones for all three slant incident angles. The measured spot sizes are listed in Table 4. The fluorescence of the LYSO crystal in the GSM scattered inside the crystal is inferred to account for the enlargement of the gamma-spot size. The introduced point spread function leads to the extra diffusion of the measured gamma spot. The point spread function (PSF) was measured using the knife-edge method, employing two perpendicularly placed lead bricks to block the gamma-ray spots. The results are shown in Fig. 9, with the PSF obtained through fitting. The obtained PSF was incorporated into the simulation program and compared with experimental results. As shown in Fig. 10, the cross-sectional comparisons of the gamma spot at different positions reveal that while the intensity of the simulated profiles including the PSF is higher than the experimental values, their shape matches the experimental data more closely. In particular, for the cross-section at Y=5 mm shown in subfigure (c4), the simulation result without the PSF drops to nearly zero at X=0 mm. In contrast, both the simulation incorporating the PSF and the experimental results decreased to approximately half of their maximum values.

Fig. 9Full-screen View

(a) Polynomial-fitted curve for selected experimental data regions; (b) Results from the knife edge measurement method

Fig. 10Full-screen View

(Color online) The intensity distribution of gamma spot along different slices: the fully ideal case (“Ideal”, cyan line); the case incorporating electron position and momentum information (“PS incl.”, red line); the case with point diffusion function included (“PDF incl.”, black line); and experimentally measured 90° scattering imaging results (“Measured”, blue line). Where (a1) is the result of the slice at the short axis, and (b1), (c1), (d1), (e1), and (f1) are the slices at distances of 1, 2, 3, 4, and 5 mm from (a1) along the x-axis, respectively. In contrast, (a2) is the result of slicing at the long axis, and (b2), (c2), (d2), (e2) and (f2) are slices at distances of 1, 2, 3, 4 and 5 mm from the y-axis shift at (a2), respectively

Summary and outlook

A simulation code was developed to study the characteristics of gamma beams produced by the novel laser Compton slant scattering mode at SLEGS. The intensity spatial distributions of the LCSS gamma-ray and the corresponding Stokes parameters were calculated by considering both linearly and circularly polarized incident laser cases. The simulation showed that for a linearly polarized laser, the direction of the scattered polarized gamma-ray spatial distribution changed with the slant of the incident angle. The present study also shows that the DOP of the incident photon is almost completely transferred to the scattered gamma rays for an arbitrary slant incident angle at the SLEGS.

A test run of the spatial distribution measurement using a linearly polarized CO₂ laser at SLEGS was conducted. The measured polarization direction and size of the scattered gamma spatial distribution were in good agreement with the simulations. Next, we investigated the direction and degree of polarization at various positions of the gamma-ray spot. Attempts will be made to extract the detailed efficiency of DOP transfer from laser to gamma-ray at different incident angles in the LCSS process using the GSM and other methods.