1.

Introduction

The SHINE facility, located in Shanghai, represents a significant milestone as China’s first high-repetition-rate X-ray free-electron laser (XFEL) facility.¹ During the first phase, the facility established three beamlines, namely, FEL-I, FEL-II, and FEL-III, which cover the photon energy range from 0.4 to 25 keV. In particular, FEL-I is engineered to cover the photon energy spectrum of 3 to 15 keV and consists of three end-stations, including the Hard X-ray Scattering and Spectroscopy End-station (HSS), the Coherent Diffraction End-station for Single Molecules and Particles (CDS), and the Station of Extreme Light (SEL).^2,3 The layout is shown in Fig. 1.

Fig. 1

Optical layout of the FEL-I beamline of the SHINE facility.

As the XFEL advances, more scientists expect to conduct higher-quality scientific experiments in more cutting-edge fields.^4,5 The demand for X-rays with high brightness, high coherence, and ultra-short pulses is increasing.⁶ The energy of X-rays emitted by accelerators is constant, but each beamline typically consists of multiple experimental stations, each with potentially different requirements for X-ray energy.

In particular, during the beamline commissioning, the attenuation of XFEL photon energy can be achieved through a gas attenuator.^7,8 Gas attenuators are located at the front end of the beamline elements and achieve attenuation of X-rays at different orders of magnitude by injecting absorbent gases of various pressures.⁹ Gas attenuators have a negligible impact on the wavefront and coherence properties of the beam and play an essential role in protecting components during beamline commissioning. However, achieving stable attenuation levels with gas attenuators takes a long time, making them unsuitable for selecting beam intensity rapidly during the limited time of experiment preparation for the experimental endstations. In addition, gas attenuators typically achieve only two and three levels of attenuation and cannot be satisfied for beam diagnostics with the required six levels or more attenuation for hard X-rays.¹⁰

On the other hand, a solid attenuator enables rapid modulation of beam intensity through an array of solid attenuator plates, each varying in type and thickness, designed to attenuate the intensity of hard X-rays at various energy ranges. Typically, the construction of a solid attenuator is intended to achieve 10 or more levels of attenuation for the operating photon energy of the experimental endstation, such as the SPB and FXE instruments at the European-XFEL and coherent X-ray imaging instrument at Linac Coherent Light Source (LCLS).^11–13 This capability of the solid attenuator ensures the fulfillment of beam intensity selection for diverse experimental requirements, provides an advantage for the initial configuration of the experimental station, and satisfies the complex technical specification of assorted scientific investigations. Therefore, solid attenuators for XFEL facilities are indispensable.

Through the absorptive capabilities of attenuator plates, the attenuation of beam intensity is achieved, which converts photon energy into heat. The currently operating solid attenuator devices function within the maximum repetition rates of free-electron lasers (FELs). The continuous maximum repetition rate of LCLS is 120 Hz, whereas the European-XFEL operates in burst mode with a maximum pulse train repetition rate of 10 Hz. There have been no significant reports regarding thermal load issues for solid attenuators under these conditions. In the field of high-repetition-rate XFELs, characterized by the high average heat load and short pulse duration, the challenge of heat accumulation becomes particularly significant at the repetition rate of over 1 kHz and could result in thermal damage problems of the attenuator plates, each of which must withstand 1 to 10 W of the average heat load.

Therefore, the selection and arrangement of attenuator plates, the mechanical design of the supporting framework, the method used to mount the attenuator plates to the attenuator arm, and the design of the effective cooling scheme are all critical factors. These considerations are critical for guaranteeing the long-term durability, reliability, and safety of the solid attenuator within the beamline. They are essential for sustaining the consistent performance of the X-ray system under high-repetition-rate operating conditions.

This paper presents a systematic introduction to the physical and mechanical designs of the solid attenuator for the CDS endstation of the beamline FEL-I within the SHINE facility. Simultaneously, the issue of the thermal damage for the solid attenuator was researched, including the theoretical calculation of single-pulse damage, verification of thermal analysis without water cooling at the repetition rate of 1 kHz, and effective thermal managing of the cooling scheme design at a high repetition rate of up to 10 kHz. The solid attenuator design and theoretical verification of the thermal damage played a crucial role in ensuring the stable operation and sustained performance of the solid attenuator in the high-repetition-rate operating conditions of hard XFEL facilities.

2.

Design of Solid Attenuator

The attenuation of beam intensity during the beamline commissioning process is primarily aimed at protecting optical components and minimizing radiation damage. However, the rapid selection of experimental conditions is also necessary to attenuate beam intensity at experimental instruments. Therefore, the beam intensity must be attenuated to more levels, with each level having three stages of fine adjustment. The selection of attenuator plates needs to balance flexibility with strong radiation resistance.

2.1.

Optical Design

The SHINE facility’s hard X-ray beamlines cover a photon energy range of 3 to 15 keV. For effective hard X-ray photo energy attenuation, single-crystal silicon, boron carbide (${\mathrm{B}}_4\mathrm{C}$), and CVD diamonds were selected as optimal attenuator plate materials. In the lower energy range of 3 to 5 keV, both CVD diamond and ${\mathrm{B}}_4\mathrm{C}$ are effective in achieving significant attenuation by adjusting the thickness. Conversely, single-crystal silicon is deployed to attenuate the photon energy for the range exceeding 7 keV. Figure 2 displays the transmittance curves of these three materials across the operating energy range with different thicknesses.

Fig. 2

Transmission of CVD diamond (a), ${\mathrm{B}}_4\mathrm{C}$ (b), and single-crystal silicon (c) plate.

Table 1 shows the combination schemes for attenuator plates; on each axis are seven mounting positions available for clamping attenuator plates, and at least one mounting position of each axis is empty and reserved for maximum attenuation combination schemes.

Table 1

Attenuator combination schemes.

	Axis 1	Axis 2	Axis 3	Axis 4	Axis 5
Position 1	CVD $20\mu \mathrm{m}$	CVD $160\mu \mathrm{m}$	${\mathrm{B}}_4\mathrm{C}$ 1 mm	${\mathrm{B}}_4\mathrm{C}$ 2 mm	${\mathrm{B}}_4\mathrm{C}$ 4 mm
Position 2	CVD $40\mu \mathrm{m}$	${\mathrm{B}}_4\mathrm{C}$ 2 mm	${\mathrm{B}}_4\mathrm{C}$ 4 mm	Si $400\mu \mathrm{m}$	Si $800\mu \mathrm{m}$
Position 3	CVD $80\mu \mathrm{m}$	CVD $100\mu \mathrm{m}$	CVD $200\mu \mathrm{m}$	CVD $400\mu \mathrm{m}$	CVD $800\mu \mathrm{m}$
Position 4	CVD $160\mu \mathrm{m}$	CVD $200\mu \mathrm{m}$	CVD $400\mu \mathrm{m}$	CVD $800\mu \mathrm{m}$	CVD 1.6 mm
Position 5	CVD $200\mu \mathrm{m}$	Si $250\mu \mathrm{m}$	Si $500\mu \mathrm{m}$	Si 1 mm	Si 2 mm
Position 6	Blank	Si $500\mu \mathrm{m}$	Si 2 mm	Si 4 mm	Si 5 mm
Position 7	Blank	Blank	Blank	Blank	Blank

The attenuated intensity of the beam is calculated as

Eq. (1)

$$I_{\mathrm{att}}=\prod _{i=1}^{n=5}{T}_i*I_0,$$

where $I_0$ is the pulse intensity without attenuation and $T_i$ is the transmission of the absorber plate. The precision of the attenuating at every grade is evaluated as

Eq. (2)

$$\mathrm{error}=\frac{I_{\mathrm{att}}-I_0*{10}^{(-\mathrm{grade})}}{I_0*{10}^{(1-\mathrm{grade})}}.$$

Through the theoretical calculation, 10-grade attenuation of each energy point in the optimal combination scheme is achieved, and the error in attenuation intensity grades does not exceed 6%. Fig. 3 shows the error of the attenuator combination at every grade.

Fig. 3

Error of attenuator combination at every attenuation grade.

In the simulation process, it is assumed that the attenuator plate absorbs the photon energy and converts it into heat energy. Therefore, the attenuator plate with the highest absorption rate will withstand the high heat load because it will absorb the most photo energy in every combination.

The thinnest and thickest attenuator plates of three types of material are listed in Table 2, by which the absorption rate is beyond 90%. The thinnest attenuator plates have the highest damage risk by a single pulse, or thermal stress, and severe distortion by multi-pulse accumulation based on the high heat load due to the action of the high absorption rates. The attenuator plates with high damage risk are displayed in Table 2.

Table 2

Absorption rate of the thinnest and thickest plates of three materials.

Thinnest plate	CVD 80  μm	B4C 1 mm	Si 250  μm
Absorption	0.92	0.90	0.99
Thickest plate	CVD 1.6 mm	${\mathrm{B}}_4\mathrm{C}$ 3.2 mm	Si 4 mm
Absorption	0.99	1.00	1.00

2.2.

Mechanical Design

The solid attenuator operates within a high vacuum environment, a necessity due to its integration with X-ray optical elements, where it is imperative to maintain a vacuum level below ${10}^{-6}\mathrm{Torr}$. The central chamber of the solid attenuator features a cylindrical design, accommodating various types of flanges. A significant flange is dedicated to an ion pump, which actively sustains the vacuum degree. The structure includes five arm-inserting flanges; each attenuator arm is equipped with a motorized linear translator situated within the vacuum, coupled with a connecting flange and a copper tube for water cooling. At both the chamber’s forefront and rear, two CF flanges and bellows facilitate connections to the beamline’s conduit. This configuration is illustrated in Fig. 4, showcasing the comprehensive design tailored to ensure optimal performance and vacuum integrity of the solid attenuator within the beamline infrastructure.

Fig. 4

Mechanical scheme of the solid attenuator chamber.

The attenuator arm of the solid attenuator is a critical mechanism for fixing and positioning the attenuator plates into the optical path in a vacuum environment. The design of the attenuation arm is important for implementing an effective clamping scheme and cooling solution for the attenuation plates. This section will detail the mechanical structure design of the attenuation arm.

The main body of the attenuator arm is constructed with 6063-O aluminum alloy, as depicted in Fig. 5. The main framework of the attenuation arm features seven square frames with a size of 22 mm for mounting the attenuation plates. Attenuation plates are secured by square pressure pieces with protrusions on both sides, which can be adjusted and tightened with bolts to satisfy the attenuator plates of various thicknesses.

Fig. 5

(a) Mechanical structure of the attenuator arm. (b) A cross-sectional view shows the connection between the water-cooling pipe and the aluminum alloy frame, with an indium film applied in the contact area.

Water cooling pipes of copper with a diameter of 8 mm are wound around both sides of the main framework. At the top position of the main frame is the cooling pipe designed with a 2R bending radius to meet the requirements of pipe bending technology. On each side of the main frame, the copper pipe is clamped by an aluminum alloy press block with fixed bolts. To enhance the thermal conductivity between the pipes and the aluminum alloy main frame, an indium film of 0.5 mm thickness is applied in the contact area between the cooling pipe and the aluminum frame to fill the contact gap and achieve the optimal heat transfer.

3.

Damage Analysis of the Solid Attenuator under High-Energy Pulse

The physical design of the solid attenuator was carried out based on the design requirements of the CDS. The mechanical design aims to achieve the necessary mechanical performance of the solid attenuator. During the attenuation of high-energy X-rays by the solid attenuator, interactions between the X-rays and the material may result in thermal, optical, or mechanical effects, leading to a rapid temperature rise in localized regions of the solid attenuator. This could cause material melting, evaporation, or micro-structural damage, significantly impacting the stability of the optical performance and material performance of the solid attenuator. Therefore, theoretical verification is conducted to analyze the single-pulse damage and multi-pulse thermal damage of the solid attenuator, ensuring effective X-ray attenuation while maintaining stability in optical performance and material performance. This section provides an in-depth discussion of the analysis of single-pulse damage and multi-pulse thermal damage of the solid attenuator.

3.1.

Single-Shot Ablation Calculation

Because the solid attenuator is the critical device that protects equipment in the end-station from the FEL radiation, the radiation damage resistance evaluation of absorption materials is necessary. A rigorous evaluation criterion is the single atomic energy deposition of the material, defined as¹⁴

Eq. (3)

$$\eta =\frac{E_{\mathrm{photon}}{\sigma }_{\mathrm{abs}}N}{A}.$$

This parameter depends on the atomic absorption cross-section of the absorbing material ${\sigma }_{\mathrm{abs}}$, the irradiated area of the light source $A$, the photon energy $E_{\mathrm{photon}}$, and the number of single-pulse photons $N$. For SHINE’s FEL-1, the light source parameters are a single-pulse energy of 0.9 mJ, and the beam radius ($1/e^2$) is 1.5 mm in the current design. Calculating the single atomic energy deposition curves for the three materials yields the results shown in Fig. 6.

Fig. 6

Single atomic energy deposition of three absorption materials.

The limitation of the atomic energy deposition is the melting dose of the materials, which is calculated as $3k_B{T}_{\mathrm{melt}}$. The thermal properties of the three absorptions are listed in Table 3, and all materials do not exceed the limitation of their atomic energy deposition for the unfocused beam with low fluence.

Table 3

Thermal parameters of the absorption materials.

Materials	Unit	CVD diamond	Si	B4C
Heat conductivity	W/mK	1500	156	39
Heat capacity	$\mathrm{J}/(\mathrm{kg}·\mathrm{K})$	502	703	1000
Density	$\mathrm{kg}/{\mathrm{m}}^2$	3515	2330	2520
Melt point	K	3550	1690	2720
Limitation of atomic energy deposition	eV/atom	0.92	0.44	0.70
Uniaxial yield strength	GPa	1.2	0.124	0.155
Young’s module	GPa	1100	131	440
Poisson ratio		0.07	0.27	0.21
Thermal expansion coefficient	${10}^{-6}$	1.0	2.56	5.6
$T_{\mathrm{crac}}$	K	3043	814	149

The instantaneous pulse irradiation on the attenuator plate causes a temperature rise. The pulse intensity is printed on the plate surface with a Gaussian type, and the highest temperature is in the center and is calculated as¹⁴

Eq. (4)

$$T_{\max }=\frac{4\ln 2Q}{\pi c_p\rho b^2{l}_{\mathrm{abs}}},$$

where $Q$ is the energy of a single pulse, $l_{\mathrm{abs}}$ is the attenuate length along the beam path, and $b$ is the beam’s radius. $c_p$ and $\rho$ are the heat capacity and the mass density of materials, respectively. Figure 7 shows the results. Si has the highest temperature rise at a low photon energy range, which is fit to use at the high energy range of up to 10 keV.

Fig. 7

Highest temperature rise by a single pulse.

The non-uniform temperature distribution causes internal thermal stress. The stress limitation $T_{\mathrm{crac}}$ that will cause material cracking for the heat stress is calculated as¹⁵

Eq. (5)

$$T_{\mathrm{crac}}=\frac{3(1-\nu )G}{\alpha E}.$$

The result is listed in Table 3; ${\mathrm{B}}_4\mathrm{C}$ has the most minor temperature limitation at 149 K. From Fig. 7, the highest temperatures of all energy ranges do not exceed the limitation, which can resist damage from instant thermal stress.

3.2.

Thermal Analysis of the Solid Attenuator in High Repetition Rate

At high repetition rates, X-ray optical devices are subjected to rapid and repetitive exposure to intense X-ray beams, leading to significant high heat generation and thermal cumulative effect within the optical components. The high heat can cause temperature gradients and thermal expansion and even thermal damage to the optical elements. Therefore, thermal analysis is crucial to assess the thermal effects and ensure the optical performance stability and material performance stability of optical devices under high-repetition-rate operation. Through thermal analysis, the temperature and stress of the optical device under high repetition rates were investigated. The thermal damage of the optical device was mitigated by effective cooling design, ensuring the functionality and precision of X-ray optical components in high-repetition-rate applications.

The thermal analysis of the solid attenuator in the condition of the repetition rates of 1 and 10 kHz was primarily conducted by multi-physics analysis. The heat flux of the attenuator plate in the repetition rate of 1 kHz is illustrated in Fig. 8, with the peak value reaching $0.1595\mathrm{W}/{\mathrm{mm}}^2$ and the energy being 0.9 W.

Fig.8

Heat flux density at the center of the attenuator plate.

3.2.1.

Thermal analysis for high repetition rate up to 1 kHz

At high repetition rates up to 1 kHz, the maximum absorbed heat energy by the attenuator plate reached 0.9 W; it was expected that the high-heat issue of the solid attenuator could be addressed through its thermal radiation. The thermal-structural coupling module in Ansys was primarily utilized for the thermal analysis of the solid attenuator in 1 kHz repetition rates. After the theoretical calculation, the thermal simulation results, as displayed in Fig. 9, show that the highest temperature and the maximum thermal stress of three types of solid attenuators in the case of 1 kHz repetition rates were below the allowable value of the material property. In particular, by the solid attenuator ${\mathrm{B}}_4\mathrm{C}$ 1 mm, the highest temperature was reached at 123.6°C, and the correspondent maximum thermal stress was 12.6 MPa, mainly due to the relatively high thermal gradient in the footprint area, low thermal conductivity, and high thermal expansion coefficient of the material property. By contrast, the solid attenuator CVD $80\mu \mathrm{m}$, known for its superior thermal conductivity and low coefficient of thermal expansion, exhibits a maximum operational temperature of 117°C.

Fig. 9

Thermal analysis results of high repetition rates up to 1 kHz.

However, as shown in Fig. 9, all three types of solid attenuators could operate normally up to 1 kHz repetition rate. Through its thermal radiation properties, it was theoretically demonstrated that the solid attenuator plate will not experience thermal damage issues.

3.2.2.

Water-cooling design for high repetition rate up to 10 kHz

When the repetition rate of the X-ray is increased to 10 kHz, the maximum absorbed heat energy by the attenuator plate reached 9 W. Through its thermal radiation, the results of the thermal analysis are shown in Fig. 10; the lowest temperature recorded on the attenuator arm of any solid attenuator without a cooling scheme surpassed 300°C. The heat dissipation capabilities of thermal radiation alone are insufficient to guarantee the stable operation of the solid attenuator. Therefore, an effective cooling scheme for the solid attenuator at a 10 kHz repetition rate was essential.

Fig. 10

Temperature and stress of the solid attenuator in 10 kHz.

At a 10 kHz repetition rate, a water-cooling system with a flow velocity of 0.5 m/s was designed to handle the high thermal load of the solid attenuator. The inlet temperature of the cooling water was precisely maintained at 20°C. To verify the cooling effectiveness of the water-cooling system for the solid attenuator plate at a 10 kHz repetition rate, an analysis with a coupled fluid-thermal-structural-field module in COMSOL Multiphysics was performed.

After the multi-physics analysis, the maximum temperature and thermal stress of the solid attenuator were displayed in Fig. 10; the water-cooling system achieved a good effect of heat dissipation for the solid attenuator under the repetition of up to 10 kHz. In particular, by implementing the cooling scheme, the temperature of the solid attenuator ${\mathrm{B}}_4\mathrm{C}$ was reduced from 469°C without water cooling to 139°C with water cooling, and the maximum thermal stress of the solid attenuators reached 189 MPa. The maximum temperature and thermal stress by all solid attenuators were acceptable and allowed based on the material property. The effective water cooling ensured that the solid attenuator would operate stably at high repetition frequencies.

The theoretical validation of the solid attenuator and water-cooling system designs was conducted through a study on damage issues of the solid attenuator at various repetition frequencies, single-pulse ablation, and thermal analysis of the solid attenuator under the repetition rate of 1 and 10 kHz. The validation ensured the attenuation performance of the solid attenuator while preserving the optical performance stability and material performance of the solid attenuator. All three damage analyses provided theoretical support for the normal operation of the CDS in the FEL-I beamline.

4.

Discussion

A solid attenuator is essential for controlling the light intensity during the experimental preparation phase at experimental endstations. The solid attenuator reduces light intensity by absorbing photon energy through absorption materials and converting it to thermal energy. This means that the attenuation materials may accumulate heat and risk thermal fatigue damage as the pulse repetition frequency increases. It is necessary to design a solid attenuator for the SHINE facility’s FEL-1 experimental station using materials with good thermal properties such as CVD diamond, Si, and ${\mathrm{B}}_4\mathrm{C}$ as attenuation materials. By designing a combination scheme for the attenuator plates, it is possible to achieve up to 10 levels of attenuation capacity within the 3 to 15 keV energy range of hard X-rays, with each level of attenuation achieving better than 6% precision, meeting the requirements of the experimental station. Considering the high repetition modes of the SHINE facility, the mechanical structure of the plate clamping framework and the water-cooling solution were carefully designed to effectively conduct heat from the attenuation plates. Analyzing the thermal load of the attenuator plates and water-cooling system under different repetition conditions is critical. Using the thermal analysis, we examined the temperature and thermal stress distribution of the attenuator under 1 and 10 kHz repetition conditions, obtaining the following simulation results:

According to the current operational planning of the SHINE facility, the preliminary beam commissioning at the experimental endstations will be conducted at low repetition rates to prevent excessive radiation damage to optical components and samples. During the pre-experimental tuning phase, the repetition rate will be increased to approach the experimental frequency, with 10 kHz being the maximum repetition rate for the current experimental endstation will operation. The design of the solid attenuator is capable of meeting the operational requirements of the experimental stations. However, further research is needed on many aspects of the mechanical structure, such as assessing the mechanical stability of the entire attenuator arm when operating in water cooling mode.