Introduction

The High Energy Photon Source (HEPS) is a 4th generation synchrotron radiation light source that has been under construction in Beijing since 2019 [1]. The HEPS accelerator system consists of three separate components, which include a storage ring [2], booster [3], and linac [4], as well as three transfer lines [5]. The 49-meter-long linac serves as an injector for the booster. The output beam energy and macro pulse repetition rate of the linac are 500 MeV and 50 Hz, respectively. The linac comprises a gridded thermal-cathode electron gun, a conventional bunching system, 8 S-band constant-gradient traveling-wave accelerating structures, an RF transmission system, a vacuum system, a control system, and a diagnostic system [6].

The linac was designed to meet the requirements of the different operation modes of a light source [4]. There are two basic operating modes: the high-bunch charge mode and high-brightness mode [7]. The high bunch charge mode requires the linac to provide a maximum bunch charge of 7.0 nC at its exit. To meet this requirement, a high transmission efficiency is one of the objectives in the design of the linac. Meanwhile, the electron gun should provide a bunch charge as high as 10 nC, or equivalently, 10 A of current with 1 ns of the pulse full width at half maximum (FWHM). Owing to this high bunch charge mode, the space charge and wakefield effects have received significant attention for the design of linear accelerators in the field of physics [4]. Accordingly, the electron gun was optimized in a high-current scenario. A multi-objective genetic algorithm (MOGA) [8] and EGUN code [9] were introduced to optimize the HEPS electron gun; MOGA is an optimization technique, which is a search method for solving multi-objective optimization-related problems. The gun was optimized under space-charge-limited conditions. The optimal results are presented and discussed in this study.

Considering another scenario, the light source would operate in the high-brightness mode, in which the linac is required to provide a bunch charge over a wide range varying from 0.5 to 7 nC. Therefore, the gun current needs to be adjustable, ranging from 0.5 A to 10 A with 1 ns of the pulse FWHM. The requirements of the HEPS electron gun are listed in Table 1.

To acquire such a wide range of pulse charges, a cathode-grid assembly was employed to adjust the potential difference between the grid and cathode. The grid-limited flow was simulated using the CST tracking solver [10], a popular simulation tool used worldwide. Grid-limited guns are widely used in traditional linacs. Simulation studies regarding gridded thermionic cathode guns have been presented [11-15]. Typical examples of these studies are listed in Table 2, including the gun parameters and simulation methods for grid-limited flows. A 2-D simulation requires an axial symmetry of the grid; however, most grid models do not exhibit an axial symmetry. Therefore, 3-D simulations of the grid-limited flow have been recently adopted owing to the lack of restrictions on symmetry.

The grid of a practical cathode-grid assembly has significantly small internal structural dimensions. For example, the radius of a grid filament can be as small as 0.03 mm. Therefore, gun simulations using grid models are challenging. In this study, the setting details are introduced, including the mesh structures. The simulation results demonstrate that the grid has a significant influence on the beam current, beam blocking rate by the grid, beam emittance at the gun exit, and beam trajectory shapes in the gun. These results are presented and discussed in this study.

The electron gun was manufactured and tested prior to installation in the HEPS linac tunnel, and the test facility and experimental results were presented. The measured data of the grid-limited current is compared with the simulation results.

This study is structured per the following scheme. Section 2 introduces the electron gun system. The gun optimization technique with MOGA under a space-charge-limited flow of 10 A is presented in Sect. 3. The 3-D simulation of the grid-limited flow was performed to analyze the grid effect on the beam, and the results are reported in Sect. 4. The test facility and experimental results of the electron gun are presented and discussed in Sect. 5, which is followed by the conclusions section.

The electron gun system of the HEPS

The electron gun system comprises a cathode-grid assembly, beam-focusing electrode, anode, pulsed high-voltage power supply, filament power supply, pulser, bias power supply, isolation transformer, and control system. Figure 1 presents a schematic of the HEPS electron gun system.

Fig. 1Full-screen View

(Color online) Schematic of the HEPS electron gun system.

A high-voltage power supply, an in-house-developed solid-state modulator, was used to provide a stable high voltage of 150 kV between the beam-focusing electrode and the anode. The solid-state modulator provided a sufficient beam energy, whereas the pulser and DC bias power supply were used to generate the required shape of the beam pulse. To generate the required 1 ns of the pulse FWHM, the pulser and bias power supply were connected in parallel with the cathode and grid. The pulser generated pulsed signals with 1 ns of the FWHM and a magnitude as high as 1 kV. The DC bias power supply is a necessary supplement to generate a well-shaped beam pulse. Typically, the DC voltage generated by the bias power supply has the following two basic functions: 1) it acts as an emission holder when the pulser magnitude is lower than the DC bias voltage; 2) it can eliminate distortion at the base of the pulse. A typical distortion is the tail following the main pulse owing to the impedance mismatch between the pulser and cathode-grid assembly.

The cathode-grid assembly is mainly composed of a cathode and grid. As a typical dispenser cathode, it is heated up to approximately 1000 ℃ to obtain a sufficient emission density by a filament power supply [18]. The grid was constructed as a gridding plane, which was mounted in parallel at a close distance but was isolated from the cathode surface. The cathode-grid assembly, which is a key component of the electron gun system, was carefully selected according to the capability of the emission current and the predicted lifetime of the cathode; type Y796 from CPI [16] was selected owing to its promising emission current, which was higher than 13 A in a short pulse.

Optimization of the electron gun using MOGA

In this section, the MOGA based on NSGA-II [19] is used to optimize a diode gun with a current higher than 10 A under a space-charge-limited flow, corresponding to the high-bunch-charge mode of the HEPS.

The NSGA-Ⅱ can be used to find multiple optimal objectives by searching several individuals, where the individuals are the input parameters for the simulations, and the objectives are the outputs of the simulations. Simulations were performed using the EGUN code, which is an electron optics and gun design program.

Considering the outputs of the EGUN simulation, the following three beam parameters were used as the objectives: a beam current of higher than 10 A, obtaining the 4 times RMS emittance value [20–22] less than 30 mm mrad, and limiting the beam radius at the gun exit to under 8 mm. The objectives of the beam current and emittance are owing to the high bunch-charge mode of the HEPS and the requirements listed in Table 1. To avoid a divergent beam at the exit of the gun, the beam radius at the gun exit is limited to under 8 mm (the radius of the cathode), as one of the objectives. However, the three objectives of the EGUN simulations were not adequate for the final design decision of the HEPS gun. The electric fields on the electrodes are also important for a stable operation of the gun. The electric fields on the electrodes are not included in the output of the EGUN simulation, and therefore are not included in the NSGA-Ⅱ study. For this study, the final design is an artificial selection of the results obtained from the NSGA-Ⅱ study with a compromise of the beam qualities, electric fields on the electrodes, and distance between the electrodes. The surface electric field was calculated by using the POISSON code [23]. Because stability is crucial for HEPS, the maximum electric fields on the electrodes and the distance between the electrodes should be conventional values. A well-used formula $EV ~3.5V^{1.25}$ is used to determine the limit of the surface electric field [24], where E (kV/mm) is the surface electric field and V (kV) is the gap voltage between the electrodes. For the 150 kV electron gun, the surface electric field was approximately 10 MV/m. A pulsed electron gun can have a relatively higher limit of the surface electric field of up to 20 MV/m [24]. The limit of the distance between the electrodes can be determined by referring to the Kilpatrick criterion $\left(\frac{V}{E}\right)E^3{e}^{-\left(\frac{17}{E}\right)}=1800$ [25], where E (kV/mm) is the surface electric field, V (kV) is the gap voltage between the electrodes. For a 150 kV electron gun, the distance between the electrodes should not be less than 17 mm.

As shown in Fig. 2(a), eight geometrical parameters of the electrode are used as individual or decision variables; the parameters are as follows: θ1, θ2, L1, L2, R0, θ3, θ4, and D. L1 and L2, and θ1 and θ2, are the lengths and slope angles of the beam-focusing electrode, respectively, and R0 is the radius of the arc. θ3 and θ4 are the slope angles formed by connecting the lines between the arc center and two arc endpoints, respectively. D is the distance between the cathode and anode. The shape of the anode may also affect the beam quality; however, this is not as critical as the beam-focusing electrode or the distance between the cathode and anode. Therefore, the shape of the anode was treated as a constant in our study. The objective function was edited to restrict the corresponding objectives. A beam current cutoff value of 10 A was defined in the objective function. Solutions above this cut-off value had their fitness unchanged, whereas those below this value were defined as less fit [26]. Similarly, a beam radius cutoff value of 8 mm was defined for the objective function. Solutions greater than 8 mm were defined as having a poor fit and were neglected. In addition, a cutoff curve was defined to avoid areas of solutions that presented a high emittance at the exit of the electron gun. The curve decreased with the generation number because the emittance was expected to decrease as the number of generations increased. Solutions below the cutoff curve had their fitness unchanged, and those above this value were defined as less fit.

Fig. 2Full-screen View

(a) The 8 geometrical parameters of the electrodes as individual, or decision variables. (b) Evolution results of the electron gun optimization. Each point in the same color corresponds to the same generation number.

In the research process using NSGA-Ⅱ, the population size, generation number, and ranges of the decision variables were carefully determined. The evolution results for 20 generations and 200 populations are shown in Fig. 2(b). Each point in Fig. 2(b) represents the result of the EGUN simulation, and the generation of evolution is illustrated using different colors. Blue indicates the initial generation whereas red indicates the final generation. Each point in the same color is a result of the same generation. The results indicate that the emittance converges with the evolution of the generations, and a higher beam current leads to a higher beam emittance.

The results in the region between 10 and 12 A is the area of focus because most results have a 4 times RMS emittance value of lower than 20 mm·mrad. The case with the lowest 4 times RMS beam emittance value and a gun current of 12 A is shown in Fig. 3(a), where the 4 times RMS emittance at the gun exit was as low as 8.6 mm·mrad. However, as shown in Fig. 3(a), this result was not selected for the final design. For an injector linac with mature technologies, an extremely low emittance of the electron gun is unnecessary for the physical design of the linac [27]. Moreover, the closest distance between the electrodes is 13 mm, which is less than the aforementioned limitation. Based on comparison, a gun current of 12 A and a 4 times RMS emittance value of 15.0 mm·mrad was chosen for the final design. Figure 3(b) presents the gun simulation of the final chosen case. Compared to the case shown in Fig. 3(a), the final case had a lower surface electric field. The surface area with an electric field higher than 10 MV was also significantly smaller than that shown in Fig. 3(a). The closest distance between the electrodes was 27 mm, which was far from the aforementioned limitation. With the assistance of MOGA, the 4 times RMS emittance value of the HEPS electron gun is lower than that of a conventional gun; the 4 times RMS emittance value of the BEPCⅡelectron gun [28] is 19.5 mm·mrad under the same gun current of 12 A and beam energy of 150 keV.

Fig. 3Full-screen View

(a) The lowest emittance from the NSGA-Ⅱ study: the 4 times RMS emittance value at the gun exit is 8.6 mm mrad with a beam current of 12 A, the maximum surface electric field on the electrode is 15.8 MV/m, and the closest distance between the electrode is 13 mm; (b) Final design of the HEPS electron gun: the 4 times RMS emittance value at the gun exit is 15 mm mrad with a beam current of 12 A, the maximum surface electric field on the electrode is 12.5 MV/m, and the closest distance between the electrode is 27 mm.

Analysis of grid-limited flow

As indicated in Sect. 1, the HEPS requires the gun current to be adjustable, ranging from 0.5 to 10 A with 1 ns of the pulse FWHM. We attempted to use a cathode-grid assembly to achieve the required adjustment of the current range and short pulses. Therefore, simulations are significant for investigating the effect of the grid on the beam quality.

The grid of a cathode-grid assembly usually has a fine structure. According to the specifications of the Y796 cathode-grid assembly, the grid is constructed by crisscross filaments. The diameter of the filament was as small as 0.03 mm and the distance between the two adjacent filament axes was approximately 0.17 mm. The distance between the cathode surface and the grid plane was approximately 0.20 mm. The area of the Y796 cathode was 2 cm², or equivalently 16.2 mm in diameter. The front view of the grid plane is shown in the upper-left part of Fig. 4, and a magnified view of a fraction of the grid plane is shown in the lower-left. The aforementioned dimensions of the filament and cathode are also presented in Fig. 4. The cutting planes of the cathode and grid are shown in the upper-right part of Fig. 4, and a fraction of the cutting plane is zoomed in and shown in the lower-right part.

Fig. 4Full-screen View

(Color online) The grid structure and mesh condition in CST.

A large mesh number is required to simulate the cathode-grid assembly using CST. In the simulation, a local fine mesh was adopted near the cathode and grid regions. The fine mesh sizes are also shown in Fig. 4. In the transverse dimensions, the mesh size is 0.03 mm, as shown in the left part of Fig. 4. While in the longitude dimension, the mesh size is as small as 0.005 mm near the cathode surface and 0.01 mm near the grid plane, as shown in the right part of Fig. 4. The remaining of the gun body has a coarse mesh, which is 1 mm on the beam-focusing electrode and anode. The grid and focusing electrode are set to a potential of -150 kV while the anode is set to 0 V. The potential at the cathode was set to a value lower than that on the grid. The space-charge-limited model was chosen as the emission model in our simulations.

The perveance is expressed as $I/V^{\frac{3}{2}}$, where $I \left(\text{A}\right)$ is the beam current and $V \left(\text{V}\right)$ is the gun voltage. As shown in Fig. 3(b), for a space-charge-limited gun, the perveance remains constant because $I$ has a linear relationship with $V^{\frac{3}{2}}$, or equivalently the Child-Langmuir law of a diode [24]. While for a grid-limited gun, we assumed that the cathode and grid form a space-charge-limited diode gun. Therefore, in the region between the cathode and grid, the perveance $I_{\text{c}}/V_{\text{g}}{}^{\frac{3}{2}}$ should remain constant, where $I_{\text{c}} \left(\text{A}\right)$ is the beam current upstream of the grid and $V_{\text{g}} \left(\text{V}\right)$ is the potential difference between the grid and cathode. Downstream of the grid, the beam is accelerated and focused until the gun exit, and $I_{\text{b}}$/$V_{\text{b}}{}^{\frac{3}{2}}$ remains a measure of the space charge forces [29], where $I_{\text{b}} \left(\text{A}\right)$ is the beam current downstream of the grid and $V_{\text{b}} \left(\text{V}\right)$ is the potential difference between the anode and focusing electrode.

Figure 5(a) presents the beam currents versus the potential difference between the grid and cathode $\left(V_{\text{g}}\right)$. While the $V_{\text{g}}$ varies from 10 to 200 V, the beam current downstream of the grid $\left(I_{\text{b}}\right)$ varies from 0.5 to 13.7 A, and the beam current upstream of the grid $(I_{\text{c}})$ varies from 0.6 to 22.4 A. The current-blocking rate of the grid increases as $V_{\text{g}}$ increases. Based on the simulation result, once $I_{\text{c}}$ reaches 22.4 A, 39% of the beam is blocked. Figure 5(b) presents the perveance $I_{\text{c}}$/$V_{\text{g}}{}^{\frac{3}{2}}$ versus $V_{\text{g}}$. The perveance $I_{\text{c}}$/$V_{\text{g}}{}^{\frac{3}{2}}$ remained nearly constant as $V_{\text{g}}$ varied from 100 to 200 V. This indicates that the cathode and grid act as a space-charge-limited diode gun only if the potential difference between them is sufficiently high. As part of the complete electron gun, the electric field between the cathode and grid overlaps with a small portion of the electric field generated by the focusing electrode and anode. In particular, when $V_{\text{g}}$ is low, the perveance $I_{\text{c}}$/$V_{\text{g}}{}^{\frac{3}{2}}$ does not remain constant. Figure 5(c) presents a plot of 4 times the RMS emittance values at the gun exit versus $I_{\text{b}}$. The simulation results demonstrate that the grid would have a negative effect on the beam emittance owing to the “lens effect” [11]. The 4 times RMS emittance values of the space-charge-limited gun, which has no grid, is shown in Fig. 5(c) for comparison with the grid-limited flow. The plot of the beam radius at the exit of the gun versus the $I_{\text{b}}$ is also shown in Fig. 5(c). A lower beam current results in a smaller beam radius at the gun exit.

Fig. 5Full-screen View

Simulated results: (a) The beam current upstream of the grid $(I_{\text{c}})$, downstream of the grid $\left(I_{\text{b}}\right)$, and the current blocking rate by the grid versus the potential difference between the grid and cathode $\left(V_{\text{g}}\right).$ (b) The perveance $I_{\text{c}}/V_{\text{g}}{}^{\frac{3}{2}}$ versus the potential difference between the grid and cathode $\left(V_{\text{g}}\right)$. (c) The plot of 4 times RMS emittance values and beam radius at the gun exit versus the beam current downstream of the grid $\left(I_{\text{b}}\right)$.

The beam trajectory in the gun and the zoomed-in beam rays near the grid region are shown in Fig. 6(a), Fig. 6(b), and Fig. 6(c), under the conditions that the beam current downstream of the grid $\left(I_{\text{b}}\right)$ are 11.6, 5.7, and 0.5 A, respectively.

Fig. 6Full-screen View

(Color online) Beam trajectories of the guns and the zoomed-in beam rays at small parts of the grid regions under the potential differences between the grid and cathode of (a) 175 V, (b) 100 V, and (c) 10 V.

The potential difference between the grid and cathode $\left(V_{\text{g}}\right)$ was 175 V, as shown in Fig. 6(a). The overall beam trajectory shown on the left side of Fig. 6(a) is approximately the same as that of the non-grided gun shown in Fig. 3(b). A magnified view of a small portion of the beam rays near the grid region is shown in the right part of Fig. 6(a). This indicates that the beam rays were slightly distorted after the grid.

In the case of the grid-limited flow shown in Fig. 6(b), the $V_{\text{g}}$ was 100 V and the beam current downstream ($I_{\text{b}}$) of the grid was 5.7 A. As shown in the left part of Fig. 6(b), the overall beam trajectory is more convergent compared to the case shown in Fig. 6(a). The perveance of $I_{\text{b}}$/$V_{\text{b}}{}^{\frac{3}{2}}$ was lower, indicating lower space-charge forces. However, the beam downstream of the grid was forced by the same electric focusing force as in Fig. 6(a). Therefore, the beam trajectory downstream of the grid was more convergent. The zoomed-in beam rays are clearly distorted after passing through the grid, as shown in the right part of Fig. 6(b).

In the case shown in Fig. 6(c), $V_{\text{g}}$ is 10 V. The beam trajectory on the left side of Fig. 6(c) is the most convergent of the three cases because the perveance $I_{\text{b}}$/$V_{\text{b}}{}^{\frac{3}{2}}$ is the lowest. The beam rays are significantly distorted after passing through the grid, as shown in the right part of Fig. 6(c).

Upon a comparison of the three cases, the gun current can be varied within the required range by adjusting the potential difference between the grid and the cathode. In addition, a lower emission from the diode results in a more convergent trajectory and greater distortion of the beam rays after passing through the grid. The beam radii at the gun exit are marked on the left side of Figs. 6(a), (b), and (c) for comparison. The distortion of the beam rays is owing to the “lens effect” and leads to an emittance growth [11].

Test bench and test results

The electron gun was manufactured and tested before being installed in the HEPS linac tunnel. The test bench is shown in Fig. 7(a). The electron gun was connected to a vacuum chamber equipped with a beam-focusing coil, a Faraday cup, a sight glass, and an ion pump. The Faraday cup was shifted out of the beamline, and the viewport on the vacuum chamber was positioned opposite to that of the cathode-grid assembly. The current measured using the Faraday cup is shown in Fig. 7(b). The vacuum pressure was maintained at a 1×10^–7 Pa level during the test. The repetition rate of the solid-state modulator and pulser was 50 Hz. The applied net potential difference between the grid and cathode was varied to obtain a variable beam current. However, compared to the simulated $I_{\text{b}}-V_{\text{g}}$ curve, as presented in Fig. 5(a), the measured curve has a lower slope rate.

Fig. 7Full-screen View

(Color online) (a) Photograph of the test bench. (b) Experimental and simulated $I_{\text{b}}-V_{\text{g}}$ curves.

This difference may be attributed to three factors, the first of which may be the dimensional errors of the gap distance between the grid and cathode. To verify this and reduce the simulation time, the complete gun model was reduced to the diode region, including only the cathode and grid. $I_{\text{c}}$ resulted from the diode simulation and $I_{\text{b}}$ was calculated by multiplying the blocking rate. The $I_{\text{b}}-V_{\text{g}}$ curve from the diode simulation nearly agrees with the $I_{\text{b}}-V_{\text{g}}$ curve from the complete simulation; the grid and cathode distance (C-G) was 0.2 mm in both cases. With a C-G of 0.3 mm, the $I_{\text{b}}-V_{\text{g}}$ curve from the diode simulation satisfies the experimental curve only if $V_{\text{g}}$ is below 200 V, as shown in Fig. 7(b). Second, the actual pulser voltage may be different from the indicator on the pulser control panel owing to the impedance mismatch between the pulser and cathode grid assembly. Third, the diode simulation verified that the longitudinal mesh independence was achieved; however, transverse mesh independence was hardly achieved because increasing the transverse mesh would lead to a significant increase in the emission density, which is beyond the capacity of the software.

The experimental results verified that the beam current can be continuously adjusted over a large range by adjusting the potential difference between the grid and cathode. The electron gun is tested for its long-term stability. The peak-to-peak amplitude stability, which is defined as (I_max - I_min)/(I_max + I_min), is measured under different beam currents. The amplitude stabilities are 7.2%, 4.9%, 2.2%, 1.6%, 0.8%, 0.6%, and 0.4% under the beam currents of 0.5 A, 1.0 A, 2.0 A, 4.0 A, 6.0 A, 8.0 A, and 10.0 A, respectively. These are well below the requirement of 10%.

Conclusion

To meet the requirements of providing a large bunch charge with an adjustable range, the electron gun for the HEPS linac was optimized using MOGA under a space-charge-limited flow, and then simulated under a grid-limited flow with a 3-D CST tracking solver. The gun optimization technology with MOGA is suitable for ensuring a specifically required beam quality at the exit of the gun. The 3-D simulation technology was used to research an electron gun equipped with a Y796 type assembly. The influence of the grid on the beam current and beam quality was analyzed through simulations. Adjustment of the current by the grid voltage was experimentally verified. After passing the test, an electron gun was installed on the linear accelerator of the HEPS.