Finite element analyses of a linear-accelerator electron gun
Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.
I. INTRODUCTION
A thermionic electron gun is a key component for the production and acceleration of electrons and positrons in linear accelerators. Because a thermionic electron gun works under high operational temperatures, it is necessary to analyze its operation under thermal load. Any geometrical change as a result of internal temperature distribution could reflect on the output beam parameters1 and potentially degrade the performance of the accelerator. Finite element analysis has been shown to be a valuable tool in performing thermal analyses where the main objective has been the evaluation of thermal quantities such as temperature and heat flux. Thermal stresses arising from high thermal gradients can be directly combined with mechanical stresses by the use of super position in linear analyses, thus providing the total stress which can then be used to determine the stability of the gun.2
For the Beijing Electron Positron-Collider upgrade project3 (BEPCII), a thermionic triode electron gun4 was designed to obtain high emission current and low emittance as per requirements of the collider. As the gun is thermal and has to work under thermal load around 1000 °C for several hours, therefore, it is important to check its performance under hot conditions. A 2D finite element thermal and structural analysis of the BEPCII gun has been reported5 that could not provide a complete scenario because the grid and the anode were not taken into account. This work presents a comprehensive 3D finite element analysis so that the gun could be operated for long duty cycles without any thermal failure to meet the designed beam parameters of the accelerator. A schematic of the gun is shown in Figure 1.
The three dimensional (3D) structural model of the gun was accomplished in Computer Aided Three-dimensional Interactive Application (CATIA)6 and then transported to ANSYS7 software (Version 14) for finite element analysis. Transient thermal and structure modules were used to analyze thermal and structure behaviors under thermal conditions. We calculated the temperature distribution, heat flux, and deformation at all the electrodes and various crucial components of the gun. We also calculated the electron beam trajectories of the gun using the SLAC electron beam trajectory program EGUN8 before and after structural anomalies where emission current and emittance of the beam were measured. Finally, we compared the results of simulation with the experimental values and drew our conclusion in Secs. II–IV.
II. THERMAL AND STRUCTURAL ANALYSIS
After assigning the standard material properties to the components under analysis, the applied temperatures to cathode and anode were 1000 °C and 30 °C, respectively, which set boundary conditions of the problem. The gun attained steady state temperature in 1800 s. We considered conduction as the main source of heat transfer and calculated the temperature distribution. A uniform temperature (1013.4 °C) over the cathode was observed throughout. The increase in temperature (13.4 °C) was due to the internal heat generation of the material. The grid showed a variation of temperature ranging from 934 °C to 1000 °C from the center towards its outer circumference. This distribution was because of the insulator at the edge of this grid that contained the heat and consequently enhanced the temperature at the circumference of the grid.
In the disc, holding the cathode, the temperature of 999 °C appeared on the inner circumference (toward cathode), while it was reduced in the radial outward direction to 693 °C at the outer circumference. This large gradient was due to its bigger volume. Similarly, the inner circumference of the focusing electrode, the temperature was 961 °C, while at the outer edge the temperature was reduced due to larger distance from cathode. However, at the anode the heat intensity was low so that no variation of temperature was seen. Figure 2 presents the temperature distribution on whole electron gun, while Fig. 3 presents the variations of temperatures on different components along with time to reach steady state. Table I presents the temperature and corresponding heat flux values of all components of electron gun in steady state condition.
Temperature distribution on the gun components. The inset describes the temperature at the cathode assembly.
Values of temperature, heat flux, stresses, and deformation on gun components at steady state condition.
| Transient thermal analysis | Transient structural analysis | ||||
|---|---|---|---|---|---|
| No. | Part name | Temperature (°C) | Heat flux (W/mm2) | Stress (MPa) | Deformation (mm) |
| 1 | Full gun | 1013.4 | 6.0042 | 57.17 | 0.16452 |
| 2 | Cathode | 1013.4 | 6.0393 × 10−12 (reference or source) | 14.032 | 0.16452 |
| 3 | Anode | 30.0 | 0.03257 | 0.337 | 0.03250 |
| 4 | Grid (center, outer diameter) | 1000.1, 934.14 | 4.9298, 0.5554 | 16.037 | 0.16452 |
| 5 | Insulator | 1013.4, 915.47 | 6.0042, 0.70596 | 57.17 | 0.12786 |
| 6 | Focusing electrode | 961.59 | 2.9772 | 56.35 | Axial 0.07259; radial 0.10986 |
| 7 | Disc (Outer diameter, inner diameter) | 693.05, 999.44 | 2.8270, 0.00722 | 8.99 | 0.1279 |
Heat flux was extreme in the beginning when 1000 °C was first applied to the cathode and then decreased as the gun approached steady state condition. Simulation results predicted the change in heat flux from 13.32 to 2.98 W/mm2 for the focusing electrodes, 12.95–2.83 W/mm2 for the disc supporting the cathode insulator, 23.82–4.93 W/mm2 for the grid, and 0.00188–0.59 W/mm2 for the insulator between the focusing electrode and the insulating pipe. The maximum heat flux variation over the entire gun, 27.53–6.00 W/mm2, appeared on the insulator supporting the cathode due to maximum radiation and temperature. Figure 3 also presents the variation of heat flux with gun stability time.
After the thermal analysis was completed, structural analyses were performed to predict the structural deformation under defined thermal load. A maximum deformation of 0.165 mm appeared on the cathode and the grid due to the high temperature and internal heat capacity of the material. The high stress area was also subject to high temperatures and heat flux. The insulator reduced the temperature and heat flow but the material expansion behavior under high temperature caused stresses to be transferred. The insulator and focusing electrode faced the maximum stresses (∼57 and 56 MPa), respectively, due to being in-contact with the cathode directly. However, due to better dissipation of heat they did not suffer any remarkable deformation. Similarly, the anode did not face stresses and therefore had no deformation in its structure. The deformation of the components can be seen in Fig. 4. A summary of the thermal and structural analyses at steady state condition is given in Table I.
III. BEAM OPTICS ANALYSIS
The geometrical deformations in different electrodes calculated by the ANSYS were used to define the new dimensions of the gun. We used the selected components (electrodes) only to study the beam dynamics as the rest of the components were beyond the scope of beam profile calculations. The EGUN software was used to simulate the trajectories before and after the defined thermal loads. Figures 5 and 6 give the beam trajectories in cold and hot conditions, respectively, with same input potentials (150 kV at the anode with respect to the cathode and focusing electrode), at the exit of the anode which was at 80 mm from the cathode.4 Table II presents the beam parameters before and after deformation produced by the temperature in the structure of the gun in steady state condition.
Beam characteristics before and after structural deformation.
| Parameters | Cold condition | Hot condition |
|---|---|---|
| Current (A) | 12.066 | 12.121 |
| Maximum emission density (A/cm2) | 14.6 | 14.9 |
| Average emission density (A/cm2) | 5.60 | 5.52 |
| Total emittance (Pi mm mR) | 20.33 | 20.02 |
| Normalized emittance (Pi mm mR) | 16.61 | 16.36 |
| Perveance (μA V−3/2) | 0.2077 | 0.2086 |
It was evident that the gun suffered an insignificant variation in its beam parameters. The calculated emittance was actually very slightly lower in the hot condition. As the cathode and anode changed by an equal numerical amount, there was no impact on the beam dynamics. The electrodes suffered no change in structure in the axial direction where a minute deformation could cause a change in the beam characteristics. Even, the small emittance variation was closer to the experimental values,4 and hence, proved agreement in the test and simulation results of the gun under operational temperature of 1000 °C.
IV. CONCLUSIONS
As evident from the beam optics analysis, it is confirmed that a small variation in structure of the gun may have an adverse effect on the beam quality. Under operational temperature conditions, we only observed radial deformations which were very minute and insignificant in nature. These changes were consistent in the numerical values between the electrodes. Hence, the beam suffered no loss in its characteristics. There were no changes in the axial direction. We calculated the same values of the beam parameters as were the designed requirements of the BEPCII linac gun system. It is very important to study the behavior of the gun in the cold and hot conditions as these are two different frames of reference. At the design stage, the so called cold conditions are to be considered only. A 3D finite element analysis confirms the physical stability and integrity of the components for long duty cycles under the thermal load. The gun is working under its operational temperature of 1000 °C without any thermally induced failures for the BEPCII collider to serve as a charm quark factory (the BESIII collaboration) for basic and applied (synchrotron radiation) research, respectively.
ACKNOWLEDGMENTS
One of the authors (Munawar Iqbal) acknowledges the Chinese Academy of Science, Beijing for providing funding. Thanks are also due to W. B. Herrmannsfeldt from SLAC for his valuable discussions to improve this article.
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