Cavity geometry optimization

Geometric optimization of normal cells is essential for achieving a high accelerating efficiency. In a linear accelerator, the kinetic energy of an electron gain can be expressed as [13]: $W=\sqrt{Z_{\text{eff}}PL,}$ (2) where Z_eff represents the effective shunt impedance, P represents the microwave power loss, and L represents the longitudinal length. With increasing Z_eff, this accelerator was shortened longitudinally. During cavity geometry optimization, we aimed to obtain the maximum longitudinal shunt impedance. Fig. 2 displays the two-dimensional model used for the geometry optimization. An axisymmetric structure can be realized based on two-dimensional models, and the relative RF characteristic parameters can be determined. Further, this method can significantly reduce the optimization time and hence greatly improve efficiency. Reduced coupling cell length and disk thickness will lead to a dramatically improved effective shunt impedance; however, the cavities will easily deform during processing. The beam pipe radius and nose radius are also critical to the longitudinal shunt impedance. However, a small beam pipe radius and nose radius result in a low capture coefficient because more bunches collide with the beam pipe. Moreover, a small nose radius generates a high BDR, and the stability of the accelerator is weakened. Therefore, appropriate values for these parameters were determined.

Fig. 2Full-screen View

Two-dimensional model of a normal cell constituting an accelerating cavity and coupling cavity.

The π/2 mode was selected as the working mode of the electron linear accelerator for maximal adjacent mode separation and frequency robustness during operation. According to the biperiodic structure theory, to maximize the longitudinal shunt impedance, the coupling cell should have a small volume and a very weak internal electromagnetic field. In our model, the coupling cells are only 1.5 mm in length; therefore, their effective shunt impedance and quality factor can be ignored.

The RF characteristics of the normal cells are presented in Table 2: f_a indicates the frequency of the accelerating cells, f_c represents the frequency of the coupling cells, Z_eff is the effective longitudinal shunt impedance, and Q₀ is the unloaded quality factor.

Design and simulation of cavity chain

As the nose weakens the electric coupling through the beam hole, magnetic coupling was adopted instead. We implemented magnetic coupling slots between the accelerating and coupling cells as portrayed in Fig. 3.

Fig. 3Full-screen View

(Color online) Vacuum model of one normal cell comprising accelerating and coupling cells.

First, the coupling coefficient between cavities was determined. To avoid the subadjacent coupling effect, the adjacent magnetic coupling slots were arranged orthogonally, as shown in Fig. 3. The dispersion equation for a coupled cavity chain can be expressed as [13]: $f_{\phi }=\frac{f_0}{\sqrt{1+k\cos \phi }},$ (3) where k refers to the magnetic coupling coefficient between cavities and φ is the phase shift between cavities. The separation between adjacent modes of the dominant π/2 mode must be considered to provide enough bandwidth between them. To achieve this, k should be 2%–3%, as a large value will lead to a loss of accelerating efficiency [12]. According to our calculations, when k was 2.7%, the adjacent mode separation of 10 MHz was obtained. In bunching cavities, the stored power is inversely proportional to the magnetic coupling coefficient [15]. Thus, for bunching cells, we predesigned a unique on-axis electric field distribution, formed only via modification of the coupling coefficient between bunching cells, to obtain a feasibly high capture rate. The procedure was the same as that for the normal cells described above.

Design of external coupler and waveguide window

To feed RF power into the accelerator, an external coupler comprising a unique coupler cell and an external coupling hole was connected to the rectangular waveguide. A vacuum model of the accelerator with a coupler was built into the CST, as shown in Fig. 4. The results, including the on-axis electric field distribution and S₁₁ parameter, are displayed in Fig. 5.

Fig. 4Full-screen View

(Color online) Vacuum model of cavity chain, external coupler, and waveguide for RF simulation in CST.

Fig. 5Full-screen View

(a) Magnitude of on-axis electric field of accelerating structure. (b) Smith plot of S₁₁ parameter for accelerating structure.

The external coupling coefficient is given by [13]: $\beta =\frac{Q_0}{Q_{\text{e}}},$ (4) where $Q_0$ is the unloaded quality factor of the accelerating structure and Q_e refers to the external quality factor. When the beam current was extremely weak, the optimal external coupling coefficient was 1. However, if the beam loading is nonnegligible, the optimum external coupling coefficient can be calculated by [13]: ${\beta }_{\text{opt}}={\left(\frac{I}{2}\sqrt{\frac{ZL}{P_0}}+\sqrt{1+\frac{I^{2}ZL}{4P_0}}\right)}^2,$ (5) where $I$ is the output beam current, $P_0$ is the input power, and $Z$ and $L$ are the effective longitudinal shunt impedance and length of the accelerator, respectively. According to our design, the output beam current was approximately 100 mA, the average energy was approximately 9 MeV, and the input RF power was 2.4 MW. Consequently, the optimum external coupling was approximately 1.96.

Waveguide windows such as klystrons, magnetrons, and accelerators are widely incorporated in electric vacuum devices. The functions of the waveguide window are to translate RF power with low loss, and provide isolation between the vacuum within the accelerator and the SF6 inside the waveguide. For this accelerator, we optimized and fabricated a waveguide window based on a 2.4 mm-thick quartz dielectric slice, as shown in Fig. 6.

Fig. 6Full-screen View

(Color online) (a) Components of waveguide window system: SF6 (green section) in the waveguide close to the power source and high vacuum (blue section) in the external coupler, separated by quartz slice (gray section). (b) Mechanical design of waveguide window, including copper connector, cooling water pipe, and BJ84 rectangular flange. (c) S parameter plots of waveguide window. Blue and orange lines correspond to S₁₁ and S₂₁. S₁₁ is lower than -20 dB at 9.3 GHz, demonstrating the feasibility of the proposed waveguide window design.

According to classical transmission line theory, when RF breakdown occurs in the accelerator, the terminal is mismatched, and the incident wave is fully reflected. Currently, transmission waveguides contain SW components. The RF window should be positioned far from the antinode of the SW and near the wave node, as indicated in Fig. 7, to reduce the probability of dielectric breakdown on the surface of the quartz window.

Fig. 7Full-screen View

(Color online) Magnitude of SW electric field inside waveguide and coupler when RF breakdown occurs in accelerator and input RF power is fully reflected.

Accelerating electric field buildup time

The field buildup time of an RF structure is closely related to its loaded quality factor. Unloaded quality factor Q₀ of the cavity chain was obtained via CST simulation. The loaded quality factor can be directly calculated using Q₀ and external coupling coefficient β. $Q_{\text{L}}=\frac{Q_0}{1+\beta }$ (6)

Based on the results of the RF analysis, Q_L was calculated as approximately 3055. In the field construction process inside the accelerator, basic parameters, such as the electromagnetic field and input impedance within the structure, change exponentially. In particular, the amplitude of the electric field in the cavity increases exponentially with time, as: $\frac{E}{E_{\text{steady}}}=1-e^{-\frac{{\omega }_{0}t}{2Q_{\text{L}}}}=1-e^{-\frac{t}{t_{\text{F}}}}.$ (7)

Further, at the end of the transient time $4\cdot t_{\text{F}}$, the magnitude of the electromagnetic field was calculated to reach approximately 98% of the steady state. During the electromagnetic field construction, the field distribution is time-varying, reaching 9.0 MeV at the steady state. According to theoretical calculations, there exists an optimal injection time $t_{\text{opt}}$ at which the injected electron beam is stably accelerated to 9.0 MeV and continues after this time [14]. $t_{\text{opt}}=\left(\ln \frac{I}{2}\sqrt{\frac{{\beta }_e{P}_0}{Z{T}^{2}L}}\right)·t_{\text{F}}.$ (8)

We can obtain that $t_{\text{opt}}\approx 2.46\cdot t_{\text{F}}$. Compared with the 10 μs microwave macro pulse width, the transient field buildup time is only 0.27 μs, and can thus be ignored.

Thermal DC gun

We adopted a thermal cathode DC gun as the electron source, constituting a cathode, heating filament, focusing electrode, anode, insulating ceramic shell, and connector to the accelerator. The emission model was simulated using the CST particle module. The emission current at 12.5 kV high voltage is 320 mA, and the perveance is 0.23 μP. The simulation results and basic parameters are shown in Fig. 8, while the basic parameters of the DC gun are listed in Table 3.

Fig. 8Full-screen View

(Color online) (a) Beam simulation of thermal DC gun in CST. (b) Mechanical design of thermal DC gun.

Beam dynamics study

Our design process involved a beam dynamics study using the ASTRA codes. The apertures were carefully set based on the nose position and the radius. We matched the actual accelerating structure and achieved an accurate beam loss calculation. The pulse beam current of 100 mA and capture ratio of 32% were achieved. The results of the beam dynamics calculations are displayed in Fig. 9.

Fig. 9Full-screen View

(Color online) Statistical results of beam dynamics simulation, along the accelerating structure longitudinally: (a) Kinetic energy (blue line) and pulse beam current (orange line); (b) RMS beam spot radius (blue line) and transverse beam emittance (orange line).

The accelerating structure generates weak RF focusing/defocusing on the electron beams during their transit. Depending on the electric field distribution of the symmetric accelerating cell, the electrons were alternately focused and defocused. However, their momentum is greater when the electrons are focused than when they are defocused, leading to an overall focusing effect.

Along the light-speed section, the energy of the accelerating electrons gradually increases, and the space charge force decreases. Benefiting from the RF focusing effect, application of an additional solenoid is unnecessary in our design for reducing the additional space cost and inconvenience. Fig. 10 shows the beam spot and the transverse and longitudinal phase–space distributions at the exit of the accelerator.

Fig. 10Full-screen View

(Color online) Beam information at the exit of the accelerator, for 10⁵ macroparticles during the beam dynamics calculation: (a) Transverse beam spot (dashed line is the beam pipe radius of 1.5 mm); (b) Transverse phase space.

High-power experiment platform and conditioning

The assembled cavity chain, waveguide coupler, and quartz waveguide window were brazed with a silver-based alloy. Subsequently, a cooling water pipe, thermal DC gun, and titanium window were welded to the accelerator structure using an argon arc. After vacuum-leak detection and cathode activation of the thermal DC gun, the accelerator structure was complete, as shown in Fig. 13.

Fig. 13Full-screen View

(Color online) Whole accelerator with all components, including thermal DC gun, titanium window, cooling pipes, and ion pump.

Using the waveguide and titanium windows, the vacuum inside the accelerator tube was sealed and isolated from the SF6 gas in the high-power waveguide transmission system. A CF63 flange was installed to connect to the magnetic spectrometer and measure the energy spectrum of the output beam. A titanium getter pump was welded onto the waveguide to maintain low vacuum in the accelerating structure. The vacuum degree of the accelerating structure should remain lower than 10^-6 Pa. With fixed performance of the thermal DC gun, the corresponding applied high voltage can be adjusted to change the emission current: The emission and pulse beam currents increased as the voltage increased. The mismatch between the initial kinetic energy and accelerating field caused a drop in the capture ratio at excessive voltages (>13 kV). Therefore, we adjusted the high voltage in the range of 12–13 kV for the high-power experiment.

Subsequently, the RF characteristics of the completed accelerator were determined. For this, the reflection coefficient, SW ratio, quality factor, and external coupling coefficient were calculated. An R&S ZVA60 Vector Network Analyzer was employed as the measuring instrument. No significant frequency shift was observed after brazing. The simulation results were slightly higher than the external coupling coefficient of 1.8. The reason for this may be an error in the waveguide port calibration before the cold test, as well as the unsatisfactory electrical contact between the waveguide window and measurement port.

Based on a study on the RF breakdown phenomenon of a high-gradient accelerating structure, we know that the RF BDR is closely related to the accelerating gradient and RF pulse width. The relationship between the BDR, accelerating gradient, and pulse width can be expressed as [19-21]: $\frac{\text{BDR}}{E_{\text{acc}}^{30}{t}_{\text{p}}^5}=\text{const}\text{.}$ (9)

In our high-power experiment, the klystron pulse was long, up to 10 μs, and the ignition rate was high. Moreover, the pulse must be conditioned in advance to reduce the BDR and improve the stability during high-power experiments. The RF power fed into the accelerator was gradually increased. To avoid irreversible damage to the cavity wall, the accelerating structure was fully conditioned to control the BDR below 10^-4 /pulse, with the input RF power of 2.4 MW [22-23].

We built a high-power experimental platform to obtain such results for the accelerator. A compact 2.4 MW X-band high-power multibeam klystron was installed as the RF power source to provide input RF power for the accelerator. The circulator separates the klystron and accelerator, and these components are connected by a waveguide filled with high-pressure SF₆ gas. We installed several directional couplers to monitor the incident wave in the accelerator and the wave reflected from the accelerator. To measure the output beam current, a Faraday cup with an integrated circuit was installed at the exit of the accelerator.

Additionally, a Tektronix DPO4034 oscilloscope was employed to sample electrical signals, including the klystron's emitting current and the collector current of the thermal DC gun, the emission current and high voltage, and the output beam current collected by the Faraday cup. Moreover, the electrical signals were denoised to eliminate high-voltage interference from the high-voltage modulator. A Rode & Schwarz NRP-Z81 power meter was incorporated to measure the incident and reflected wave signals of the accelerator. The beam current waveform, energy spectrum, capture coefficient, and output beam spot size were measured and evaluated during the high-power experiments.

Results of high-power experiment

The signals of the output beam current and high voltage applied to the thermal DC gun were sampled using a Tektronix DPO4034 oscilloscope. Accordingly, the best data are displayed in Fig. 14, for which the pulse width is 9.8 μs, the pulse beam current is 100 mA, and the repetition rate is 50 Hz (i.e., the operating duty ratio is 0.5‰). Because of some mismatch between the klystron and modulator, the input RF power is not strictly flat and decreases slowly with pulse time. This imperfect input RF pulse causes a slight decline in the waveform of the output beam current. The ratio between the output beam current and emission current from the thermal DC gun was regarded as an approximate estimate of the capture ratio. Under the conditions in Fig. 14, the capture ratio of (31.2±0.5)% was determined, which is just below the predicted value of 32%, possibly owing to processing and measurement errors.

Fig. 14Full-screen View

(Color online) Signals of output beam current and high voltage applied on thermal DC gun.

A magnetic spectrometer was installed at the exit of the linear accelerator, as depicted in Fig. 15, to measure the beam energy spread. Further, to reduce the beam spot size and improve the energy resolution, a slit with the length of 38 mm and width of 0.2 mm was inserted at the entry of the magnetic spectrometer during the test. The size of the slit significantly affected the relative brightness of the screen, thereby affecting the energy resolution. With varying magnetic field, electrons with different kinetic energies exhibit unique drifting trajectories. The beam energy spread was evaluated based on the position and brightness of the YAG screen. The energy spectra of the output beams corresponding to different input powers are presented in Fig. 16. For the 2.4 MW input power, the kinetic energy of the output beam was 9.04 MeV and the FWHM of the energy spectrum is approximately 3.5%.

Fig. 15Full-screen View

(Color online) (a) Schematic of energy spread measurement experiment. (b) Image of energy spread measurement setup inside shielding room.

Fig. 16Full-screen View

(Color online) Energy spread measurement results with different input RF power.

A mirror was placed at the angle of 45° to the beamline, and the light was reflected from the YAG screen. A CCD camera with a focusing lens was used to capture images. The CCD camera has a resolution of approximately 50 m/px. The spot size of the output beam was estimated using an image on a YAG screen. The brightness distribution of the images can be used to determine the RMS diameter of the beam because the brightness of the optical transition radiation is proportional to the number of incoming particles. For the input RF power of 2.4 MW and pulse beam current of 100 mA, the beam spot image was captured by the CCD camera, and the calculated RMS radius of the RMS beam spot was approximately 0.5 mm, as depicted in Fig. 17.

Fig. 17Full-screen View

(Color online) (a) Beam spot photo captured by CCD camera. (b) Brightness analysis result post processing.