Introduction
Radiotherapy is an effective way to relieve the cancer burden worldwide [1, 2]. In 2014, scientists reported the superiority of using an ultrahigh dose rate (FLASH) for radiating lung tumors in mice [3]. Subsequently, FLASH-RT has become a topic of particular interest in radiotherapy research [4]. Radiotherapy facilities employing different particles, including photons [5, 6], electrons [7, 8], and protons [9, 10], are underway to apply FLASH radiotherapy in clinical settings. Very high-energy electrons (VHEE) are considered potential candidates for realizing FLASH radiotherapy for deep-seated tumors in the near future. VHEE radiotherapy, which was first proposed in 2000 [11], utilizes electrons with energies ranging from 50 to 200 MeV [12] to treat tumors to realize fine conformality and reduce treatment time [13, 14]. In recent years, various VHEE radiation experiments have been performed in linear accelerator platforms [15, 16]. Facilities for the future clinical application of VHEE-FLASH radiotherapy were also proposed by the SLAC National Accelerator Laboratory [8] and the Compact Linear Collider (CLIC) radio frequency (RF) group at the European Organization for Nuclear Research (CERN) in collaboration with the Lausanne University Hospital (CHUV) [17]. A research team at Tsinghua University also proposed a compact VHEE facility based on the developed X-band high-gradient technology.
The layout of the proposed compact VHEE facility is illustrated in Fig. 1. The facility is powered by an X-band 50-MW klystron. A pulse compression device enhances the power from the klystron to 150-MW, 300-ns pulses. The linear accelerator includes a buncher and two X-band high-gradient structures. Electrons from a pulsed direct-current (DC) gun were bunched and accelerated to 100 MeV. This VHEE beamline is supposed to deliver 40-Hz, 24 nC/pulse electrons to generate a dose rate of 40 Gy/s at a field of 6 cm ×6 cm, which can be applied in FLASH radiotherapy research. The pulse compression devices and high-gradient structures have been preliminarily studied [18, 19]. This paper introduces research on a prototype of the buncher.
Linear accelerating structures can be divided into three types: standing-wave (SW), traveling-wave (TW), and backward traveling-wave (BTW) structure. The BTW structure is selected as the buncher in this study for the following reasons: compared with the SW structure, the BTW structure can be operated without a circulator, and its filling time is shorter, which is more favorable in the case with a pulse compressor; compared with the TW structure, the BTW can accomplish transverse bunching without a solenoid. Moreover, the BTW structure exhibits a higher shunt impedance than the TW structure. However, BTW structures are less commonly used than SW and TW structures, and only S-band BTW structures have been reported [20-23]. In this study, we expanded the application of BTW structures to a higher frequency (11.424 GHz, X band).
The remainder of this paper is organized as follows. Section 2 introduces the beam dynamics and RF design of the BTW structure. The fabrication and low-power tests of this structure are presented in Sect. 3. In Sect. 4, detailed high-power experimental results are presented. Finally, the conclusions are presented in Sect. 5. The appendices show the existing and developed methods used in this study. Appendix A introduces the equivalent circuit model and illustrates its applications. In Appendix B, we develop a method for calculating the single-cell parameters from the field distribution using the circuit model. This method can be used to design the X-band BTW structure. In Appendix C, we apply the equivalent circuit model in the time domain, which can be used to calculate the transient beam parameters of a buncher. Appendix D presents the beam dynamics equations used in this study.
Design of the BTW structure
The X-band BTW structure groups the DC electron beam into bunches (via the bunching section) and accelerates them to approximately 8 MeV (via the accelerating section). The length of the buncher structure in a compact VHEE accelerator should be as short as possible. Since the buncher shares the same power supply system with the X-band high-gradient structure, the filling time of the BTW structure should not be longer than that of the X-band high-gradient structure, which is 95 ns [24].
The beam dynamics design of the BTW structure is similar to that of the SW structure and involves the following steps. First, the cavity shape was optimized. After optimization, the electric field distribution along the z-axis of a single cell with different lengths was calculated to construct the field distribution of the entire structure. The constructed field was used to calculate the beam parameters along the structure. The beam parameters at the exit were optimized by adjusting the length and field amplitude of each cell in the bunching section. Finally, the RF design and simulation were performed to realize the optimized constructed field distribution.
The RF design of a BTW-type buncher is different from that of SW and TW bunchers. The developed method for designing a BTW structure is to simulate the RF parameters of each single cell and then calculate the field distribution of the entire structure using the equivalent circuit model [25]. However, this method ignores the influence of the coupling holes when simulating the single cell. In this study, we introduce a method for calculating the parameters of single cells from the field distribution, simplifying the design process of the BTW structure. This method is described in Appendix B.
The cell shape of the BTW structure is illustrated in Fig. 2. A “nose” structure was adopted to improve the shunt impedance. Coupling holes are shaped like “kidneys” to enable convenient fabrication. Because the input power of this structure is much smaller than that of the high-gradient structure, the shunt impedance and quality factor are not as important. Instead, we focused more on the fabrication and tuning, considering that this is the first fabrication attempt of an X-band BTW structure. The working mode of the structure is selected as 5π/6 to make the first several bunching cells longer, which is beneficial for fabrication and tuning. The accelerating gradient of the accelerating section is set to 44 MV/m, with a maximum surface electric field of approximately 200 MV/m, which proved feasible in the high-gradient experiment [18].
An industrial thermionic cathode-diode electron gun was used as the electron source. The parameters of the DC electron gun are listed in Table 1. An ellipse can be used to represent the electrons emitted from the thermionic cathode in phase space. The geometric emittance is the ellipse area divided by π, and normalized emittance is the geometric emittance multiplied by the normalized momentum of the emission electron. The relevant values in optimizing the beam parameters are the capture rate, energy spread, and phase spread. The capture rate determines the pulsed beam current. As an accelerator used in radiotherapy, the energy spread of a buncher should be as small as possible. Moreover, the phase spread produces an energy spread when the high-gradient structures further accelerate the bunches.
| Parameters | Value |
|---|---|
| Perveance (μP) | 0.347 |
| Voltage (kV) | 12.5 |
| Emission current (mA) | 485 |
| Waist radius (mm) | 0.46 |
| Geometric emittance (mm‧mrad) | 32.7 |
| Normalized emittance (mm‧mrad) | 7.26 |
This study uses dynamic equations to calculate the beam parameters, as introduced in Appendix D. The beam dynamics optimization results of the BTW structure are shown in Fig. 3. The average energy of the bunch at the exit is 7.8 MeV, with a capture rate of 32%, as shown in Fig. 3(a) and (b). The root-mean-square (RMS) energy spread is 1.7 MeV, while the RMS phase spread is 13°. During calculation, the electron beam from the DC gun within an RF period is divided into 100 longitudinal slices. Figure 3 (c) shows the phase spaces of each capture slice. The iris radius is 2 mm, and the envelope of the captured electron is within this restriction, as shown in Fig. 3 (d). The relative phase velocity of a single cell (
A 3D electromagnetic simulation was performed using the CST Studio suite [26]. Figure 4(a) shows the vacuum model of the BTW structure. The structure consists of 8 cells representing the bunching section and 16 cells representing the accelerating section, to give a total length of 238 mm. The width of the input waveguide was 10.16 mm to match the BJ-100 standard waveguide; therefore, the last cell was lengthened by 0.73 mm. The width of the output waveguide was 3.31 mm, and a step waveguide was designed to match it with a standard waveguide. The input and output couplers both adopted a quasi-symmetric shape to suppress the dipole field.
The model was simulated using a frequency-domain solver at the working frequency point, through which the field distribution along the z-axis and reflection coefficient at the input port can be obtained. By applying the method introduced in Appendix B, the frequencies of each cell and coupling coefficients of adjacent cells can be derived. After repeatedly adjusting the radius and coupling hole of each cell, the simulated cell parameters of the BTW structure converged to the designed values derived from the optimized field distribution, as shown in Fig. 5. The simulated coupling factors of the input and output couplers were 29.3 and 101, respectively. In contrast, their designed values were 29.7 and 102, respectively. The filling time of the structure calculated using Eq. (17) in Appendix B was 95 ns.
When the simulated cell parameters converged to the designed values, the simulated electric field distribution also converged to the designed value. The 2D field distribution at the cross-section is shown in Fig. 4 (b). The longitudinal field distribution on the z-axis is shown in Fig. 6. The field amplitude distribution is nearly the same as the constructed one with the circuit model, and the phase advance is concentrated on the working mode, 5π/6.
The Simulated S-parameters in CST are shown in Fig. 7. The simulated reflection coefficient at the working frequency is -40 dB, and the transmission loss is -5.1 dB. The S-parameters calculated using the equivalent circuit model are also presented. The S-parameters fit well in the frequency range next to the working point (11.40-11.47 GHz). Relatively obvious distinctions between the CST and circuit models were observed at higher frequencies, possibly owing to fitting errors in the circuit model and the narrowness of the first several cells.
Figure 8 shows the surface electric field, magnetic field, and modified Poynting vector of the BTW structure. Only the input coupler and two cells are shown because the maximum surface fields are located in the acceleration section. The maximum surface electric field was located at the nose of the cells, whereas the maximum magnetic field and modified Poynting vector were located at the coupling hole between adjacent cells. The maximum field values and other parameters are listed in Table 2.
| Parameters | Value |
|---|---|
| Cell radius, Rc (mm) | 7.72-8.80 |
| Cell length, L (mm) | 4.81-10.93 |
| Coupling hole, θ (°) | 15.2-33.4 |
| Quality factor Q | 3600-6500 |
| Shunt impedance, ZT2 (MΩ/m) | 25.8-139 |
| Group velocity, vg | 0.0051-0.021c |
| Filling time, tf (ns) | 95 |
| Pulse width, D (ns) | 230 |
| Cell’s stored energy, u (mJ) | 1.1-15.8 |
| Accelerating gradient, Ea (MV/m) | 43.6 |
| Peak surface, E (MV/m) | 190 |
| Peak surface, H (kA/m) | 720 |
| Peak surface, Sc (MW/mm2) | 3.8 |
| Pulse heating, ΔT (K) | 105 |
| Reflection, S11 (dB) | −40 |
| Transmission, S21 (dB) | −5.1 |
Fabrication and low-power test
A 3D computer-aid design (CAD) model of the BTW structure is shown in Fig. 9. The couplers consist of two halves, each processed by the milling machine. The single cell was processed using a lathe, while its coupling holes, cooling channels, and tuning holes were processed using a milling machine. The tuning pins were brazed in the tuning holes for tuning during low-power measurements. After machining, each part was brazed for further testing.
After fabrication, RF measurements were applied to the structures. Bead-pull field measurements were performed to tune the structure, as shown in Fig. 10. The details of the experimental setup are similar to those in Ref. [18]. According to the nonresonant perturbation theory [27], the electric field is proportional to the square root of the reflection variations in the presence and absence of a perturbing object.
After obtaining the field distribution, the tuning method for nonuniform TW accelerating structures [28] was applied. Based on the tuning method, the frequency of the cells in the accelerating section was approximately 4 MHz below the designed value. Therefore, we tuned the cells by pushing the tuners onto the structure. However, the measurement results showed that the frequency of the first cell (i.e., the output coupler) was approximately 50 MHz lower than the designed value, which was beyond the tuning range. This frequency shift was previously evaluated as a fabrication deviation because of a lack of experience. To reduce the influence of the deviation on this BTW structure, we tuned the cells of the bunching section away from the designed frequencies to counteract part of the reflection from the first cell. This machining fault can be avoided in the future by conducting more detailed checks during the low-power tests.
The field measurement results before and after tuning are shown in Fig. 11. Before tuning, the average phase advance of the accelerating section was 144°. After tuning, this value is about 150°, corresponding to the working mode, 5π/6. Because of the fabrication error of the first cell, the field distribution of the bunching section was different from that of the designed section. We used the measured results after tuning to calculate the beam dynamics, with the capture rate decreasing from 32% to 25%. This is acceptable for a prototype; however, more careful machining and checking should be performed in the future. The S-parameters after tuning are shown in Fig. 12; the reflection on the working frequency is -25 dB, and the transmission loss is -5.1 dB.
High-power test
After the low-power microwave test, the thermionic cathode electron gun was welded to the BTW structure. The structure was then installed and subjected to high-power testing at the Tsinghua X-band high-power test stand (TpoT-X) [29]. The high-power experimental setup is shown in Fig. 13. A previous study tested an X-band two-stage pulse compression system with a correction cavity chain at TpoT-X [19]. The BTW structure was installed at the output of the pulse compression system. The pulse compression system can output a three-time, 230-ns flattop pulse in the one-stage pulse compression mode (with the second compressor detuned). The one-stage output is used as the input pulse for the BTW structure.
An RF waveguide window was installed between the pulse compressor and BTW structure to avoid interference in the vacuum inside the two systems, as shown in Fig. 13 (a). A high voltage was applied to the thermionic cathode using an electron gun power supply. A titanium window was installed at the exit of the structure. The beam was tested and measured under atmospheric conditions.
The structure was conditioned after installation, and the system operated at a repetition rate of 40 Hz. When the vacuum was worse than 1×10-5 Pa or the reflection from the structure was five times larger than the normal one, the auto-conditioning system recorded it as a breakdown event and shut down the microwave source for 30 s. If the structure operated without breakdown for 60 s, the klystron output increased by a set value. After conditioning with 2.2×106 pulses, the BTW structure reached a maximum input power of 5.5 MW. After conditioning, the BTW structure operated with an input power of 5 MW for 4.2×105 pulses, and a breakdown rate of 2×10-4/pulse was recorded. Therefore, the high-power performance of the BTW structure was verified. Subsequently, the thermionic cathode was activated. The measured perveance of the electron gun was 0.315 μP, which is 10% smaller than the designed value. Beam tests were conducted after activation.
The measurement results are shown in Fig. 14. The waveforms obtained during the high-power tests are presented in Fig. 14(a). Among them, the input, output, and reflected waves were measured using a directional coupler, and the beam current was collected by a current collector. The input wave was a 5-MW pulse from a pulse compressor. The output pulse was about 100 ns later than the input pulse. Owing to the dispersion effect, the shape of the output pulse differs from that of the input pulse. The pulsed beam current has similarities with the output wave in terms of transient behavior. Both pulses are magnified and plotted in Fig. 14 (b). The pulsed beam current can be roughly divided into a rising edge (1000-1130 ns), a steady state (1130-1190 ns), and a falling edge (1190-1260 ns), which is in accordance with the output pulse. According to the equivalent circuit model, the output pulse reflects the field in the first cell. Therefore, when the first cell reaches the steady state, the beam current also does. The falling edge of the beam current is earlier than the output pulse because the cells behind the first cell, whose field also influences the bunching process, reach the falling edge earlier than the first cell. The steady state of the beam current is short because of the long filling time and short input pulse. The current waveform calculated from the measured input wave using the time-domain circuit equation introduced in Appendix C is shown in Fig. 14 (b). The calculated pulsed current wave fundamentally fits the measured value; however, any discrepancy between the calculated and measured pulse currents may be due to the inaccuracy of the transient beam loading calculation method.
A bending magnet is typically used to measure the energy of a charged-particle bunch. However, the magnet was too large for installation at the exit of the BTW structure on our platform. Therefore, a series of steel sheets were used to measure the range of the electron beam and calculate its energy. The experimental setup is shown in Fig. 13 (b). The measurement results are shown in Fig. 14 (c). The practical range is 3.95 g/cm2. According to the standard GB/T 25306-2010, the most probable energy source is:
The beam spot was measured using a yttrium aluminum garnet (YAG) screen and recorded using a charge-coupled device (CCD) camera, as shown in Fig. 13 (c). The beam projection image after the pseudo-color processing, the beam density distributions at the x and y cross sections at the beam center (indicated by the green lines), and the Gaussian fitting curves (indicated by the red lines) are shown in Fig. 14 (d). According to the fitting results, the RMS radii of the beam are 1.0 and 0.95 mm in the x and y direction, respectively.
A comparison of the designed and measured values of the BTW structure is presented in Table 3. Considering the loss of waveguide and quality factor degradation of the structure after fabrication, its input power was set to 5.0 MW, which was higher than the design value of 4.6 MW. The accelerating gradient was calculated by dividing the beam energy at the exit by the length of the structure. The measured value was 3% higher than the designed value. The breakdown rate is 2×10-4. A lower breakdown rate must be attained to apply this buncher in a radiotherapy scenario. In the future, rounding the coupling hole should be considered to reduce the breakdown rate. The measured pulsed current was smaller than the designed value because of the decreased capture ratio and electron gun emission. Although the beam parameters, including the current and beam spot, were not as good as the design, the high-gradient and large-current performances of the BTW structure were preliminarily verified. In the future, we will attempt to correct the fabrication error of the output coupler to ensure that the capture ratio is as designed, and the magnetic coupling holes between adjacent cells will be optimized with smooth rounding [22] to improve its high-gradient performance.
| Parameters | Designed value | Measured result |
|---|---|---|
| Input power (MW) | 4.6 | 5.0 |
| Accelerating gradient (MV/m) | 43.6 | 45.0 |
| Breakdown rate (/pulse) | - | 2×10-4 |
| Capture ratio | 32% | 25% |
| Current (mA) | 155 | 108 |
| Energy (MeV) | 7.8 | 8.0 |
| rx (RMS) (mm) | 0.69 | 1.0 |
| ry (RMS) (mm) | 0.69 | 0.95 |
Conclusion
This study presents the prototype X-band BTW accelerating structure for future very high-energy electron radiotherapy facilities. A method for calculating the parameters of single cells using field distribution was derived to simplify the design process. The BTW structure was simulated and designed in the CST using this method after dynamic beam optimization. The simulated field distribution fits well with the constructed distribution. A time-domain circuit equation was applied to analyze the transient beam parameters of the buncher in the unsteady state. The BTW structure was fabricated at Tsinghua University and high-power tested at the Tsinghua X-band High-power test stand. The structure was powered with 5-MW microwave pulses from a pulse compressor, with an average gradient of 45 MV/m. The electron bunches were accelerated to 8 MeV with a pulsed current of 108 mA. Both the high-gradient and large-current performance of the BTW structure were proven preliminarily in the high-power experiment.
Expanding global access to radiotherapy
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