A proton beam energy modulator for rapid proton therapy

Radiation therapy is an effective treatment to cancer, either by itself or in combination with other treatment methods. During the process of radiation therapy, high energy beams of photons or protons deposit energy in tissues via atomic or nuclear interactions. The deposited energy can potentially eradicate cancerous tissues, but it can also damage cells in healthy organs as well. The key figure of merit in radiation therapy, the therapeutic ratio,^1,2 describes the trade-off between the possible treatment benefits of tumor eradication and the complications in healthy organs.

A high therapeutic ratio can be expected in proton therapy due to the favorable feature of the proton Bragg peak³ on the Bragg curve depicting the rate of ionizing radiation loss when a beam travels through matter as a function of distance. The Bragg curves of protons in the radiotherapeutic energy range have been simulated and measured,^4,5 where the Bragg peaks occur at the end of the range right before the protons come to a stop, indicating a well-localized radiation energy deposition. This feature enables precise and concentrated dose delivery at the tumor location, so healthy organs nearby can receive much less dosage, thus improving the therapeutic ratio.

A three-dimensional beam scanning system plays a key role in precise proton therapy.^6–8 In the two transverse directions with respect to the beam propagation direction, scanning is often done by deflecting the beam trajectory with magnets. In the longitudinal direction, scanning is done by modulating the beam energy as the Bragg peaks are located at different distances in matter for proton beams of different energies.

In conventional proton therapy machines, beam energy modulation is performed by inserting passive energy degrading absorbers of different thicknesses in steps;^6–8 as a result, the modulation process driven by motors is slow. The use of the passive energy modulation method limits the capabilities of the proton source and beam delivery system and increases the treatment time so that the treatment results are more susceptible to organ motion. At the same time, the passive energy modulators also introduce an increase in the energy and momentum spread in the proton beam or distort the beam shape, compromising the outcome of the treatment plans. Therefore, a fast and active beam energy modulator is desirable in the development of proton therapy machines.

The linear accelerator (linac) solution for proton beam scanning has been proposed and investigated in recent years.^9–15 In these approaches, energy modulation happens before or on the gantry over long distances and is limited by the rate of change for the electromagnets on the gantry. Here, we present a new approach for rapid energy modulation and scanning by individually coupled radiofrequency (RF) cavities inserted after the final bend of the gantry. The individual coupling scheme makes it possible to design fully optimized cavities for a high shunt impedance while the peak electric field and magnetic field are minimized to reduce the RF breakdown probability at a high operating gradient. The compact high-gradient structure makes it easy to insert the energy modulator module into existing proton therapy devices, such as cyclotrons. Another unique advantage of our approach is that with the RF energy modulator running at a high repetition rate, the accelerating or decelerating gradient can be tuned for each pulse by changing the amplitude and phase of the klystrons¹⁶ that drive the linac. In this way, the proton beam energy can be changed rapidly to achieve active depth scanning.

This paper is structured as follows: Section II presents the full rapid proton beam delivery system that includes the rapid energy modulator. The system design demonstrates the feasibility of the our approach. Section III presents the S-band energy modulator cavity design with multi-physics simulation results, including RF simulations, beam dynamics simulations, and thermal simulations. A single-cavity prototype has been designed, fabricated, and tested. Section IV presents the structure fabrication and the RF measurement results. Section V presents conclusions and future work.

A schematic of the rapid proton beam delivery system using RF cavities is shown in Fig. 1, with a proton source, a gantry with three bending magnets, an RF energy modulator, and an RF beam deflector. The goal of such a system is to deliver a proton beam that covers a scanning area of 25 × 25 cm² with a depth variation of 12 cm within 1 s for a dose of 50 Gy/L/s.

Such a system design can be adapted to various proton sources with different beam energies. Here, we choose the proton source to be a 150 MeV cyclotron, which is commercially available. A scanning depth variation of ±12 cm can be achieved with ±30 MeV energy modulation on the 150 MeV beam. Note that the bunch length of the proton beam generated by a cyclotron is normally on the order of a few tens of millimeters, which is longer than what can be effectively manipulated by S-band RF cavities. Therefore, a bunch compressor is needed to shorten the beam before the energy modulator section. The bunch compression can be introduced by a lower-frequency cavity at the zero crossing point of the cavity voltage. An acceptable bunch length into the energy modulator is evaluated by beam simulations, which will be explained later in this paper, to achieve a small energy spread after the energy modulator.

The proton beam gets transported to the gantry comprised of permanent or superconducting magnets to bend the beam trajectory. The gantry is designed to have an energy acceptance of ±3 MeV, while the typical energy spread of the initial proton beam is an order of magnitude smaller. Beam trajectories are shown in Fig. 1 for 153 MeV and 147 MeV through three 1.5 T bending magnets.

After the gantry, the beam enters the energy modulator to change the depth of the delivered dose. It is also required that the beam be rastered in the transverse plane to provide a full coverage of the target. This approach is compatible either steering with electromagnets or an RF deflector. We intend to develop and implement this approach with an RF deflector to match the timescale of our energy modulation and maximize the dose rate delivery. This paper focuses on the design and experimental test of the energy modulator.

We choose fully optimized elliptical cavities¹⁷ for the energy modulator. The geometry of a single cavity with dimensions is shown in Fig. 2. We performed the following simulations on the cavity: RF simulations to study the accelerator performance, beam dynamics simulations to study the beam phase space evolution in a 50-cell energy modulator structure, and thermal simulations to study the temperature rise when the structure is pulsed.

Eigenmode simulations were performed with periodic boundaries assigned at the two ends of the single cavity. The operating mode we chose is the fundamental transverse magnetic (TM) mode of the cavity to provide an intense interaction with the proton beam. The optimization goal in the RF design is to maximize the shunt impedance to increase the accelerating gradient with a given input power while minimizing the surface electric and magnetic field to lower the probability of RF breakdowns. The cavity period, 2.36 cm, corresponds to 160° of phase advance per cell for the 150 MeV proton beam. When the phase advance between two periodic boundaries is 160°, the longitudinal (defined as the z direction) electric field E_z in a single cavity is plotted on the beam axis in Fig. 3.

To demonstrate the energy modulation approach, we designed a single-cavity prototype, where only one cavity is powered from the coupling waveguide. The coupler is designed to provide critical coupling. The geometry of the single-cavity prototype is shown in Fig. 4(a). Driven modal simulations were performed when the single cavity is excited at the WR284 waveguide port. Figure 4(b) shows the electric field plot of the fundamental TM mode in the single cell in the driven modal simulation.

Table I lists the key parameters of the single cavity design with the coupler in the critical coupling regime. To provide an average gradient of 30 MV/m, 400 kW of input power is required to be fed into this cell. The peak surface E field in this case is 68 MV/m, and the peak H field is 99 kA/m.

The method of feeding individual cells not only enables a high shunt impedance from a relatively small beam aperture¹⁸ but also allows flexible phase control of each cavity to match the changing β value for the low-β proton beam (β = v/c = 0.5067 for the 150 MeV beam). The phase flexibility is critical in proton applications in the therapeutic energy range, as the beam β changes with the energy modulation. Figure 5 shows a driven modal simulation of a five-cell structure. Each cell is driven individually with an equal RF power level and a phase difference of 160° between neighboring cells. The 160° phase advance is forced by running the klystrons that will power each individual cell with a 160° phase difference.

Beam dynamics simulations were performed in ACE3P and IMPACT¹⁹ with 50 cavities of the S-band structures. The average gradient in these energy modulator cavities is set to 30 MV/m. To achieve an energy spread of within 3 MeV after the 50 cavities, the initial bunch length needs to be as short as 7 mm (full length), and we set the initial bunch length as 7 mm in these simulations. The initial bunch length can be tuned with the bunch compressor before the energy modulator.

The proton bunch with a charge of 11 fC starts with 150 MeV before the energy modulator, and it can get accelerated or decelerated depending on its relative phase with the RF field. As the β value changes, the phase difference between cells is also changed accordingly in groups of 10 cells. In the acceleration case, for example, the phase advance per cell is 160° for cell nos. 1–10, 158° for cell nos. 11–20, 156° for cell nos. 21–30, 154° for cell nos. 31–40, and 152° for cell nos. 41–50. In the deceleration case, the phase advance per cell is 160° for cell nos. 1–10, 162° for cell nos. 11–20, 164° for cell nos. 21–30, 168° for cell nos. 31–40, and 171° for cell nos. 41–50.

The final beam energy distributions in the acceleration case and in the deceleration case are shown in Figs. 6(a) and 6(b), respectively. An energy modulation of ±30 MeV is shown in the simulations. The full energy spread is about 3 MeV in both cases, while it can be further reduced by using a shorter proton bunch to start with.

To deliver a high radiation dose, we plan to run the energy modulator at a high repetition rate of 1 kHz–10 kHz for 1 s. The gradient in the energy modulator is swept linearly from −30 MV/m to 30 MV/m during the treatment. An input RF power of 400 kW is required to provide the peak gradient of ±30 MV/m.

Thermal simulations were carried out in High Frequency Structure Simulator by Ansys (HFSS) to calculate the temperature rise in a multi-cell structure. Figure 7(a) shows the temperature distribution in the model of two cells with periodic boundaries at t = 1 s. Each cavity is fed by an RF power source with a duty factor of 2% from t = 0 to t = 1 s. The input RF power varies between 0 kW and 400 kW to achieve the linear sweep of the gradient. We simulated the equivalent thermal model by powering each cavity with a continuous power of (8/3) kW for 1 s.

The initial copper block temperature is 22.0 °C (room temperature), and no active cooling is included in the simulation, given the short timescale of the RF pulse and the thermal mass of the RF deflector. In practice, active cooling will be added for thermal tuning of the cavities.

Figure 7(b) shows the maximum, minimum, and average temperature change in the structure with time. After 1 s of high-power operation, the peak temperature rises to 61.6 °C. The structure cools back down to room temperature in about 20 s. The temperature rise is practical for the high repetition rate operation.

For a temperature rise of 39.6 °C in the copper structure, the cavity frequency shift is 1.87 MHz, which is well within the tunable frequency range of the klystron. Note that the actual frequency shift will be smaller than 1.87 MHz, as we plan to power the cavity for 1 s and then cool down to room temperature.

Based on the model in Fig. 4(a), a single-cell prototype has been designed and fabricated for an experiment driven by a high-power S-band klystron. Figure 8 shows the drawing of the split-block design. A few diagnostics are added, including an RF probe mounted on the wall of a matching waveguide with a coupling coefficient of around −65 dB to provide a real-time measurement of the field in the single-cell cavity and two Faraday cups at both ends of the beam pipe to monitor dark current. The cavity frequency can be tuned mechanically with a tuner.

Figure 9(a) shows one of the two halves of the cavity, which later were brazed together at the splitting surface, and Fig. 9(b) shows the completed structure after brazing.

RF measurements were performed with a vector network analyzer, and the experimental results are shown in Fig. 10. The cavity shows a good resonance at the design frequency in Fig. 10(a), and a critical coupling with the S₁₁ circle is almost going through the origin in Fig. 10(b). The experimental results agree very well with design simulations.

We designed, built, and tested a rapid energy modulator with RF cavities at the S-band for proton therapy devices. The cavities can provide 30 MV/m of average gradient to a 150 MeV proton beam with 400 kW of microwave power fed into each individual cell. Beam simulations have demonstrated ±30 MeV of energy modulation with a final energy spread of 3 MeV in a 50-cell energy modulator. Thermal simulations have shown that the high repetition rate operation with a duration of 1 s is practical. A single-cell prototype has been built and tested, showing a very good agreement with the design simulations. The current design is optimized for the 150 MeV cyclotron beam, but it can be easily adapted to other proton sources with different beam parameters.

A high-power S-band test stand will be commissioned for the single-cavity structure test at the Next Linear Collider Test Area (NLCTA) at SLAC. The output microwave power from an S-band klystron will be fed into the WR284 waveguide and coupled into the single-cell cavity. With this prototype, we will be able to demonstrate the high-power operation of the energy modulator cavity and measure RF breakdown statistics.

A similar single-cavity structure has also been designed at the C-band to be tested at a high-power klystron test stand at the Los Alamos National Laboratory. These structures can also operate at cryogenic temperatures to increase the operating gradient.²⁰ 

This work was supported by the U.S. Department of Energy (DOE) (Contract No. DE-AC02-76SF00515). The authors thank Billy Loo, Reinhard Schulte, Bruce Faddegon, Matthew Murphy, and Eric Abel for helpful discussions. The authors also thank Ben Bigornia for help with the machine drawings and Andy Nguyen for help with vacuum cleaning and structure brazing.

The data that support the findings of this study are available from the corresponding author upon reasonable request.