1 Introduction

Linac has been widely used for cancer treatment. In China, Tsinghua University and the Beijing Medical Equipment Institute (BMEI) completed an 8–10 MeV traveling-wave linac for medical application in 1998 ^[1]. And efforts have been made by other groups to produce medical accelerators. According to the World Health Organization, up to 4000 sets of medical accelerators are needed in China^[2].

Low-energy linac can treat 85% of the tumors which need radiotherapy. In most cases, electron beams of different energies are required to treat tumors at different depths. This is achieved by an energy-switch placed in a side cavity. By changing the device position in the cavity, one can change the field distribution in the accelerating tube^[3]. Considering high shunt impedance, good stability and small size, side-coupled accelerating structure is a good candidate for medical use^[4]. We designed a side-coupled accelerating structure with an energy switch. According to Ref.[5], The final energies were 6 and 4 MeV. 3D CST microwave studio (MWS)^[6] was used for designing the models, and ASTRA^[7] for simulation of beam dynamics. The design requirements are shown in Table 1.

For side-coupled accelerating structure, the coupling cavity is placed alternately between two accelerating cavities with a magnetic coupling^[8]. Due to asymmetry of the structure, the accelerating field will offset from the centerline resulting in an asymmetric electric field. Especially for electrons of low energies, the electric field symmetry in the first cell is essential. Based on Ref.[9], we conducted the calculation and improved the structure symmetry.

RF heating should be considered too. The considerable energy dissipation from the nose cones may induce a remarkable temperature rise, causing dangerous thermo-mechanical stress due to the non-uniform temperature distribution^[10]. To evaluate this important issue, we performed the thermo-mechanical analysis by ANSYS Workbench^[11].

2 Accelerating structure

The compact side-coupled linac is operated on π/2 mode. It consists of seven accelerating cavities and six coupling cavities. Fig. 1 shows the models of accelerating and coupling cavities with their optimized longitudinal electric field.

Fig. 1Full-screen View

Models of accelerating (a) and coupling cavities and their longitudinal electric field curves.

To accelerate electrons continuously, the length of each cavity must be βλ/2, where λ is the RF wavelength and β = v/c is electron traveling speed over light speed. The accelerating cavity is 50 mm long, while ones of two bunching cavities are 21 and 45 mm respectively. In order to maximize electric field at the electron bunch entrance, the first accelerating cavity was designed as half-cavity structure. Except the first cell, each accelerating cavity is of a Ω-shape, with a nose cone angle of 20°. The accelerating cavity hole is 4 mm in radius. To meet the requirements of mechanical strength and heat exchange, the web thickness is 3 mm. To get high shunt impendence and Q factor, key parameters of the nose cone are optimized. Resonant frequency of the cavity is fixed at 2998±0.5 MHz ^[12]. The effective shunt impedance of each accelerating cavity is ~100 MΩ/m, and the Q factor of 18730 and R/Q = 456. At the nose cone, the surface electric field reaches to s maximized at E_max/E_average = 4, where E_average is the average electric field on the axis.

In placing coupling cavities on accelerating cavities, the side-coupled structure operating on π/2 mode will introduce two periodic units (ACA and CAC, A denotes accelerating cavity and C denotes coupling cavity). The frequency gap of the two units on π/2 mode is named as stop band. To ensure the whole tube to operate on π/2 mode, the geometries of ACA and CAC must be adjusted to make the stop band as small as possible^[13-15]. The resonant frequency of an optimized accelerating cavity and coupling cavity should be 3021.2 MHz and 3076.9 MHz, respectively, when the coupling coefficient is 3.5%. With coupling slots, the effective shunt impedance of the accelerating cavity will decrease by 3%.

Bi-periodic system has large frequency spaces between operating mode and the adjacent modes^[13]. Fig. 2(a) shows the resonant mode (π/2 mode) of the ACA unit. It can be seen that, on π/2 mode, there is only little electric field exiting around the coupling slot in the side cavity. The phase shift between two adjacent accelerating cavities is π. Fig.2(b) shows the model of the whole accelerating cavity.

Fig. 2Full-screen View

Electric field profiles of the resonant mode (a) and the whole accelerating tube (b)

3 Beam dynamics

Two samples of energy switch are shown in Fig. 3. By moving the plunger (s), one can make the coupling unsymmetrical, hence the reduction or increase of electric field downstream. We chose the switch with one plunger^[16]. The switch was placed in the fourth coupling cavity.

Fig. 3Full-screen View

Schematics of the energy switch.

To calculate the beam dynamics, we converted the accelerating field (calculated by CST) into ASTRA format as its input field file. The effect of space charge was considered in the simulation process. A total of 10000 macro particles were used for initial simulations. After scanning all the parameters, full beam dynamics simulation was carried out with 1000000 ASTRA macro particles. The electrons were assumed to be generated from a DC gun. The transverse distribution was radially Gaussian with beam spot size of Φ1 mm (RMS). The longitudinal distribution was uniform with bunch length of 0.7 ns. The initial energy spread and normalized emittance were assumed to be 0.5% and 1.0 π·mm·mrad, respectively ^[17-19].

Fig. 4(a) shows the field distributions on the axis when the plunger is 5.21 mm or 7.91 mm long. At the two positions of the energy switch, the resonant frequencies of the whole structure have a difference of 0.41 MHz. The energy growth curves are shown in Fig. 4(b), and the beam sizes at the end of linac are shown in Fig.4(c). Using the electric field (Fig. 4, upper parts), the electrons can be accelerated from 10 keV to 6081 keV with an average electric field strength of 23.8 MV/m. At the end of accelerating tube, the RMS beam diameter is about 1.42 mm, and the RMS energy spread is 242.7 keV. Using the electric field (Fig. 4, lower parts), the final energy is 4001 keV, with a 0.4-mm increase in RMS beam diameter (which still meets the design requirements) and RMS energy spread of 152.7 keV.

Fig. 4Full-screen View

Longitudinal electric fields of the accelerating tube (a), energy growth curves (b) and RMS beam bunch diameters (b) at different positions of energy switch.

4 Asymmetry analysis

To reduce its electric field asymmetry, the first cavity uses coaxial coupling instead. As shown in Fig. 5, by enlarging the regions of the coupling cavity near the outer and inner radii, the magnetic energy is concentrated in the outer and inner regions and the electric energy in the middle region^[20]. Coupling is accomplished through a pair of coupling slots 180° apart cut into the web. This preserves symmetry about the beam axis, and minimizes the beam perturbation. Further, by rotating the coupling slots 90° at each half of accelerating cavity, the coupling slots are at maximum separation, thereby further reducing the direct coupling between accelerating cavities through the slots.

Fig. 5Full-screen View

Model of the coaxial coupling cavity (a) and electric field distribution in the cavity (b)

The longitudinal electric field, which may be expanded into monopole and multi-poles, can be expressed as^[21]:

where b is the bore radius, and ΔE_d-average /(2b) is the average amplitude gradient of the dipole electric field. The dipole contribution can be quantified as:

We calculated ΔE_d/E_Z of the former structure and the modified it at b=4 mm above and below the axis. The results are shown in Fig. 6. For the former structure, ΔE_d/E_Z = 0.698%, while it is 0.075% for the optimized structure, i.e. a 10-times improvement in asymmetry of electric field.

Fig. 6Full-screen View

Symmetry of the prior (a) and modified (b) structures.

5 Thermo-mechanical analysis

Due to power dissipation in the wall, the structure material is heated by the electromagnetic field. This has a strong impact on the mechanical properties and leads to structure deformation. The loss density (W/m²) coming from metallic losses can be expressed by: ^[22]

where, P_L is the average surface power loss, R_S is the surface resistance, and H_t is the tangential magnetic field.

We used HFSS module in ANSYS Workbench to calculate the electromagnetic field of one periodic unit (CAC) with copper as the wall material. Then, the electromagnetic results were used to calculate the surface power distribution. The thermo-mechanical analysis was performed assuming an infinite sequence of accelerating cavities with a boundary condition of perfect insulation^[23]. The usual air convection cooling was taken into account. The duty cycle was 2%, and the mesh size of the thermo-mechanical analysis was about 80 000 elements.

The thermo-mechanical analysis results are shown in Fig. 7. The maximum temperature at the nose cone is 72.5°C.High initial stress is produced at the nose cone and the web where the heat flows away difficultly. Deformation is proportional to the distance to the axis. Maximal deformation of about 73 μm occurs at the outer edge of coupling cavity.

Fig. 7Full-screen View

Thermo-mechanical analysis results.

6 Conclusion

The physical calculation and design of a side-coupled accelerating structure have been done. An optimized geometry with high shunt impedance and Q factor was obtained. With the energy switch, the electrons could be accelerated from 10 keV to 6081 keV or 4001 keV. The beam characteristics met the design requirements. The accelerating field symmetry in the first cavity was studied, and an optimal design with symmetry improvement of about 10 times was obtained. The thermo- mechanical analysis results of the temperature, equivalent stress and deformation distributions provide estimation for future cooling system.