High-gradient low-$\beta$ accelerating structure using the first negative spatial harmonic of the fundamental mode

The development of high-gradient accelerating structures for low-$\beta$ particles is the key for compact hadron linear accelerators. A particular example of such a machine is a hadron therapy linac, which is a promising alternative to cyclic machines, traditionally used for cancer treatment. Currently, the practical utilization of linear accelerators in radiation therapy is limited by the requirement to be under 50 m in length. A usable device for cancer therapy should produce 200–250 MeV protons and/or $400–450\mathrm{MeV}/\mathrm{u}$ carbon ions, which sets the requirement of having $35\mathrm{MV}/\mathrm{m}$ average “real-estate gradient” or gradient per unit of actual accelerator length, including different accelerating sections, focusing elements and beam transport lines, and at least $50\mathrm{MV}/\mathrm{m}$ accelerating gradients in the high-energy section of the linac. Such high accelerating gradients for ion linacs have recently become feasible for operations at S-band frequencies. However, the reasonable application of traditional S-band structures is practically limited to $\beta =\mathrm{v}/\mathrm{c}>0.4$. However, the simulations show that for lower phase velocities, these structures have either high surface fields ($>200\mathrm{MV}/\mathrm{m}$) or low shunt impedances ($<35\mathrm{M}\mathrm{\Omega }/\mathrm{m}$). At the same time, a significant ($\sim 10\%$) reduction in the linac length can be achieved by using the $50\mathrm{MV}/\mathrm{m}$ structures starting from $\beta \sim 0.3$. To address this issue, we have designed a novel radio frequency structure where the beam is synchronous with the higher spatial harmonic of the electromagnetic field. In this paper, we discuss the principles of this approach, the related beam dynamics and especially the electromagnetic and thermomechanical designs of this novel structure. Besides the application to ion therapy, the technology described in this paper can be applied to future high gradient normal conducting ion linacs and high energy physics machines, such as a compact hadron collider. This approach preserves linac compactness in settings with limited space availability.

Figure 1

Left: 3D layout rendering of the 15-cell $\beta =0.3$ negative harmonic structure. Right: Fabricated cell prototype of the $\beta =0.3$ negative harmonic structure.

Figure 2

Realistic (blue) and ideal (center) amplitude (left) and phase (center) distributions of traveling wave field in the middle of the $\beta =0.42$ $5\pi /6$ magnetic-coupled disk-loaded waveguide cell (right) as simulated in CST Microwave Studio.

Figure 3

Effective shunt impedance of a $\pi$-mode pillbox cavity as a function of phase velocity for different frequencies. Beam apertures are 6 mm.

Figure 4

Schematics of the accelerator scheme with the focusing lattice.

Figure 5

Phase slippage of the beam center in a 28.5 cm long $\beta =0.3$ section. The dots represent different cells.

Figure 6

The results of beam dynamics simulations in $\beta =0.3$ $50\mathrm{MV}/\mathrm{m}$ section produced by track. Beam envelope development along the section (x—blue; y—red).

Figure 7

BTW structure model (left) and electric field distribution in the nose part for the $50\mathrm{MV}/\mathrm{m}$ gradient (right). Red color corresponds to $200\mathrm{MV}/\mathrm{m}$.

Figure 8

The dispersion curve of disk-loaded periodic waveguide structures with a magnetic coupling ($n=0$ curve corresponds to the fundamental harmonic, $n=-1$ curve corresponds to the first negative harmonic).

Figure 9

Shunt impedance of the 20-cells BTW structures with different geometry and designed to operate at different spatial harmonics, as a function of beam velocity. The geometry of FHS and NHS cells with no noses is similar except for the cell length.

Figure 10

Profile of the $\beta =0.3$ NHS cells with the optimized parameters.

Figure 11

Electric (left), magnetic (center) and modified Poynting vector (right) field maps in the optimized $\beta =0.3$ NHS cell.

Figure 12

Shunt impedance (left) and peak field normalized to the accelerating gradient (right) of the NHS structure with noses as a function of designed operation mode.

Figure 13

Energy gain (in color) of $45\mathrm{MeV}/\mathrm{u}$ $12\mathrm{C}6+$ beam at $-20$ degrees synchronous phase in 15 cells section of $\beta =0.3$ NHS as simulated in CST Particle Studio.

Figure 14

Left: The design of input and output rf power couplers. Right: Profile of the complex amplitude of the electric field along the NHS constant gradient section with 42.7 MW input power.

Figure 15

Group velocity (left) and shunt impedance (right) variation in the cells along the structure.

Figure 16

Reflection (S11, red) and transmission (S21, green) characteristics of the NHS 15-cells structure with couplers.

Figure 17

Temperature map of the full structure (left) and cell #12 (right) in the steady-state regime.

Figure 18

Transient temperature analysis results. Left: in large time scale. Right: with rf pulse resolution. The results are taken at the point with the maximal temperature.

Figure 19

ansys mesh for transient thermal analysis model.

Figure 20

Von Mises stress (left) and the first principal total strain (right) maps of the cell #12 at the end of the fifth pulse.

Figure 21

Left, low cycle fatigue and, right, high cycle fatigue of copper. The black line is the value for the designed structure.

Figure 22

Finished NHS test cell with all features included.

Figure 23

Turned cell on CMM (left and top right), profile scan taken of the cell showing all dimensions within $\pm 10$ microns tolerances.

Figure 24

Single-cell rf test stand design (left) and assembly (right).

Figure 25

Simulated (black), measured (red) and corrected (blue) magnitudes of the power transmission ($S_{21}$) in a single cell NHS mockup.