Quasi-Alvarez drift-tube linac structures for heavy ion therapy accelerator facilities

Next generation heavy ion therapy and research facilities require efficient accelerating structures. Particularly, at low beam energies, right after the standard scheme of the ion source, low-energy beam transfer, and radio-frequency quadrupole (RFQ), several options for accelerating structures are available including the classic drift-tube linac (DTL), the interdigital H-mode DTL (IH-DTL), and superconducting quarter-wave resonators. These structures need to integrate the beam acceleration with the focusing channel, nowadays typically provided by permanent-magnet quadrupoles (PMQs). The frequency of operation needs to be in line with that of the RFQ structure, and it has been chosen at 750 MHz for practical considerations for the Next Ion Medical Machine Study (NIMMS) that is the application focus of this manuscript. While classic DTL structures at low ion beam energies do not provide enough space for PMQs at that frequency within a single $\beta \lambda$ period, IH-DTL structures do not provide the regular focusing channel with consequences on the beam quality. For these reasons, quasi-Alvarez drift-tube linac (QA-DTL) structures are reevaluated in this manuscript as they might fill this gap. They have not received much attention in the literature so far and therefore their design is described in detail. The design procedure presented here may serve as a blueprint for DTL design in general. In addition to the overall rf design, axial field stabilization with a new technique and multiphysics studies of the rf structure are described. A cost estimation completes the NIMMS QA-DTL study.

Figure 1

(a) The NIMMS reference synchrotron layout for the NIMMS facility. (b) The full high-frequency linac design for ${\mathrm{C}}^{6+}$ acceleration [8]. Note the schematic layouts are not to scale.

Figure 2

A schematic illustration of various QA-DTL design options compared to classic DTL design. A long drift tube is placed every $n\beta \lambda$.

Figure 3

A schematic illustration of the QA-DTL superperiod inside a tank (horizontal plane view). It comprises two half-length long drift tubes with PMQ and two small drift tubes without. The entire structure is designed by combining a set of these superperiods.

Figure 4

From the top: the schematic of the linac (quadrupole positions in black, gap positions in green), the 6 rms x and y envelopes, the average kinetic energy, and the quadrupole gradients.

Figure 5

Beam distributions at the entrance ($5\mathrm{MeV}/\mathrm{nucleon}$, left diagrams) and exit ($30\mathrm{MeV}/\mathrm{nucleon}$, right diagrams) of the full QA-DTL option. Note the different scales for the $\phi \text{−}W$ plane.

Figure 6

A cross-sectional view of a drift tube. The drift tube is rotationally symmetric with respect to the beam axis. The geometry of a half drift tube is determined by eight parameters which are shown here. A kind of midsphere, centered on the drift tube, eases the production of the stem-to-drift-tube junction.

Figure 7

Left: A 3D view of the cooling channel of a NIMMS facility structure drift tube. Right: Cooling channel cut in the symmetry planes. The area shown in blue is the water passage. Inner connections are clearly visible.

Figure 8

A comparison of different cooling strategies on the evacuation of the heat dissipation in long and small drift tubes. The heat profile is plotted at the duty cycle of 10%. Note the different scales. Only the outer copper shell is shown, open areas contain cooling circuits and the PMQ in vacuum.

Figure 9

The deformation of drift tubes at the duty cycle of 10%. Case A uses stem cooling in all drift tubes and case C uses drift-tube cooling. The deformation is scaled by a factor of 300 for better illustration.

Figure 10

A schematic arrangement of magnetic blocks and easy-axis direction of a 16-segment PMQ.

Figure 11

Top: 3D model of the PMQ. Bottom: Comparison of the 3D simulation results to the 2D approximation of the magnetic field of the PMQ.

Figure 12

Distribution of valid solutions obtained by a random search among 10,000 randomly generated parameter sets. All solutions with ${\mathrm{ZTT}}_{sp}$ higher than 95.0 and a maximum surface electric field below $38\mathrm{MV}/\mathrm{m}$ are plotted. The result of the genetic algorithm is shown as a red cross.

Figure 13

A cross-sectional view of electric and magnetic field distribution in a QA-DTL cavity at $4\mathrm{MV}/\mathrm{m}$.

Figure 14

Comparison of the axial electric field profile of the QA-DTL at $4\mathrm{MV}/\mathrm{m}$ obtained in 2D comsol and 3D hfss simulations.

Figure 15

The 3D model of the NIMMS QA-DTL tank design at $4\mathrm{MV}/\mathrm{m}$.

Figure 16

(a) The electromagnetic field distribution in the cell boundary plane cutting through a post coupler. The intensity of the electric field is shown by colors normalized to one. Arrows show the direction of the electric field. (b) Corresponding horizontal cross-section with the same scaling. (c) The equivalent circuit of the ${\mathrm{PC}}_0$ mode of the post coupler.

Figure 17

Tilt sensitivity of stabilized and nonstabilized NIMMS QA-DTL at $4\mathrm{MV}/\mathrm{m}$.

Figure 18

A comparison of construction costs of different parts of a QA-DTL at the two values of an average axial electric field of $4\mathrm{MV}/\mathrm{m}$ (blue) and $8\mathrm{MV}/\mathrm{m}$ (red).

Figure 19

The estimated total costs (construction and rf power source costs) of NIMMS QA-DTL as a function of the average axial electric field. The calculation has been performed based on three different rf costs of 2, 5, and 10 EUR/W. The dashed line shows only the costs related to the construction of the structure.