Design study of compact medical fixed-field alternating-gradient accelerators

We have studied the various conditions and limitations for achieving compact fixed-field alternating-gradient (FFAG) accelerators to be widely used in heavy-ion cancer therapy. For the case of a normal-conducting FFAG accelerator, our linear calculation indicates 12-cell radial sectors with a field index of 10.5 as a suitable configuration. We found that its ring circumference can be as small as 70 m and that triple-cascade rings are needed to accelerate a carbon beam from $40\mathrm{k}\mathrm{e}\mathrm{V}/\mathrm{u}$ to $400\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{u}$. In this paper, we report a systematic analysis based on a linear optical model, a comparison of various types of FFAG, and a design example with some technical concerns. An important result is that viable radial-sector designs are possible with circumference factor $C$ significantly lower than the value 4.45 previously quoted.

Figure 1

Basic elements of a radial-sector FFAG.

Figure 2

Stability islands of the 12 cell radial-sector type are compared in the $k\mathrm{\text{−}}C$ plane for three different configurations: (a) singlet, (b) doublet, and (c) $D\mathrm{\text{−}}F\mathrm{\text{−}}D$ triplet. Similar stability regions are observed for all three configurations.

Figure 3

Magnitudes of vertical $\beta$ function for the case of the 12-cell singlet configuration. The higher order stability islands are associated with large phase advances and betatron oscillations.

Figure 4

Ring radii calculated for the first stability region of 8, 12, and 16 cells. Doublet radial-sector configurations are assumed. Straight lines correspond to momentum ratios of 2.0, 3.0, and 4.0, respectively, where orbit excursions are less than 1 m.

Figure 5

Lengths of drift space per cell as a function of orbit excursion. Here, all the solutions satisfying a ring radius of less than 11 m are plotted. For momentum ratios above 3.0, fulfilling the constraints of both orbit excursion and drift length may not be possible.

Figure 6

Required spiral angles for 8, 12, 16 cells to fulfill the condition for orbit excursion of 1 m or less.

Figure 7

Overall view of the triple-cascade radial-sector FFAG system.

Figure 8

$\beta$ functions of the (a) LE, (b) ME, and (c) HE rings at extraction orbit.

Figure 9

Racetrack shape of a preliminary MA core.

Figure 10

Frequency dependence of complex impedance ($Z=R+jX$) of the racetrack-shaped MA core described in Fig. 9.

Figure 11

Frequency dependence of the cavity impedance ($Z_{\mathrm{c}\mathrm{a}\mathrm{v}}=R_{\mathrm{c}\mathrm{a}\mathrm{v}}+j{X}_{\mathrm{c}\mathrm{a}\mathrm{v}}$) for the LE-FFAG ring. Here, four cores per cell and a gap capacitance of 70 pF are assumed.

Figure 12

Vertical tune shifts for the case of the LE ring. A pole gap of 1 cm is assumed and the vertical tune at injection is adjusted to the value listed in Table , using the linear optical model described in the text.

Figure 13

Fast-extraction system estimated for tightly spaced lattice configuration of the HE-FFAG ring. Assuming brute-force extraction, at least eight kickers and two septum magnets are needed to obtain a beam separation of 420 mm.

Figure 14

Dynamic apertures for the (a) LE, (b) ME, and (c) HE rings. Top and bottom figures correspond to injection and extraction orbits, respectively. 1000 turns of tracking are performed.