Interdigital $H$-mode drift-tube linac design with alternative phase focusing for muon linac

We have developed an interdigital H-mode (IH) drift-tube linac (DTL) design with an alternative phase focusing (APF) scheme for a muon linac, in order to measure the anomalous magnetic moment and electric dipole moment (EDM) of muons at the Japan Proton Accelerator Research Complex (J-PARC). The IH-DTL accelerates muons from $\beta =v/c=0.08$ to 0.28 at an operational frequency of 324 MHz. The output beam emittances are calculated as $0.315\pi$ and $0.195\pi \mathrm{mm}\mathrm{mrad}$ in the horizontal and vertical directions, respectively, which satisfies the experimental requirement.

Figure 1

Configuration of low-emittance muon beam.

Figure 2

Cell arrangement in accordance with synchronous phase.

Figure 3

Optimized phase (${\varphi }_s$) array results as function of cell (gap) number.

Figure 4

Three-dimensional model of IH cavity in CST MW Studio calculation.

Figure 5

Effects of ridge tuner (RT), cavity taper (CT), stem radius ($R_{\mathrm{stem}}$), and drift tube radius ($R_{\mathrm{DT}}$) adjustment. Horizontal axis is the distance from the cavity start on the beam axis, and vertical axis is the $E_z$ normalized at the peak value. Black: longitudinal electric field along z before optimizations, blue: field after optimizations with RT and CT, red: field after optimizations with $R_{\mathrm{stem}}$ and $R_{\mathrm{DT}}$.

Figure 6

Beam velocity distribution as a function of distance along the IH structure (black) and synchronous phase in each position (red). ${\beta }_x$ (top) and ${\beta }_y$ (bottom) along beam axis.

Figure 7

Emittance growth ($\mathrm{\Delta }ϵ$) along beam axis (z). Red: emittance growth in the x-direction ($\mathrm{\Delta }{ϵ}_x$), blue: emittance growth in the y-direction ($\mathrm{\Delta }{ϵ}_y$), green: emittance growth in the y-direction without the vertical electric field ($E_y$) and the horizontal magnetic field ($H_x$).

Figure 8

Calculated phase space distributions at IH exit. (a) the horizontal divergence angle $x^{\prime }$ vs $x$, (b) the vertical divergence angle $y^{\prime }$ vs $y$, (c) $y$ vs $x$, and (d) $\mathrm{\Delta }W(W-4.5\mathrm{MeV})$ vs $\mathrm{\Delta }\varphi$.