Three-Dimensional Spiral Beam Injection:Design Principles and Experimental Verification

TL;DR

This work addresses the challenge of injecting and storing low-$\gamma$ beams in a compact storage ring by introducing a three-dimensional spiral injection method that relies on strong x–y coupling produced by a solenoidal fringe field. The authors develop a kinematic framework based on backward-tracking, derive axis-symmetric x–y correlations using a flat-beam model, and identify representative Twiss-parameter sets that realize the required correlations; they further employ a data-driven tSVD analysis in the $r$-$\mathrm{vertical}$-$\theta$ space to locate a dominant feature direction governing injection success. The experimental program uses an $80\ \mathrm{keV}$ DC electron beam and three rotating quadrupoles to shape the four-dimensional phase space, with direct visualization, wire-scan measurements, and model–measurement consistency showing good agreement with simulations and validating the core injection principle. The results yield practical design guidelines that prioritize correlated multivariate phase-space structures over individual Twiss parameters and demonstrate a viable path toward pulsed-beam storage in compact, solenoid-based devices, advancing precision beam control in new energy regimes.

Abstract

A proof of principle experiment of Three-dimensional spiral beam injection scheme has been carried out. This injection scheme requires a strongly x-y coupled beam to meet magnetic field distribution through solenoid magnet fringe field. In this paper, we introduce outline of experimental setup, results of x-y coupling adjustment with DC electron beam of 80 keV. The results of this experiment will be evaluated and improvements for actual operation will be discussed.

Figures (44)

• Figure 1: Conventional beam injection vs. 3-D injection scheme.
• Figure 2: Image of the 3-D spiral beam injection for this demonstration experiment. OPERA-3D model opera and flat-shaped beam samples are shown.
• Figure 3: Black: Three-dimensional spiral trajectories with flat $x$–$y$ correlation, corresponding to the type-1 configuration shown in Fig. \ref{['fig:ribbon_soukan']}. Green: Trajectories with opposite $x$–$y$ correlation, referred to as type-2. Red circle in the figure denotes entrance of storage magnet as shown in fig. \ref{['fig:miniSolOPERA']}. A clear divergence along the solenoid axis is observed in this case.
• Figure 4: Vertical diverging as a function of $B_RL$ along each trajectory. Beam samples are same as Fig. \ref{['fig:A1_A1Reverse_3D']}.The red dashed line indicates the bottom surface of the iron yoke of the storage solenoid magnet (see fig. \ref{['fig:miniSolOPERA']}). As the beam spreads in the vertical direction for $\mathrm{vertical}>$ -0.2m in Fig. \ref{['fig:A1_A1Reverse_3D']}, the corresponding $\langle BrL \rangle$ distribution shown here also broadens.
• Figure 5: Strong correlation of flat-shaped beam samples at the injection point(vertical=-0.55 m in fig. \ref{['fig:A1_A1Reverse_3D']}). These strong correlations result from the axisymmetric solenoidal field. Black circles (green triangles) are as in ten black (green) trajectories in fig. \ref{['fig:A1_A1Reverse_3D']}