New Geometrical-Optimization Approach using Splines for Enhanced Accelerator Cavities' Performance

Over the past decades accelerator scientists made a huge effort in advancing the technology of particle accelerators, which lead to state-of-the-art fabrication techniques as well as simulation tools. Combining these advancements with the large boosting in computing speed provides large flexibility and motivation to investigate new accelerator geometries. In this paper, we describe a new optimization approach for the geometry of accelerating cells. This approach uses a set of control points with variable positions to control a nonuniform rational B-spline (NURBS), which describes the cavity shape. INTRODUCTION AND DESCRIPTION In this section, we describe a new optimization approach for the geometry of accelerating cells. This approach uses a set of control points with variable positions to control a nonuniform rational B-spline (NURBS) [1, 2], which describes the cavity shape. The positions of the control points are then optimized using differential-evolution optimization to maximize/minimize the defined optimization function. This function is defined by the user and depends on the cavity parameters such as the shunt impedance, wall losses, peak surface fields...etc The set of control points used in our optimization for nose-shaped accelerator cells is shown in Fig. 1. The figure shows only a half-cell since we optimize for symmetric cells. Three sets of points control the cavity shape. • First, four fixed points (black points) including the origin are defined using the cavity outer radius (b), iris radius (a), and cell width or periodicity (p). Typically, the iris radius is fixed, and the outer radius is used for frequency adjustments while the periodicity can be either fixed or added as a design variable. • The second set of points are the green ones which only move horizontally (D0, D2 and D3) or vertically (D1). These points provide a guideline for the cavity cell shape. Point D0 is fixed vertically at the outer radius and provides extra control on the outer contour (upper quarter). It also forces the outer curvature to be convex. Point D1 and D2 are both fixed vertically at the iris radius and provides extra control on the nose shape. They also force the nose curvature to be concave. Point D3 is fixed horizontally at half the period edge minus the minimum separation between cells (t). ∗ mamdouh@slac.stanford.edu D0