1. LARGE SCALE SHAPE OPTIMIZATION FOR ACCELERATOR CAVITIES*
Volkan Akcelik, Kwok Ko, Lie-Quan Lee, Zenghai Li, Cho Ng, Liling Xiao, SLAC
ABSTRACT: We present a shape optimization method for designing accelerator cavities with large scale computations. The objective is to find the best accelerator cavity shape with the desired spectral response. The forward problem is the large scale Maxwell equation in frequency domain. The design variables are CAD parameters defining the cavity shape. We use scalable algorithms with a discrete adjoint approach. The algorithm is tested with two realistic cavity design examples.
Maxwell Eigenvalue Shape Optimization
Motivation for accelerator modeling
Conventional cavity design using trial-and-error approach on desktop computers is costly in terms of human effort and computational time.
We develop state-of-the art constrained optimization techniques on parallel computers for large-scale shape optimization of accelerator cavities.
The objective is to determine the optimum design variables giving the desired spectral response.
Design variables are CAD parameters defining the shape of a cavity.
Eigenvalue shape optimization
First order optimality conditions
Consider shape optimization problem in the following form:
Adjoint equation
Design equation
Gradients are computed using a discrete adjoint approach.
The nonlinear problem is solved using a quasi-newton method
Shape Design of Choke-Mode Cavity
Choke-mode cavity
The accelerator mode is trapped inside the cavity by means of a choke structure, and unwanted modes are coupled out from the cavity.
Design objectives
Maximize the external Q for the accelerating mode.
Minimize the external Q for the higher-order-modes.
Set the accelerating mode frequency to GHz.
Set field flatness for the accelerating mode throughout the structure.
Constrain the shunt impedance for accelerating mode.
Results of shape optimization
Definition of design parameters
Optimum design parameters in mm
Initial and optimum external Q values for HOM modes
Initial (black) and optimum (red) cavities
Shape Design of Crab Cavity
Design objectives
Minimize the maximum magnetic field on the cavity surface.
Constrain the operating frequency.
Apply additional bound constraints to design variables.
Method of solution
Challenging problem: As cavity deforms, the location of maximum magnetic field may jump.
Use Lp norm in the objective function.
Start the optimization with small p. As p increases, Lp norm approaches to the infinity norm.
Use a quasi-Newton method with an active set strategy.
Results of shape optimization
Definition of design parameters
Initial and optimized field values for two design examples
Initial and optimized field values in different stages of optimization
* Work supported by .US Department of Energy Offices of HEP, ASCR and BES under contract DE-AC02-76SF00515.