Preliminary Study On Optimization Of Superconducting Structure By Function Approximation Approach

Since 1960, the superconducting radio frequency(SRF) technology has developed increasingly, and been adopted by the international accelerator projects in the frontier field. The SRF cavities are hardcore for accelerators and the performance can dramatically affect the stability and the cost of an accelerator. The traditional optimization approach of SRF cavity is to observe different univariate performance curves and choose the parameters. The final geometry structure is decided by a few iterations. But the method can’t provide the theoretically optimal solution. And the way to find an optimized cavity structure by method of exhaustion is time-consuming and hard to realize. We adopted an untraditional method to attain the optimal cell shape in theory.This paper takes single-cell elliptical cavities as example. The relationship between microwave properties and geometry dimensions of an SRF cavity is treated as a continuous function equivalently. We attempt to use a multivariate polynomial function to approximate the continuous function, and then find the minimum point of multivariate polynomial function to acquire the mathematically optimal result. Firstly, I proved that the boundary of electro-magnetic field defined by Poisson Equation can be described by Stone-Weierstrass theory mathematically. Then the approach is use to optimize elliptical SRF cavity to demonstrate the work flow and validity. It was found that the figures of merit, which meet the actual application requirements, can be attained by selecting different weight factors. We used this method to optimize 1.3GHz 9cell SRF cavity for ILC, and attained figures of merit in line with expectations.Conclusion: This paper has demonstrated necessity and sufficiency of function approximation to solve the optimization problem of SRF cavities. By introducing a group of weight factors, the evaluation method of cell shape of elliptical cavities has been established. The significance of low loss shape mentioned in references has been explained by selecting different weight factors, and the optimal results coincide with theoretical expectations.