High-Temperature Superconductor Coatings for Beam Impedance Reduction in Particle Colliders: Nonlinear Effects

Sergio Calatroni,Ruggero Vaglio

doi:10.1109/tasc.2021.3053299

Abstract

Coating of surfaces facing particle beams with high-temperature superconductors (HTS) for reducing the beam coupling impedance is being considered for the next generation of hadron colliders, such as the FCC-hh at CERN, where HTS would be exposed to the high-frequency wakefields generated by the particle bunches and to the strong field of the steering magnets. In this frame, we present a simple model for the calculation of the microwave response of HTS exposed to a strong external magnetic field, which takes into account the nonlinearity of the pinning potential of the vortex lattice. The equation of motion of the vortex lattice is solved in first-order approximation, and we calculate the amplitude of the third-harmonic components in the electric field produced by vortex oscillation. We deduce the time-dependent surface impedance, which could serve as a boundary condition in the simulation codes for the calculation of beam-stability phenomena in particle accelerators. Finally, time-integration of the surface impedance allows exploring the dependence of the surface impedance on surface currents, useful for analyzing the experimental results obtained using simple resonators in terms of our model.

Highlights

S EVERAL new applications of high-temperature superconductors (HTS) have been discussed in the scientific literature in recent years, requiring operation of HTS at high frequency and in presence of a strong magnetic field
One notable example is the case for beam coupling impedance reduction in future particle colliders, such as the FCC-hh at CERN [1] or CPPC in China [2], where the high-frequency image currents produced by the beam would flow on the inner surface of a screen, coated with HTS, lining the inside of the magnets which steer the beam
In this article, following [29], we develop a simple model based on the single-vortex Gittleman and Rosenblum (GR) approach and we introduce a nonlinear pinning potential for vortices in HTS

Summary

INTRODUCTION

S EVERAL new applications of high-temperature superconductors (HTS) have been discussed in the scientific literature in recent years, requiring operation of HTS at high frequency and in presence of a strong magnetic field. Equation (3) modified could in principle be inserted in beam dynamics numerical simulation codes and would be fully sufficient for evaluating the effect of HTS nonlinearities on particle beam stability [32], through the calculation of Erf and of its effect back on the beam itself It is useful for a better physics insight to analyze the single mode ω behavior, and it is easy to show that the generated EM field contains a large component at the same frequency of the forcing RF current, and odd harmonics whose. CALATRONI AND VAGLIO: HIGH-TEMPERATURE SUPERCONDUCTOR COATINGS FOR BEAM IMPEDANCE REDUCTION IN PARTICLE COLLIDERS amplitude increases for increasing amplitude of the forcing term, the main contribution given by the third harmonic signal For this purpose, it is convenient to rewrite (3) in adimensional units, introducing the following adimensional parameters: y = x/ξv, τ = ωt, arf = φoJrfo/kξv, r = ω/ωo, where ωo = k/η is the depinning frequency, a key parameter characterizing the RF behavior of the vortex lattice. We note that the fundamental and the third harmonic are clearly distinguishable in Fig. 2, and the substantial equivalence between numerical simulation and first-order solution confirm that the third harmonic component is the dominant high-order term generated by the assumed nonlinear potential

COMPLEX RESISTIVITY IN THE NONLINEAR CASE

SURFACE IMPEDANCE IN A THICK FILM

CONCLUSION