Superconducting radio frequency

The ultra-low electrical resistivity of a superconducting material allows an RF resonator to obtain an extremely high quality factor, Q.

The resonant frequency driven in SRF cavities typically ranges from 200 MHz to 3 GHz, depending on the particle species to be accelerated.

The most common fabrication technology for such SRF cavities is to form thin walled (1–3 mm) shell components from high purity niobium sheets by stamping.

An antenna is needed in the setup to couple RF power to the cavity fields and, in turn, any passing particle beam.

The full SRF cavity containment system, including the vacuum vessel and many details not discussed here, is a cryomodule.

SRF requires chemical facilities for harsh cavity treatments, a low-particulate cleanroom for high-pressure water rinsing and assembly of components, and complex engineering for the cryomodule vessel and cryogenics.

There are the proceedings of CERN accelerator schools,[2][3][4] a scientific paper giving a thorough presentation of the many aspects of an SRF cavity to be used in the International Linear Collider,[5] bi-annual International Conferences on RF Superconductivity held at varying global locations in odd numbered years,[6] and tutorials presented at the conferences.

The motivation for using superconductors in RF cavities is not to achieve a net power saving, but rather to increase the quality of the particle beam being accelerated.

Shortcomings of these materials arise due to their underlying physics as well as their bulk mechanical properties not being amenable to fabricating accelerator cavities.

At present, the de facto choice for SRF material is still pure niobium, which has a critical temperature of 9.3 K and functions as a superconductor nicely in a liquid helium bath of 4.2 K or lower, and has excellent mechanical properties.

A few simple approximations derived from the complex theories, though, can serve to provide some of the important parameters of SRF cavities.

Instead, the calculations are performed by any of a variety of computer programs that solve for the fields for non-simple cavity shapes, and then numerically integrate the above expressions.

The Geometry Factor is given by and then The geometry factor is quoted for cavity designs to allow comparison to other designs independent of wall loss, since wall loss for SRF cavities can vary substantially depending on material preparation, cryogenic bath temperature, electromagnetic field level, and other highly variable parameters.

The critical parameter for SRF cavities in the above equations is the surface resistance Rs, and is where the complex physics comes into play.

The superconductor's residual resistance arises from several sources, such as random material defects, hydrides that can form on the surface due to hot chemistry and slow cool-down, and others that are yet to be identified.

The pinned fluxon cores create small normal-conducting regions in the niobium that can be summed to estimate their net resistance.

The plot below shows the ideal Qo values for a range of residual magnetic field for a baked and unbaked cavity.

There are many phenomena that can occur in an SRF cavity to degrade its Q vs E performance, such as impurities in the niobium, hydrogen contamination due to excessive heat during chemistry, and a rough surface finish.

The insight gained could lead to simpler cavity fabrication processes as well as benefit future material development efforts to find higher Tc alternatives to niobium.

[10] Later the similar phenomenon was observed with nitrogen doping and which has been the current state-of-art cavity preparation for high performance.

In the equation for Vwake, the ratio R/Qo serves as a good comparative measure of wakefield amplitude for various cavity shapes, since the other terms are typically dictated by the application and are fixed.

The calculation of electromagnetic field buildup in a cavity due to wakefields can be complex and depends strongly on the specific accelerator mode of operation.

The damping is accomplished by preferentially allowing dipole and all HOMs to leak out of the SRF cavity, and then coupling them to resistive RF loads.

The leaking out of undesired RF modes occurs along the beampipe, and results from a careful design of the cavity aperture shapes.

The aperture shapes are tailored to keep the TM01 mode "trapped" with high Qo inside of the cavity and allow HOMs to propagate away.

Another approach is to place the HOM loads directly on the beampipe as hollow cylinders with RF lossy material attached to the interior surface, as shown in the adjacent image.

Further, such loads must sometimes operate at cryogenic temperatures to avoid large thermal gradients along the beampipe from the cold SRF cavity.