In this chapter we have seen a simple pillbox cavity evolve into a re-entrant cavity and then into coupled standing wave and travelling wave cavities. The assumption that X-band structures could reach higher gradients at small apertures was made looking at Figure 3.3, that overlooked the effects of re-entrant and coupling on shunt impedance and therefore gradient. Figure 3.54 shows the maximum gradient of cavities with 2 mm aperture radii. The blue bars show plain pillbox cavities without coupling or nose cones and the red bars show the increase in gradient‡ with
nose cones. The green and teal bars then show the gradient calculated for 10 cm and 30 cm standing wave cavities respectively. We can see that once coupling is added, the higher frequency structures’ gradients are reduced more than the lower frequency cavities.
‡Peak fields limited byS
3.6 Summary 117
Fig. 3.54 Figure showing maximum gradient with and without re-entrant and coupling. The 10 and 30cm structures are side-coupled standing wave structures.
The reduction in gradient caused by the addition of inter-cell coupling was not seen with backwards travelling wave structures. Only one that was investigated was calculated to reach the required gradient. The 3 GHz travelling wave structure did not perform better than the X-band structures as it was limited by shunt impedance and input power. The only feasible cavity for this application was the 15 cmφ= 5π
6
constant gradient backwards travelling wave structure which was calculated to reach 65 MV/m. The 3 GHz side-coupled standing wave cavity was calculated to
reach 63.3 MV/m and in Figure 3.3 one can see that the shunt impedance does not
reduce much by increasing the aperture radius. For this reason, alongside the beam dynamics study presented in Chapter 5 the possibility of increasing the aperture diameter further will be investigated.
Chapter 4
Large Aperture High
Gradient Cavity
Optimisation
4.1
Large Aperture Optimisation
At the end of the previous chapter it was decided to optimise multi-cell S- & C- band cavities with 2 mm septum thickness as shunt impedance scales with septum thickness and this is the smallest septum successfully demonstrated in this frequency range. Even with a scaled septum S- & C-band demonstrated the highest shunt impedance for a larger 4 mm aperture radius as is shown in Figure 3.8, where the gradient is calculated with the shunt impedance and input power at 100 MW/m
withSc limited to 4 W/µm2 . The small aperture optimisation chapter used the
modified Poynting vector as a single limit on peak fields. However as was seen in Figure 3.53 this resulted in very high peak surface electric fields. Peak surface electric field is widely regarded as a gradient limiting quantity, thus it is necessary to implement a limit for high gradient optimisation. There is lots of available high gradient data at X-band from the CLIC high gradient test program, however there is very little data available at lower frequencies. The TERA foundation performed single cell high gradient tests of S- and C-band cavities at the CLIC Test Facility (CTF) at CERN [123, 67, 91]. One single cell cavity was tested at both S- and C-band, so although informative, the conclusions that can be drawn from this data are limited.
Results from the TERA 3 GHz high gradient test program are shown in Figure 4.1. The results from winter 2012 are considered to be from an under-conditioned cavity [124], and the value of the peak surface electric field is uncertain as there was no direct probe inside the cavity. These uncertainties are accounted for with
120 Large Aperture High Gradient Cavity Optimisation
multiple fits to the data. The blue fit indicates a maximum surface electric field of ≈ 240 MV/m for a breakdown rate of 10−6 bpp/m. The more conservative
black fit indicates maximum surface electric field of ≈ 160−180 MV/m. The
C-band single cell structure tested yielded slightly higher peak surface electric fields for a given BDR, however the frequency dependence of peak surface electric field is questionable, this is discussed in [125]. For this reason along with the error uncertainties in the data a maximum surface electric field of 200 MV/m for both
S- and C-band cavities was decided. This is also the limit used in the CLIC high gradient test program [120].
The peak field limitSchas also been revised for this study. In the small aperture
optimisation Scmax =4 W/µm2 because it was considering 12 GHz power sources
which typically have maximum pulse lengths of 1.5µs. In this optimisation study
we are considering lower frequencies of ≤5.7 GHz and power sources in this range
can typically pulse up to 5 µs. Sc scales with BDR as
BDR∝Sc15t5
[82] as such the new Scmax =2 W/µm2. The simulations in this chapter have been
done using the Eigenmode solver in CST. A tetrahedral mesh was used with 40 cells per wavelength and third order curved elements.
Fig. 4.1 Scaling fits taken from the TERA publication on the 3 GHz single cell high gradient test results [67].