LOS POBLADORES TEMPRANOS

Side-coupled standing wave structures were also investigated at both S- and C- band with a 4 mm aperture radius. The quadruplet simulated in CST is shown in Figure 4.6, with the π

2 mode excited. Both the S- and C-band cavities had their

nose cones individually optimised following the same methodology as mentioned in the previous section. The coupling slots were also individually optimised. The S-band structure shown in Figure 4.6 still only requires 2% coupling so has a regular length side-coupled cavity. The C-band structure shown in Figure 4.7 has had the length of the side-coupled cavity increased to increase the coupling to >4%

without lowering the cell further down into the accelerating cavity and reducing the shunt impedance. Table 4.3 shows the main figures of merit for a C-band side-coupled structure. At a gradient of 48.5 MV/m the surface electric field peaks

at 212 MV/m on the nose cone. This allows for no further optimisation to increase

the gradient as that would increase the peak field further above the limit. Both the peak surface electric field and Sc are limiting the gradient in this case.

4.3 Standing Wave 127

Fig. 4.6 Cross section of S-band side-coupled standing wave structure quadruplet model used in simulation with periodic boundaries. Electric field plot showing the

π

2 mode.

5.7 GHz SCSWS

Parameter Value Units

f Frequency 5.7 GHz S Septum Thickness 2 mm rc Accelerating Cell Radius 16.9 mm

rsc Coupling Cell Radius 7.2 mm

l Accelerating Cell Length 15.7 mm lsc Coupling Cell Length 20 mm

Ncell Number of Accelerating Cells 19

d Coupling Slot Depth 1.4 mm k Coupling factor 4.2 % Q₀ Q-factor 7804

tf ill Filling time 220 ns

Z Shunt Impedance 61.2 MΩ/m Eacc Gradient 48.5 MV/m

Epeak Peak Surface E-field 212 MV/m

Hpeak Peak Surface H-Field 320 kA/m

Sc Modified Poynting Vector 2 W/µm2

Table 4.3 Parameter table for the 5.7 GHz side-coupled standing wave cavity.

Gradient is limited by 12.8 MW input power, and available shunt impedance.

Figure 4.7 shows the surface magnetic field profile of the C-band side-coupled standing wave quadruplet simulated. This peak field is a result of the amount of

128 Large Aperture High Gradient Cavity Optimisation

coupling required for the 19-cell cavity. The peak field can be reduced by increasing the length of the side-coupled cell and reducing the slot depth however this is already a ‘long cell’. Increasing the length further requires a reduction in cell radius to tune it to the correct operating frequency, and the capacitive region in the side-coupled cell becomes too small. The capacitive gap in the side-coupled cell could be reduced to tune the coupling cell, but it has been limited at 3 mm to keep peak fields small.

4.3 Standing Wave 129

3 GHz SCSWS

Parameter Value Units

f Frequency 3 GHz

S Septum Thickness 2 mm rc Accelerating Cell Radius 36 mm

rsc Coupling Cell Radius 12.4 mm

l Accelerating Cell Length 29.8 mm lsc Coupling Cell Length 29.8 mm

Ncell Number of Accelerating Cells 10

d Coupling Slot Depth 1.5 mm k Coupling factor 2.3 % Q₀ Q-factor 13260

tf ill Filling time 700 ns

Z Shunt Impedance 75.3 MΩ/m Eacc Gradient 53.8 MV/m

Epeak Peak Surface E-field 210 MV/m

Hpeak Peak Surface H-Field 262 kA/m

Sc Modified Poynting Vector 0.9 W/µm2

Table 4.4 Parameter table for the 3 GHz side-coupled standing wave quadruplet. Gradient is limited by 12.8 MW input power, and available shunt impedance.

The main parameters and figures of merit for the 3 GHz side-coupled standing wave quadruplet seen in Figure 4.6 are shown in Table 4.4. The coupling requirement for this structure is only 2% so it was unnecessary to use a long coupling cell to reduce the peak surface magnetic field on the coupling slots. The peak surface magnetic field was only 262 kA/m at 2.3%; slightly more coupling than is necessary. The

3 GHz quadruplet was calculated to achieve a gradient of 53.8 MV/m outperforming

its C-band counterpart by 5.3 MV/m, with lower peak fields. Sc was much lower

than the limit of 2 W/µm2, but increasing the size of the nose cone to increase

gradient further would have also raised Epeak which was already over the limit at

130 Large Aperture High Gradient Cavity Optimisation Parameter S-band bTW C-band bTW C-band SW S-band SW Units f Frequency 3 5.7 5.7 3 GHz l Cell Length 24.8 13.1 15.7 29.8 mm Ncell Number of cells 15 22 19 10

vg_/ c k Group Velocity k-factor -0.2 -0.04 -0.5 -0.0 4.2 2.3 %

tf ill Filling time 0.8 0.4 1.4 4.4 µS

Z Shunt Impedance 85.4 65.6 61.2 75.3 MΩ/m

Pin Input Power 10 10 11.4 11.6 MW

Eacc Gradient 48.6 47.5 46.8 51.1 M V/m

Epeak Peak Surface

E-field

204 200 200 200

Hpeak Peak Surface

H-field 153 256 302 267 kA_/ m Sc Peak Modified Poynting Vector 1.6 1.53 1.74 0.8 W_/ µm2

Table 4.5 parameters for each large aperture structure considered with the input power reduced to bring the peak surface electric field within limits. Group Velocity indicates the values at the start and end of the structures. The C-band bTW did not have enough power to fill the entire structure with 10 MW input power. Values in red exceed target values.

The figures of merit for each full large aperture structure considered in this chapter are summarised in Table 4.5 where the input power, for some structures, has been reduced to operate within the peak surface electric field limit of 200 MV/m.

Comparing all of the structures, the S-band structures are calculated to reach higher gradients than the C-band structures for both standing and travelling wave. This could be due to the same limits imposed on both despite the frequency difference. The limit of 2 mm septum thickness was imposed on both structures and shunt impedance strongly varies with septum thickness. Relative to the cell length, the S-band structures have a thinner septum. Additionally, as discussed at the start of the chapter C-band structures are likely to exceed the peak surface electric field of S-band structures at the same breakdown rate, however the data for this frequency is limited and the frequency dependence of the peak surface electric field before breakdown is contested in the literature. The C-band backwards travelling wave structure did not have enough power to fill the end cell when the power was reduced to 10 MW. The nose cones could be reduced to lower Epeak instead but this would