Nose Cone Optimisation Study

A nose cone optimisation study was performed to investigate the effect of varying the nose cone parameters, shown in Figure 3.9, for different frequency cavities. The plots contain both S- and X-band single cell cavities, 3 and 12 GHz respectively. This is not to compare the frequencies with one another, but to see if the general trends differ between the extremes of the frequencies investigated. Values are normalised to the accelerating gradient achieved with 50 MW input power per metre. The nominal parameters chosen for the study are shown in Table 3.1.

Figure 3.10 shows the effect of varying the distance between the nose cones (Gc)

on some chosen important cavity figures of merit. The lower left plot indicates an optimum value of Gc which produces the highest shunt impedance per unit

3.3 Single Cell Re-entrant Cavities 79

Fig. 3.9 Diagram labelling the parameters on a nose cone geometry. Nominal nose cone parameters

Parameter X-band S-band Units

f Frequency 12 3 GHz A Aperture Radius 2 2 mm Rin Inner nose radius 0.5 4 mm

Ron Outer nose radius 0.5 4 mm

Ric Inner corner radius 1 5 mm

Gc Nose cone gap 6 20 mm

CA Nose cone angle 65 65 deg Lf Nose cone flat 0 0 mm

Table 3.1 The nominal nose cone parameters used in the nose cone optimisation study.

electric field increases - shown in the top left plot - and this raises the shunt impedance. After the peak value the shunt impedance decreases due to the transit time factor. The peak surface magnetic field increases as the gap between the nose cones decreases despite the peak fields increasing. This is due to the nose cone angle remaining constant, thus further reduction of the gap causes the protruding section extend further into the magnetic peak region of the cavity, and enhances the fields.

80 Small Aperture High Gradient Cavity Optimisation

Fig. 3.10 The effect of the gap between the nose cones on shunt impedance and peak fields for both S and X-band.

Figure 3.11 shows the effect of increasing the blend radius on the inner (Rin)

and outer (Ron) edges of the nose cone. In both cases one parameter was kept

constant as the other varied. For both frequencies Rin has a greater effect on the

shunt impedance than Ron, and both increase Z as the ‘point’ of the nose cone

sharpens. However both have a similar effect on the peak surface electric field. This is a useful result for optimisation because by reducingRon the peak surface electric

field, which is widely regarded as a limiting factor on high gradient operation, is reduced with minimal impact on the shunt impedance. The peak surface magnetic field remains constant which is to be expected given the distance of the nose cones from the magnetic peak region of the cavity. The nose cone radii have no effect on the magnetic peak fields so they have been omitted.

3.3 Single Cell Re-entrant Cavities 81

Fig. 3.11 The effect of the nose cone radii on shunt impedance and peak fields for both S and X-band. Rx on the x-axis refers to the radii in the plot legend.

Figure 3.12 shows the effect of varying the nose cone angle on some important figures of merit. The shunt impedance decreases as the nose cone angle increases as does the peak surface electric field this is explained by the width of the base of the cone with respect to the height as was shown in Figure 2.13. As the nose cone angle decreases the field enhancement factor increases. The peak surface magnetic field does not change for S-band but for X-band it reduces slightly. One would expect the magnetic peak to increase as the cone angle pushes the base of the nose cone further into the magnetic peak section of the cavity, but this effect is not seen. The X-band cavity is more sensitive to changes in the nose cone angle than the S-band cavity. This is most visible in theZ plot in the bottom left. Z/Eacc stays

82 Small Aperture High Gradient Cavity Optimisation

Fig. 3.12 The effect of the nose cone angle on shunt impedance and peak fields for both S and X-band.

Figure 3.13 shows the effect of introducing and increasing the length of the flat section of the nose cone. The trends are similar for both frequencies but are much more pronounced in the lower frequency case, due to a larger range of values being used. The peak surface electric field decreases as the flat ‘blunts’ the sharp nose cone. In the lower frequency case this is rapid at the start then it saturates as the flat section extends further away from the electric peak region. As expected the peak surface magnetic field increases as the flat raises the radius Ron further into

the magnetic peak region. The shunt impedance reduces more rapidly than the peak surface electric field, so it is not the most effective parameter in reducing

Epeak as Rin is the most critical parameter for Z. A more effective optimisation

would be to reduceRon as that will have a lesser effect onZ for the same reduction

in Epeak This study was done to investigate the effect of varying the nose cone

parameters on the peak fields and shunt impedance, within the range of frequencies we are interested in. It will be referred to throughout this work to inform structure optimisation process. Throughout this thesis, every single structure presented has the nose cones individually optimised for the highest gradient within peak field limits. Every single parameter is optimised in every case, using the lessons learned in this nose cone study about which parameters are more effective for the desired outcome.