Full structure

In the previous sections the coupler cell and the end cells have been tuned to 2.9985 GHz by adjusting the length of the gap between the nose cone. The bottle-

neck of the coupler has been adjusted to achieve roughly critical coupling. In this section the end cells are added to the 3-cell coupler model with normal accelerating and coupling cells between to form an 11-cell prototype structure. The vacuum model is shown in Figure 4.17.

138 Large Aperture High Gradient Cavity Optimisation

Fig. 4.17 CST vacuum model of the 11-cell prototype structure.

Previously the length of the side-coupled cell was reduced by 0.4 mm to achieve

field flatness after the addition of the power coupler. The magnitude of the electric field along axis is plotted in Figure 4.18 and shows the cavity is no longer field flat.

Fig. 4.18 Magnitude of the electric field along axis of the 11-cell prototype structure with a reduction in coupling of 0.4 mm.

Figure 4.19 showsS₁₁ for the 11-cell model shown in Figure 4.17. The cavity

is no longer well matched reflecting more than half the power at the operating frequency. There is also an unwanted mode near 3 GHz.

4.4 Final Prototype Structure 139

Fig. 4.19 .

The reduction in accelerating cell length was swept again to find the optimum. Reducing the length of the coupling cells by a further 0.05 mm was necessary to

achieve the electric field distribution shown in Figure 4.20 and plotted in the top plot of Figure 4.21.

Fig. 4.20 The 11-cell prototype electric field distribution after final optimisation.

The bottleneck of the power coupler was also re-optimised to achieve critical coupling that is shown in Figure 4.21. The final results shown in this figure were obtained running a high mesh simulation (70 cells per wavelength) as this is the final characterisation before manufacturing the structure.

140 Large Aperture High Gradient Cavity Optimisation

Fig. 4.21 Electric field distribution along the beam axis of the prototype model after final optimisation (Top). S-parameters of prototype structure after final optimisation simulations (Bottom).

The resonance peak in the bottom left plot of Figure 4.21 is slightly off frequency which was initially thought to be acceptable due to the large tuning ability provided by the tuning pins which are added in Chapter 6. After the drawings of this cavity had been completed and sent to the manufacturer an additional simulation was done using the Eigenmode solver to confirm the final dispersion curve of the prototype structure. This is shown in Figure 4.22. Only modes 7-12 appear as one one expect in a typical dispersion curve. Mode 12 is the accelerating π/2 mode and mode 13

is the side-coupled π/2 mode. It is clear that the stopband has not closed and

thus the accelerating mode lies on a plateau rather than the steepest past of the dispersion curve. The accelerating mode will be unstable due to its proximity to its neighbour mode 11.

4.4 Final Prototype Structure 141

Fig. 4.22 Dispersion curve of the final prototype structure. The stop-band between the twoπ/2 modes has not been adequately closed.

The final tuning simulations for the full prototype were performed using the frequency domain in CST, with a field monitor set up at 2.9985 GHz to observe the

fields at this frequency. Due to the final structure being completed in great haste to meet a non-negotiable deadline, the widening of the stopband was regrettably overlooked until after the manufacture of the disks. It was assumed that because field flatness had been satisfied the stopband was also closed. Reducing the length of side-coupled cell simply detuned them and took them far away from the resonant accelerating cells. Figure 4.23 shows the accelerating mode of the final prototype structure at 2.998 69 GHz. The mode is only slightly off frequency but unfortunately

the field is not completely flat as is shown in Figure 4.24. The mode should be able to be bought to the correct frequency with the tuning pins presented in Chapter 6. This will allow a high power test of the cavity to still be successfully completed. However it is unlikely the large 20 MHz stop-band between the accelerating π/2

mode and the side-coupled π/2 mode, can be closed with the tuning pins. It may

be possible to send the machined disks for further machining to take a millimetre off of the side-coupled cells before bonding, and bring the structure within the range of the tuning pins.

142 Large Aperture High Gradient Cavity Optimisation

Fig. 4.23 Ez of the accelerating mode of the final prototype structure at 2.99869

GHz.

Fig. 4.24 The Z-component of the electric field on axis of the accelerating mode of the final prototype structure.

Chapter 5

Beam Dynamics

Transverse and longitudinal beam dynamics were introduced in Chapter 2 alongside many other concepts necessary for designing an RF cavity. The primary goal of an RF cavity is to accelerate a beam of charged particles to the desired output energy, but it is also important to produce enough output current. Beam dynamics must be considered from the very start of the cavity design process and throughout to ensure the RF design is optimal for that specific application. In the case of the ProBE linac the beam current must be sufficient to ensure imaging of each patient in a clinically acceptable period of time. A significant beam loss of around 90% of particles is inherent in all cyclinac schemes due to the large frequency mismatch between the 72.8 MHz cyclotron and the high frequency (3-12 GHz) linac,

a small transverse aperture can contribute more loss considering the relatively large transverse emittance c.10 mm−mrad obtained from therapy cyclotrons. In this

chapter the beam dynamics studies that were undertaken alongside, and informed the RF cavity optimisation are presented. Both a small aperture and a large aperture scheme were considered. By minimising the beam aperture radius, one can maximise the shunt impedance and thus accelerating gradient of a cavity. However, a smaller aperture means the transverse beam size must be kept to a minimum requiring more focussing magnets between cavities. More magnets between cavities means less space for accelerating cavities, and shorter cavities require higher gradients to achieve the same acceleration. Therefore a large aperture scheme was also studied to see if the optimal was longer cavities with lower gradient, that require less intense focussing between cavities. Following that the cavity length is investigated to ensure that is also the optimum. In this study the starting energy is 230 MeV and the final energy is 330 MeV.

144 Beam Dynamics

5.1

Cyclotron Linac Beam Matching

The ProBE booster linac is a normal conducting pulsed machine, the RF power is pulsed to enable higher peak powers to be utilised while the average power is suitably low to prevent excess heating. A typical 50 MW klystron foreseen to power this linac can be pulsed at a maximum repetition rate of 200 Hz with a maximum pulse length 5 µs, corresponding to a maximum duty cycle of 0.1%, meaning the

linac is off for the vast majority of the time - 99.9%. At PSI [59] cyclotron beam ‘chopping’ has been successfully demonstrated, to reduce activation of the linac during ‘off time’ [126]. This enables the cyclotron beam to be pulsed at 200 Hz to match the klystron repetition rate, with a rise time of 1 µs. Within each 5 µs flat

top ‘pulse’ from the cyclotron are 357, 0.8 ns long pulses, bunched at the cyclotron

frequency of 72.8 MHz which corresponds to every 13.7 ns. 1 period of RF at 3 GHz

is 0.3 ns long thus each proton bunch from the cyclotron sees just over 2.5 RF

periods in the linac. These concepts are visualised in Figure 5.1.

Fig. 5.1 Timing diagram for the cyclinac scheme, showing, from top to bottom, the linac RF pulses, the cyclotron pulses, the linac RF in each pulse and the proton intensity profile [67].

The Christie Varian ProBeam cyclotron [127] has an extraction current at 230 MeV up to 800 nA. Taking into account the duty cycle at 200 Hz from the cyclotron linac frequency mismatch, the average current entering the linac is 0.8 nA.

To achieve the required imaging current of 3.2 pA [128] the linac must have a total

transmission of only 0.4%. If the structure needs to operate with a lower duty cycle, the transmission required through the structure to deliver the same dose must