Mechanical optimization of superconducting cavities in continuous wave operation

Several planned accelerator facilities call for hundreds of elliptical cavities operating cw with low effective beam loading, and therefore require cavities that have been mechanically optimized to operate at high $Q_L$ by minimizing $df/dp$, the sensitivity to microphonics detuning from fluctuations in helium pressure. Without such an optimization, the facilities would suffer either power costs driven up by millions of dollars or an extremely high per-cavity trip rate. ANSYS simulations used to predict $df/dp$ are presented as well as a model that illustrates factors that contribute to this parameter in elliptical cavities. For the Cornell Energy Recovery Linac (ERL) main linac cavity, $df/dp$ is found to range from 2.5 to $17.4\mathrm{Hz}/\mathrm{mbar}$, depending on the radius of the stiffening rings, with minimal $df/dp$ for very small or very large radii. For the Cornell ERL injector cavity, simulations predict a $df/dp$ of $124\mathrm{Hz}/\mathrm{mbar}$, which fits well within the range of measurements performed with the injector cryomodule. Several methods for reducing $df/dp$ are proposed, including decreasing the diameter of the tuner bellows and increasing the stiffness of the enddishes and the tuner. Using measurements from a Tesla Test Facility cavity as the baseline, if both of these measures were implemented and the stiffening rings were optimized, simulations indicate that $df/dp$ would be reduced from $\sim 30\mathrm{Hz}/\mathrm{mbar}$ to just $2.9\mathrm{Hz}/\mathrm{mbar}$, and the power required to maintain the accelerating field would be reduced by an order of magnitude. Finally, other consequences of optimizing the stiffening ring radius are investigated. It is found that stiffening rings larger than 70% of the iris-equator distance make the cavity impossible to tune. Small rings, on the other hand, leave the cavity susceptible to plastic deformation during handling and have lower frequency mechanical resonances, which is undesirable for active compensation of microphonics. Additional simulations of Lorentz force detuning are discussed, and the results are compared to measurements on the ERL injector cavities.

Figure 1

Power required to maintain a constant accelerating gradient as a function of current and detuning. Parameters from the Cornell ERL main linac are used.

Figure 2

Detuning of a Cornell ERL injector cavity in the presence of microphonics.

Figure 3

Section view of a CAD model of a Cornell ERL main linac cavity. In the model shown, the cavity has stiffening rings at the same radius used in ILC cavities.

Figure 4

Section view of a CAD model of a Cornell ERL injector cavity.

Figure 5

ANSYS mesh of the ERL 7-cell cavity with helium tank. The tan bellows-like part on the right is the simplified tuner. It is supported by the rigid blue plate. In this model, the stiffening rings between the cells have a 155 mm inner diameter.

Figure 6

$df/dp$ of the 7-cell cavity for several wall thicknesses from 2 to 4 mm and tuner stiffnesses from 50 to $200\mathrm{kN}/\mathrm{mm}$, as a function of the radial position of the stiffening ring, given as a fraction of the iris-equator distance [i.e. $(r_{\mathrm{ring}}-r_{\mathrm{iris}})/(r_{\mathrm{equator}}-r_{\mathrm{iris}})$].

Figure 7

Measured $\Delta f$ versus $\Delta p$ of the 2-cell cavities for different tuner positions. The prediction from ANSYS simulations is also shown, which assumes the stiffness of the tuner is $31\mathrm{kN}/\mathrm{mm}$.

Figure 8

$df/dL$ of the Cornell ERL 7-cell main linac and 2-cell injector cavities.

Figure 9

Spring model of the longitudinal stiffness of the 7-cell assembly (above) and the 2-cell assembly (below).

Figure 10

$K$ of the two cavity assemblies, with data from both a simulation of the full model and from simulations of individual parts, put together using the equations in Fig. 9.

Figure 11

$dF/dp$ of the cavities, showing both the nominal result and the result if no pressure is applied to the end walls. In the latter case, the magnitude of $dF/dp$ decreases nearly to zero.

Figure 12

Comparison of the breakdown of $df/dp$ to the full simulation. The open markers correspond to the 2-cell cavity.

Figure 13

One method of decreasing $df/dp$ is reduction of the diameter of the bellows used in conjunction with the Saclay tuner.

Figure 14

Required force for frequency tuner and maximum stress in the cavity at maximum tuning. Inset are images showing deflection in the cavity for selected stiffening ring radii. Blue locations are least deflected, and red locations are most deflected.

Figure 15

Effect of gravity on a cavity seated on its enddishes.

Figure 16

Frequencies of the first 6 mechanical resonances of the 7-cell cavity for various stiffening ring radii.

Figure 17

Lorentz force detuning coefficients from ANSYS of the ERL injector and main linac cavities. The ILC cavity is also shown for comparison, with measurement reported from 20.

Figure 18

Lorentz force detuning measurement of an ERL injector cavity.