Superconducting resonator used as a phase and energy detector for linac setup

Booster linacs for tandem accelerators and positive ion superconducting injectors have matured into standard features of many accelerator laboratories. Both types of linac are formed as an array of independently-phased resonators operating at room temperature or in a superconducting state. Each accelerating resonator needs to be individually set in phase and amplitude for optimum acceleration efficiency. The modularity of the linac allows the velocity profile along the structure to be tailored to accommodate a wide range charge to mass ratio. The linac setup procedure, described in this paper, utilizes a superconducting resonator operating in a beam bunch phase detection mode. The main objective was to derive the full set of phase distributions for quick and efficient tuning of the entire accelerator. The phase detector was operated in overcoupling mode in order to minimize de-tuning effects of microphonic background. A mathematical expression was derived to set a limit on resonator maximum accelerating field during the crossover search to enable extracting unambiguous beam phase data. A set of equations was obtained to calculate the values of beam phase advance and energy gain produced by accelerating resonators. An extensive range of linac setting up configurations was conducted to validate experimental procedures and analytical models. The main application of a superconducting phase detector is for fast tuning for beams of ultralow intensities, in particular in the straight section of linac facilities.

Figure 1

Layout of the superconducting linac booster. The main components are: two target areas TA1 and TA2; the superbuncher C1; split loop resonator (SLR) modules C2 and the time-energy lens C3; 90 degrees achromatic bend A1 and 180 degrees achromat A2. The insert in the left top corner shows a rendered image of a cryostat module housing three SLR.

Figure 2

Low frequency phase detecting mode for distributions of $E$-field (a) and $H$-field (b) in a SLR.

Figure 3

The four lowest mechanical modes in SLR identified using Strand7.

Figure 4

Experimental setup utilizing a superconducting SLR as a beam phase detector.

Figure 5

The dependence of bunch phase advance $\mathrm{\Delta }{\mathrm{\Psi }}_{\det }$ as a function of bunch relative energy change $\mathrm{\Delta }E/E$ as per Eq. (7). The numbers in brackets corresponds to vertical axis scaled down by a factor of 10. The parameter $k$ is shown as a number next to the right vertical axis. The two solid lines with arrow heads show graphically how to determine $\mathrm{\Delta }{\mathrm{\Psi }}_{\det }$ if parameters $\mathrm{\Delta }E/E$ and $k$ are known. The two dashed lines with arrow heads illustrate how to define $\mathrm{\Delta }E/E$ if the parameters $\mathrm{\Delta }{\mathrm{\Psi }}_{\det }$ and $k$ are identified.

Figure 6

Time dependence of the instantaneous resonance frequency deviation $\mathrm{\Delta }F$ from the reference frequency of the unlocked SLR at 4.2 K in the ambient cryostat environment.

Figure 7

Example of SLR rf field, generated by a bunched beam passing through the resonator. The energy of the ${{}^{58}\mathrm{Ni}}^{+22}$ beam is 185 MeV and the beam current is 7 nA. The last (12th) linac resonator is used as the phase detector.

Figure 8

Relative beam bunch phase $\mathrm{\Delta }{\mathrm{\Psi }}_{\det }/\mathrm{\Delta }{\mathrm{\Psi }}_{\det \max }$ shown by open circles as detected by the superconducting phase detector as a function of the cosine of the operating phase of the linac accelerating resonator $\cos (\mathrm{\Delta }{\mathrm{\Psi }}_{\mathrm{acc}})$. The straight solid line is the theoretical prediction of the same relationship. The energy of ${{}^{58}\mathrm{Ni}}^{+22}$ beam produced by terminal and linac stripper is 185 MeV and beam current is 7 nA. The last (12th) linac resonator is configured as the phase detector.

Figure 9

Phase shift of the bunch phase measured with superconducting SLR 4.3 with respect to the master oscillator as a function of time. Each segment signifies the operation condition of the rf resonators. 1.1 stands for the first SLR in the first module cryostat, etc. RTB (yellow area) stands for room temperature buncher and SB (pink area) for super buncher. Examples of typical operating conditions of resonator 1.2: UNL- operation SEL in unlocked mode; PL- phase locked condition; $\varphi 1$, $\varphi 2$, and $A\varphi$ are two crossovers and acceleration phase correspondingly.

Figure 10

MWS $E$-field distribution along the axis of the 150 MHz SLR.

Figure 11

MWS $H$-field distribution along the axis of the 150 MHz SLR.