Redundant field survey data of cyclotron with imperfect median plane

Abstract

An accurate and detailed field map is important for cyclotron beam dynamics studies. During the long history of cyclotron studies, many techniques have been developed by cyclotron pioneers for the treatment of median plane field map. In this paper, we take the TRIUMF 500 MeV cyclotron as an example to study the asymmetric field resulting from imperfect median plane symmetry. The “Gordon approach” and a highly accurate compact finite differentiation method are used to investigate the historical field survey data. The redundancy in the survey data is revealed by the expansion method, which also makes it possible to correct the error in the measurement. Finally, both the azimuthal field Bθ and the axial gradient of the axial field dBz /dz in the median plane are corrected using the radial field map Br . The influence of the correction is examined by recalculating the equilibrium orbit properties of the TRIUMF cyclotron. The result shows significantly increased vertical centering errors of the closed orbits. A further simulation study suggests that these centering errors can be reduced to below 1.5 cm by adjusting the trim coils' Br field within the output limits of our trim coils' power supplies. The error in the measurement field data may explain why the calculated trim coils' settings during the cyclotron commissioning in 1974 encountered difficulty.

Intensity limit in compact H- and H+ 2 cyclotrons

“…[24]. We also reproduced the calculation shown in [25, figure 2] using equation (2.20) to calculate the electric focusing, and a CYCLOPS run with the historical magnetic survey data CYC581 [26]. The result is presented in figure 3.…”

Constant-tune cyclotrons

“…The magnetic field off the median plan can be obtained from extrapolation using Maxwell's equations, see for instance ref. [12].…”

Cyclotrons: Why/how are their dynamics different?

“…This suggests 𝛾 ∼ 10 as a rough upper limit for cyclotron economic viability. More recent designs exist up to 𝛾 = 3, and one is included in this issue [39], but none have been built beyond 𝛾 = 1.6: the PSI cyclotron and it has already been running for over 50 years [17,36].…”

“…These two parts can be expanded by Maxwell equations to give all the three field components in the median plane. The technique can be found in the thesis of Mort's final graduate student, Dong-O Jeon [21], and has been applied here by Lige Zhang [39] to analyze some self-consistency issues in the TRIUMF magnetic field data. Mort Gordon was a remarkable man.…”