Linac Alignment Algorithm: Analysis on 1-to-1 Steering

Abstract

In a linear accelerator, it is important to achieve a good alignment between all of its components (such as quadrupoles, RF cavities, beam position monitors et al.), in order to better preserve the beam quality during acceleration. After the survey of the main linac components, there are several beam-based alignment (BBA) techniques to be applied, to further optimize the beam trajectory and calculate the corresponding steering magnets strength. Among these techniques the most simple and straightforward one is the one-to-one (1-to-1) steering technique, which steers the beam from quad center to center, and removes the betatron oscillation from quad focusing. For a future linear collider such as the International Linear Collider (ILC), the initial beam emittance is very small in the vertical plane (flat beam with γǫy = 20 − 40nm), which means the alignment requirement is very tight. In this note, we evaluate the emittance growth with one-to-one correction algorithm employed, both analytically and numerically. Then the ILC main linac accelerator is taken as an example to compare the vertical emittance growth after 1-to-1 steering, both from analytical formulae and multi-particle tracking simulation. It is demonstrated that the estimated emittance growth from the derived formulae agrees well with the results from numerical simulation, with and without acceleration, respectively. Linac alignment problemThe basic problem of linac misalignment can be sketched in Figure 1. The most ideal case is that all the elements of a linac are aligned on a straight line. In that case, there is no dispersive or wake-field-related emittance growth, if the beam is also injected on the axis. In practice, however, the linac components are scattered randomly with respect to the survey axis (treated as a straight line here) as shown in Figure 1. The beam will get a dipole kick when it pass by a quadrupole off center. If the offset is ∆y, the kick iswhere K 1 denotes the normalized quadrupole strength,Bρ , Bρ the beam rigidity which is proportional to beam energy, δ p the energy offset of the particle.In formula (1) it is shown that particle with different energy offset δ p (and same initial coordinates) will get different dipole kick from the same quadrupole misalignment, and then perform different motion and have different trajectory. That will introduce dispersion and the dispersive emittance growth which is δ p -correlated. In comparison, without the quadrupole misalignments (dipole kicks), the chromatic difference only from the quadrupole kick is relatively small, and all the particles will have "same" betatron linear oscillation under the quadrupole focusing.On the other hand, the beam centroid will follow the straight line without misalignment. With misalignment, it is also kicked and will perform "betatron" oscillation along the linac. Such an off-center distribution of the charges will generate wake field when it couples with the linac component impedance. The wake field has a longitudinal position correlation in the bunch, and wi...

A Linac Simulation Code for Macro-particles Tracking and Steering Algorithm Implementation

“…At the mean time this code is optimized for linac alignment or steering algorithm implementation. Some study results using this simulation code can be found in [1] [2] [3].…”

A Linac Simulation Code for Macro-Particles Tracking and Steering Algorithm Implementation

“…At the mean time this code is optimized for linac alignment or steering algorithm implementation. Some study results using this simulation code can be found in [1] [2] [3].…”