Polarization control in spin-transparent hadron colliders by weak-field navigators involving lattice enhancement effect

Hadron polarization control schemes for Spin Transparent (ST) synchrotrons are analyzed. The spin dynamics and beam polarization in such synchrotrons are controlled by spin navigators (SN) which are special small insertions of weak magnetic fields. An SN stabilizes the beam polarization and allows for setting any desirable spin orientation at an interaction point in the operational regime, including a frequent spin flip. We present a general approach to design of SNs. We distinguish different types of SNs, namely, those not causing closed orbit perturbation as well as those producing local and global orbit distortions. In the second case, the concept of the spin response function in an ST synchrotron is applied and expanded to reveal the effect of the SN strength enhancement by magnetic lattice of the synchrotron. We provide conceptual schemes for SN designs using longitudinal and transverse magnetic fields allowing for polarization control at low as well as high energies. We also develop the ST concept for ultra-high energies. This development may enable and stimulate interest in polarized beam experiments in possible polarized collider projects such as Large Hadron Collider (LHC), Future Circular Collider (FCC) and Super Proton Proton Collider (SPPC).

A novel non-adiabatic approach to transition crossing in a circular hadron accelerator

Crossing the transition energy is always a delicate process, representing a potential source of strong perturbations of the dynamics of charged particle beams in a hadron circular accelerator. Since the first generation of multi-GeV rings, intense studies have been devoted to understanding the possible harmful mechanisms involved in transition crossing and to devise mitigation measures. Nowadays, several circular particle accelerators are successfully operating across the transition energy and this process is well mastered. In a completely different context, stable resonances of the traverse phase space have been proposed as new means of manipulating charged particle beams. While the original aim of such a proposal was multi-turn extraction from the CERN Proton Synchrotron to the Super Proton Synchrotron, many more applications have been proposed and studied in detail. In this paper, the two topics, i.e. transition crossing and stable resonances, have been brought together with the goal of providing a novel and non-adiabatic approach to perform a clean transition crossing. The idea presented here is that by judiciously using sextupoles and octupoles it is possible to generate stable islands of the horizontal phase space. These islands represent a second closed orbit whose properties can be selected independently of those of the standard, i.e. central, closed orbit. This provides a means of performing a non-adiabatic change of the transition energy experienced by the charged particles by displacing the beam between the two closed orbits.

Adaptive feedforward control of closed orbit distortion caused by fast helicity-switching undulators

A new correction algorithm for closed orbit distortion based on an adaptive feedforward control (AFC) has been developed. At SPring-8, two helicity-switching twin-helical undulators (THUs) had been implemented with conventional feedforward corrections. However, the validity of these corrections turned out to be expiring due to unforeseen variation in the error magnetic fields with time. The developed AFC system has been applied to the THUs dynamically updating the feedforward table without stopping the helicity switching amid user experiments. The error sources in the two THUs are successfully resolved and corrected even while the two THUs are switching simultaneously with the same repetition period. The actual operation of the new AFC system enables us to keep the orbit variations suppressed with an accuracy at the sub-micrometre level in a transparent way for light source users.

HOLDITCH-TYPE THEOREMS FOR THE POLAR MOMENT OF INERTIA UNDER THE 1-PARAMETER CLOSED PLANAR HOMOTHETIC MOTION

In this study, during the 1-parameter closed homothetic motion, the Holditch-Type Theorems are presented for the polar moments of inertia of the closed orbit curves of three non-collinear points.

CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C1 VECTOR FIELDS

Let M be a closed n-dimensional smooth Riemannian manifold, and let X be a $C^1$ -vector field of $M.$ Let $\gamma $ be a hyperbolic closed orbit of $X.$ In this paper, we show that X has the $C^1$ -stably shadowing property on the chain component $C_X(\gamma )$ if and only if $C_X(\gamma )$ is the hyperbolic homoclinic class.

Closed orbit feedback system for the fast ramping hadron synchrotrons

The realization of a fast and robust closed orbit feedback (COFB) system for the on-ramp orbit correction at SIS18 synchrotron of FAIR project is reported in this thesis. SIS18 has some peculiar behaviors including on-ramp optics variation, very short lengths of the ramps (200 ms to 1 s) and a cycle-to-cycle variation of beam parameters. The realized fast COFB system being robust against above mentioned features of SIS18 is a first of its kind and the course to its realization led to some novel contributions in the field of closed orbit correction. A new method relying on the discrete Fourier transform (DFT)-based decomposition of the orbit response matrix (ORM) has been introduced, exploiting the symmetry in the arrangement of beam position monitors (BPMs) and the corrector magnets in the synchrotrons. A nearest-circulant approximation has also been introduced for synchrotrons having slight deviation from the symmetry, making the method applicable to a vast majority of synchrotrons. Moreover, the performance and the stability analysis of COFB systems in the presence of ORM mismatch between the synchrotron and the feedback controller is presented. The COFB systems are divided into slow and fast regimes and a new stability criterion consistent with measurements, is introduced. The practicality of the criterion is verified experimentally at COSY Jülich and is used for the analysis of various sources of ORM mismatch at SIS18. The commissioning of the SIS18 COFB system is also reported in detail which relies on Libera Hadron as the main hardware resource for the controller implementation. The on-ramp orbit correction is demonstrated for the horizontal plane of SIS18, for the disturbance rejection up to 600 Hz.

Photodetachment of the H– ion in a forced harmonic potential

The photodetachment of a H– ion in a forced harmonic potential driven by a general time-dependent oscillating electric field has been investigated in the semi-classical closed orbit theory for the first time. It is found that the driven electric field frequency can affect the photodetachment cross-section of this system greatly. If the frequency of the driving electric field is equal to the harmonic frequency, a resonance phenomenon occurs in the classical motion of the detached electron. The interference effect between the returning electron wave travelling along the closed orbit with the initial outgoing wave gets stronger, causing the photodetachment cross-section to oscillate in a complicated manner. When the frequency of the driving electric field is unequal to the harmonic frequency, the driving electric field can weaken or strengthen the oscillatory structure in the photodetachment cross-section. In addition, the strength and initial phase in the driving electric field can also influence the photodetachment dynamics of the system. Our work provides a new method for controlling the photodetachment of negative ions in a harmonic potential and may guide future experimental research for cavity dynamics or in the ion trap.