Vladimir Balandin

Hamiltonian methods for the study of polarized proton beam dynamics in accelerators and storage rings

The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket (3) and Hamiltonian function (5). After this extension it becomes possible to apply the methods of the theory of Hamiltonian systems to the study of polarized particles beam dynamics in circular accelerators and storage rings. Some of those methods have been implemented in the computer code FORGET-ME-NOT [1], [2].

Computation and analysis of spin dynamics

A method is described that allows the computation and analysis of high-order spin maps for general non-autonomous optical systems. It is shown how the equations of motion in curvilinear coordinates resulting from the Thomas-BMT equation can be solved within a differential algebraic framework in SU(2) and SO(3) representations. The resulting maps are subjected to a spin-orbit normal form transformation, and the nonlinear orbit dependencies of the invariant polarization axis as well as the orbit dependent spin tune can be obtained. For the case of electron machines, the resulting invariant polarization can be used to determine the radiative equilibrium polarization via the Derbenev-Kondratenko approach. Both the computation of the spin map as well as the algorithm for the computation of the invariant axis have been implemented in the code COSY INFINITY [2] [3] [4].

Operation of Free Electron Laser FLASH Driven by Short Electron Pulses

The program of low charge mode of operation is under development at free electron laser FLASH aiming in single mode radiation pulses. A short pulse photoinjector laser has been installed at FLASH allowing production of ultrashort electron pluses with moderate compression factor of the beam formation system. Here we present pilot results of free electron laser FLASH operating at the wavelength λ = 13.1 nm and driven by 70 pC electron bunches. Relevant theoretical analysis has been performed showing good agreement with experimental results.

Emittance Reduction Possibilities in the PETRA III Magnet Lattice

PETRA III is a third generation light source at DESY that has been operated as a user facility since 2010 with a horizontal emittance of 1 nm · rad at a beam energy of 6 GeV. Recently an upgrade for additional photon beamlines has been carried out, and the recommissioning of PETRA III started in February 2015 [1]. Because the current optics solution for the upgraded storage ring predicts about 20% increase in the horizontal emittance, it motivates us to study a question whether or not there are optics modifications which allow the reduction of the emittance without significant changes in the present magnet arrangement. In this paper we present the results of the first look at this problem mostly limiting our consideration to the capabilities of the linear optics of the separate storage ring parts. STORAGE RING OVERVIEW The current layout of the PETRA III storage ring [2,3] is shown in Fig. 1, and one sees that it does not look like a conventional synchrotron light source constructed from large number of identical cells accommodating insertion devices. This is a result of a long history of the modifications of the facility. The former electron-positron collider PETRA has been turned into a pre-acceleratorPETRA II for HERA, and then, after the shutdown of HERA, PETRA II has been converted into the synchrotron light source. PETRA II has consisted of four identical quadrants, each of them mirror symmetric with respect to the center of a straight section. Therefore one octant (half of quadrant or one eight of the ring) has reflected all lattice and optics properties of the machine. For PETRA III [2] it was decided to accommodate all insertion devices in one octant. The octant extending from North-East to East was redesigned, and the FODO lattice was replaced by a sequence of the doublebend achromat (DBA) cells (in the following we will refer to this section as the “new octant”). Besides that, for the additional emittance reduction, twenty 4 m long damping wigglers were installed in the straight sections West and North. As concerning the chromaticity correction, no sextupoles were placed in the DBA lattice, and the chromaticity correction was performed globally using old sextupoles in the remaining seven octants [4]. In the recent upgrade [3] two new experimental halls were built, one in the North and one in the East, each housing 5 new photon beamlines. In order to accommodate new insertion devices, the part of the hardware of arcs in two old octants is removed and replaced by DBA-like cells (the extensions North and East), and for the rest of these arcs (shortened octant arcs) the FODO structure is kept. No new ∗ nina.golubeva@desy.de sextupoles are added but several old sextupoles are uninstalled that leads to some reduction of the dynamic aperture (∼ 20% predicted, which is acceptable).

Algorithms for the treatment and analysis of spin dynamics in SU(2) and SO(3)

A method is described that allows the computation and analysis of high-order spin maps for general non-autonomous optical systems. It is shown how the equations of motion in curvilinear coordinates resulting from the Thomas-BMT equation can be solved within a differential algebraic framework in SU(2) and SO(3) representations. The resulting maps are subjected to a spin-orbit normal form transformation, and the nonlinear orbit dependencies of the invariant polarization axis as well as the orbit dependent spin tune can be obtained. For the case of electron machines, the resulting invariant polarization can be used to determine the radiative equilibrium polarization via the Derbenev-Kondratenko approach. Both the computation of the spin map as well as the algorithm for the computation of the invariant axis have been implemented in the code COSY INFINITY [2] [3] [4].