CALCULATIONS OF ELECTRON BEAM MOTION IN ELECTRON COOLING SYSTEM FOR COSY

Results of calculations of electron beam motion in cooler for COSY (Juelich, Germany) are shown. The aim of the calculations is to study excitation of the beam galloping due to magnetic and electric field ripples, imperfection of bending field in toroids, transverse electric field in the end of accelerating tube etc. Dependences of the beam temperature on different parameters of magnetic and electrostatic systems are presented. Methods of correction of electron beam motion in order to decrease its transverse velocity are shown. INTRODUCTION In low energy electron coolers temperature (transverse velocity) of electron beam is not very important parameter because motion of electrons is adiabatic along full length of coolers from electron gun to collector and there is no significant excitation of transverse velocity. But in electron cooling systems for high energy, longitudinal Larmor length for electrons is high. Because of this, motion is not adiabatic and strong excitation of transverse temperature of the beam in possible. In such case investigation of electron motion in order to prevent strong increasing of electron transverse temperature is important task. There are several one-particle effects which can increase transverse temperature of electron during the flight in magnetic field of the electron cooler: 1) magnetic field ripples, 2) electric field ripples, 3) excitation on transverse electric field in the end of the acceleration tube, 4) excitation on transverse magnetic field in transition between different values of magnetic field, 5) entry and leaving from bending parts. In linear approximation, transverse beam motion in the system can be divided to for modes. First one is transverse shift of the beam relatively the reference line of the system without transverse velocity. Second one is dipole mode, in which all electrons of the beam with the same longitudinal coordinate move in transverse direction synchronously in the same direction, i.e. centre of mass of the beam moves, but there is no motion of electrons relatively the centre of mass. Third mode is synchronous motion of electrons relatively the centre of mass, but centre of mass doesn’t move. In literature such motion is called galloping. And the fourth mode appears in systems where quadruple component of transverse magnetic field exists. This mode changes transverse profile of the beam by compressing it in one direction and stretching in perpendicular direction. In systems with axial symmetry only galloping (third mode) can exist. Since in points 1-4 from the list above we suppose axial symmetry, only galloping can be excited there. In point 5 excitation of all modes is possible. Influence of quadruple component on the temperature of the beam is very weak and it can be adjusted by field index in bends of the cooler. According to this, we need only two different types of additional correctors: dipoles and axial lenses, for correction of beam motion. ELECTRON COOLER FOR COSY Electron cooler for COSY (Juelich, Germany) is constructed to work in wide range of operating electron energy: 25 keV (injection) – 2 MeV (maximum energy for the ring) [1]. Magnetic field in cooling section is 2 kG. Cooling time ~10 sec. Figure 1: Electron cooler for COSY. Strict requirements on size of the cooler, forces us to make its shape so complicated (fig. 1). In such shape acceleration and deceleration tubes are placed in one high voltage vessel. Length of acceleration tubes is 2 m. Along full trajectory from gun to collector electrons move in longitudinal magnetic field. Magnetic system of high voltage vessel consists of two sets of identical coils, producing longitudinal magnetic field in acceleration and deceleration tubes. Transport line between high voltage vessel and cooling section consists of three 90° bends, one 45° toroid, two straight sections for technical purposes and two sections with variable profile of magnetic field for minimization of excitation of transverse motion in transition between different values of magnetic field. Cooling section consists of special coils with possibility to adjust straightness of magnetic force line by rotating each coil independently [2]. Bending field in 90° bends (82 G for 2 MeV electrons) is made with special coils (fig. 2). Each bend includes 4 coils. We are THPMCP004 Proceedings of COOL09, Lanzhou, China 134 04 Electron Cooling planning to change current in every coil independently, so one can regulate both value of the field and field index.