Turn-by-Turn Measurements for Systematic Investigations of the Micro-Bunching Instability

While recent diffraction-limited storage rings provide bunches with transverse dimensions smaller than the wavelength of the observed synchrotron radiation, the bunch compression in the longitudinal plane is still challenging. The benefit would be single cycle pulses of coherent radiation with many orders of magnitude higher intensity. However, the self-interaction of a short electron bunch with its emitted coherent radiation can lead to micro-bunching instabilities. This effect limits the bunch compression in storage rings currently to the picosecond range. In that range, the bunches emit coherent THz radiation corresponding to their bunch length. In this paper, new measurement setups developed at the Karlsruhe Institute of Technology are described for systematic turn-by-turn investigations of the micro-bunching instability. They lead to a better understanding thereof and enable appropriate observation methods in future efforts of controlling and mastering the instability. Furthermore, the described setups might also be used as high repetition rate bunch compression monitors for bunches of picosecond length and below. MICRO-BUNCHING INSTABILITY The micro-bunching instability (MBI) is a longitudinal instability that arises due to the self-interaction of a bunch with its emitted electro-magnetic field. This interaction can be modelled by a synchrotron-radiation impedance whose real part corresponds to the emitted radiation. The impedance has a low frequency cutoff due to the shielding of the vacuum chamber [2] and a high frequency cutoff due to the particle energy. The shielded wavelengths can be approximated with the shielding cutoff λ = 2h √ h/R with h being the beam pipe height and R the particles radius of curvature, while the high frequency cutoff can be approximated by the critical frequency of the synchrotron radiation fc = 3γ c/(4πR). Therefore, the impedance has significant strength if γ √ h3R−3 ' 2.While this applies to almost all light sources, only a few heavy particle machines reach high enough energies. However, also future colliders will be confronted with high amount of synchrotron radiation. In order to generate a significant wake potential, the bunch spectrum and the impedance need to overlap. As a rule ∗ Funded by the German Federal Ministry of Education and Research (Grant No. 05K16VKA) & Initiative and Networking Fund of the Helmholtz Association (contract number: VH-NG-320). M. Brosi, P. Schönfeldt and J. Steinmann acknowledge the support of the Helmholtz International Research School for Teratronics (HIRST). † johannes.steinmann@kit.edu 1 For a good summary of the topic see Ref. [1]. of thumb, storage rings with a few meters bending radius and some tens of centimeters beam-pipe height typically have a cutoff around hundred gigahertz, leading to a critical bunch length around ten picoseconds. At first, the additional wake potential leads to potential well distortion and a change of bunch shape. Then, above a critical bunch charge, a self-amplified system is formed since the distorted bunch shape increases the wake potential further. This leads to the formation of sub-structures on the bunch profile and a blowup of the bunch in phase space. The blow-up is much faster and stronger than the damping time and no equilibrium is reached. The bunch is blown up, until the wake potential becomes negligible. Then, the radiation damping shortens the bunch, until the threshold is hit again. Consequently, a sawtooth behaviour is observed. Due to the characteristic bunch size of a few picoseconds and even smaller substructures, signatures of the instability can be seen in the terahertz frequency range where outbursts of coherent radiation are observed. Obviously, the behaviour is beam current dependent, too. The relevant time scales when observing the MBI reach from a few turns during the start of a burst, over some milliseconds between consecutive bursts, to minutes and hours when analyzing current dependent changes. Consequently, the diagnostics need to be single shot, turn-by-turn and be able to record for long time scales. In this paper, we will present recent diagnostic systems developed and evaluated at the Karlsruhe Institute of Technology (KIT).