Profile distortion by beam space-charge in Ionization Profile Monitors

Measuring the transverse beam size in the Large Hadron Collider by using Ionization Profile Monitors is a difficult task for energies above injection during the energy ramp from 450 GeV to 6.5TeV. The beam size decreases from around 1mm to 200um and the brightness of the beam is high enough to destroy the structure of any form of interacting matter. While the electron trajectories are confined by an external electro-magnetic field which forces the electrons accordingly on helix paths with certain gyroradii, this gyration is heavily increased under the influence of the electric field of the beam. Smaller beam sizes, which go hand in hand with increased bunch electric fields, lead to larger gyroradii of the ionized electrons, which results in strongly distorted profiles. In addition, this distortion becomes more visible for smaller beam sizes as the extent of gyration grows compared to the actual beam size. Depending on the initial momentum distribution of the electrons, emerging from the ionization process with the highly relativistic beam, the profile distortion is affected significantly. In order to be able to perform reliable investigations into the effects of space charge a good knowledge of such initial momentum distributions is essential. The theoretical calculation of electron initial momenta will be discussed in order to obtain reliable results from the simulation of the electron movement within the ionization chamber which are used to investigate the effect of space charge on the registered profiles. An analytical approach to the mechanism of profile distortion is presented, which is based on the increased gyration of electrons after they left the space charge region. Their parallel movement close to the detector is unaffected by the bunch field and can therefore be described as a purely circular movement. A description of the profile distortion for single gyroradii, which is based on convolution, is built upon that mechanism along with the option of restoring the corresponding initial profile. A method for the correction of the registered profiles is presented, which is based on the partitioning of the detector profile with respect to the gyroradii of electrons. The distortion of the emerging partial profiles is described via convolution with corresponding point spread functions. Partial corrections can be obtained via deconvolution and together they yield the beam profile. A way of separating the electron signal with respect to the gyroradius in the form of an electron sieve is presented as well.