Coherent structures in an electron beam
  The formation and evolution of coherent structures in a low-energy electron beam produced in a Malmberg-Penning trap is investigated by means of CCD diagnostics. The electrons are emitted from a thermionic cathode and their energy is controlled by an acceleration grid. By varying the spatial distribution of the energy of emitted electrons, different space charge effects are observed, as, e. g., a sharp or a gradual transition to a space charge dominated regime. The variation of the coherent structures along the beam is studied by varying the electron density or/and the value of the confined magnetic field. The observed processes are interpreted using a tridimensional particle-in-cell code which solves the Vlasov-Poisson system in zeroth order drift approximation. 
Andrea Illiberi, Giovanni Bettega, Marco Cavenago, Franca De Luca,   Roberto Pozzoli, Massimiliano Rome', Yuri Tsidulko