Simulation of electron bunch trajectories through a Booster Cavity PITZ Group Tatiana Kozlova Supervisor: Marek Otevrel DESY, 7 September 2010

Group: Photo Injector Test Facility at DESY, Location Zeuthen (PITZ) The general goal of the group: to develop electron beams sources for linear colliders and free electron lasers PITZ setup

Booster Cavity The energy of the electron bunch is increased The electromagnetic field inside the booster can also deflect the beam The purpose: To simulate booster steering free trajectories To keep the beam on-axis

V-Code program. Booster section Goal: to obtain a simplified model of the booster cavity Input parameters: Output parameters: Transformation function (f ) V-Code is a beam dynamics simulation tool which is based on the moment approach.

Algorithm for finding transformation function - 1st order moments (simplified notation: ) - coefficients expanded using norm. Legendre polynomial

Practical steps for receiving the transformation function To figure out the acceptable initial parameters for the 1st order moments of electron bunch; To add the function of automatical loading the initial data and receiving the data from the V-Code; To receive 1st order moments of electron bunch (positions and angles of the centroid of the bunch) after the booster for different initial parameters (positions and angles in front of the booster and the reference phase); To obtain the view of booster transformation function.

Results : The acceptable initial parameters for the 1st order moments of electron bunch The maximal proper initial parameters for ensemble: The output beam energy as a function of the field phase for different field amplitudes. The output beam energy as a function of the field amplitude.

Results: The function of automatical loading the initial data and receiving the data from the V-Code Problem: a large number of calculations Initial parameters (range, steps) Output data file MatLab program C++ program Transformation function Set of Initial data Set of output data V-Code program

Results: The view of booster transformation function The linear basis functions: , where C000 C001 C010 x 0.0253 0.0013 y x’ 0.572 -0.504 y’

Results: The view of booster transformation function

Results: Electromagnetic field phase influence Phase scan of the beam position after the booster for different input parameters Blue cross – [0, 0, 0]; red line – [0.6, 0, 1]; green line – [0.6, 0.6, 0.6]; purple line – [1, 0, 0]; blue line – [1, 1, 1].

Summary Special thanks to my supervisor Marek Otevrel & Simulations of Booster were performed in V-Code program; The domain of acceptable parameters was found: The program of automatical loading and receiving data was added to the V-Code; 2D projections of the transformation function which represent the real booster were received in linear approximation; The investigation of electromagnetic field phase influence on the output position of the beam was performed. Special thanks to my supervisor Marek Otevrel & Thank you for your attention