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

2. 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

3. 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

4. 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.

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

6. 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.

7. 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.

8. 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

9. 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’

10. Results: The view of booster transformation function

11. 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].

12. 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