# Longitudinal Jitter Analysis of a Linear Accelerator Electron Gun
## 3 Results and Discussions  
To study bunching process in pre-injector caused by gun timing jitter in longitudinal direction, simulation was done by PARMELA software [12] at 136.8 keV pulsed beam by adjusting electron trigger timing without changing other parameters. To reach maximum total energy and stable beam at the linac exit, the energy spread has to be less than \(\pm\)0.5% and the emittance 0.1 mm mrad [6]. These parameters are affected the most by the bunching process, and therefore are studied in detail. In the beginning, gun trigger timing had no longitudinal jitter then beam parameters at A0 exit were calculated, as shown in Figure 7, which is composed of beam phase spectrum, beam profile, phase spread vs. energy spread and energy spectrum.  
The values of transverse section, average energy, energy spread, phase of the reference particle and normalized XY emittances were 1.9 cm \(\times\) 2 cm, 47.56 MeV 10.30%, 118.15\({}^{\circ}\) and 98.12, 98.76 mm mrad (38), respectively. To compare simulation results, 30 ps jitter was considered to calculate beam parameters which are shown in Figure 8.  
Figure 6: Persistently stored waveforms measured by the BCT1 and BCT2 under the condition with certain timing jitters.  
Figure 7: Nominal beam parameters at the A0 exit without any timing jitter.  
The corresponding parameters of transverse section, average energy, energy spread, phase of the reference particle and normalized XY-emittance were 1.8 cm \(\times\) 2 cm, 51.62 MeV, 10.81%, 124.39\({}^{\circ}\) and 100.70, 21.54 mm mrad (38), respectively. Then, the longitudinal jitter of the electron gun trigger timing was simulated from 0 ps to 350 ps. The beam parameters at A0 exit were calculated and are shown in Figures 9 and 10, respectively.  
Figure 8: Beam parameters at A0 exit with 30 ps longitudinal jitter.  
Figure 9: Variations in the beam energy, energy spread, and phase as a function of the gun timing.  
Consequently, the bunching efficiency from the gun to the A0 exit of the Linac changed in a range of 54.70% (from maximum 83.15% to minimum 28.45%), as shown in Figure 11.  
From the simulation results, it is obvious that the electron gun trigger timing longitudinal jitter affects the beam performance, including the beam size (profile), average energy, energy spread, emittance and phase of the reference particle. The simulation results of the beam performance are apparently different; the maximum and minimum percentage difference of beam size, average energy, energy spread, phase of reference particle and XY-emittances are 100%, 13.27%, 42.24%, 9.89\({}^{\circ}\) and 65.01% and 86.81%, respectively. Therefore, the electron trigger timing should be adjusted to optimize the longitudinal phase of the electron beam to achieve good beam performance and to keep injection efficiency to the storage ring as high as possible. A comparison between maximum and minimum values of beam parameters is given in Table 1.  
Figure 11: Variations in the bunching efficiency as a function of the gun timing.  
Figure 10: Variations in the \(x\) and \(y\) normalized emittance as a function of the gun timing.