Abstract

Thermionic-cathode radio-frequency electron gun (RF gun) has been a compact electron source of accelerators for more than two decades. In an RF gun, electrons pulled out from the cathode by the high gradient field setup in its microwave cavity are rapidly accelerated to relativistic energy such that space charge effects are less significant. Motivated by the need of a high quality electron source for the NSRRC ultrashort beam facility, we studied a 2998 MHz, 1/2+1/2+1 cell, thermionic cathode RF gun with on-axis coupled structure (OCS RF gun). OCS RF gun features simplicity of frequency tuning during fabrication due to its axial symmetry. We started with circuit analysis that provides a reliable model through the investigation. Microwave properties and electron beam characteristics of designed OCS RF gun has been evaluated by 2D simulations of SUPERFISH and PARMELA as well as 3D simulations of HFSS and CST-PS. Operating parameters are optimized to obtain a 2.5 MeV electron beam with quasi-linear energy chirp that allows aggressive bunch compression in the RF linac located downstream after proper beam selection. We have also investigated power distribution of back-streamed electrons that eventually lost onto the surface of thermionic cathode. A prototype of the designed OCS RF gun structure has been fabricated for low power microwave test. Measured frequencies and longitudinal electric field profile of the cavity structure agree well with the results predicted in the simulation studies.

Abstract

Thermionic-cathode radio-frequency electron gun (RF gun) has been a compact electron source of accelerators for more than two decades. In an RF gun, electrons pulled out from the cathode by the high gradient field setup in its microwave cavity are rapidly accelerated to relativistic energy such that space charge effects are less significant. Motivated by the need of a high quality electron source for the NSRRC ultrashort beam facility, we studied a 2998 MHz, 1/2+1/2+1 cell, thermionic cathode RF gun with on-axis coupled structure (OCS RF gun). OCS RF gun features simplicity of frequency tuning during fabrication due to its axial symmetry. We started with circuit analysis that provides a reliable model through the investigation. Microwave properties and electron beam characteristics of designed OCS RF gun has been evaluated by 2D simulations of SUPERFISH and PARMELA as well as 3D simulations of HFSS and CST-PS. Operating parameters are optimized to obtain a 2.5 MeV electron beam with quasi-linear energy chirp that allows aggressive bunch compression in the RF linac located downstream after proper beam selection. We have also investigated power distribution of back-streamed electrons that eventually lost onto the surface of thermionic cathode. A prototype of the designed OCS RF gun structure has been fabricated for low power microwave test. Measured frequencies and longitudinal electric field profile of the cavity structure agree well with the results predicted in the simulation studies.

Contents

Abstract i
Acknowledgement ii
List of Figure viii
List of Table xv

Chapter 1 Introduction
1.1 Background 1
1.1.1 Brief History 1
1.1.2 The NSRRC Ultrashort Beam Facility 2
1.1.3 The Side-coupled Structure Thermionic RF Gun at NSRRC 3
1.2 On-Axis Coupled Structure RF Gun 5
1.3 Research Purpose and Methodology 6

Chapter 2 Principles of RF Electron Gun
2.1 Pillbox Cavity from Cylinder Waveguide 8
2.2 Parameters of an Accelerator Cavity 12
2.2.1 Energy Gain and Transit Time Factor 12
2.2.2 Cavity Losses and Shut Impedance 13
2.2.3 The Quality Factor 14
2.2.4 Equivalent Circuit 15
2.3 RF Electron Gun 16
2.3.1 Mechanism 16
2.3.2 Coupled Cavity Modes 17
2.4 Beam Dynamics 19
2.4.1 The Emittance 19
2.4.2 RF Acceleration 21
2.4.3 F Effect on Transverse Phase Space 23
2.4.4 RF Effect on Longitudinal Phase Space 24
2.4.5 Space Charge Effect 26

Chapter 3 Literature Review
3.1 The OCS gun designed by KHI 28
3.1.1 Simulation Results of the OCS gun designed by KHI 29
3.1.2 Measurement Results of the OCS gun designed by KHI 33
3.2 The OCS type RF gun designed by MAX-Lab 36

Chapter 4 Design and Simulations of Tuning
4.1 Design Specifications 40
4.2 Circuit Analysis of Three-cell Coupled Cavities 42
4.2.1 The Equivalent RLC Circuit 42
4.2.2 Resonant Frequencies 45
4.2.3 Coupling Coefficients between Cavity Cells 47
4.2.4 Field Ratio 48
4.2.5 Input Coupling 51
4.2.6 The Special Case for π/2-mode 53
4.3 Simulation Tools 55
4.3.1 SUPERFISH 55
4.3.2 PARMELA 55
4.3.3 HFSS and CST PS for 3D Simulation 56
4.4 SUPERFISH Simulations 57
4.4.1 Convergence Test by a Pillbox Cavity 57
4.4.2 Dimension of the Structure 58
4.4.3 Frequency Tuning 59
4.4.4 Field Ratio Tuning 60
4.4.5 Mode Separation 61
4.4.6 Microwave Properties after Tuned in SUPERFISH 62
4.5 HFSS Simulations 63
4.5.1 Convergence Test and Mesh Settings 63
4.5.2 Optimization of Mode Separation 64
4.5.3 Asymmetric Structure Module 66
4.5.4 Tuning and Results 68

Chapter 5 Electron Beam Properties
5.1 PARMELA Simulations 73
5.1.1 Beam Properties of Designed OCS Gun 74
5.1.2 Comparisons of the OCS and SCS type RF Guns of NSRRC 76
5.2 CST PS Simulations 89
5.2.1 Output Beam Dynamics of the OCS Gun of NSRRC 90
5.2.2 Beam Dynamics of Back-Streamed Particles 93
5.2.3 Back-bombardment of the OCS RF Gun in different Field Ratio 95
5.3 Summary of Beam Properties 97

Chapter 6 Fabrication & Microwave Measurement
6.1 Fabrication of the OCS Gun of NSRRC 99

6.2 Principles of Measurement- Quality Factor and Field Distribution 101
6.2.1 Impedance Method for Determination of Quality Factor 101
6.2.2 Bead-Pull Method for Determination of On-axis Field Distribution 103
6.3 Results of Microwave Cold Test 104
6.3.1 Measured Resonant Frequencies and Tuner Test 104
6.3.2 Measured On-axis Field Distribution 105
6.3.3 Quality Factor and Input Coupling 106

Chapter 7 Conclusions 108


Appendix A Derivations and Formulae
A.1 Beam Dynamics 108
A.2 Circuit Model for Tuning an OCS gun 112
A.3 Solutions of Single Variable Cubic Function 114

Appendix B Programming Codes
B.1 MATLAB Codes for Computing Resonant Frequencies 115
B.2 SUPERFISH Codes of the well-tuned NSRRC OCS RF Gun 116
B.3 MATLAB Codes for Evaluating ω-ωβ Plot 117
B.4 PARMELA Codes 118

Appendix C Tuning Procedures
C.1 2D Tuning by SUPERFISH 119
C.2 3D Tuning by HFSS 122

Appendix D Simulation Setups
D.1 Setups of Eigen-mode Calculations in HFSS 126
D.2 Setups of Driven-mode Calculations in HFSS 127
D.3 Setups of CST PS Simulation 128

Appendix E Layout of the OCS RF gun of NSRRC 129

References 133


















List of Figure

Figure 1.1 Setup of the NSRRC ultrashort beam facility. 2
Figure 1.2 Layouts of the 2998MHz thermionic RF electron gun of NSRRC. 3
Figure 1.3 The side-coupled structure, standing wave, thermionic cathode RF gun optimized by NSRRC and its field distribution when operating in π/2-mode, 2998MHz. 4
Figure 1.4 Distributions of the 2.5 MeV electron beam at gun exit with peak fields of 32MV/m and 75 MV/m at half-cell and full-cell, respectively. 4
Figure 1.5 The Schematics of an OCS-gun. 5
Figure 1.6 Research flow diagrams for design and analysis of an RF gun. 7

Figure 2.1 A pillbox cavity with length d and radius a. 10
Figure 2.2 Fields inside a TM010 mode pillbox cavity. 11
Figure 2.3 Equivalent circuit of a single cavity resonator. 15
Figure 2.4 The equivalent circuit of the cavity chain coupled by nth identical cavities. 18
Figure 2.5 Schematics of the RF gun structure for n+1/2-cell. 21

Figure 3.1 Cross section schematics of OCS type RF gun proposed by KHI. 28
Figure 3.2 Emittance of output beam and back bombardment power as functions of field ratio e_b calculated by EMSYS. 30
Figure 3.3 Energy spectra of back-bombarding beam. Dotted line: e_b=1.0; Solid line: e_b=2.6. 30
Figure 3.4 Radial distribution of back-bombarding power density on the cathode surface. 31
Figure 3.5 Energy spectrum at the RF gun exit. The energy spread (FWHM) is less than 30keV. 31
Figure 3.6 Simulated energy distributions versus time at the gun exit in a macropulse with different peak accelerating field applied in to the RF gun designed by KHI. 32
Figure 3.7 Time dependent energy distribution of the RF gun designed by KHI with 65MV/m maximum accelerating field. 32
Figure 3.12 Graph of KHI’s OCS type RF gun system installed to the FEL device. 35
Figure 3.13 The OCS type RF gun designed by MAX-lab. 37
Figure 3.14 The field contour of the OCS type RF gun designed by MAX-lab, simulated by SUPERFISH. 37
Figure 3.15 Accelerating fields on beam axis at π/2-mode (left) and at 0-mode (right.). 37
Figure 3.16 Transverse phase space distributions at gun exit with Icathode=0mA (left), Icathode=100mA (middle) and Icathode=600mA (right). 38
Figure 3.17 The energy distribution at gun exit with Icathode=0mA (left), Icathode=100mA (middle) and Icathode=600mA (right). 38
Figure 3.18 The layout of the OCS type thermionic RF gun designed by MAX-lab with improved cooling in between the cells and around the cathode 39

Figure 4.1 Equivalent circuit of three-cell coupled cavity chain. 42
Figure 4.2 Results of convergence test of a 2998 MHz pillbox cavity. 57
Figure 4.3 The initial dimension setup of the OCS gun of NSRRC. 58
Figure 4.4 Field magnitude distribution and contour of coupling-cell (left) and full-cell (right) after tuned to 2998.09 and 2998.05 MHz, respectively. (SUPERFISH) 59
Figure 4.5 Field magnitude distribution and contour after tuned to 2998 MHz, eb=1. (SUPERFISH) 59
Figure 4.6 On-axis field magnitude distribution and contour of tuned OCS gun of NSRRC after tuned. (SUPERFISH) 60
Figure 4.7 Frequency sweep of the OCS gun of NSRRC after tuned. (SUPERFISH) 61
Figure 4.8 The field contour and on-axis field distribution of zero-mode (left) and π-mode (right). (SUPERFISH) 61
Figure 4.9 The mesh cross section view of the OCS RF gun of NSRRC. (HFSS) 63
Figure 4.10 Result of convergence test of the OCS RF gun of NSRRC. (HFSS) 63
Figure 4.11 Mode test of the OCS RF gun of NSRRC after tuned by SUPERFISH. 65
Figure 4.12 Mode test of the OCS gun of NSRRC with optimized mode separation and result from the theoretical evaluations. 65
Figure 4.13 Field patterns of the OCS RF gun of NSRRC. (eigen-mode, HFSS) 65
Figure 4.14 Schematics (left) and HFSS module (right) of the coupling structure, waveguide and pumping pipe in cross section view. 66
Figure 4.15 The side, top and front view of the OCS type RF gun of NSRRC with external structures. 67
Figure 4.16 The mesh spacing of HFSS simulations for tuning the OCS gun of NSRRC. 67
Figure 4.17 Field patterns of the well-tuned OCS type RF gun of NSRRC simulated by HFSS (Driven mode). 70
Figure 4.18 S11 parameter spectrums. (HFSS) 70
Figure 4.19 On-axis electric field distribution of tuned OCS gun of NSRRC. (HFSS) 71
Figure 4.20 VSWR and input coupling of the tuned OCS RF gun of NSRRC. (HFSS) 71
Figure 4.21 Smith chart of the tuned OCS RF gun of NSRRC. (HFSS) 71
Figure 4.22 On-axis field distribution of the tube of tuned OCS gun of NSRRC.(HFSS) 72
Figure 4.23 On-axis field distribution of drift tube of tuned OCS gun of NSRRC.(HFSS) 72
Figure 4.24 On-axis field distribution of pumping pipe of tuned OCS gun of NSRRC.(HFSS) 72
Figure 5.1 Energy distribution at exit of OCS RF gun of NSRRC with different accelerating gradients. 74
Figure 5.2 Energy distribution at exit of OCS RF gun of NSRRC. 75
Figure 5.3 Energy spectrum at exit of OCS RF gun of NSRRC. 75
Figure 5.4 Particle number distribution at exit of OCS RF gun of NSRRC. 75
Figure 5.5 Real space and phase space distribution at exit of OCS RF gun of NSRRC. 76
Figure 5.6 On-axis field distribution of the OCS RF gun with different field ratio. 77
Figure 5.7 On-axis field distribution of the SCS RF gun with different field ratio. 77
Figure 5.8 Schematics of the definition of top 10% energy particles 77
Figure 5.9 Distributions of particle loss and output charge in different field ratio of the OCS RF gun of NSRRC. 79
Figure 5.10 Distributions of the r.m.s. transverse emittance and the r.m.s. transverse emittance of top 10% energy particles in different field ratio of the OCS RF gun of NSRRC. 79
Figure 5.11 Real space distribution of electrons at the exit of the OCS RF gun of NSRRC with different field ratio. 80
Figure 5.12 Phase space distribution of electrons at the exit of the OCS RF gun of NSRRC with different field ratio. 80
Figure 5.13 Longitudinal energy distributions at the exit of the OCS RF gun of NSRRC with different field ratio. 81
Figure 5.14 Phase spaces of selected top 10% energy particles at the exit of the OCS RF gun of NSRRC with different field ratio. 81
Figure 5.15 Distributions of particle loss and output charge in different field ratio of the SCS RF gun of NSRRC. 83
Figure 5.16 Distributions of the r.m.s. transverse emittance and the r.m.s. transverse emittance of top 10% energy particles in different field ratio of the SCS RF gun of NSRRC. 83
Figure 5.17 Real space distribution of electrons at the exit of the SCS RF gun of NSRRC with different field ratio. 84
Figure 5.18 Phase space distribution of electrons at the exit of the SCS RF gun of NSRRC with different field ratio. 84
Figure 5.19 Longitudinal energy distributions at the exit of the SCS RF gun of NSRRC with different field ratio. 85
Figure 5.20 Phase spaces of selected top 10% energy particles at the exit of the SCS RF gun of NSRRC with different field ratio. 85
Figure 5.21 Comparison of particle losses and output charge of OCS and SCS RF gun. 87
Figure 5.22 Comparison of output charge of top 10% energy particles of OCS and SCS gun. 88
Figure 5.23 Comparison of emittance of OCS and SCS RF gun. 88
Figure 5.24 Comparison of emittance of top 10% of energy particles of OCS and SCS RF gun. 88
Figure 5.25 A cross snapshot of the electron beam accelerating in the thermionic OCS RF gun of NSRRC. 89
Figure 5.26 Electron distributions at exit of the OCS RF gun of NSRRC. (CST PS) 90
Figure 5.27 Energy spectrum at exit of the OCS RF gun of NSRRC. (CST PS) 90
Figure 5.28 Energy spectrum in the gun structure at the moment that first bunch just arrives the gun exit. (CST PS) 91
Figure 5.29 Energy spectrum in the gun structure at the moment that second bunch just arrives the gun exit. (CST PS) 91
Figure 5.30 Distributions of electron beam position and energy of the OCS RF gun of NSRRC. The particle number of simulation is not large enough so that the stepped distribution of beam takes place in this figure. 92
Figure 5.31 The back-bombarded current distribution on cathode surface. 93
Figure 5.32 Energy spectrum of back-bombarded electrons on cathode surface. 94
Figure 5.33 The back-bombarded electron distribution on cathode surface. 94
Figure 5.34 Back-bombarded power and charge within different field ratio. 95
Figure 5.35 Energy spectrum of back-bombardment within different field ratio. 96

Figure 6.1 Experiment setup of the cold test for the OCS gun of NSRRC. 98
Figure 6.2 Layout cross section view of the OCS gun prototype of NSRRC. 99
Figure 6.3 Resonant frequencies response of the OCS gun of NSRRC when R_full varies. 100
Figure 6.4 Input coupling and field ratio versus R_fullof the OCS gun of NSRRC. 100
Figure 6.5 Equivalent circuit for the coupling system of RF source and cavity resonator. 101
Figure 6.6 Measured and simulated (HFSS) S_11 parameter of prototype. 104
Figure 6.7 Measured and simulated (HFSS) frequency response versus p of the prototype. 105
Figure 6.8 Simulated (HFSS) VSWR and field ratio versus p of the prototype. 105
Figure 6.9 Measured and simulated (HFSS) on-axis field distribution. 106

Figure C.1 The fitted tuning curve of the coupling-cell. 119
Figure C.2 The fitted tuning curve of the full-cell. 120
Figure C.3 The response of gun frequency with varying R_half. 120
Figure C.4 The fitted tuning curve of the gun with varying R_half. 120
Figure C.5 Field balance tuning curves when varying the radius of iris between coupling- and full- cell. 121
Figure C.6 Field balance tuning curves when varying R_full. 121
Figure C.7 Parameter sweep results of ΔR_f=-0.3~0 mm in tuning step 1. 123
Figure C.8 Parameter sweep results of ΔR_f=-0.3~-0.2 mm in tuning step 1. 123
Figure C.9 Parameter sweep results of Δs=0~+4.5 mm in tuning ne step 2. 124
Figure C.10 Parameter sweep results of ΔR_f=-0.25~-0.15 mm in tuning step 3. 124
Figure C.11 Parameter sweep results of R_(h,cpl)=-0.05~0.05 mm in tuning step 4. 125

Figure D.2 The solution setup of the convergence test in eigen-mode of HFSS simulation. 126
Figure D.1 Meshing settings of the gun structure in eigen-mode of HFSS simulation. 126
Figure D.3 The mesh settings in driven-mode of HFSS simulation. 127
Figure D.4 Setups of driven-mode calculations in HFSS. 127
Figure D.5 Setups of particle source (left) and meshing (right) in CST PS. 128
Figure D.6 Setups of the PIC solver parameters in CST PS. 128










List of Table

Table 1.1 Designed parameters of the NSRRC ICS experiment. 2

Table 2.1 Quantities of cylinder waveguide. 9
Table 2.2 Values of x_mn. 10

Table 3.1 Optimized parameters of the OCS gun designed by KHI. 29
Table 3.2 The desired parameters of the OCS type thermionic RF gun designed by MAX-lab. 36
Table 3.3 Performance of OCS gun designed by MAX-lab, simulated by SUPERFISH. 36

Table 4.1 Desired Parameters of the OCS Type Thermionic RF Gun of NSRRC. 40
Table 4.2 Microwave parameters of the OCS gun designed by KHI. 46
Table 4.3 The result of evaluating resonant frequencies. 46
Table 4.4 Microwave properties of tuned OCS gun of NSRRC. (SUPERFISH) 62
Table 4.5 Microwave properties of individual cells of tuned OCS gun of NSRRC. (SUPERFISH) 62
Table 4.6 Resonant frequencies and quality factors calculated by HFSS (eigen-mode). 64
Table 4.7 Micorwave parameters desired and achieved. (Drievn-mode, HFSS) 69

Table 5.1 Input parameters of PARMELA calculation. 73
Table 5.2 Parameter Comparison of OCS and SCS RF gun under designed circumstances. 87
Table 5.2 Beam Properties of the OCS RF gun of NSRRC calculated by PARMELA. 97
Table 5.3 Bam Properties of the OCS RF gun of NSRRC calculated by CST PS 97

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