1. LCLS-II Injector Impedance Study
Liling Xiao, Zenghai Li
Computational Electrodynamics Department, RFARD, TID
L.Xiao and Z. Li, June 03, 2015

2. LCLSII-Injector Model
Mechanical model-> EM model
Beampipe r=0.59inch ~ 15mm, fc=5.87GHz
Evaluate the major beam line components’ impedances (longitudinal/transverse, trapped modes).
Perform the whole injector dark current simulation from the gun, and from the CM.
L.Xiao and Z. Li, June 03, 2015

3. APEX GUN/Buncher – Studied
E-field
H-field
F= MHz, Q0=31719

4. Beamline Components 2D Slots (2) Stripline BPM (2) VAT valve (2)
Light box
ICT
YAG
L.Xiao and Z. Li, June 03, 2015

5. Accelerator Modeling with ACE3P
SLAC’s suite of conformal, high-order, C++/MPI based parallel finite-element electromagnetic codes
A unique capability for high-fidelity and high-accuracy accelerator simulation and modeling with its six application modules
ACE3P (Advanced Computational Electromagnetics 3P)
Frequency Domain: Omega3P – Eigensolver (damping)
S3P – S-Parameter
Time Domain: T3P – Wakefields and Transients
Particle Tracking: Track3P – Multipacting and Dark Current
EM Particle-in-cell: Pic3P – RF guns & klystrons
Multi-physics: TEM3P – EM, Thermal & Structural effects
L.Xiao and Z. Li, June 03, 2015

6. Wakefield Simulations Using ACE3P-T3P (Limitation: β=1 and no-intrusion along the beampipe)
Maxwell’s equations are cast into a second-order wave equation by combining Ampere’s and Faraday’s laws
Solves a linear system of equations Ax = b at every time step. The implicit time advancement scheme is unconditionally stable.
The Weiland indirect Wakefield integration method is used to determine the Longitudinal Wakefield.
The Transverse Wakefield is obtained through the Panofsky-Wenzel theorem by taking derivative of the integration of the Longitudinal Wakefield.
L.Xiao and Z. Li, June 03, 2015

7. Convergence Study - VAT-Valve Wakefield Simulations (Assuming β=1)z
Model and Mesh
Converged with mesh quality
Converged with time step
Results are converged with mesh size=3mm and dt=0.75ps for 6mm bunch length.
In the following simulations, the similar mesh quality and time step are used.
L.Xiao and Z. Li, June 03, 2015

8. VAT-Valve: Longitudinal Short-Range Wakefield
Kloss factor=0.66V/pC
Qb=100pC, fb=1MHz, I=Qb.fb=0.1mA,
P=(Qb.kloss).I=6.6mW
The heating due to the instantaneous energy loss cause no problems for the VAT-valve structure assuming 6mm of the bunch length.
L.Xiao and Z. Li, June 03, 2015

9. VAT-Valve: Longitudinal Long-Range Wakefield
~2.7GHz
frms=11.25GHz
Snap Shots of Wakefield
L.Xiao and Z. Li, June 03, 2015

10. VAT-Valve: Longitudinal Trapped Modes
The mode excited by the beam around 2.7GHz is most dangerous, and can generate the resonant heating.
ACE3P-Omega3P:
F=2.669GHz, Q0=14976
β=0.914
R=R/Q.Q0=847kΩ, I=0.1mA,
P=R.I2=8.5mW
The heating due to the resonant mode is comparable to the instantaneous energy loss, and cause no problems for the VAT-valve structure for 6mm of the bunch length.
L.Xiao and Z. Li, June 03, 2015

11. VAT-Valve: Transverse Short-Range Wakefield
Kick Factor_y=40V/pC/m
Kick Factor_x=32V/pC/m
L.Xiao and Z. Li, June 03, 2015

12. VAT-Valve: Transverse Long-Range Wakefield
Beam offset=2mm Wy
~3.4GHz
~3.0GHz
~2.7GHz
~ longitudinal mode Wx
The y-dipole trapped modes have bigger effects on the beam than the x-dipole.
L.Xiao and Z. Li, June 03, 2015

13. VAT-Valve: Y-Dipole Trapped Modes
F=3.00GHz
R/Q_z=3.7Ω/structure
β=0.914
Q0=17613
Dipole center offset 6.1mm
F=3.42GHz
R/Q_z=3.7Ω/structure
β=0.914
Q0=19970
Dipole center offset 9.2mm
Even the beam on z-axis, the y-dipole trapped modes can be excited due to the unsymmetrical structure on the y-direction, and thus their effects on the beam need to be evaluated.
L.Xiao and Z. Li, June 03, 2015

14. Stripline BPM/Light Box Wakefield Simulations (Assuming β=1)
For short-range wakefield
For long-range wakefield and trapped mode study
T3P can calculate wakefield when one can see only vacuum region along the structure from the beampipe at one end.
Therefore, we calculate the short-range wakefield for two stripline BPMs/LightBox together with an extra straight section connecting the larger end at one end of the structure to the same cross section as the other end.
L.Xiao and Z. Li, June 03, 2015

15. BPM: Longitudinal Short-Range Wakefield
Loss Factor=0.024V/pC/BPM
Qb=100pC, fb=1MHz, I=Qb.fb=0.1mA,
P=(Qb.kloss)I=0.24mW
The heating due to the instantaneous energy loss cause no problems for the StripLine BPM structure assuming 6mm of the bunch length.
L.Xiao and Z. Li, June 03, 2015

16. Kick Factor_y/x=4V/pC/m/BPM
BPM: Transverse Short-Range Wakefield
Kick Factor_y/x=4V/pC/m/BPM
L.Xiao and Z. Li, June 03, 2015

17. LightBox: Longitudinal Short-Range Wakefield
Loss Factor=0.1V/pC/lightbox
Qb=100pC, fb=1MHz, I=Qb.fb=0.1mA,
P=(Qb.kloss)I=2mW
The heating due to the instantaneous energy loss cause no problems for the LightBox structure assuming 6mm of the bunch length.
L.Xiao and Z. Li, June 03, 2015

18. Kick Factor_y=70V/pC/m/Light Box Kick Factor_x=60V/pC/m/Light Box
LightBox: Transverse Short-Range Wakefield
Kick Factor_y=70V/pC/m/Light Box
Kick Factor_x=60V/pC/m/Light Box
L.Xiao and Z. Li, June 03, 2015

19. Some of Trapped Modes in BPM and Light Box
F=960MHz
F=3.30GHz
F=3.45GHz
F=2.87GHz
There are many trapped modes in the stripline bpm and light box. Some of them are closed to the pick up, and their effects on the beam will be evaluated.
L.Xiao and Z. Li, June 03, 2015

20. Injector Components Impedances
(beam length=6mm, β=1)
Component
KLoss
(V/pC)
Kick Factor_x
(V/pC/m)
Kick Factor_y
LongitudinalTrapped Modes
Transverse Trapped Modes
VAT-Valve
0.66 32 40
2.7 GHz
3.0 GHz, 3.4 GHz
Stripline BPM
0.024 4
Laser Box
0.2 60 70
ICT
YAG-Screen
L.Xiao and Z. Li, June 03, 2015

21. Emittance Degradation Due to Wake_T
Use the LightBox_wy to estimate emittance degradation
BPM
LightBox
Short-range Wake_T
valve

22. Initial Beams Gaussian distribution (case-1)
εx,y = 8.74 μm (Feng Zhou)
σx,y=5.3 mm
σz =5.3 mm (wake calculation used 6mm)
βx,y=3.412
αx,y,z=0
(case-2)
εx,y = 1 μm (Feng Zhou)
σx,y= 3 mm
βx,y= 9
Beam Energy: 750 keV
Beam offset: 1 mm

23. Emittance Degradation (using LightBox Wake_T)
Gaussian distribution (case-1)
εx,y = 8.74 μm (Feng Zhou)
σx,y= 5.3 mm
σz =5.3 mm (wake calculation used 6mm)
βx,y= 3.412
αx,y,z=0
Beam Energy:750 keV
100,000 particles
Beam offset: 1 mm
Emittance_init = μm
Emittance_after_lightbox = μm
Negligible degradation
(x, xp)
(z, xp)(head tail)

24. Emittance Degradation (Using LightBox Wake_T)
Gaussian distribution (case-2)
εx,y = 1 μm (Feng Zhou)
σx,y= 3 mm
σz =5.3 mm (wake calculation used 6mm)
βx,y= 9
αx,y,z=0
Beam Energy:750 keV
100,000 particles
Beam offset: 1 mm
Emittance_init = μm
Emittance_after_lightbox = μm
0.8% increase
(x, xp)
(z, xp) (head tail)

25. (x, xp) (z, xp (head tail))
3.3nC charge – (just to show the wakefield effect)
(x, xp) (z, xp (head tail))

26. Summary
Have build the injector EM model that can be used for wakefield simulation and dark current evaluation.
Have finished VAT-Valve, stripling BPM, and Laser Box wakefield simulations.
The valve has the largest loss factor than the BPM and laser box. Its broadband heating generated by the beam is around 6.6mW for the beam σ=6mm, Qb=100pC, and frep=1MHz. The resonant heating is around 8.5mW.
The laser box has the largest transverse kickers than the VAT and BPM. Its effect on the beam is under investigated.
It is found that the transverse trapped modes in the Valve have larger center shift. Their effects on the beam need to be evaluated.
Will simulate ICT and YAG including longitudinal and transverse wakefields, and determine the possible trapped modes generated by the beam.
L.Xiao and Z. Li, June 03, 2015