L.Xiao and Z. Li, June 03, 2015

LCLS-II Injector Impedance Study

Liling Xiao, Zenghai LiComputational Electrodynamics Department, RFARD, TID

L.Xiao and Z. Li, June 03, 2015

LCLSII-Injector Model

Mechanical model-> EM modelBeampipe 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.

F=186.378MHz, Q0=31719

APEX GUN/Buncher – StudiedE-field

H-field

L.Xiao and Z. Li, June 03, 2015

Beamline Components

VAT valve (2)

Stripline BPM (2)

Light boxICT YAG

Slots (2)

2D

L.Xiao and Z. Li, June 03, 2015

• 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

Accelerator Modeling with ACE3P

L.Xiao and Z. Li, June 03, 2015

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.

Wakefield Simulations Using ACE3P-T3P(Limitation: β=1 and no-intrusion along the beampipe)

L.Xiao and Z. Li, June 03, 2015

Convergence Study - VAT-Valve Wakefield Simulations (Assuming β=1)

Model and Mesh Converged with time stepConverged with mesh quality

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.

y

z

L.Xiao and Z. Li, June 03, 2015

VAT-Valve: Longitudinal Short-Range WakefieldKloss factor=0.66V/pC

The heating due to the instantaneous energy loss cause no problems for the VAT-valve structure assuming 6mm of the bunch length.

Qb=100pC, fb=1MHz,

I=Qb.fb=0.1mA,

P=(Qb.kloss).I=6.6mW

L.Xiao and Z. Li, June 03, 2015

VAT-Valve: Longitudinal Long-Range Wakefield

Snap Shots of Wakefield

~2.7GHz

frms=11.25GHz

L.Xiao and Z. Li, June 03, 2015

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

R/Q=56.6Ω/structure @ 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

VAT-Valve: Transverse Short-Range WakefieldKick Factor_y=40V/pC/m Kick Factor_x=32V/pC/m

L.Xiao and Z. Li, June 03, 2015

VAT-Valve: Transverse Long-Range Wakefield

Wy

~2.7GHz~ longitudinal mode

~3.0GHz

~3.4GHz

Wx

The y-dipole trapped modes have bigger effects on the beam than the x-dipole.

Beam offset=2mm

L.Xiao and Z. Li, June 03, 2015

VAT-Valve: Y-Dipole Trapped Modes

F=3.00GHzR/Q_z=3.7Ω/structure R/Q_y=25Ω/structure @ β=0.914Q0=17613Dipole center offset 6.1mm

F=3.42GHzR/Q_z=3.7Ω/structure R/Q_y=8.7Ω/structure @ β=0.914Q0=19970Dipole 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

Stripline BPM/Light Box Wakefield Simulations (Assuming β=1)

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.

For short-range wakefield For long-range wakefield and trapped mode study

L.Xiao and Z. Li, June 03, 2015

BPM: Longitudinal Short-Range WakefieldLoss 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

BPM: Transverse Short-Range WakefieldKick Factor_y/x=4V/pC/m/BPM

L.Xiao and Z. Li, June 03, 2015

LightBox: Longitudinal Short-Range WakefieldLoss 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

LightBox: Transverse Short-Range WakefieldKick Factor_y=70V/pC/m/Light Box Kick Factor_x=60V/pC/m/Light Box

L.Xiao and Z. Li, June 03, 2015

Some of Trapped Modes in BPM and Light Box

F=2.87GHz

F=960MHz

F=3.45GHz

F=3.30GHz

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

Injector Components Impedances

Component KLoss (V/pC)

Kick Factor_x(V/pC/m)

Kick Factor_y(V/pC/m)

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 4

Laser Box 0.2 60 70

ICT

YAG-Screen

(beam length=6mm, β=1)

Emittance Degradation Due to Wake_T

Use the LightBox_wy to estimate emittance degradation

Short-range Wake_T

valve

BPM

LightBox

Initial BeamsGaussian 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

• σz =5.3 mm (wake calculation used 6mm)

• βx,y= 9

• αx,y,z=0

• Beam Energy: 750 keV• Beam offset: 1 mm

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 = 8.738 μm• Emittance_after_lightbox = 8.741 μm• Negligible degradation

(x, xp)

(z, xp)(head tail)

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 = 0.9998 μm• Emittance_after_lightbox = 1.008 μm• 0.8% increase

(x, xp)

(z, xp)(head tail)

• 3.3nC charge – (just to show the wakefield effect)

(x, xp) (z, xp (head tail))

L.Xiao and Z. Li, June 03, 2015

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.

Summary