beam optimization with fast particle tracking (fpt) · beam optimization with fast particle...

Beam Optimization with

Fast Particle Tracking (FPT)

LCLSII Physics Meting, 10/07/2015

Lanfa Wang

• Motivation

• Physics Model of FPT

• Benchmark with ELEGANT

• Results for new injector beam

2

Motivation

LCLSII Physics meeting, 10/07/2015, L. Wang

Complexity of LCLS-II beam dynamics (compared with

LCLS)

• Strong space charge at injector (CW gun, low beam energy)

• Strong CSR effect (more bending magnets in transportation line)

Strong LSC in linac (long by-pass beamline, low beam energy)

• Low beam energy

For design/optimization purpose, we need a fast program,

which should includes wakefield, CSR and space charge.

• ELEGANT provide detail tracking and including all the collective effects

above, but it is not fast enough

• LiTrack is fast, but CSR and LSC is not included

3

Strong Impact of CSR and space charge

LCLSII Physics meeting, 10/07/2015, L. Wang Ji Qiang, et.al. WEP070, FEL15

without CSR

and space charge

with CSR

+space charge

4

Introduction to FPT


Original for collective effects, Longitudinal space charge is

added recently, it includes

Geometric wake and resistive wall wake;

1D CSR in free space (and 2D CSR with shielding)

1D/2D LSC (uniform beam, Gaussian beam, or arbitrary

beam)

5

CSR


1D free space CSR [Saldin, E.L. et al. Nucl.Instrum.Meth. A398

(1997) 373]

Pro: Fast computation

con: no shielding, no 2D effect

2D CSR with shielding

Pro: shielding effect, resistive wall effect; 2D effect ;

con: slow computation for very short bunch

0 2 4 6 8 10-50

0

50

100

150

200

250

300

350

400

k (1/mm)

Z (

)

Real, Zhou

Imaginary,Zhou

Real, Wang

Imaginary,Wang

6

2D CSR


=6μm (50THz) , 𝜎𝑟=0.1mm

CSR Field at end of the LCLSII BC2 magnet

Integrated field after the magnet

Apply to arbitrary pipe cross-section

Fast CER computation;

Ante-chamber

7

Shielding and CSR energy loss


long wavelength dominant;

frequency up to 50 THz is need

-50 0 50 1000

0.5

1

1.5

z (fs)

I (k

A)

beam of 100pC at Undulator Begin, sigz= 29.8906(fs)

-100 -50 0 50 1000

100

200

300

400

500Beam Spectrum

Frequency (THz)

Ma

gn

itu

de

|I(

f)|

100pC

-200 -100 0 100 200 300 400 5000

0.5

1

1.5

z (fs)

I (k

A)

beam of 300pC at Undulator Begin, sigz= 113.57(fs)

-20 -10 0 10 200

100

200

300

400Beam Spectrum

Frequency (THz)

Ma

gn

itu

de

|I(

f)|

300pC

LCLS-II Beam spectrum

-2 -1 0 1 2 30

0.1

0.2

0.3

q

bunc

h de

nsity

-2 -1 0 1 2 30

10

20

30

8

Micro-bunch instability driven by CSR (KEK DR)


f up to 0.5THz f up to 1.5THz

N=8.5E10

N=5.5e10

No Saw-tooth instability observed with long

wavelength CSR

Short wavelength (High frequency) CSR is

important for micro-bunch instability

μm CSR is needed for LCLS-II

KEK DR:

• beam energy 1.1GeV; Circumference 135.5m

• Bunch length 6.53 mm;

(L. Wang, H. Ikeda, K. Oide K. Ohmi and D. Zhou,

TUPME017, IPAC13)

9

Longitudinal Space charge (LSC)


1D free space for round Gaussian and uniform beam

Pro: Fast computation; good for long wavelength

con: 2D effect (energy spread, damping) is not included

2D LSC with arbitrary beam and chamber [L. Wang, Y. Li, PRSTAB, 18, 024201 (2015)]

Pro: 2D effect and shielding effect; good for all wavelength • Field spread converts to slice energy spread;

• Large slice energy spread for short wavelength;

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

1.2

/(ka)

Z||(a

rb. u

ints

)

Round uniform beam

10

LCLS 6/19/2014 data, 1kA, 4GeV, 180pC, BC2 R56 = 24.7mm (Yuantao, Ding)


LH =2.2uJ,Initial E =10.3keV

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40LH =3.7uJ,Initial

E =11.4keV

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40

LH =5uJ,Initial E =12.3keV

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40LH =7.2uJ,Initial

E =13.8keV

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40LH =9.9uJ,Initial

E =15.6keV

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40

LCLS 4GeV, 180pC, 1kA, LH off

t (fs)

E

(M

eV)

-100 0 100-40

-20

0

20

40

11

ELEGANT Space Charge Model


Elegant uses round uniform beam

model with 𝑎 = 3𝜎; good

approximation at long wavelength.

1D LSC

3D space charge

To be released

12

Benchmark FPT with ELEGANT


• x-px plane: sigma_x = 0.1227mm, sigma_x' = 0.1411e-4, alphax=-0.524,

emittance_normalized = 0.3 mm-mrad

• y-py plane: same as x-px plane

• z-pz plane: sigma_z = 0.979mm, sigma_dE = 1keV, alphaz = 0.368e-3

Initial beam at 100MeV

13

Without collective effects


• Initial Ideal Gaussian beam from 100MeV of LCLS linac

• Without wake, CSR and space charge

• compare Beam at BC2 END

Beam energy 1.6GeV Beam energy 1.644GeV

Red: ELEGANT

Blue: FPT

14

With wake (RF structure, beam pipe)


Peak current is lower due to the

effect of wake

15

Wake+CSR


Peak current increases

with CSR

16

Wake+CSR+LSC


The LSC kicker is compared with ELEGNAT and analysis

For design, we can consider the long wavelength effect only (NOT instability);

which includes the de-chirp effect and also a small number of macro-particle can

be used;

For instability, the main issue is how to handle noise.

some ideas to reduce the noise and improve the resolution; under going

-2000 -1000 0 1000 2000

-0.1

-0.05

0

0.05

0.1

t(fs)

E

(M

eV

)

0 5 10 150

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Bu

nc

hin

g

(m)

FPT: 8 Millions particles

ELEGANT: 50 Millions particles

FPT play trick at L1: Ez 𝑁𝑠𝑖𝑚

𝑁𝑟𝑒𝑎𝑙

For 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑓 > 0.25𝑓𝑐~𝑐

4∆𝑠

Micro-bunching at 2~3um; ubi starts from very beginning

17

Micro-bunch instability by ELEGANT and IMPACT (FEL15, TUP066)


50MP, 1024bins, ELEGANT 624MP, 2048 bins, IMPACT

~2.3μm

Amp=0.15%

~3μm

Amp=0.15%

At undulator begin

Wake+CSR+Spacecharge

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2x 10

5

(m)

ZL

SC (

)

BC1BEG

BC2BEG

DL1BEG

DL2BEG

DL1END

DL2END

18

LSC for emittance 0.45um


bc1beg=120m

bc2beg=335m

dL1beg=928m

dL1end=1030m

dL2beg=2770m

dL2end=3100m

0 500 1000 1500 2000 2500 3000 3500 40000

50

100

150

200

250

300

350

s(m)

(

m)

x

y

Bunching factor 6.7 and 10 are used

Long-by-pass contributed largest

LSC at L1 (blue) and L2 (black)

also important

The wavelength at peak is close

19

Optimization with FPT


20

300pC beam at 100MeV (Feng Zhou)


-20 -15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

em

itta

nc

e (m

-ra

d)

t (ps)

Bunch emittance=4.3463e-07/4.3506e-07 (m-rad)

X-emittance

Y-emittance

Head

21

Optimization with FPT, LSC off, example for New 300pC


Zero chirp

High peak current >1kA

Smooth current profile • L1 phase=20.8 degree

• Linearizer phase= 155 degree

• L2 Phase= 29.6 degree

• BC1= 80mrad (R56~-33mm)

• BC2= 43.8mrad (R56~-40mm)

Confirmed with ELEGANT with CSR,

(LSC off)

Need to check LSC effect, the impact

on the current profile is likely small.

This is just one example, it can be

further improved with more study

ELEGNAT

Head

22

100pC beam


-15 -10 -5 0 5 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

em

itta

nc

e (m

-ra

d)

t (ps)

X-emittance

Y-emittance100MeV (Feng Zhou)

4GeV at Undulator Begin

• Peak current: 12A

• Emittance: 0.25um

• Peak current: >1.1kA

• Small chirp

Linearizer = 163o

R56BC2= -34 mm

Continue study, matching...

23

Summary


FPT provide fast computation with good agreements with

ELEGANT; it provides flexibilities for different models (2D

LSC, CSR shield effect, transverse SC also straight

forward, etc.)

Preliminary study shows optimization with FPT works

well (>1kA, flat current profile)

We demonstrated that the collective effects can be

minimized

24

Next


Optimization with (wake+CSR)+LSC

- Optimization with long wavelength effect (not instability), therefore a

small number of particles is required

- Micro-bunch instability (LSC) resolution is limited ~ > 2∆𝑠, improve

the resolution

- Noise reduction schemes

integrated S2E optimization (MOGA/People) with GPT

(injector)+FPT (linac), especially for low charge

…..

Ultimate goal: online optimization.

Lots of works to be done and can be done to improve the

beam quality (we already have very good emittance)!

25 LCLSII Physics meeting, 10/07/2015, L. Wang

beam optimization with fast particle tracking (fpt) · beam optimization with fast particle...

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