Magnetic Compression of High Brightness Beams:

Survey of Experimental Results

Scott G. AndersonICFA Sardinia

July 2002

July 2, 2002 S. G. Anderson - ICFA Sardinia 2

Magnetic Compression

• Motivation — increase brightness, need sub-ps bunches

• Problems — 6D phase space deterioration caused by collective effects– Acceleration fields – Coherent Synchrotron Radiation

(CSR) – Velocity fields – Space-charge

• Experiments– CTF, TTF, SDL, APS, UCLA, …– Features of the data

• Phase space dilution – emittance growth, momentum spectrum

• Phase space filamentation filamentation – both longitudinal and transverse– Comparisons with theory/simulation

• Simulations reproduce rms quantities, but not intricate phase space structures seen in expt.

July 2, 2002 S. G. Anderson - ICFA Sardinia 3

Operating Principle of Magnetic Compression

Acceleration ahead of crest of rf wave + chicane dipoles acts as lens + drift.

δz δz

acceleratingwave

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CTF II Emittance Measurements*

• Large bend plane emittance growth observed as a function of compression

• Only CSR and/or space-charge were reasonable sources of

• PARMELA predicts 10% of measured

• CSR-TRACK predicts 60% of measured

*from: H. H. Braun, et al., Phys. Rev. Lett. 84, 658 (2000).

July 2, 2002 S. G. Anderson - ICFA Sardinia 5

CTF II Emittance and Momentum Distribution Measurements*

*from: H. H. Braun, et al., Phys. Rev. ST Accel.

Beams 3, 124402 (2000).

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CTF II Emittance versus Horizontal Size

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TTF

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TTF

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SDL

0 0.2 0.4 0.6 0.8 1 1.2 1.40

100

200

300

400

500

600

700

Cu

rren

t (A

)

Time (ps)

1 1.5 2 2.5020406080

100120140160

Cu

rren

t (A

)

Time (ps)

1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

Cu

rren

t (A

)

Time (ps)

RF zero phasing measurement of electron

beam time profile.

No compression

Mild compression

Strong compression

1

2

3

4

5

6

123

4

5

687

• Strong micro-bunching with compression — source not agreed upon.

July 2, 2002 S. G. Anderson - ICFA Sardinia 10

APS?

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UCLA Experiment

• Lower energy (< 12 MeV) — space-charge may play significant role in compression

• This allows/requires emittance measurement using slits:

• Transverse phase space is directly measured

July 2, 2002 S. G. Anderson - ICFA Sardinia 12

Interferometer Data

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 12 14 16 18 20 22

Autcorrelation Data

Delay [psec]

σt = 0.63 ps

0

1

2

3

4

5

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

SimulationData

Dipole FieldDelay Arm Position

Nor

mal

ized

Si g

n al

July 2, 2002 S. G. Anderson - ICFA Sardinia 13

Emittance Versus PWT Phase

5

10

15

20

25

55 60 65 70 75 80 85 90

Normalized Emittance [mm mrad]

Linac Phase [deg]

Sharp increase is a consistent feature in

data

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Bifurcation of Transverse Phase Space

σz = 4 ps σz = 0.6 ps

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Varying Phase or Field

5

10

15

20

25

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Changing CurrentChanging Phase

Pulse Length [psec]

Em

itta

nce

[mm

mra

d]

• Emittance growth and phase space structure is a function of compression.

July 2, 2002 S. G. Anderson - ICFA Sardinia 16

Emittance Growth Vs Beam Size

0

5

10

15

20

25

30

35

1 1.2 1.4 1.6 1.8 2 2.2 2.4

σx [mm]Em

itta

nce Growth

[m

m m

rad]

July 2, 2002 S. G. Anderson - ICFA Sardinia 17

Simulation

• Different codes model different processes (acceleration fields versus velocity fields.)

• Codes employed:– TREDI: Solves Lienard-Wiechert potentials.– PARMELA: Provides input distributions for TREDI.

Point-to-point space charge for comparison.– ELEGANT: CSR only calculation.

• Simulations indicate that for this experiment, acceleration fields do not contribute much emittance growth, the space charge fields are the dominant effect.

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Simulation

• Simulation is difficult. Number of macro-particles is low because of time-intensive space-charge calculations.

• Sharp emittance increase when bifurcation begins is missing in simulations.

0

5

10

15

20

25

55 60 65 70 75 80 85 90

Emittance dataPARMELA simulationTREDI simulationELEGANT simulation

Em

itta

nce

[mm

mra

d]

PWT Phase [deg.]

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Heuristic Model

• To analyze the effect of space-charge in the compressor, we model the beam as a series of longitudinal slices.

• Since the beam energy spread is heavily correlated to slice position, we assume that there is no energy spread (no dispersion) within a single slice.

• Space-charge forces push a slice based on the fields at it’s centroid due to the other slices.

• Use standard envelope equations to evolve the sizes of single slices.

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Configuration Space ‘gymnastics’ in the Model

Configuration Space Long. Phase Space

Beam “folds over” in configuration space.

(no space-charge)

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Space-charge in the model

• In simple model integrate space-charge force in last magnet to get x’ between slices

• Model predicts size dependence

• In simulation use 3D ellipsoidal fields

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

x/a

ellipsoid edge

Cartoon of config. space evolution.

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Simple calculation with the model

0.0

0.5

1.0

1.5

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

0.0 0.5 1.0 1.5 2.0 2.5

Em

itta

nce

[mm

mra

d]

x’ [

mra

d]

s/R σ0

• Kick applied between two slices in the last magnet.

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Slice Model Simulation

Trace space bifurcation

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5

-1

-0.5

0

0.5

-1.5 -1 -0.5 0 0.5

Configuration space

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1 1.2

Input size dependence

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Bifurcation in PARMELA

19.5

20

20.5

21

21.5

22

22.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4z [mm]

-4

-3

-2

-1

0

1

2

3

4

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 [ ]z mm

0

100

200

300

400

500

600

700

19.55 20.3 21.05 21.8γ

z phase space Energy distribution Config. space

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Summary of UCLA Experiment

• Features of the data:– Trace space bifurcation– Emittance growth inversely proportional to beam

size

• Simulation shows that space-charge is the dominant effect

• Slice model simulation, and PARMELA/TREDI simulations show same features as data, but not as pronounced. Possible pre-existing structure in phase space and/or CSR combines with space-charge effects to accentuate behavior seen in data.

• Blue statements seem applicable to other experimental data as well!