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Start to End for ERLP (EMMA Workshop 26-28/02/07)

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Bruno Muratori

ASTeC Daresbury Laboratory

Cockcroft Institute

- (M. Bowler, C. Gerth, F. Hannon, B. McNeil*, H. Owen, S. Smith, N. Thompson, E. Wooldridge)

* - Strathclyde University, Glasgow

- Overview of codes used in the design of ERLP
- Main parameters of ERLP
- Overview of Optics and Start to End model of ERLP
- Gun & Injector
- Injector transfer line – various approaches
- Analytic
- ASTRA & quadrupoles
- GPT & full model
- ELEGANT

- Linac to first arc
- RF focusing treatment

- Outstanding Work

- Injector Design (assumed S2E does not start before this)
- ASTRA

- Optics Layout strategy for ERLP
- MAD8

- Space Charge for the ERLP
- Analytical estimate
- ASTRA / GPT

- Start to End (S2E) model for the ERLP
- MAD8 / ELEGANT
- GENESIS

- Beam Breakup for the ERLP
- bi (Beam Instability code)

- Gun Energy 350 keV
- 4 ps long bunches, 80 pC, at injection
- 8.35 MeV Injection line around 15 m
- 35 MeV Beam Transfer System (BTS)
- Bunch repetition rate 81.25 MHz
- Bunch spacing 12.3 ns
- Average current 13 µA
- Initial emittance (norm) between 2 mm mrad and 3 mm mrad
- Transverse beam size ~ 1-16 mm throughout
- ~ 0.4 ps long bunches at FEL

Lattice Matching

Lattice Matching

GENESIS

ASTRA

Elegant

Elegant

106 particles

250k particles

250k particles

250k particles

Booster to FEL

8.35/35MeV

FEL Interaction

FEL to Dump

8.35/35MeV

Gun to Booster

0 to 8.35MeV

MAD8

MAD8

Gun & Injector

Gun

electrons

JLab GA

anode

electrons

Injector (TL1)

- Modelling with ASTRA taking into account space charge.
- Gun → solenoid #1 → buncher → solenoid #2 → booster
- Bunch length/shape from a GaAs cathode?Modelling for various bunch lengths (15 ps, 20 ps, 25 ps).
- Similar beam parameters can be achieved by adjusting the solenoid/buncher settings.

Injector Line (TL2)

- AT 8.35 MeV space charge still an issue
- ASTRA does (did ?) not model dipoles
- Try to ignore dispersion effects & Replace dipoles with quadrupoles (obviously wrong but …)
- Make sure resulting Twiss parameters almost identical
- Look at emittance growth using ASTRA and initial Gaussian parameters
- Validity of analytical formula with quadrupoles ?

- Horizontal focusing given by (equivalent for vertical)
- Sigma matrix transformation
- New emittance
- Gaussian bunch (in s)

- Comparison gives ‘upper bound’ as long as flow laminar
- Not true for r = 1.0 mm and r = 0.5 mm

- Comparison gives ‘upper bound’ as long as flow laminar
- Not true for r = 0.5 mm (laminarity depends on εN so varies)

- Variation of beam size not taken into account → average has to be taken for meaningful comparison

- Quadrupole ‘k’ value higher than space charge equivalent but also more local → small perturbation & can be ignored

- ASTRA distribution from gun and booster (C. Gerth & F. Hannon)
- Emittance outside transverse plane
- Gaussian good approximation for emittance growth estimate

- All results so far in good agreement & can use analytical estimate for a rough guess provided laminarity insured
- Different algorithms also agree
- Emittance increase appears to be comparable to the analytical estimate in all cases considered
- Dispersion may be left out for a rough estimate
- Next: Include bends → use GPT (required modifications in fringe field treatment)

- Spikes unphysical & related to calculation of emittance in magnetic elements → agreement with ASTRA

GPT & TL2 with dipoles (beam size & angle)

- Comparison with ASTRA & quadrupole model:
- ASTRA: 2.8 mm mrad (x), 3.3 mm mrad (y)
- GPT: 3.0 mm mrad (x), 3.9 mm mrad (y)

Starting with Gaussian parameters at the start of the injector line

Starting with Gaussian parameters at the start of the injector line

Linac to first Arc

- Lattice matching with MAD8
- Keep Twiss parameters low (β < 50 m)
- Dispersion free after injection/extraction bends and arcs
- 1st arc: isochronous
- 2nd arc: R56 = -R56 bunch compressor
- Exact matching point at the entrance of the FEL

- Tracking with elegant (TL2: E = 8.35 MeV, l = 10m, 4 dipoles, 12 quads)Space charge effects?
- Different focusing strength of the linac in MAD8 and elegant and other models → re-matching after the linac

- Different code use different models (sometimes very !)
- MAD8 / ELEGANT give different focusing
- Must be accommodated in optics design
- Probably both wrong !

- Important to get this correct as overall effect could be high …

- Couplers can have a strong influence on the transfer matrix
- Hard to model
- Strongly affects focusing

- Theory vs. Experiment very limited despite being relatively easy to do … (difference in orbit method)

after acceleration

Before acceleration

Transfer Line 2 / Linac

Longitudinal Phase Space

- Tracked bunch at end of TL2 → linac
- ELEGANT used
- Off crest acceleration for bunch compression later in chicane

Outward arc / Compression

after linac

- 4-dipole chicane R56(BC) = 0.28 m
- For optimum compression set the off-crest phase in main linac toφrf = 9°

after BC

4

1

3

2

- Track distribution obtained from ASTRA after the booster through injector transfer line with GPT
- Try different kinds of linac focusing
- Chambers model
- Direct numerical integration
- Krafft model
- ELEGANT (different types exist within this)
- ASTRA
- GPT ? (given field maps – even 3D)
- Experimental verification very much desired – could be done on ERLP booster and / or linac at different energies & off-crests

- Optics with no real problems so far & straightforward
- Injector layout still being optimised → parameters may vary (emittance & bunch length due to varying laser spot size and pulse length)
- Good agreement between ASTRA and GPT and analytical result for drifts & quadrupoles (provided flow is laminar)
- Good agreement with dipoles correctly modelled
- Distribution still to be tracked including latest parameters
- Off-crest of 9° not a must if not going through FEL & compressing bunch later
- RF focusing still to be studied but maybe not essential

- Vinokurov’s Formula …

- Elliptical beam with charge density
- Electric field
- Transverse motion (round beam) paraxial approximation, laminar flow

- On boundary, ,
- With external focusing
- Envelope for KV distribution
- Therefore laminar flow given by

- Horizontal focusing given by (equivalent for vertical)
- Sigma matrix transformation
- New emittance
- Gaussian bunch (in s)

- Laminar flow not always valid e.g. :
- 4 ps, normalised emittance of 5 mm mrad, beam size 1 mm
- relativistic gamma ~ 17, max. current = 8 A
- LHS = 0.025, RHS ~ 0.05 → flow not laminar

- Complete s2e …

Outward arc / Compression

- 4-dipole chicane R56(BC) = 0.28 m
- For optimum compression set the off-crest phase in main linac toφrf = 9°
- Here bunch not fully compressed φrf = 7.8° K2 = 120 m-3→ rms bunch length = 0.4 ps

after linac

after BC

Outward arc/ Compression

Longitudinal Phase Space after Bunch Compressor

Sextupoles off

- Sextupoles can be used to linearise the curvature induced by the sinusoidal rf during acceleration by varying T566.
- The compression factor is then limited by the uncorrelated energy spread.
- Simulation results appear to be too good!! - rms bunch length ~ 230 fs

Sextupoles

K2 = 90 m-3

- Sextupoles in the outward arc help to achieve the shortest possible bunch length
- Can actually make bunch length too short for lasing! (in theory)
- Adjustable in real machine to optimise lasing properties
- In practice we are likely to see disruptive effects not apparent in the model

- Modelling of the FEL interaction with GENESIS 1.3:
- FEL parameters were estimated from steady-state codes for given (rms) electron bunch parameters:- radiation wavelength for max. gain = 4.4 µm- intra-cavity peak power at saturation ~ 100 MW
- elegant2genesis was used to generate GENESIS input distribution: - bunch is discretised into slices of a radiation wavelength- rms values are calculated for each slice- bunch is generated with 8192 particles per slice
- GENESIS was run in time-dependent mode with seed beam equivalent to intra-cavity peak power at saturation
- Number of particles were reduced randomly to give the required slice charge for the elegant input file.

FEL Interaction

before FEL

- Seed option in GENESIS:Uniform intensity distribution over the entire bunch!!! Not exact representation of pulse structure.
- The main aim was to get an electron bunch with a realistic energy spread for the beam transport to dump.
- Next steps: - modelling of Gaussian seed pulse- modelling of the cavity

after FEL

Mean energy loss

0.86%

Full energy spread

~4%

FEL Interaction

Predictions for mean energy loss and full energy spread of steady-state codes are in good agreement with GENESIS results.

Decompression / Deceleration

- Matching of return arc: R56 = -R56 (BC) in order to decompress the bunch
- Apertures were included in the elegant tracking.They were chosen to be 10% smaller than the vacuum chamber dimensions to approximately account for the effect of misalignment.
- No particles were lost during the recirculation even with the sextupoles turned off.

FEL Interaction

After deceleration

Sextupoles off

- The deceleration phase φdecis given byφdec = φrf + π.
- To achieve exactly the injection energy during deceleration, the deceleration phase needs to be reduced slightly to account for the mean energy loss of about 0.8% in the FEL process.
- Sextupoles can be used to straighten out the energy spread.

- Initial calculations & running the code bi (E. Wooldridge)
- Assume TESLA 9-cavity HOM’s
- Threshold current 5.12 mA
- Beam Breakup not a problem for ERLP as current much lower

- Various …

- 4 ps long bunches, 80 pC
- 8.35 MeV Injection line (TL2) between 10 m and 15 m
- 35 MeV Beam Transfer System (BTS)
- Initial emittance (norm) between 1 mm mrad and 2 mm mrad
- Transverse beam size ~ 1-16 mm throughout BTS
- 0.4 ps long bunches at FEL

- ASTRA - used for Gun to Booster (C Gerth & F Hannon)
- How do we treat dipoles in Injector line ?
- Analytical approach (N Vinokurov)
- GPT (General Particle Tracer) recently acquired
- TRACE-3D (Linear Space Charge only)

ASTRA dipole version requires 3D space charge mesh:

- slower than 2D version

- requires more particles (300k), which makes it even slower!

- in the bends the space charge field needs to be recalculated more often ...

Segment 1: 39 h 29 min

Segment 2: 11 h 16 min

Segment 3: 39 h 29 min

3.8 days (3GHz Pentium 4, elegant tracking < 1s)

‘Test bunch’ was set up with beam parameters similar to the tracking results from the injector:

βx / βy = 2 m

αx / αy = 0

εnx / εny= 3 µm

Bunch length (rms) = 1.2 mm (Gaussian)

Energy spread ∆E/E = 0.1% (no chirp)

Transfer Line 2

Elegant (2k)

ASTRA (1k)

without sc

1%

Transfer Line 2

Elegant (2k)

ASTRA (300k)

with sc

εnx~ 6 µm

εny ~ 4 µm

Transfer Line 2

After 1st dipole

Elegant (2k)

ASTRA (300k)

with sc

Energy spread growth occurs in the dipoles!

Tracking of straight line with 2D and 3D version gave same results.