P. Emma, G. StupakovP. Emma, G. StupakovOct. 31, 2002Oct. 31, 2002

Limitations of Electron Beam Limitations of Electron Beam Conditioning in Free-Electron LasersConditioning in Free-Electron Lasers

Limitations of Electron Beam Limitations of Electron Beam Conditioning in Free-Electron LasersConditioning in Free-Electron Lasers

transverse emittance:transverse emittance:

energy spread:energy spread:

< 1 < 1 mm at 1 Å, 15 GeV at 1 Å, 15 GeV

< 0.05%< 0.05% at at IIpkpk = 4 kA, = 4 kA, KK 4, 4, uu 3 cm, …3 cm, …

SASE FEL needs very bright electron beam…SASE FEL needs very bright electron beam…

Requirement is eased if Requirement is eased if correlationcorrelation establish establish between energy and ‘emittance’ (between energy and ‘emittance’ ( ~ ~ xx22))

Energy spread is easy,… but presentEnergy spread is easy,… but presentguns produce guns produce NN > > 2 2 mm~~

Lu

FEL Electron Beam ConditioningFEL Electron Beam Conditioning

ee

LCLSLCLS

r/ x

undulatorundulatoree

Relative energy deviation, Relative energy deviation, uu, of each , of each ee should be increased should be increased

in proportion to the square of its norm. betatron amplitude, in proportion to the square of its norm. betatron amplitude, rr

(natural focusing: (natural focusing: xx,,yy = 0) = 0)

conditioncondition

Notconditioned

Notconditioned

Slippage in Slippage in TrackingTracking (with (with LCLSLCLS-like -like FODO lattice)FODO lattice)

ConditionedConditioned

NNmm 33101044

NNmm 0 0

Conditioning Prior toConditioning Prior toAcceleration and CompressionAcceleration and Compression

Locate conditioner near start of accelerator…Locate conditioner near start of accelerator…

ee bunch for FEL compressed from bunch for FEL compressed from zz00 to to zzff

and and

accelerated from accelerated from 00 to to u u ……

Acceleration Acceleration reducesreduces relative energy spread, but relative energy spread, but compression compression increasesincreases it… it…

Relative energy deviation at low-energy conditioner is…Relative energy deviation at low-energy conditioner is…

SOLENOID-2SOLENOID-1

h h

k, L k, L

I

RF RF

e

z0

x0

Solenoid FEL Beam ConditionerSolenoid FEL Beam Conditioner

(see also N. Vinokurov; NIM A 375, 1996, pp. 264-268)

R56 = 1/h

+

T216 = T436 = T511 = T533 = k2L/2

A ‘One-Phase’ Conditioner (for simplicity)A ‘One-Phase’ Conditioner (for simplicity)

SOLENOID

h h

k, L

I

RF RF

e

Energy conditioning is Energy conditioning is provided for provided for hh > 0… > 0…

Equate to earlier result…Equate to earlier result…

Conditioner parameters (left) are given by FEL parameters (right)Conditioner parameters (left) are given by FEL parameters (right)

R56 = 1/h

Conditioning and Emittance GrowthConditioning and Emittance Growth

Transverse emittance growth due to solenoid chromaticity…Transverse emittance growth due to solenoid chromaticity…

……is set by FEL parameters, is set by FEL parameters, notnot conditioner… conditioner…

Relative transverse emittance growth…Relative transverse emittance growth…

‘‘RF-Quad’ EffectRF-Quad’ Effect

Conditioner adds kick dependent on Conditioner adds kick dependent on zz00……

Head (Head (zz00 > 0) is de-focused and tail is focused (RF-quad effect)… > 0) is de-focused and tail is focused (RF-quad effect)…

Solenoid conditioner generates same undesirable RF-quad effect Solenoid conditioner generates same undesirable RF-quad effect as TMas TM210210-type conditioner. Is there some fundamental connection?-type conditioner. Is there some fundamental connection?

For LCLS using natural focusing (For LCLS using natural focusing (uu 72 m)… 72 m)…

A “two-phase” conditioner is A “two-phase” conditioner is muchmuch worse. worse.

Numerical ExampleNumerical Example

Particle Tracking Through Solenoid SystemParticle Tracking Through Solenoid System

With

If this is a general result, then conditioning a short wavelength FEL If this is a general result, then conditioning a short wavelength FEL looks looks impossible.impossible.

Go to Gennady’s half of talk…Go to Gennady’s half of talk…

After Solenoid-1After Solenoid-1 After Solenoid-2After Solenoid-2

wow!wow!