1. Limitations of Electron Beam Conditioning in Free-Electron Lasers
P. Emma, G. Stupakov
Oct. 31, 2002

2. Energy spread is easy,… but present
SASE FEL needs very bright electron beam…
transverse emittance:
eN < 1 mm at 1 Å, 15 GeV
energy spread:
sd < 0.05% at Ipk = 4 kA, K  4, lu  3 cm, …
Energy spread is easy,… but present
guns produce N > 2 mm ~
Requirement is eased if correlation establish between energy and ‘emittance’ (d ~ x2)

4. FEL Electron Beam Conditioning
undulator e- e-
LCLS
r/sx Lu
Relative energy deviation, du, of each e- should be increased in proportion to the square of its norm. betatron amplitude, r
(natural focusing: ax,y = 0)
condition

5. Slippage in Tracking (with LCLS-like FODO lattice)
eN  1 mm, sd  0
Conditioned
eN  1 mm
sd  310-4
Not
conditioned

6. Conditioning Prior to Acceleration and Compression
Locate conditioner near start of accelerator…
e- bunch for FEL compressed from sz0 to szf and accelerated from g0 to gu …
Acceleration reduces relative energy spread, but compression increases it…
Relative energy deviation at low-energy conditioner is…

7. Solenoid FEL Beam ConditionerRF
k, L
k, L RF
SOLENOID-1
SOLENOID-2
R56 = 1/h h -h -I
sx0
sz0 - +
T216 = T436 = - T511 = -T533 = k2L/2
(see also N. Vinokurov; NIM A 375, 1996, pp )

8. A ‘One-Phase’ Conditioner (for simplicity)
k, L RF
SOLENOID
R56 = 1/h h -h +I
Energy conditioning is provided for h > 0…
Equate to earlier result…
Conditioner parameters (left) are given by FEL parameters (right)

9. Conditioning and Emittance Growth
Transverse emittance growth due to solenoid chromaticity…
Relative transverse emittance growth…
…is set by FEL parameters, not conditioner…

10. ‘RF-Quad’ Effect Conditioner adds kick dependent on z0…
Head (z0 > 0) is de-focused and tail is focused (RF-quad effect)…
Solenoid conditioner generates same undesirable RF-quad effect as TM210-type conditioner. Is there some fundamental connection?

11. Numerical Example For LCLS using natural focusing (bu  72 m)…
A “two-phase” conditioner is much worse.

12. Particle Tracking Through Solenoid System
With
After Solenoid-1
After Solenoid-2
wow!
If this is a general result, then conditioning a short wavelength FEL looks impossible.
Go to Gennady’s half of talk…