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

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)

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

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

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…

Solenoid FEL Beam Conditioner RF 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. 264-268)

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)

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

‘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?

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

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…