11 Application of Accelerators and Storage Rings
695
Fig. 11.18 Evolution of the microbunch structure at z = 12L g0 , 14L g0 , 16L g0 , 18L g0 . Upper
subplots: distribution of particles in (ψ, η) phase space. Three FEL buckets are indicated by dashed
curves. Lower subplots: normalized charge density as function of ψ
developed [14, 23]. More realistic cases require sophisticated simulation codes such
as FAST [24], GENESIS [11] or GINGER [25]. These are indispensable for the
design of short-wavelength FELs.
3D Gain Length
The 3D gain length L g is typically 30–50% longer than the 1D gain length
L g0 . According to [23] L g can be expressed in terms of three dimensionless
parameters: X γ = L g0 4πσ η /λ u (energy spread parameter), X d = L g0 λ l /
4πσ 2
r
(diffraction parameter, σ r rms beam radius) and X ε = L g0 4πε/(β av λ l ) (angular
695
Fig. 11.18 Evolution of the microbunch structure at z = 12L g0 , 14L g0 , 16L g0 , 18L g0 . Upper
subplots: distribution of particles in (ψ, η) phase space. Three FEL buckets are indicated by dashed
curves. Lower subplots: normalized charge density as function of ψ
developed [14, 23]. More realistic cases require sophisticated simulation codes such
as FAST [24], GENESIS [11] or GINGER [25]. These are indispensable for the
design of short-wavelength FELs.
3D Gain Length
The 3D gain length L g is typically 30–50% longer than the 1D gain length
L g0 . According to [23] L g can be expressed in terms of three dimensionless
parameters: X γ = L g0 4πσ η /λ u (energy spread parameter), X d = L g0 λ l /
4πσ 2
r
(diffraction parameter, σ r rms beam radius) and X ε = L g0 4πε/(β av λ l ) (angular