696
M. Dohlus et al.
spread parameter, ε emittance, β av average beta function).
L g = L g0 (1 + Λ)
(11.87)
Λ = a 1 X
a 2
d + a 3 X
a 4
ε + a 5 X
a 6
γ + a 7 X
a 8
ε X
a 9
γ +
+ a 10 X
a 11
d X
a 12
γ + a 13 X
a 14
d X
a 15
ε + a 16 X
a 17
d X
a 18
ε X
a 19
γ
a 1 = 0.45, a 2 = 0.57, a 3 = 0.55, a 4 = 1, 6,
a 5 = 3.0, a 6 = 2.0, a 7 = 0.35, a 8 = 2.9,
a 9 = 2.4, a 10 = 51, a 11 = 0.95, a 12 = 3.0,
a 13 = 5.4, a 14 = 0.7, a 15 = 1.9, a 16 = 1140,
a 17 = 2.2, a 18 = 2.9, a 19 = 3.2.
Gain Guiding
Gain guiding counteracts the diffractive widening of the FEL beam since most of
the light is generated in the central core of the electron beam [26]. Gain guiding
permits the FEL beam to follow slow, “adiabatic” motions of the electron beam and
is thus crucial for the tolerable deviation of the electron beam orbit from a perfectly
straight line in the long undulator of an x-ray FEL.
Transverse Coherence
The fundamental Gaussian mode TEM00 has its highest intensity on the beam axis
while higher modes extend to larger radial distances. The TEM00 mode grows
fastest along the undulator, owing to its superior overlap with the electron beam.
Near saturation it dominates and the FEL radiation possesses a high degree of
transverse coherence, as verified by double-slit diffraction experiments [27].
Seeding
FEL “Seeding” means to provide an initial electromagnetic wave at the entrance
of the undulator with the help of an external laser pulse of adequate wavelength.
Various seeding methods have been proposed to improve the longitudinal coherence
properties of SASE radiation, and to reduce the relative timing jitter between
pump and probe signals in time domain experiments aiming at femtosecond level
resolution. Direct seeding requires a coherent signal well above the shot-noise level.
In the VUV such signals may be obtained by high harmonic generation (HHG)
in a gas [28, 29]. At shorter wavelengths, self-seeding [30] may be applied: a
SASE signal, produced in a short undulator, is passed through a monochromator
and serves as narrow-band seed radiation in the main undulators following further
downstream. In a high-gain harmonic generation (HGHG) FEL [31], the electron
beam is energy-modulated in an undulator by interaction with a powerful laser.
A magnetic chicane converts the energy modulation to a density modulation. A
second undulator causes the density-modulated beam to emit coherent radiation
at a higher harmonic frequency. In an echo-enabled harmonic generation (EEHG)
FEL [32], a second modulator followed by a second chicane are inserted before
the radiator. The electron beam interacts twice with two laser pulses in the two
modulators. The longitudinal phase space distribution becomes highly nonlinear,
M. Dohlus et al.
spread parameter, ε emittance, β av average beta function).
L g = L g0 (1 + Λ)
(11.87)
Λ = a 1 X
a 2
d + a 3 X
a 4
ε + a 5 X
a 6
γ + a 7 X
a 8
ε X
a 9
γ +
+ a 10 X
a 11
d X
a 12
γ + a 13 X
a 14
d X
a 15
ε + a 16 X
a 17
d X
a 18
ε X
a 19
γ
a 1 = 0.45, a 2 = 0.57, a 3 = 0.55, a 4 = 1, 6,
a 5 = 3.0, a 6 = 2.0, a 7 = 0.35, a 8 = 2.9,
a 9 = 2.4, a 10 = 51, a 11 = 0.95, a 12 = 3.0,
a 13 = 5.4, a 14 = 0.7, a 15 = 1.9, a 16 = 1140,
a 17 = 2.2, a 18 = 2.9, a 19 = 3.2.
Gain Guiding
Gain guiding counteracts the diffractive widening of the FEL beam since most of
the light is generated in the central core of the electron beam [26]. Gain guiding
permits the FEL beam to follow slow, “adiabatic” motions of the electron beam and
is thus crucial for the tolerable deviation of the electron beam orbit from a perfectly
straight line in the long undulator of an x-ray FEL.
Transverse Coherence
The fundamental Gaussian mode TEM00 has its highest intensity on the beam axis
while higher modes extend to larger radial distances. The TEM00 mode grows
fastest along the undulator, owing to its superior overlap with the electron beam.
Near saturation it dominates and the FEL radiation possesses a high degree of
transverse coherence, as verified by double-slit diffraction experiments [27].
Seeding
FEL “Seeding” means to provide an initial electromagnetic wave at the entrance
of the undulator with the help of an external laser pulse of adequate wavelength.
Various seeding methods have been proposed to improve the longitudinal coherence
properties of SASE radiation, and to reduce the relative timing jitter between
pump and probe signals in time domain experiments aiming at femtosecond level
resolution. Direct seeding requires a coherent signal well above the shot-noise level.
In the VUV such signals may be obtained by high harmonic generation (HHG)
in a gas [28, 29]. At shorter wavelengths, self-seeding [30] may be applied: a
SASE signal, produced in a short undulator, is passed through a monochromator
and serves as narrow-band seed radiation in the main undulators following further
downstream. In a high-gain harmonic generation (HGHG) FEL [31], the electron
beam is energy-modulated in an undulator by interaction with a powerful laser.
A magnetic chicane converts the energy modulation to a density modulation. A
second undulator causes the density-modulated beam to emit coherent radiation
at a higher harmonic frequency. In an echo-enabled harmonic generation (EEHG)
FEL [32], a second modulator followed by a second chicane are inserted before
the radiator. The electron beam interacts twice with two laser pulses in the two
modulators. The longitudinal phase space distribution becomes highly nonlinear,