11 Application of Accelerators and Storage Rings
697
leading to density modulations at a very high harmonic number initiated by a modest
energy modulation.
11.1.2.3 Technical Requirements
Very bright electron beams are required to drive ultraviolet and x-ray FELs. Higher
peak current and smaller cross sections reduce the gain length (see Eq. (11.82)).
High peak currents require longitudinal bunch compression, but the energy spread is
increased by this process (which affects the gain length through X γ in Eq. (11.87)).
Very low-emittance beams can be generated by specially designed particle sources
with photocathode or with thermionic emission. The beam cross section in the
undulator can be reduced by stronger focusing (i.e., smaller β av ), but the increased
angular spread will eventually degrade the FEL gain (through X ε in Eq. (11.87)).
The FEL design optimization is therefore multi-dimensional and beyond our scope
here. Typical requirements on electron beams are
I 0 ≥ 1 kA, σ η < ρ/2, ε ∼ λ l / (4π) .
(11.88)
These requirements apply to the “slice” beam qualities defined on the scale of the
coherence length (see Eq. (11.85)). For harmonic generation FELs, the slice energy
spread should be much smaller than the ρ-parameter of the final amplifier because
the additional energy modulation imposed on the beam becomes the effective energy
spread there. Beam current, slice emittance and energy spread should be “flat”
along the bunch in order not to increase the final radiation bandwidth. However,
there are proposals for introducing, on purpose, some longitudinal variation of the
electron energy within the bunch to generate a controlled frequency chirp in the FEL
radiation pulse [33].
High-quality electron beams as described can be produced with linear accelerators but not with storage rings, mainly due to synchrotron radiation effects.
11.2 Accelerators in Industry
K. H. W. Bethge · J. Meijer
11.2.1 Introduction
Accelerators in their earliest stages of development served exclusively as tools of
fundamental research; today they find application over a broad range of technical,
industrial and medical areas.
697
leading to density modulations at a very high harmonic number initiated by a modest
energy modulation.
11.1.2.3 Technical Requirements
Very bright electron beams are required to drive ultraviolet and x-ray FELs. Higher
peak current and smaller cross sections reduce the gain length (see Eq. (11.82)).
High peak currents require longitudinal bunch compression, but the energy spread is
increased by this process (which affects the gain length through X γ in Eq. (11.87)).
Very low-emittance beams can be generated by specially designed particle sources
with photocathode or with thermionic emission. The beam cross section in the
undulator can be reduced by stronger focusing (i.e., smaller β av ), but the increased
angular spread will eventually degrade the FEL gain (through X ε in Eq. (11.87)).
The FEL design optimization is therefore multi-dimensional and beyond our scope
here. Typical requirements on electron beams are
I 0 ≥ 1 kA, σ η < ρ/2, ε ∼ λ l / (4π) .
(11.88)
These requirements apply to the “slice” beam qualities defined on the scale of the
coherence length (see Eq. (11.85)). For harmonic generation FELs, the slice energy
spread should be much smaller than the ρ-parameter of the final amplifier because
the additional energy modulation imposed on the beam becomes the effective energy
spread there. Beam current, slice emittance and energy spread should be “flat”
along the bunch in order not to increase the final radiation bandwidth. However,
there are proposals for introducing, on purpose, some longitudinal variation of the
electron energy within the bunch to generate a controlled frequency chirp in the FEL
radiation pulse [33].
High-quality electron beams as described can be produced with linear accelerators but not with storage rings, mainly due to synchrotron radiation effects.
11.2 Accelerators in Industry
K. H. W. Bethge · J. Meijer
11.2.1 Introduction
Accelerators in their earliest stages of development served exclusively as tools of
fundamental research; today they find application over a broad range of technical,
industrial and medical areas.