Measuring the Electron Beam Energy in a Magnetic Bunch ... - DESY

up with and then interact with the electron bunch, giving it an energy spread which is
correlated along the bunch. For an rms bunch length, σ z , dipole length, L B and dipole
bend radius, R, the CSR-induced rms relative energy spread per dipole for a Gaussian
bunch under steady-state conditions is
Nre
LB
Δ ECSR
≈ 0.22
(2.3.4)
2 / 3 4 / 3
γR
σ
z
Where N is the number of electrons, r e is the classical electron radius and gamma is the
Lorentz energy factor [15]. Since the bunch length is shorter after each bend, the local
energy spread generated in the last bend of the chicane will be the largest.
Aside from the increase in emittance, bunch compressors can also cause
something called a micro-bunching instability when a density modulation created by the
impedance of geometric wakefields, longitudinal space-charge, or CSR get caught in a
feedback loop in which these energy modulations are coupled into density modulations
via the momentum compaction of the chicane. For example, the CSR creates an energy
modulation of the bunch and the dispersion chops the beam up into slices with lengths
that are comparable to the coherent synchrotron radiation wavelengths. These microbunches
then interact with one another, experiencing resonant oscillatory motion that can
break the macro-beam apart. Although it was initially suspected that CSR would be the
primary driver of the microbunching instability, the longitudinal space-charge effects in
the injector are now the primary focus of concern. The microbunching instability can be
avoided by increasing the residual energy spread of the bunch with a laser heater that
imposes a periodic energy modulation over the bunch and then smears it out
longitudinally via dispersion [16].
At FLASH, a single chicane is used as the first bunch compressor and a
symmetric double-chicane is used as the second bunch compressor (Fig. 2.3.4). The
microbunching instability is more likely in the second chicane, due to the added bending
of the double-chicane design and the higher energy of the beam [13]. In general, the gain
of the instability increases with the inverse of the characteristic wavelength of the
modulation squared. It is cut off for wavelengths that are shorter than R 56 *C*δ. For the
first bunch compressor, R 56 , C and δ are larger than for the second bunch compressor and
so the cut-off occurs at longer wavelengths, making the microbunching less effective.
With careful balancing of CSR and other effects, this can be avoided and the second
chicane can be used to compensate for CSR-based emittance growth generated in the
upstream bunch compressor [17].
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