Abstract
The effects of a correlated linear energy/velocity chirp in the electron beam in the free electron laser (FEL), and how to compensate for its effects by using an appropriate taper (or reverse-taper) of the undulator magnetic field, is well known. The theory, as described thus far, ignores velocity dispersion from the chirp in the undulator, taking the limit of a ‘small’ chirp. In the following, the physics of compensating for chirp in the beam is revisited, including the effects of velocity dispersion, or beam compression or decompression, in the undulator. It is found that the limit of negligible velocity dispersion in the undulator is different from that previously identified as the small chirp limit, and is more significant than previously considered. The velocity dispersion requires a taper which is nonlinear to properly compensate for the effects of the detuning, and also results in a varying peak current (end thus a varying gain length) over the length of the undulator. The results may be especially significant for plasma driven FELs and low energy linac driven FEL test facilities.
Highlights
The electron beams typical of plasma accelerators possess small emittance, a large energy spread, and are very short compared to beams from more conventional linac sources
With regard to the free electron laser (FEL) gain, the large energy spread is potentially the most deleterious feature at first glance, but measurements and simulations imply that a large proportion of the energy spread is corellated with the temporal bunch coordinate
It has been shown that the beam dispersion in the undulator may be more important than previously acknowledged for presently achievable cases, especially in the realm of plasma driven FEL’s, and the constraint on when it is relevant is ∼ an order of magnitude tighter than the previously identified condition of a ‘small’ chirp
Summary
The free electron laser (FEL) is established as the brightest source of coherent hard x-rays in the world, with facilities currently operational in the USA [1] and Japan [2], and about to come online in Switzerland [3] and Hamburg [4] in the near future. With regard to the FEL gain, the large energy spread is potentially the most deleterious feature at first glance, but measurements and simulations imply that a large proportion of the energy spread is corellated with the temporal bunch coordinate This chirp in the beam energy causes a detuning in the FEL resonant frequency along the length of the bunch, and it is well known that this can be compensated for with an appropriate tapering of the undulator magnetic field [11]. With the increased interest in novel accelerator concepts as FEL drivers, e.g. use of plasma accelerators [12,13,14,15] or the synthesis of broadband beams from linacs as in [16, 17], the case of larger chirps has become more relevant In this regime, dispersive effects can no longer be ignored, and the beam current and energy spread are a function of propagation distance through the undulator. Note that typically the term ‘taper’ refers to the technique of reducing the undulator magnetic field, and ‘reverse-taper’ refers to the opposite; in the following, for brevity, we use the term ‘taper’ in a more general sense as altering the magnetic field, either increasing or decreasing
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