Formation of electron bunches for harmonic cascade x-ray free electron lasers

Abstract

The operation of x-ray free electron lasers (FELs) relies on extremely high quality electron beams. Two FEL projects employing the technique of self-amplified spontaneous emission define the state-of-the-art situation: peak current of few kiloamperes, emittance of 1 mm-mrad or less, and an energy spread of 1 MeV or less [1,2]. Creation of electron bunches with these parameters is a difficult and elaborate process consisting of the electron bunch production, acceleration, and compression. A significant understanding was gained in the underlying physics over the past decade [3‐7]. The main phenomena affecting electron bunches includes space charge effects, wakefields, and coherent synchrotron radiation (CSR). Nonlinearity of the waveform of the accelerating field in the linac and nonlinear time-of-flight characteristics of bunch compressors also play an important role. More demanding for the electron beam quality are FELs that are designed to generate temporally coherent x-rays. These FELs, called high-gain harmonic generation FELs or harmonic cascade FELs (HC FELs) [8‐10], employ a laser to seed the radiation at a lower harmonic of the output FEL radiation. Very often several FEL cascades are used to obtain the radiation at the x-ray wavelength. In these cases, the radiation produced in one cascade by one group of electrons proceeds ahead and interacts with other electrons from the same electron bunch in the next cascade. Thus, relatively long electron bunches are needed to accommodate this technique. It is important to have a constant peak current (i.e. a flat electron density distribution) over the entire bunch length, and a discussion of the means to obtain this is one of the objectives of this paper. We also propose a technique aiming for control of the peak current spikes at the edges of the electron bunch. Those spikes often occur after the final bunch compression and are capable of inducing unwanted wakefields and coherent synchrotron radiation. It is largely anticipated that HC FELs will be used for the production of relatively long temporally coherent x-ray pulses with a narrow bandwidth. However, a nonlinear energy modulation of electrons in the electron bunch can cause a frequency chirp in the output signal [11,12] which broadens the bandwidth significantly beyond the Fourier transform limit. 1 The rf harmonic linearizer [13] often helps to remove major nonlinear components in the energy modulation of electrons, but, frequently, even the remaining modulation significantly broadens the bandwidth, in particular, when strong linac structural wakefields are present. In this paper we propose a complementary technique which employs a specially shaped distribution of electron density and the wakefields themselves in order to avoid the remaining energy modulation of electrons. We also give a simple recipe on how to find such a distribution and demonstrate its usefulness with a practical example. The overall goal for a design of the electron beam delivery system responsible for the formation of the electron bunches for HC FEL is to obtain a so-called flat-flat distribution, i.e., flat in the peak current and flat in the energy, which means that there are no peak current and energy modulations of electrons along the electron bunch. The technique discussed in this paper allows achievement of this goal on a macroscale comparable to the bunch length, but does not deal with the peak current and energy fluctuations on a microscale of few tens of microns often caused by the microbunching instability. This problem has already been addressed in the literature (see [4,14] and references therein).