Accelerator, Laser, and Coherent Optoelectronics R&D Lab (ALCOL)

Abstract

Density modulations on electron beams can improve machine performance of beam-driven accelerators and FELs with resonance beam-wave coupling. The beam modulation is studied with a masked chicane by the analytic model and simulations with the beam parameters of the Advanced Superconducting Test Accelerator (ASTA) in Fermilab. With the chicane design parameters (bending angle of 18°, bending radius of 0.95 m and R56 ~ - 0.19 m) and a nominal beam of 3 ps bunch length, the analytic model showed that a slit-mask with slit period 900 mm and aperture width 300 mm induces a modulation of bunch-to-bunch spacing ~100 mm to the bunch with 2.4% correlated energy spread. With the designed slit mask and a 3 ps bunch, particle-in-cell (PIC) simulations, including nonlinear energy distributions, space charge force, and coherent synchrotron radiation (CSR) effect, also result in beam modulation with bunch-to-bunch distance around 100 mm and a corresponding modulation frequency of 3 THz. The beam modulation has been extensively examined with three different beam conditions, 2.25 ps (0.25 nC), 3.25 ps (1 nC), and 4.75 ps (3.2 nC)，by tracking code Elegant. The simulation analysis indicates that the sliced beam by the slit-mask with 3 ~ 6% correlated energy spread has modulation lengths about 187 mm (0.25 nC), 270 mm (1 nC) and 325 mm (3.2 nC). The theoretical and numerical data proved the capability of the designed masked chicane in producing modulated bunch train with micro-bunch length around 100 fs.

introduction

 

We have been investigating the masked chicane technique [1 – 3] with the available beam parameters such as the 50 MeV photoinjector of the Advanced Superconducting Test Accelerator (ASTA), which is currently being constructed and commissioned in Fermilab [4]. Downstream of the ASTA 50 MeV photoinjector beamline, a magnetic bunch compressor, consisting of four rectangular dipoles, is adopted and a slit-mask is designed and inserted in the middle. Based on this slit-masked chicane, the bunching performance and the ability of sub-ps microbunch generation are studied.

 

In order to evaluate bunching performance with nominal beam parameters, the masked chicane has been analyzed by the linear bunching theory in terms of bunch-to-bunch distance and microbunch length. Elegant code is employed to examine the theoretical model with the ASTA nominal beam parameters (RMS bunch length sz,i is 3 ps and energy ratio τ is around 0.1). The Particle-In-Cell (PIC) simulation (CST-PS) includes space charge and CSR effect and nonlinear energy distribution over macro-particle data. For Elegant simulations, bunch charge distribution and the beam spectra are mainly investigated with three different bunch charges, 0.25 nC, 1 nC, and 3.2 nC, under two RF-chirp conditions of minimum and maximum energy spreads. The corresponding bunch length for the maximally chirped beam is 2.25, 3.25, and 4.75 ps and the correlated energy spread is 3.1, 4.5, and 6.2 % respectively for bunch charge of 0.25 nC, 1 nC, and 3.2 nC

 ANALYTIC DESIGN

The designed chicane consists of four dipoles and a slit mask with slit spacing, W, and aperture width, a, is inserted in the middle of the bunch compressor (dispersion region). Before the beam is injected into the masked chicane, a positive linear energy-phase correlation is imposed by accelerating the beam off the crest of the RF wave in the linear accelerator. The chicane disperses and re-aligns the particles with respect to their energies in phase space. The input beam is then compressed and the phase space ellipse is effectively rotated toward the vertical. In the middle of the chicane, the beam is partially blocked by the transmission mask and holes are introduced in the energy-phase ellipse. In the second half of the chicane, the beam is deliberately over-bunched and the beam ellipse is slightly rotated past the vertical. In this step, the linear energy-phase correlation is preserved by over-bunching, accompanied with a steeper phase-space slope. Consequently, the projection of the beam ellipse on the time axis generates density modulations at a period smaller than the grid spacing.

With a masked chicane, one can control the microscopic structure of a bunch under compression by adjusting the grid period and/or by varying the chicane magnetic field. In principle, if a grid period (or slit-spacing) is smaller than a hundred microns, a modulation wavelength of the bunched beam is possibly cut down to a few tens of microns. The beamline for the mask is originally designed with the four dipoles having bending angle of 18o, bending radius R = 0.95 m, and dipole separation D = 0.68 m. The 125 mm thick tungsten mask with a slit-array is designed with period of W = 900 mm and aperture width of a = 300 mm (~ 33 % transparency).

For the ASTA 50 MeV chicane, R56 (longitudinal dispersion) = - 0.192 m and hx (maximum transverse dispersion) = - 0.34 m. The bunch-to-bunch spacing (or modulation wavelength), Dz, is defined by the final bunch length divided by the number of micro-bunches in a compressed beam [2]. The final bunch length is

                                (1)

, where h1 is the first order chirp, sz,i is the initial bunch length, sδi is the initial un-correlated RMS energy spread, and τ is the energy ratio. The energy ratio is normally ~ 0.1 at ASTA photoinjector beamline. Concerning correlated energy spread sδ, we have

                                                         (2)

The correlated energy spread, sd, and transverse emittance, εx, normally determine a transverse beam size at the mask by

                           (3)

, where βx,mask is the beta function and hx,mask is the transverse dispersion at the mask [5, 6]. After passing through a slit-masked chicane, the number of microbunches of the compressed beam is determined by the transverse beam size at the mask, sx,mask , and the slit period, W, by

                                                                     (4)

The correlated energy spread,sd, and transverse emittance, εx, normally determine a transverse beam size at the mask by

                                 (5)

The bunch-to-bunch spacing of modulated beam, Dz, can thus be derived to be

    (6)

With the calculated bunch-to-bunch spacing, the bunch length of microbunches can be evaluated by sz,m = T×Dz, where T (= a/W) is the mask transparency (~ 33 % here), assuming the time pattern of the beam is similar to the mask pattern6.

We examine bunch lengths, compression ratios, and bunch-to-bunch distances with respect to correlated energy spreads, sd, for the beam with ASTA nominal parameters [4]. When sd  reaches 0.468%，which corresponds to sd = - sz,i/R56 and h1 = - 1/R56, the beam is maximally compressed and the final rms bunch length tends to be minimal. One can see that continuously increasing sd renders the beam less compressed and would make the beam rather stretched instead of being compressed. The bunch length via the magnetic chicane is thus mainly governed by an amount of beam energy-spread determined by a beam injection condition with respect to RF-phase. As shown in Fig. 2(b), the compress ratio is apparently in inverse proportion as a final bunch length (rms), which therefore becomes infinite when the beam is maximally compressed. Figure 2(c) shows bunch-to-bunch distance (bunch modulation length) with correlated energy spread, sd. The analytic calculation points out that the distance becomes ~ 100 mm with correlated energy spread of ~ 2.4%. With a 33.3% mask transparency, it is predicted that the ~ 100 mm spaced bunch produces a microbunch length of ~ 33 mm, corresponding to 100 fs in time.