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The Microbunched Electron Cooling (MBEC) proposed by D. Ratner is a promising cooling technique that can find applications in future hadron and electron-ion colliders. In this paper, we develop a new framework for the study of MBEC which is based on the analysis of the dynamics of microscopic 1D fluctuations in the electron and hadron beams during their interaction and propagation through the system. Within this framework, we derive an analytical formula for the longitudinal cooling rate and benchmark it against 1D computer simulations. We then calculate the expecting cooling time for a set of parameters of the proposed electron-ion collider eRHIC in a simple cooling system with one chicane in the electron channel. While the cooling rate in this system turns out to be insufficient to counteract the intrabeam scattering in the proton beam, we discuss how the electron signal can be amplified by two orders of magnitude through the use of plasma effects in the beam.

Echo-enabled harmonic generation has been used to seed a free-electron laser and has been demonstrated up to the 75th harmonic, producing 32 nm light from a 2,400 nm laser. The production of coherent radiation at ever shorter wavelengths has been a long-standing challenge since the invention of lasers 1 , 2 and the subsequent demonstration of frequency doubling 3 . Modern X-ray free-electron lasers (FELs) use relativistic electrons to produce intense X-ray pulses on few-femtosecond timescales 4 , 5 , 6 . However, the shot noise that seeds the amplification produces pulses with a noisy spectrum and limited temporal coherence. To produce stable transform-limited pulses, a seeding scheme called echo-enabled harmonic generation (EEHG) has been proposed 7 , 8 , which harnesses the highly nonlinear phase mixing of the celebrated echo phenomenon 9 to generate coherent harmonic density modulations in the electron beam with conventional lasers. Here, we report on a demonstration of EEHG up to the 75th harmonic, where 32 nm light is produced from a 2,400 nm laser. We also demonstrate that individual harmonic amplitudes are controlled by simple adjustment of the phase mixing. Results show the potential of laser-based manipulations to achieve precise control over the coherent spectrum in future X-ray FELs for new science 10 , 11 .

In the past, calculation of wakefields generated by an electron bunch propagating in a plasma has been carried out in linear approximation, where the plasma perturbation can be assumed small and plasma equations of motion linearized. This approximation breaks down in the blowout regime where a high-density electron driver expels plasma electrons from its path and creates a cavity void of electrons in its wake. In this paper, we develop a technique that allows us to calculate short-range longitudinal and transverse wakes generated by a witness bunch being accelerated inside the cavity. Our results can be used for studies of the beam loading and the hosing instability of the witness bunch in plasma-wakefield and laser-wakefield acceleration.

In this paper, we propose a new approach to measuring ultrafast dynamics with free-electron lasers (FELs). Ultrafast experiments are among the most promising avenues of research at x-ray FELs, with the potential to reveal the chemical dynamics of charge separation, conical intersection crossing, and biologically mediated reactions. Pump-probe scanning is the standard approach to measure dynamics at x-ray FELs, but at the shortest timescales, and particularly for x-ray pump, x-ray probe experiments, the scans require challenging beam setups and can introduce systematic errors. Here, we propose an alternative approach using the randomness of the self-amplified spontaneous emission (SASE) process to drive many simultaneous pump-probe experiments on each shot. Measuring the fluctuations in the incident beam’s time profile on a shot-to-shot basis enables the reconstruction of ultrafast dynamics down to the coherence length of the FEL without the need for pump-probe scans. Because of similarity to ghost imaging, in which spatial properties are reconstructed by measuring the incident probe’s transverse properties, we call this “pump-probe ghost imaging.” In this paper, we describe the method and simulate an example experiment. We also describe an alternative implementation that uses only spectral measurements, avoiding the need for direct time-domain diagnostics and extending the method to the attosecond regime.

This paper discusses the extension to different electron beam aspect ratio of the Child-Langmuir law for the maximum achievable current density in electron guns. Using a simple model, we derive quantitative formulas in good agreement with simulation codes. The new scaling laws for the peak current density of temporally long and transversely narrow initial beam distributions can be used to estimate the maximum beam brightness and suggest new paths for injector optimization.

Microbunched electron cooling is a promising cooling technique that can find applications in future hadron and electron-ion colliders to counteract intrabeam scattering that limits the maximum achievable luminosity of the collider. To minimize the cooling time, one would use amplification cascades consisting of a drift section followed by a magnetic chicane. In this paper, we first derive and optimize the gain factor in an amplification section for a simplified one-dimensional model of the beam. We then deduce the cooling rate of a system with one and two amplification cascades. We also analyze the noise effects that counteract the cooling process through the energy diffusion in the hadron beam. Our analytical formulas are confirmed by numerical simulations for a set of model parameters.

The technique of microbunched electron cooling (MBEC) is a coherent cooling scheme with possible applications in high-energy hadron and electron-ion machines. In our previous work we analyzed the cooling of the hadron energy spread and transverse emittance using a one-dimensional (1D) technique that tracked the microscopic fluctuations in the hadron and electron beams. However, in order to obtain analytical expressions for our key quantities, we limited ourselves to calculating and optimizing only the initial values of the cooling rates. In this paper, we extend our approach so that it properly addresses the issue of the long-term, dynamic evolution of the hadron beam. In order to do so, it becomes necessary to consider the synchrotron motion of the hadron beam, in conjunction with the effects of diffusion and intrabeam scattering (IBS). With these modifications, our formalism allows us to develop a simple numerical tool that can effectively model the final state of hadron beam after many passages through the MBEC cooler.

We propose a scheme that combines the echo-enabled harmonic generation technique with the bunch compression and allows one to generate harmonic numbers of a few hundred in a microbunched beam through up-conversion of the frequency of an ultraviolet seed laser. A few-cycle intense laser is used to generate the required energy chirp in the beam for bunch compression and for selection of an attosecond x-ray pulse. Sending this beam through a short undulator results in an intense isolated attosecond x-ray pulse. Using a representative realistic set of parameters, we show that 1 nm x-ray pulse with peak power of a few hundred MW and duration as short as 20 attoseconds (FWHM) can be generated from a 200 nm ultraviolet seed laser. The proposed scheme may enable the study of electronic dynamics with a resolution beyond the atomic unit of time (∼24 attoseconds) and may open a new regime of ultrafast sciences.

The technique of microbunched electron cooling (MBEC) is an attractive coherent cooling scheme with potential applications in future high-energy circular colliders. In our previous work, we analyzed the cooling of the energy spread using a one-dimensional (1D) technique that tracks the dynamics of microscopic fluctuations in the hadron and electron beams. In this paper, we extend this approach so that it covers the transverse emittance cooling as well. In order to do so, it is necessary to consider the betatron motion of the hadron beam and take into account effects of the momentum dispersion in the modulator and kicker regions. We derive relatively simple analytical expressions for the emittance and energy spread cooling times in terms of the various beam and lattice parameters, allowing us to perform fast optimization studies for an MBEC configuration. Verified through comparison with simulation, our theory can also incorporate features such as plasma amplification stages, which are crucial components of a realistic cooling system.