We propose undertaking a demonstration experiment on suppressing spontaneous undulator radiation from an electron beam at BNL's Accelerator Test Facility (ATF). We describe the method, the proposed layout, and a possible schedule. There are several advantages in strongly suppressing shot noise in the electron beam, and the corresponding spontaneous radiation. The self-amplified spontaneous (SASE) emission originating from shot noise in the electron beam is the main source of noise in high-gain FEL amplifiers. It may negatively affect several HG FEL applications ranging from single- to multi-stage HGHG FELs. SASE saturation also imposes a fundamental hard limit on the gain of an FEL amplifier in a coherent electron-cooling scheme. A novel active method for suppressing shot noise in relativistic electron beams by many orders-of-magnitude was recently proposed. While theoretically such strong suppression appears feasible, the performance and applicability of this novel method must be evaluated experimentally. Several practical questions about the proposed noise suppressor, such as 3D effects and/or sensitivity to the e-beam parameters also require experimental clarification. To do this, we propose here a proof-of-principle experiment using elements of the VISA FEL at BNL's Accelerator Test Facility.

Shot noise in the electron beam distribution is the main source of noise in high-gain FEL amplifiers, which may affect applications ranging from single- and multi-stage HGHG FELs to an FEL amplifier for coherent electron cooling. This noise also imposes a fundamental limit of about 10{sup 6} on FEL gain, after which SASE FELs saturate. There are several advantages in strongly suppressing this shot noise in the electron beam, and the corresponding spontaneous radiation. For more than a half-century, a traditional passive method has been used successfully in practical low-energy microwave electronic devices to suppress shot noise. Recently, it was proposed for this purpose in FELs. However, being passive, the method has some significant limitations and is hardly suitable for the highly inhomogeneous beams of modern high-gain FELs. I present a novel active method of suppressing, by many orders-of-magnitude, the shot noise in relativistic electron beams. I give a theoretical description of the process, and detail its fundamental limitation.

FEL-based coherent electron cooling (CEC) offers a new avenue to achieve high luminosities in high energy colliders such as RHIC, LHC, and eRHIC. Traditional treatments consider the FEL as an amplifier of optical waves with specific initial conditions, focusing on the resulting field. CEC requires knowledge of the phase space distribution of the electron beam in the FEL. We present 1D analytical results for the phase space distribution of an electron beam with an arbitrary initial current profile, and discuss approaches of expanding to 3D results.

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We review the statistical description of the chaotic time evolution of the radiation from a self-amplified spontaneous-emission free-electron laser in the linear region before saturation. A high-gain, self-amplified spontaneous-emission (SASE) free-electron laser (FEL) [1, 2], based on modern beam technology, has the advantage of operating without a resonator and hence is capable of generating coherent radiation with wavelength down to the x-ray region. The LCLS at SLAC has recently achieved high gain and saturation at 1.5 {angstrom} [3]. A review of SASE theory can be found in ref. [4]. In this paper, we have considered the linear regime before saturation. In the nonlinear saturation regime, SASE is no longer a Gaussian process and analytic treatment is very difficult. A valuable numerical simulation analysis of the statistical behavior in the nonlinear regime can be found in ref. [10,11].

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