Three-dimensional model of small signal free-electron lasers

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In the coherent electron cooling, the modern hadron beam cooling technique, each hadron receives an individual kick from the electric field of the amplified electron density perturbation created in the modulator by this hadron in a copropagating electron beam. We developed a method for computing the dynamics of these density perturbations in an infinite electron plasma with any equilibrium velocity distribution-a possible model for the modulator. We derived analytical expressions for the dynamics of the density perturbations in the Fourier-Laplace domain for a variety of 1D, 2D, and 3D equilibrium distributions of the electron beam. To obtain the space-time dynamics, we employed the fast Fourier transform algorithm. We also found an analytical solution in the space-time domain for the 1D Cauchy equilibrium distribution, which serves as a benchmark for our general approach based on numerical evaluation of the integral transforms and as a fast alternative to the numerical computations. We tested the method for various distributions and initial conditions.

Section: Conclusion and Future Plansmentioning

confidence: 99%

Section: Conclusion and Future Plansmentioning

confidence: 99%

Semianalytical description of the modulator section of the coherent electron cooling

Elizarov

Litvinenko

2013

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“…In the modulator section of the coherent electron cooling (CeC) [1], information about a hadron is recorded as a density perturbation in a co-propagating electron beam. Then, this perturbation is amplified in a free electron laser (FEL) [2,3], and thereafter, the amplified perturbation creates an electric field that accelerates or decelerates the hadron depending on its velocity deviation. Precise computation of the dynamics of shielding of a hadron in an electron beam is required to provide a theoretical description of CeC device and obtain the correct parameters' values for the facility currently under construction at Brookhaven National Laboratory [4].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of shielding of a moving charged particle in a confined electron plasma

Elizarov¹,

Litvinenko²

2015

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Dynamics of shielding of a moving charged particle in a confined plasma, which represents a realistic model of an electron beam in accelerators, is studied. This is a longstanding problem in plasma physics with important applications in accelerator physics. However, only solutions for an infinite unrealistic plasma are available. We developed a novel method to solve this problem, which consists of transformation of the Vlasov-Poisson differential equations to an integral equation for the Laplace image of the electron density perturbation created by an external charge. The integral equation is then solved numerically via the piecewise polynomial collocation method and the fast Fourier transform. We present thorough analysis of the results obtained and their physical interpretation.

“…Saldin and colleagues [2] derived the dispersion relation (4) for a 1D FEL with collinear propagation of the electron and FEL's plane wave of radiation. In our recent paper [4], we expanded this derivation to include the plane waves propagating at an angle with respect to the motion of the electron beam, i.e.,k…”

Section: Dðs;áþmentioning

confidence: 99%

“…We derive constraints on the maximal number of growing modes and upper frequency cutoff for a FEL with a spatially uniform electron beam having an arbitrary energy distribution. 4 …”

Section: Dðs;áþmentioning

confidence: 99%

Counting 1D free electron laser growing modes in the presence of space charge

Wang

Litvinenko

Webb

2012

Knowing the number and structure of the free electron laser's (FEL) growing modes is of fundamental importance to its theoretical description and its applications. The one-dimensional FEL dispersion relation, including the space-charge effects, is well established in the FEL theory, but questions remain about the number of the growing solutions (modes). In this paper, we provide the definite answers to the latter question and identify the amplification bandwidth of these modes.