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@inproceedings{wang:ipac2021-wepab031,
author = {G. Wang and V. Litvinenko and J. Ma},
title = {{Frequency Dependence of Plasma Cascade Amplification}},
booktitle = {Proc. IPAC'21},
pages = {2672--2674},
eid = {WEPAB031},
language = {english},
keywords = {electron, plasma, distributed, simulation, hadron},
venue = {Campinas, SP, Brazil},
series = {International Particle Accelerator Conference},
number = {12},
publisher = {JACoW Publishing, Geneva, Switzerland},
month = {08},
year = {2021},
issn = {2673-5490},
isbn = {978-3-95450-214-1},
doi = {10.18429/JACoW-IPAC2021-WEPAB031},
url = {https://jacow.org/ipac2021/papers/wepab031.pdf},
note = {https://doi.org/10.18429/JACoW-IPAC2021-WEPAB031},
abstract = {{A new type of amplifier, plasma cascade amplifier (PCA) has been proposed for a coherent electron cooling (CeC) system. Previously, the 1D model for PCA assumes that the transverse distribution of the density perturbation in the electrons is uniform and consequently, the plasma frequency does not depend on the wavelength of the perturbation. This assumption is valid if the longitudinal wavelength of the beam frame is much shorter than the transverse width of perturbation. In this work, we explore the PCI gain at a long wavelength by assuming the perturbation in the electron density has a non-uniform transverse profile. Specifically, we solve the 3D Poisson equation for given charge distribution (longitudinal sinusoidal, transversely Gaussian, or Beer-can), average the electric field over the transverse plane, and then apply it to 1D Vlasov equation. Similar to the previous calculation, the Vlasov equation can be reduced to a Hill’s equation but the plasma frequency now depends on the longitudinal wavelength of the density perturbation in the electrons. By numerically solving Hill’s equation, we obtain the gain of a PCA and compare it with the results from 3D SPACE simulations.}},
}