AUTHOR=Hemsing Erik 

TITLE=Minimum Spectral Bandwidth in Echo Seeded Free Electron Lasers

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00035

DOI=10.3389/fphy.2019.00035

ISSN=2296-424X

ABSTRACT=<p>This paper examines the impact of non-linear longitudinal phase distortions on the spectral bandwidth in echo seeded free electron lasers (FELs). It extends the existing theory developed in Hemsing [<xref ref-type="bibr" rid="B1">1</xref>] for echo-enabled harmonic generation (EEHG) to include finite laser pulse durations. An analytic expression for the shape of the optimized longitudinal bunching envelope is derived, and is used to determine the laser and electron beam pulse durations that minimize the seeded bandwidth in the presence of arbitrary phase distortions. The time-bandwidth product (TBP) is also derived, and is shown that the TBP and the bandwidth increase by no more than <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msqrt></mml:math></inline-formula> from their transform-limited values when the bandwidth is minimized.</p>