wavefront, which are also multiplied by the harmonic factor. In order to have minimal reduction of the FEL input coupling factor, it is desirable that the size-angular bandwidth product of the UV seed laser beam be very close to the ideal i.e. diffraction-limited performance in the waist plane at the middle of the modulator undulator.'
address:
- 'European XFEL GmbH, Hamburg, Germany'
- 'Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany'
author:
- 'Gianluca Geloni,'
- Vitali Kocharyan
- and Evgeni Saldin
title: Analytical studies of constraints on the performance for EEHG FEL seed lasers
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**DEUTSCHES ELEKTRONEN-SYNCHROTRON**

**\
**

DESY 11-200

November 2011

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**Analytical studies of constraints on the performance for EEHG FEL seed lasers**

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Gianluca Geloni,

*\
European XFEL GmbH, Hamburg*

Vitali Kocharyan and Evgeni Saldin

*\
Deutsches Elektronen-Synchrotron DESY, Hamburg* $$\begin{aligned}
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**NOTKESTRASSE 85 - 22607 HAMBURG**

\[sec:uno\] Introduction
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An important goal for any advanced X-ray FEL is the production of X-ray pulses with the minimum allowed photon energy width for given pulse length, which defines the transform-limit. A well-known approach to obtain fully coherent radiation in 