Tolerance Study for the Echo-Enabled Harmonic Generation Free Electron Laser Page: 1 of 3
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
SLAC-PUB-13644
May 2009
Tolerance study for the echo-enabled harmonic generation free electron laser*
D. Xiangt and G. Stupakov, SLAC, Menlo Park, CA 94025 USAAbstract
The echo-enabled harmonic generation free electron
laser (EEHG FEL) holds great promise in generation of co-
herent soft x-ray directly from a UV seed laser within one
stage. The density modulation in the harmonic generation
process is affected by the smearing effect caused by the
fluctuations of energy and current along the beam, as well
as the field error of the dispersive elements. In this paper
we study the tolerance of the EEHG FEL on beam quality
and field quality. The diffusion effect from incoherent syn-
chrotron radiation (ISR) in the dispersion sections and the
second modulator are also studied.
INTRODUCTION
There has been continually growing interest in generat-
ing fully coherent (both longitudinally and transversely)
and powerful short wavelength radiation using the har-
monic generation free electron laser (FEL) scheme, as re-
flected by the many proposals and funded projects world-
wide [1-3]. In the classic HGHG scheme [4], the up-
frequency conversion efficiency is relatively low, so that
multiple stages are generally needed to generate coherent
soft x-rays starting with a UV seed laser with the wave-
length ~ 200 nm [5].
Recently a new method entitled echo-enabled harmonic
generation (EEHG) was proposed for generation of high
harmonics using the beam echo effect [6, 7]. In the EEHG
FEL the beam is energy modulated in the first modula-
tor and then sent through a dispersion section with strong
dispersion strength after which the modulation obtained in
the first modulator is macroscopically washed out while si-
multaneously complicated fine structures (separated energy
bands) are introduced into the phase space of the beam. A
second laser is used to further modulate the beam energy
in the second modulator. After passing through the sec-
ond dispersion section the separated energy bands will be
converted into current modulation and the echo signal then
occurs as a recoherence effect caused by the mixing of the
correlations between the modulation in the second modu-
lator and the fine structures.
The EEHG scheme has a remarkable up-frequency con-
version efficiency. It has been shown in [7] that the
Fermi@Elettra FEL may operate in a single stage to
achieve 10 nm soft x-rays from the 240 nm seed laser. Our
recent time-dependent simulation [8] also confirmed the
good performance of EEHG FEL where 3.8 nm radiation
in the water window is generated from 190 nm seed laser
* Work supported by US DOE contracts DE-AC02-76SF00515.
t dxiang@slac.stanford.eduand the bandwidth is very close to the Fourier transform
limit. In this paper we will focus on some practical consid-
erations of an EEHG FEL and the degradation effects from
unperfect beam and field qualities. We will use the typi-
cal parameters of the Fermi@Elettra FEL: E 1.2 GeV,
QE 150 keV, and En= 1.5 mm mrad.
CHOICE OF ENERGY MODULATION
AMPLITUDES
According to Ref. [7], the maximized bunching factor
for the nth harmonic may be written as,0.67
br- (n+1)1/3F(A1>(1)
where A1 AE,/QE is the dimensionless modula-
tion amplitude in the first modulator and F(A1)
Lil(Alx)e Ax2/2] ma. As shown in Fig. 2 of Ref. [7],
the maximal value of F(A1) increases with A1, but the
growth slows down when A1 > 3. In order to get suffi-
cient bunching while still keeping the slice energy spread
within a small level, it's desirable to choose A1 3. The
value of A2 does not affect the the bunching factor, but it is
related to the final slice energy spread and determines the
strength of the dispersion sections. The slice energy spread
of the beam at the entrance to the radiator is found to be,Az Az
OE 9UE t(2)
Generally speaking, using a large A2 could decrease the
required dispersion strength, which is helpful to reduce the
space for the dispersion sections. As we will show below
that the small dispersion strength also mitigates the diffu-
sion from ISR and enhances the tolerance of the field qual-
ity of the chicanes. But if A2 is too large, it may result
in a large slice energy spread which if beyond the toler-
ance will greatly degrade the FEL lasing. Thus the choice
of A2 should be made based on specific parameters of the
FEL projects. Take the Fermi@Elettra FEL project as an
example, using Xie's formulae [9], it's found that the FEL
performance will not be degraded if the slice energy spread
of the beam at the entrance of the radiator is less than 500
keV. So increasing A2 to 3 will not degrade the FEL perfor-
mance as compared to the case when A2 = 1. The corre-
sponding optimized dispersion strength are R = 8.198
56
mm and R6 = 2.625 mm for A2 1 and A2 3, re-
spectively.Presented at the 2009 Particle Accelerator Conference, 05/04/2009 -- 05/08/2009, Vancouver, Canada
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Xiang, D. & Stupakov, G. Tolerance Study for the Echo-Enabled Harmonic Generation Free Electron Laser, article, May 26, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc925885/m1/1/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.