HiSOR multimode undulator as a circularly polarized light source
A linear/helical multimode undulator, which is installed at storage ring in Hiroshima Synchrotron Radiation Center, is initially designed for the utilizing of circularly polarized light from its fundamental harmonic in the spectral range of 4 - 40 eV. Operating of the undulator in elliptical configu...
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| Zitieren: | HiSOR multimode undulator as a circularly polarized light source / G.V. Rybalchenko, N.V. Smolyakov, K. Shirasawa, M. Morita, A. Hiraya // Вопросы атомной науки и техники. — 2001. — № 1. — С. 96-101. — Бібліогр.: 12 назв. — англ. |
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Rybalchenko, G.V. Smolyakov, N.V. Shirasawa, K. Morita, M. Hiraya, A. 2015-03-18T17:49:01Z 2015-03-18T17:49:01Z 2001 HiSOR multimode undulator as a circularly polarized light source / G.V. Rybalchenko, N.V. Smolyakov, K. Shirasawa, M. Morita, A. Hiraya // Вопросы атомной науки и техники. — 2001. — № 1. — С. 96-101. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 41.60.-m, 41.60.Ap, 42.25.Ja, 07.85.Qe. https://nasplib.isofts.kiev.ua/handle/123456789/78522 A linear/helical multimode undulator, which is installed at storage ring in Hiroshima Synchrotron Radiation Center, is initially designed for the utilizing of circularly polarized light from its fundamental harmonic in the spectral range of 4 - 40 eV. Operating of the undulator in elliptical configuration may considerably extend this spectral region. This paper presents a study for the optimisation of operating parameters of a linear/helical multimode undulator with the aim to maximize the circularly polarized high-energy photons output. The comparison with the correspondent characteristics of synchrotron radiation from bending magnet is performed. The results presented here were obtained for the general case that provides a means of applying derived expressions for any kind of elliptical wiggler as well as bending magnet. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Theory and technics of particle acceleration HiSOR multimode undulator as a circularly polarized light source Мультирежимный ондулятор на накопительном кольце HiSOR как источник циркулярно поляризованного излучения Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
HiSOR multimode undulator as a circularly polarized light source |
| spellingShingle |
HiSOR multimode undulator as a circularly polarized light source Rybalchenko, G.V. Smolyakov, N.V. Shirasawa, K. Morita, M. Hiraya, A. Theory and technics of particle acceleration |
| title_short |
HiSOR multimode undulator as a circularly polarized light source |
| title_full |
HiSOR multimode undulator as a circularly polarized light source |
| title_fullStr |
HiSOR multimode undulator as a circularly polarized light source |
| title_full_unstemmed |
HiSOR multimode undulator as a circularly polarized light source |
| title_sort |
hisor multimode undulator as a circularly polarized light source |
| author |
Rybalchenko, G.V. Smolyakov, N.V. Shirasawa, K. Morita, M. Hiraya, A. |
| author_facet |
Rybalchenko, G.V. Smolyakov, N.V. Shirasawa, K. Morita, M. Hiraya, A. |
| topic |
Theory and technics of particle acceleration |
| topic_facet |
Theory and technics of particle acceleration |
| publishDate |
2001 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Мультирежимный ондулятор на накопительном кольце HiSOR как источник циркулярно поляризованного излучения |
| description |
A linear/helical multimode undulator, which is installed at storage ring in Hiroshima Synchrotron Radiation Center, is initially designed for the utilizing of circularly polarized light from its fundamental harmonic in the spectral range of 4 - 40 eV. Operating of the undulator in elliptical configuration may considerably extend this spectral region. This paper presents a study for the optimisation of operating parameters of a linear/helical multimode undulator with the aim to maximize the circularly polarized high-energy photons output. The comparison with the correspondent characteristics of synchrotron radiation from bending magnet is performed. The results presented here were obtained for the general case that provides a means of applying derived expressions for any kind of elliptical wiggler as well as bending magnet.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78522 |
| citation_txt |
HiSOR multimode undulator as a circularly polarized light source / G.V. Rybalchenko, N.V. Smolyakov, K. Shirasawa, M. Morita, A. Hiraya // Вопросы атомной науки и техники. — 2001. — № 1. — С. 96-101. — Бібліогр.: 12 назв. — англ. |
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| first_indexed |
2025-11-25T22:45:44Z |
| last_indexed |
2025-11-25T22:45:44Z |
| _version_ |
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| fulltext |
HiSOR MULTIMODE UNDULATOR
AS A CIRCULARLY POLARIZED LIGHT SOURCE
G.V. Rybalchenkoa, N.V. Smolyakova,b, K. Shirasawaa, M. Moritaa, A. Hirayaa,b
aDepartment of Physical Science and bHiroshima Synchrotron Radiation Center (HSRC),
Hiroshima University, Higashi-Hiroshima 739-8526, Japan
A linear/helical multimode undulator, which is installed at storage ring in Hiroshima Synchrotron Radiation
Center, is initially designed for the utilizing of circularly polarized light from its fundamental harmonic in the
spectral range of 4 − 40 eV. Operating of the undulator in elliptical configuration may considerably extend this
spectral region. This paper presents a study for the optimisation of operating parameters of a linear/helical
multimode undulator with the aim to maximize the circularly polarized high-energy photons output. The comparison
with the correspondent characteristics of synchrotron radiation from bending magnet is performed. The results
presented here were obtained for the general case that provides a means of applying derived expressions for any
kind of elliptical wiggler as well as bending magnet.
PACS: 41.60.-m, 41.60.Ap, 42.25.Ja, 07.85.Qe.
INTRODUCTION
Many efforts were recently made to satisfy demands
for intense beams of circular polarized electromagnetic
radiation in a wide range of experiments in materials
science and molecular biology. For this purpose, among
many other works, a linear/helical multimode undulator
[1] was installed at one of two straight sections of a
compact racetrack-type 700-MeV storage ring (HiSOR)
of Hiroshima Synchrotron Radiation Center (HSRC)
[2]. This multimode undulator was designed to enhance
the intensity and degree of circular polarization of
photon beam in comparison with those radiating from
bending magnet (BM). However, while the undulator is
operating in the helical mode, the available photon
energy is restricted to the range of 4 − 40 eV, since only
the first harmonic is generated along the undulator axis.
With the aim to extend the photon energy range, it was
proposed [3] to use the linear/helical multimode
undulator in so-called elliptical multipole wiggler
(EMPW) mode [4-6], since the configuration of the
multimode undulator allows the continuous
transformation from linear mode through elliptical to
helical mode. In that event energy of elliptically
polarized photons generated at high harmonics along the
undulator axis is considerably beyond the fundamental
energy and its intensity is reasonably strong for
utilization.
The main features of EMPW radiation can be
understood through analogy to standard synchrotron
radiation from bending magnets. More precisely, almost
the same relations describe the on-axis radiation from
elliptical wiggler and the off-plane synchrotron
radiation. It gives direct insight into physics of the
elliptical wiggler’s radiation. At the same time, it should
be pointed out that the corresponding variables in these
relations have different physical meanings for the case
of elliptical wiggler and bending magnet.
A detailed study has been conducted to evaluate and
optimise the spectral performance of the HiSOR
linear/helical multimode undulator at elliptical mode for
photon energies above 40 eV. This paper includes a
summary of the procedure and results; some of them are
derived for the general case and thus may be used for
optimisation of other electromagnetic radiation sources,
both to elliptical wigglers and to bending magnets.
RADIATION SOURCES
The HiSOR storage ring [2] with the electron beam
operational energy 700 MeV has two 180° normal-
conducting bending magnets with maximum magnetic
field 2.7 T. The radius of the electron beam’s trajectory
is 86R = cm and critical wavelength of synchrotron
radiation is 1.42cλ = nm (critical energy is 873 eV). It
generates an electromagnetic radiation with intensity
high enough to satisfy experimental needs within the
photon energy range of about 1−103 eV. It is generally
known that the elliptically polarized off-plane
component of synchrotron radiation from bending
magnet can be used as a source of circularly polarized
photons. The degree of circular polarization is zero at
the median plane and increases gradually as the vertical
observation angle increases. However, in this process
the radiation intensity falls rapidly down at high
observation angles.
The HiSOR linear/helical multimode undulator has a
similar design to those of the elliptical wiggler for
Spring-8 [7,8] and the helical undulator for UVSOR [9].
Its magnetic structure consists of two jaws, which are
placed above and below the storage ring median plane,
similar to the planar undulator. However, each of these
96 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 1.
Series: Nuclear Physics Investigations (37), p. 96-101.
jaws consists of three standard Halbach-type permanent
magnet arrays (see Fig. 1). The four outer arrays may
slide simultaneously along the stationary middle arrays.
In doing this, the pair of arrays 1 and 6 move together in
one direction through the distance d and the pair of
arrays 3 and 4 move together through the same distance,
but in the opposite direction. As it is shown in Fig. 1, d
is the relative displacement of the side arrays in
reference to their non-shifted position. Depending on its
value the undulator configuration is linear ( )0d = ,
elliptical ( )0 / 4ud λ< < and helical ( )/ 4ud λ= .
Here uλ is the length of the undulator period.
At the median plane, two central lanes (Nos. 2 and 5
in Fig. 1) generate only vertical magnetic field, same as
for a conventional undulator. In linear configuration the
horizontal components (along X -axis) of the magnetic
fields from outer arrays cancel each other and the
resulting field has only vertical component. In this case
the undulator will generate the linearly polarized
radiation. At the helical configuration the four outer
arrays generate the horizontal magnetic field only since
vertical fields of side magnets cancel each other. With
the combination of the vertical field of the central
arrays, it produces a spiral-type magnetic field. For the
chosen geometry of magnetic blocks [1], the amplitudes
of the horizontal (x) and vertical (y) magnetic field
components are close to each other at any gap.
Radiation in this situation is almost fully circularly
polarized. Between these two configurations the
undulator field is of elliptical type with different
amplitudes of horizontal and vertical components
depending on d value. The resultant magnetic field is
described as a sum of the fields generated by six arrays.
The field of each array in the regular part is sinusoidal-
type with respect to the longitudinal coordinate z .
Considering for simplicity the first harmonic only, one
can get:
( )( )
6
1
cos 2p ip i u
i
B b z dπ λ
=
= −е ,
where pB are horizontal ( p x= ) and vertical (
p y= ) components of the undulator’s fields, ipb are
the amplitudes of the fields, generated by the i -th array,
id are the corresponding array shifts:
1 6 3 4d d d d d= = − = − = and 2 5 0d d= = . From
symmetry considerations the following relations are
fulfilled on the undulator axis:
2 5 0x xb b= = , 2 5y yb b= , 1 6 3 4x x x xb b b b= = − = − ,
1 3 4 6y y y yb b b b= = = .
Substituting these relationships into Eq. , the
following expression for the undulator magnetic field on
its axis can be derived:
Fig. 1. The scheme of the multimode undulator,
operated in EMPW mode together with its vertical cut
( )
( )
max
max
cos 2 ,
sin 2 .
x x u
y y u
B B z
B B z
π λ
π λ
м =п
н
=по
Here, max sinxB u ϕ= and max cosyB v w ϕ= +
represent the amplitudes of the horizontal and vertical
fields, 2 / udϕ π λ= is the phase shift of the outer arrays,
14 xu b= , 22 yv b= are the amplitudes of the horizontal
and vertical magnetic fields at helical configuration, and
14 yw b= . It is important to note that the horizontal
component of the resulting field (2) is always out of
phase by 2π relative to the vertical regardless of the
array shift d .
The following main parameters of the linear/helical
multimode undulator were chosen to satisfy the users
needs: the length of period 10uλ = cm, number of
periods 18N = , gap varies in the range of 30 200:
mm. It provides maximum magnetic field 0.347 T in the
helical mode and 0.597 T in the linear mode [1]. The
corresponding deflection parameters are 4.58 for helical
mode and 5.57 for linear mode. They are defined here
by the following standard way:
( )max 2
, , 2x y x y uK eB mcλ π= and 2 2 2
x yK K K= + .
The energy of fundamental harmonic in helical
mode is varied from 4 eV up to 40 eV by increasing the
undulator gap from 30 mm up to 90 mm, with keeping
the fundamental harmonic circularly polarization above
99%. It is also found [3] that an operation of the
undulator with minimum gap in the elliptical
configuration, when shift d is about a few mm, provides
the regime of an elliptical multipole wiggler wherein the
photons with energy higher than 40 eV are effectively
generated at higher harmonics.
CHARACTERISTICS
97
OF ELECTRO − MAGNETIC RADIATION
Let us consider synchrotron radiation generated by
zero-emittance electron beam moving through a bending
magnet along a circular trajectory. The number of
photons (flux density I ) radiated per second, per unit
solid angle dΩ per unit relative wavelength interval
( )dλ λ , is given by the following well-known
expression [10]:
( ) ( ) ( )
2 2
2
2
3 , ,x y
d n iI F F
d d e
α γ ξ η ξ η ξ
λ λ π
й щ= = +л ыΩ
&
,
where i is the electron beam current, e is an electron
charge, α is the fine structure constant, γ is the
relativistic factor, 2cξ λ λ= , 34 3c Rλ π γ= , R is the
orbit radius, ψ is the vertical observation angle,
η γ ψ= and
( ) ( )22 2
2 3( , ) 1xF Kη ξ η ζ= + ,
( ) ( )2 2 2
1 3( , ) 1yF Kη ξ η η ζ= + .
Here ( ) 3 221ζ ξ η= + and ( )Kν ζ are the modified
Bessel functions order of 1 3,2 3ν = .
The degree of circular polarization of the radiated
photons is defined as:
( )2c x y x yP F F F F= + .
Let us now consider the radiation from elliptical
multipole wiggler with N periods. Its magnetic field is
described by the Eq. with the following conditions:
Ky>>1 and 1xK Ј . The photons with highest energy
are generated at the part of electron trajectory with the
vertical field close to max
yB and the horizontal field close
to zero. Since Ky>>1, the radiation that is emitted from
these regions may be described by the standard
expressions for synchrotron radiation. In this case, the
bending radius corresponding to max
yB is equal to
( )2u u yR Kγ λ π= , and corresponding critical
wavelength is equal to 34 (3 )c uRλ π γ= . In addition,
the respective parts of the electron’s trajectory, which
can be regarded as the arc of the circular orbit, is tilted
up or down with the angle xKψ γ= by the alternating
horizontal magnetic field. As a consequence, the
radiation generated along the undulator axis from the
2N parts of the electron’s trajectory, will be of the
same intensity and equally polarized. As a result, the
spectrum of EMPW can be obtained from Eq. for the
off-plane synchrotron radiation spectra. Thus, the right -
side part of the expression should be multiplied by the
number of the poles 2N (i.e. the total number of the
radiation sources), and use the following variable
definitions: xKη = and ( )22 3c u yKλ λ γ= [5,6].
In further analysis, the optimisation of the radiation
parameters based on two different criteria: to maximize
the photon flux density and to maximize the
performance of BM and EMPW as circularly polarized
radiation sources will be considered.
OPTIMIZATION
OF THE RADIATION INTENSITY
The maximum of the flux density may be found by
differentiating Eq. with respect to the parameters ξ and
η with equating these derivatives to zero. As a result,
one can get:
( ) ( )
( ) ( )
2 2 2 2
2 2
1 3 1 2 2 0,
3 1 2 1 0,
q q
q
η ζ η η
η ζ η η
м + − + + =п
н
й щ+ − + =п л ыо
where ( ) ( )2 3 1 3q K Kζ ζ= . Numerical solution of Eq.
gives absolute maximum at the point 0.417ξ = , 0η =
. In the case of HiSOR sources, it corresponds to the
photon energy of about 155 eV for the undulator at
linear mode (since 0xKη = = ), and to the photon
energy of 730 eV on the BM median plane.
Taking into consideration only the second equation
of , which arises from the η -derivative, the optimum
value of parameter η for every value of ξ can be
found. In the case of BM it means to find such a vertical
angle of observation, where flux density has a
maximum. In case of EMPW, the problem comes to
finding of the best value for xKη = , i.e. of the best
value for the array’s shift d . It is obvious that one of
the solutions of this equation is 0η = . More detail
analysis shows that the point of 0 0.244ξ = separates
the energy axis in two parts. For 0ξ ξі intensity has a
maximum at 0η = , which means the operation at the
BM median plane, or at the linear mode of EMPW. For
0ξ ξ< , 0η = is the point of local minimum of
radiation, and maximum of intensity is located at 0η № .
In the case of the BM, it corresponds to the non-zero
observation angle ψ η γ= above or below the bending
plane. The numerical value of 0ξ can be obtained as a
solution of the equation ( ) ( )2 3 1 3 1 3K Kξ ξ ξ= .
For HiSOR’s bending magnet and linear / helical
undulator in EMPW mode intensities at these optimum
angles versus photon energy are shown in Fig. 2.
Numerical calculations were performed for electron
beam energy 0.7 GeV and current 300mA. For the
helical / linear undulator in EMPW mode all results
were obtained at 30mm gap. Due to summation of the
98
100 1000
1E12
1E13
1E14
bending magnet:
ψ 0
orbit plane
ξ max=0.417ξ
0
=0.244
I,
ph
ot
on
s/
se
c/
m
ra
d
2 /0
.1
%
B.
W
photon energy, eV
undulator:
EMPW mode
linear mode
Fig. 2. Maximum available radiation intensity vs
photon energy. ξmax is the point of absolute maximum of
radiation. For ξ<ξ0 maximum of radiation occurs at η
0, for ξ≥ξ0 at η=0
0.0 0.2 0.4 0.6 0.8 1.0
0.5
1.0
1.5
2.0
2.5
A
point ot the absolute
maximum of IPc
2
ξ =0.233
η =0.878
Pc=0.84
η
ξ
η = -0.129+0.619ξ -0.325
Fig. 3. Functional dependence of parameter η vs ξ,
being solution of the equation 0f η∂ ∂ =
radiation from N periods, the radiation intensity from
EMPW stands out above the BM intensity by the factor
2N , but at the same time operating energy region for
BM is wider than that of EMPW.
OPTIMIZATION OF THE CIRCULAR
POLARIZED RADIATION
The optimization of the spectral output for BM and
EMPW involves a trade-off between flux density and
degree of circular polarization. As it was mentioned
above, at 0ξ ξі the radiation with maximum available
intensity is situated at 0η = and is linearly polarized.
With the increasing of η the degree of circular
polarization cP increases while the intensity decreases.
For 0ξ ξ< , optimized radiation is elliptically polarized,
but again if one wants to obtain higher degree of
circular polarization the intensity will noticeably
decreases. In order to find the best compromise between
intensity and degree of polarization, it seems natural to
maximize the product of circular polarized light
intensity ( )cIP and the degree of circular polarization
( )cP :
( )
2
2, x y
c
x y
F F
f IP
F F
ξ
η ξ =
+
: .
This figure of merit is commonly accepted [11,12] in
virtue of the fact that it is proportional to square of the
signal-to-noise ratio in circular-dichroism experiments.
Similar to the previous section, by differentiating
Eq. with respect to ξ and η and equating these
derivatives to zero, the following relations can be
derived:
( )
3 2 2
4
22
2 2
4 3
2 2
2 0,
3 13 1
1 0.
3 1
q qq
q q
η η
ζ ηζ η
η η
ζ η η
м
− − + =п ++п
н
+п − + =п +о
The root of the second equation of the system ,
corresponding to 0f η∂ ∂ = , gives the value of η such
that the function f reaches its maximum for any
predetermined ξ and seems to be most interesting from
the physical point of view. The solution of this equation
is plotted in Fig. 3, allowing the easy choice of the
devices operation parameters. For simulation reasons, it
is more convenient to use the following approximation
of this solution, which is valid within the interval
( )0.01,1ξ О :
0.3250.129 0.619η ξ −= − + .
It is important to note that Eq. is generally valid for
radiation from any kind of bending magnet as well as
elliptical wiggler. By solving of both equations of
system , absolute maximum of f is obtained at
0.223ξ = , 0.878η = , as shown at the point A in Fig. 3.
The degree of polarization cP at that is about 0.84.
The results of this optimisation have been applied to
the both HiSOR radiation sources, BM and
linear/helical undulator. In the case of BM (Fig. 4a), the
corresponding vertical angle ψ was found for any
photon energy by using the Eq. . After that 2
cf IP=
value was calculated using Eq. and Eq. (Fig. 4b). One
can see that the function f peaks at the photon energy
of 389 eV and at vertical observation angle 0.64ψ ≈
mrad, corresponding to the point A of the general
solution. As was mentioned above, for this photon
energy the degree of polarization will be about 0.84. It
is possible to obtain higher cP at larger observation
angles ψ , but photon flux will be lower.
99
0 200 400 600 800 1000 1200 1400 1600 1800
0.3
0.6
0.9
1.2
1.5
1.8
b)
a)
ψ
, m
ra
d
photon energy, eV
Optimum observation angle
for BM radiation
0 200 400 600 800 1000 1200 1400 1600 1800
4.0x1011
6.0x1011
8.0x1011
1.0x1012
1.2x1012
1.4x1012
1.6x1012
IP
c2 , p
ho
to
ns
/s
ec
/m
ra
d
2 /0
.1
%
B.
W
IPc
2 value
at the optimized angle ψ
Fig 4. a) The operation parameters for HiSOR’s
bending magnet. b) Corresponding “figure of merit”
100 200 300 400 500 600 700
2
3
4
5
6
b)
a)
Optimum side arrays
shift d for EMPW radiation
d,
m
m
photon energy, eV
100 200 300 400 500 600 700
0
1x1013
2x1013
3x1013
4x1013
5x1013
6x1013
IPc
2 value at
the side arrays shift d
IP
c2 , p
ho
to
ns
/s
ec
/m
ra
d2 /0
.1
%
B.
W
Fig. 5. a) The operation parameters for HiSOR’s
linear/helical undulator. b) Corresponding “figure of
merit”
100 1000
1E12
1E13 IPc
2
photon energy, eV
100 1000
1E11
1E12
1E13 b) I
100 1000
0.6
0.7
0.8
0.9
c)
a)
P
c
ph
ot
on
s/
se
c/
m
ra
d
2 /0
.1
%
B.
W
P
c
bending magnet
undulator in EMPW mode
Fig. 6. BM and EMPW radiation properties,
calculated for optimum operation parameters. (a)
“Figure of merit” = 2
cf IP ; (b) Flux density of
radiation I ; (c) Degree of circular polarization P
In the case of EMPW, the situation is much more
complicated since the variation of the side arrays shift
d change both vertical and horizontal magnetic fields.
At first, using Eq. , xKη = has to be found as the
function of ξ , then d and yK values have to be found
using corresponding expressions for max
,x yB , after that ξ
has to be converted to the photon energy using relation
( )23u yKλ λ γ ξ= . The result of this calculation is
shown in Fig. 5a. Figure 5b shows the value of f as a
function of the photon energy. One can see that f
peaks at 82 eV, which corresponds to 0.223ξ = . In this
case, the horizontal deflection parameter xK is equal to
0.878 , the relative displacement of the side magnetic
arrays (d) is equal to 4.6 mm and accordingly
5.252yK = .
Fig. 6 shows the dependence of EMPW and BM
radiation parameters ( f , flux density I , Pc) vs. photon
energy. They were calculated in the same manner as for
the Figs. 4,5 and, gathered together, enables us to
compare performance of both radiation sources.
Intensity of the radiation from bending magnet is 1-2
order weaker than that from elliptical wiggler. However,
the degree of polarization is larger than 0.75 up to
1000eV. In the case of EMPW, for the energy region of
40-150 eV, the value f is high enough with 0.8cP і ,
but the degree of circular polarization rapidly declines
for photon energy above 150 eV.
It is important also to check area of application of
the EMPW mode. To cover energy range above 40eV it
is necessary to use the arrays shift 6d < mm (Fig. 5a).
At such small shifts EMPW approximation
1y xK K Ј? is valid since the ratio 4.6y xK K і .
CONCLUSION
In this article the way to obtain maximum of two
different parameters: radiation intensity and product of
circular polarized light intensity and degree of circular
polarization from EMPW and BM is shown. Some
results were derived for the general case, which allows
its application to other radiation sources.
It is shown that a spectral range of circularly
polarized light, which is generated by a linear/helical
multimode undulator at helical mode, may be
considerably extended to high photon energy region by
using EMPW mode. Both EMPW and BM are found to
have a high degree of circular polarization in the
spectral region above 40 eV. The polarization
characteristics can be effectively controlled by varying
of the horizontal magnetic field in case of EMPW, or by
varying of the vertical angle of observation in case of
BM.
The photon flux density of EMPW is obviously
higher than that of BM due to the large number of
radiation sources ( 2N ). On the other hand, the BM
radiation is bending magnet field is much stronger
100
(2.7 T) than the much more intense in the high-energy
region since the EMPW field amplitude (0.597 T). From
the present analysis it is possible to conclude that the
elliptical mode of the multimode undulator has much
potential for generating of circularly polarized light at
high energy, up to 0.5 keV.
The presented results were calculated for ideal case,
i.e. for zero emittance electron beam and infinitely small
acceptance aperture. The inclusion of these real
parameters into simulation may slightly change the
spectral distributions. The effect of finite vertical
aperture on the correspondent fluxes is shown in Fig. 7.
The BM and EMPW radiations were integrated over the
vertical slits bounding the vertical observation angles.
For the BM, slit was positioned at the optimum angle
ψ η γ= , which was varied with changing of the
photon energy according to Eq. . For the EMPW the
center of the slit was positioned on-axis. Two types of
slits were analysed. The first slit size corresponds to the
angle ( )1 2ψ γ∆ = , independent with the photon
energy. The second slit uses the vertical size equal to
the full width at half maximum (FWHM) of the vertical
intensity distribution at corresponding photon energy.
For the relatively soft radiation with energies below
the critical energy, the size of FWHM is larger than
( )1 2γ and corresponding value of 2
cIP at this energy is
higher. Fig. 7 demonstrates some effects of the real
experiment parameters on the radiation characteristics,
in comparison with Fig. 6a, which was calculated for
infinitely small slit size. One can see that an ideal case
approximation is adequately enough for the optimisation
of radiation sources.
In conclusion it should be noted that using of
EMPW mode of the linear/helical multimode undulator
in addition to the usual, linear and helical modes, allows
obtaining of the radiation with various kinds of
polarization in the wide spectral region.
100 1000
1E12
1E13
BM:
FWHM slit
∆ ψ =0.5/γ slit
I P
c2 , p
ho
to
ns
/se
c/
m
ra
d/
0.
1%
B.
W
photon energy, eV
EMPW:
FWHM slit
∆ ψ =0.5/γ slit
Fig. 7. Integrated over 2 different slits f=IPc
2
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101
Introduction
Radiation sources
Conclusion
References
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