Generation of intense ultra-short X-ray pulses in wake field undulator
The generation of X-rays based on the interaction mechanism of a relativistic charged particles with alternative wake fields induced in periodic structures are studied. The optimum wake field characteristics providing the maximum flux of wake field undulator radiation in an X-ray range are obtained....
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2011 |
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| Мова: | Англійська |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2011
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| Цитувати: | Generation of intense ultra-short X-ray pulses in wake field undulator / A. Opanasenko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 82-85. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859717100733464576 |
|---|---|
| author | Opanasenko, A. |
| author_facet | Opanasenko, A. |
| citation_txt | Generation of intense ultra-short X-ray pulses in wake field undulator / A. Opanasenko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 82-85. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The generation of X-rays based on the interaction mechanism of a relativistic charged particles with alternative wake fields induced in periodic structures are studied. The optimum wake field characteristics providing the maximum flux of wake field undulator radiation in an X-ray range are obtained. Using the data on beam parameters of varied photo-injector projects, the X-ray fluxes are calculated.
Представлено результати дослідження процесу генерації рентгенівського випромінювання, заснованого на механізмі взаємодії заряджених частинок зі знакозмінними кільватерними полями, що індуковані у періодичних структурах. Знайдено оптимальні співвідношення між розмірами гофрованого хвилеводу та електронного згустка, при яких досягаються максимальні потоки випромінювання.
Представлены результаты исследования процесса генерации рентгеновского излучения, основанного на механизме взаимодействия заряженных частиц со знакопеременными кильватерными полями, индуцируемыми в периодических структурах. Найдены оптимальные соотношения между размерами гофрированного волновода и размерами электронного сгустка, при которых достигаются максимальные потоки излучения.
|
| first_indexed | 2025-12-01T08:12:59Z |
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| fulltext |
GENERATION OF INTENSE ULTRA-SHORT X-RAY PULSES
IN WAKE FIELD UNDULATOR
Anatoliy Opanasenko∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received August 12, 2011)
The generation of X-rays based on the interaction mechanism of a relativistic charged particles with alternative wake
fields induced in periodic structures are studied. The optimum wake field characteristics providing the maximum
flux of wake field undulator radiation in an X-ray range are obtained. Using the data on beam parameters of varied
photo-injector projects, the X-ray fluxes are calculated.
PACS: 41.60, 41.75.L, 41.75.H, 84.40.A
1. INTRODUCTION
Because of numerous potential applications of in-
tense X-ray beams with ultra-short duration, such
ways of their generation as the self-amplifying spon-
taneous emission in FEL’s and the inverse Compton
scattering (ICS) of intense optical laser radiation on
high charged bunches are powerfully developed at the
present time [1,2]. The ICS-based X-ray sources with
photons energies 10...40 keV (for use in medicine and
material characterization) are received a large devel-
opment due to compactness and relatively low cost
[2]. The X-ray beam fluxes of 109...1010photons/sec
in a 1% bandwidth are usually required for biological
and medical imaging. But until now, the intensity
of the most available ICS-based X-ray sources is still
less than 108 photons/sec. Therefore, the search for
methods that be able to provide the needed photon
yields remains a relevant topic. In this connection,
designing the compact wake field undulator (WFU)
with sub-millimeter period [3,4], due to advanced ac-
celerator technology, can open a new opportunities to
obtain ultra-short high-brightness X-ray beams.
The goal of this work consists in obtaining op-
timal conditions needed to generate high-flux X-ray
pulses with ultra-short duration by ultra-relativistic
electron bunches moving through an weakly corru-
gated rectangular waveguide with sub-millimetre pe-
riod.
2. WFU CHARACTERISTICS
Let us consider the WFU radiation mechanism. The
wake forces induced by a bunch of relativistic charged
particles in a periodic structure can be expressed as
a Floquet’s series
~F (~r, t) =
∞∑
p=−∞
~F (p)(~r⊥, t− z/vz) ei 2πp
D z , (1)
where ~F (p) is the pth space harmonic of the wake
force, vz is the bunch velocity, D is the waveguide
period. The synchronous (p = 0) harmonic acting
on the bunch results in the beam loading and beam
break up effects well known in RF linear accelera-
tors. It is usually assumed that the non-synchronous
(p 6= 0) spatial harmonics of the fields do not con-
tribute to change of the beam energy on the aver-
age by the period. However under certain conditions
(for example for off-axis particles in the corrugated
waveguide used in RF linacs ) the non-synchronous
spatial harmonics of transverse components of the ra-
diation reaction force give rise to undulating particles
with alternating transverse velocity
~v⊥ =
ic
2γ
∑
p 6=0
~K
(p)
⊥ ei 2πp
D z , (2)
where the WFU or deflection parameter is defined as
follows
~K
(p)
⊥ = −
~F
(p)
⊥ D
pπmcvz
. (3)
Here γ is the Lorentz factor (γ2 >> 1), c is the ve-
locity of light, m is the electron mass of rest.
The charged particle undulation with the al-
ternating velocity Eq. (2) causes emission of the
undulator-type radiation. In an X-ray range, wave-
lengths of this radiation are given as (see Ref.[5])
λp =
D
2pγ2
1 +
1
2
∑
p′ 6=0
∣∣∣K(p′)
⊥
∣∣∣
2
. (4)
As it is known, the undulator parameter of a con-
ventional magnetic undulator is proportional to the
undulator period D (K⊥ ∼ D). This property re-
stricts the use of a magnetic undulator with very
short periods. The WFU parameter, unlike one for
the magnetic undulator, is independent on the pe-
riod, and has inversely proportional dependence on
an RF structure transverse size l⊥, (K⊥ ∼ 1/l⊥) [4].
∗Corresponding author E-mail address: opanasenko@kipt.kharkov.ua
82 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2011, N5.
Series: Nuclear Physics Investigations (56), p.82-85.
This peculiarity allows to use the WFU with sub-
millimeter periods. In this case the electron energy
can be saved more than one order comparably with
the conventional centimeter-period magnetic undu-
lator. In Ref. [4] the rectangular waveguide with
periodically perturbed walls is considered as the pro-
totype of a wake field undulator. The wake forces
induced by an ultra-relativistic electron bunch with
3D Gaussian charge density distribution are calcu-
lated by a perturbation method. So, using the results
presented in Ref.[4] for Gaussian bunch moving along
a planar waveguide with weakly-corrugated metallic
surfaces (see Fig.1), we can express an absolute value
of the WFU parameter in the following form
∣∣∣K(p)
x
∣∣∣ = 8πN |εCp| re
w
e
− (vzτ)2
2σz2
∣∣∣∣∣
∞∑
m=1
e−
(πm)2(σx
2+σy
2)
2w2 ×
× sin
[πm
w
(
y +
w
2
)] ∞∑
n=0
(−1)nXn,m(x)
1 + δ0,n
×
×W
(
ωm,p,nσz
vz
√
2
− i
vzτ√
2σz
)∣∣∣∣ ,
(5)
where
Xn,m =
sin
(
πm
2 + πmy0
w
)
sh
(
2πm
w b0
)
{
sh
(
πm(x0 + b0)
w
)
×
× cos
(
πn
2b0
(x + b0)
)
+ sh
(
πm(x0 − b0)
w
)
×
× cos
(
πn
2b0
(x− b0)
)}
, W (z) = e−z2
erfc(−iz) ,
re is the classical radius of the electron , ωm,p,n are
the eigenfrequencies, vzτ = vzt− z the relative longi-
tudinal coordinate of a particle, N is the number of
electrons in the bunch, σx, σy, σz are the rms bunch
dimensions, x and y are transverse coordinates of the
particle; x0 and y0 are the transverse coordinates of
the bunch crest. The other geometry sizes can be
seen in Fig.1.
Fig.1. A rectangular waveguide with periodic
surfaces; b(z) = b0[1 + ε
∑
p Cpcos(2πpz/D)]
is the surface contour with the small parame-
ter ε, (0 < ε << 1), D is the period, z is a
longitudinal coordinate, w is the waveguide
width
3. WFU OPTIMIZATION
Let us obtain the maximum photon flux from the
WFU. For this we must find relations between di-
mension of the corrugated waveguide and the bunch
at which the absolute value of the WFU parameter
reaches the maximum. As it is shown in Ref [4] the
wake field exited by a bunch with σz ∼ D, is localized
within the bunch and moves synchronously with it
without storing into the waveguide. In addition the
transverse component of the alternating wake force
reaches the maximum at the maximum of the charge
density. So, such the wake force distribution is most
suitable for using it as a pump field.
In Fig.2 the distribution of the absolute value of
the WFU parameter |K(1)
x | is given for the bunch
(with parameters eN = 1 nC, σz = 1.2D,σx =
σy = 10µm) that moves along the corrugated
waveguide (with the dimensions b0 = D = 100 µm,
w = 5b0, ε = 0.1, and the simplest surface profile
b(z) = b0[1 + ε cos(2πz/D)]) at the transverse bunch
disposition x0/b0 = 0.7. Ibidem, the Gaussian distri-
bution of the bunch charge is imagined by the dotted
line.
Fig.2. The charge and |K(1)
x | distribution
As a first step of the WFU optimization, let us build
the dependence of the |K(1)
x (0)| taken at the crest
bunch (vzτ = 0) on relative waveguide width w/b0.
Fig.3. The |K(1)
x (0)| v.s. relative width w/b0
Analysis of dependencies such as built in Fig.3
for the different relative transverse bunch positions
(x0/b0 = 0.8, 0.7, 0.6, 0.4) shows that there is a sim-
ple correlation between the optimal values for which
the |K(1)
x (0)| reaches the maximum
w/b0 ≈ 7.5(1.33− x0/b0) . (6)
On the other hand the maximal value of the WFU
parameter is obtained if the bunch moves as close as
possible to the corrugated surface of the waveguide,
due to surface-wave character of the wake field [4]
xmax/b0 = 1− ε− 2σx/b0 . (7)
83
So, substituting Eqs. (6) and (7) into Eq. (5),
we can find the |K(1)
x (0)| as the function of
the waveguide vertical size b0 for different
transverse bunch sizes σx = σy = 10 µm
and σx = σy = 1 µm(see the next Fig.4).
Fig.4. The |K(1)
x (0)| v.s. a waveguide vertical size b0
As shown in Fig.4, the |K(1)
x (0)| reaches the maxi-
mum at the optimal values: b0 = 150 µm, b0 = 15 µm
for two chosen bunch sizes, accordingly. Scaling
analysis of Eq. (5) indicates that the WFU parameter
increases in inverse proportion with proportional re-
duction of all geometric dimensions of the waveguide
and bunch, as it is confirmed by Figs.4.
Fixing the all obtained optimal values: b0 =
150 µm, σx = σy = 10 µm, b0 = 15 µm, σx = σy =
1 µm, one can correct the small parameter ε, the rel-
ative height of the corrugations (Fig.5). As it follows
from the last figures, the optimal value of the small
parameter is ε = 0.12.
Fig.5. The |K(1)
x (0)| v.s. a small parameter ε
4. CALCULATION OF X-RAY FLUXES
On the analogy with the conventional magnetic undu-
lator [6] consisting of Nu periods, the WFU radiation
flux near the pth harmonic with bandwidth ∆ω/ω ∼=
1/pNu containing in the central cone θp ≈ 1/γ
√
pNu,
can be obtained in the form [3]
F (p) ≈ α
π
2
frepN
〈∣∣∣K(1)
x
∣∣∣
2
〉
, (8)
where α is the fine-structure constant, frep
is the bunch repetition frequency, N is
the number of electrons in the bunch,
〈...〉 = (vz/eN)
∫∞
−∞ dτ
∫ ∫
S⊥
d2~r⊥ρ(~r⊥, τ)... is the
bunch averaging,ρ(~r⊥, τ) is the charge density of the
bunch. After averaging over the bunch in Eq. (8),
the WFU radiation flux can be written as
F (p) = α
π
2
frepN
3 (8π)2√
2π
|εCp|2
(re
w
)∫ ∞
−∞
ds e−
3s2
2 up(s) ,
(9)
where the function up(s) is defined as
up(s) ≡
∣∣∣∣∣
∞∑
m=1
e−
(πm)2(σ2
x+σ2
y)
2w2 sin
[πm
w
(
y0 +
w
2
)]
×
×
∞∑
n=0
(−1)nXm,n(x0)
1 + δ0,n
W
(
ωm,p,nσz
vz
√
2
− i
s√
2
)∣∣∣∣∣
2
. (10)
One can show that for bunches with σz ≥ D, the
function up(s) is interpolated by up(s) = up(0) −
[up(0)− up(−1)]s2. So, the flux Eq. (9) can be easily
calculated by the formula
F (p) ≈ αfrepN
3π3
√
3
2
(
8
3
)2
|εCp|2
(re
w
)2
×
× [2up(0) + up(−1)] . (11)
As an instance, let us calculate flows of X-rays with
the sub-picosecond duration (στ ≈ 0.5 ps) and 30 keV
photon energy generated by an electron beam in the
sub-millimetre WFU consisting of Nu = 100 pe-
riods. The optimal sizes of the WFU and beam
obtained by Eqs. (6) and (7) are given in Table 1.
Table 1. The optimal parameters of the WFU and
bunch
b0 = D w ε xmax σz σx, σy θ1
µm µm µm µm µm rad
150 656 0.12 112 150 10 7× 10−5
Substituting the beam parameters of the var-
ied photo injector projects [7] into Eq. (11), we
calculate the fluxes given in Table 2. Here it
is supposed that the electron beams from the
selected photo injectors be able to accelerate
to the energy 690 MeV and the to compress
the bunches to required sizes given in Table 1.
84
Table 2. The X-ray fluxes from varied photo
injectors
q = eN frep F (1)
Lab nC MHz ph/s/1%bw
JLab 0.112 75 4.45× 109
JLab 0.133 748.5 5.75× 1010
Cornel 0.077 1300 1.94× 1010
Cornel 1 10 3.267× 1011
Boeing 7 6.7 2.2× 1011
FZR 1 1 3.267× 1010
BNL 1.42 357.87 3.29× 1013
BNL 10 10 3.267× 1014
LANL 1 100 3.267× 1012
CEA 3 0.1 8.82× 1010
DESY 1 0.072 2.35× 109
DESY 1 0.0325 1.06× 109
BESSY 2.5 0.025 1.276× 1010
5. CONCLUSIONS
In this paper, the optimal relations between sizes of
the WFU and bunches at which the |K(1)
x | reaches
the maximum providing the maximum WFU radia-
tion fluxes of in the X-ray range are obtained. It
is shown that the average X-ray fluxes can attain
109...1014 photons/sec/1%bw, that one can open op-
portunities to use this X-rays source in medicine
imaging and in many other applications.
References
1. JohnN.Galayda. The First Angstrom X-Ray
Free-Electron Laser // Proc. of IPAC’10. Kyoto.
2010, p.11-15.
2. M.Uesaka, et. al. Medical Application of Multi-
Beam Compton Scattering Monochromatic Tun-
able Hard X-Ray Source // Proc. of the 46 Work-
shop of the INFN ELOISATRON Project. The
Phsics and Aplications of High Brightness Elec-
tron Beam. Erice, 9-14 October, 2005, p.300-311.
3. A.Opanasenko. Wakefield undulator for generat-
ing X-rays // Proc. of RuPAC’04. Dubna, 2004,
p.278-280.
4. A.Opanasenko. Alternating wake force in rectan-
gular waveguide with periodic perturbed walls //
Proc. of RuPAC’08. Zvenigorod, 2008, p.31.
5. A.Opanasenko. Radiation of charged particles in
self-wakefield” // RuPAC’02. Obninsk, 2002, v.1,
p.264; http://arxiv.org/abs/physics /0302025.
6. K.J.Kim. Characteristics of synchrotron radia-
tion // AIP Conf. Proc. 189. 1989, v.1, p.565-
632.
7. Frank Stephan. Status and Perspectives of Photo
Injector Developments for High Brightness
Beams // Proc. of the 46 Workshop of the INFN
ELOISATRON Project. The phsics and aplica-
tions of high brightness electron beam. Erice, 9-14
October 2005, p.269-290.
ГЕНЕРАЦИЯ ИНТЕНСИВНОГО РЕНТГЕНОВСКОГО ИЗЛУЧЕНИЯ
УЛЬТРАКОРОТКОЙ ДЛИТЕЛЬНОСТИ В КИЛЬВАТЕРНО-ПОЛЕВОМ
ОНДУЛЯТОРЕ
Анатолий Опанасенко
Представлены результаты исследования процесса генерации рентгеновского излучения, основанного
на механизме взаимодействия заряженных частиц со знакопеременными кильватерными полями, ин-
дуцируемыми в периодических структурах. Найдены оптимальные соотношения между размерами
гофрированного волновода и размерами электронного сгустка, при которых достигаются максималь-
ные потоки излучения.
ГЕНЕРАЦIЯ IНТЕНСИВНОГО РЕНТГЕНIВСЬКОГО ВИПРОМIНЮВАННЯ
УЛЬТРАКОРОТКОЇ ТРИВАЛОСТI В КIЛЬВАТЕРНО-ПОЛЬОВОМУ ОНДУЛЯТОРI
Анатолiй Опанасенко
Представлено результати дослiдження процесу генерацiї рентгенiвського випромiнювання, заснованого
на механiзмi взаємодiї заряджених частинок зi знакозмiнними кiльватерними полями, що iндукованi у
перiодичних структурах. Знайдено оптимальнi спiввiдношення мiж розмiрами гофрованого хвилеводу
та електронного згустка, при яких досягаються максимальнi потоки випромiнювання.
85
|
| id | nasplib_isofts_kiev_ua-123456789-111468 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T08:12:59Z |
| publishDate | 2011 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Opanasenko, A. 2017-01-10T11:50:52Z 2017-01-10T11:50:52Z 2011 Generation of intense ultra-short X-ray pulses in wake field undulator / A. Opanasenko // Вопросы атомной науки и техники. — 2011. — № 5. — С. 82-85. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 41.60, 41.75.L, 41.75.H, 84.40.A https://nasplib.isofts.kiev.ua/handle/123456789/111468 The generation of X-rays based on the interaction mechanism of a relativistic charged particles with alternative wake fields induced in periodic structures are studied. The optimum wake field characteristics providing the maximum flux of wake field undulator radiation in an X-ray range are obtained. Using the data on beam parameters of varied photo-injector projects, the X-ray fluxes are calculated. Представлено результати дослідження процесу генерації рентгенівського випромінювання, заснованого на механізмі взаємодії заряджених частинок зі знакозмінними кільватерними полями, що індуковані у періодичних структурах. Знайдено оптимальні співвідношення між розмірами гофрованого хвилеводу та електронного згустка, при яких досягаються максимальні потоки випромінювання. Представлены результаты исследования процесса генерации рентгеновского излучения, основанного на механизме взаимодействия заряженных частиц со знакопеременными кильватерными полями, индуцируемыми в периодических структурах. Найдены оптимальные соотношения между размерами гофрированного волновода и размерами электронного сгустка, при которых достигаются максимальные потоки излучения. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Электродинамика Generation of intense ultra-short X-ray pulses in wake field undulator Генерацiя iнтенсивного рентгенiвського випромiнювання ультракороткої тривалостi в кiльватерно-польовому ондуляторi Генерация интенсивного рентгеновского излучения ультракороткой длительности в кильватерно-полевом ондуляторе Article published earlier |
| spellingShingle | Generation of intense ultra-short X-ray pulses in wake field undulator Opanasenko, A. Электродинамика |
| title | Generation of intense ultra-short X-ray pulses in wake field undulator |
| title_alt | Генерацiя iнтенсивного рентгенiвського випромiнювання ультракороткої тривалостi в кiльватерно-польовому ондуляторi Генерация интенсивного рентгеновского излучения ультракороткой длительности в кильватерно-полевом ондуляторе |
| title_full | Generation of intense ultra-short X-ray pulses in wake field undulator |
| title_fullStr | Generation of intense ultra-short X-ray pulses in wake field undulator |
| title_full_unstemmed | Generation of intense ultra-short X-ray pulses in wake field undulator |
| title_short | Generation of intense ultra-short X-ray pulses in wake field undulator |
| title_sort | generation of intense ultra-short x-ray pulses in wake field undulator |
| topic | Электродинамика |
| topic_facet | Электродинамика |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111468 |
| work_keys_str_mv | AT opanasenkoa generationofintenseultrashortxraypulsesinwakefieldundulator AT opanasenkoa generaciâintensivnogorentgenivsʹkogoviprominûvannâulʹtrakorotkoítrivalostivkilʹvaternopolʹovomuondulâtori AT opanasenkoa generaciâintensivnogorentgenovskogoizlučeniâulʹtrakorotkoidlitelʹnostivkilʹvaternopolevomondulâtore |