Proposals for experimental study of wakefield undulator radiation
The possibility of detection of a wake-field undulator radiation generated by short bunches of relativistic charged particles, moving through a periodic rf structure, is estimated. Проведена оценка возможности регистрации кильватерно-полевого ондуляторного излучения, генерируемого короткими сгустка...
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Opanasenko, A.N. 2015-04-06T14:49:23Z 2015-04-06T14:49:23Z 2006 Proposals for experimental study of wakefield undulator radiation / A.N. Opanasenko // Вопросы атомной науки и техники. — 2006. — № 3. — С. 151-153. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 29.27, 41.60.A, 41.60.B, 41.60.C https://nasplib.isofts.kiev.ua/handle/123456789/79876 The possibility of detection of a wake-field undulator radiation generated by short bunches of relativistic charged particles, moving through a periodic rf structure, is estimated. Проведена оценка возможности регистрации кильватерно-полевого ондуляторного излучения, генерируемого короткими сгустками релятивистских заряженных частиц, движущихся в периодической резонансной структуре. Проведено оцінку можливості реєстрації кільватерно-польового ондуляторного випромінювання, що генерується короткими згустками релятивістських заряджених частинок, що рухаються в періодичній резонансній структурі. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Применение ускорителей в радиационных технологиях Proposals for experimental study of wakefield undulator radiation Предложения по экспериментальному исследованию кильватерно-полевого ондуляторного излучения Пропозиції, що до експериментального дослідження кільватерно- польового ондуляторного випромінювання Article published earlier |
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Proposals for experimental study of wakefield undulator radiation |
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Proposals for experimental study of wakefield undulator radiation Opanasenko, A.N. Применение ускорителей в радиационных технологиях |
| title_short |
Proposals for experimental study of wakefield undulator radiation |
| title_full |
Proposals for experimental study of wakefield undulator radiation |
| title_fullStr |
Proposals for experimental study of wakefield undulator radiation |
| title_full_unstemmed |
Proposals for experimental study of wakefield undulator radiation |
| title_sort |
proposals for experimental study of wakefield undulator radiation |
| author |
Opanasenko, A.N. |
| author_facet |
Opanasenko, A.N. |
| topic |
Применение ускорителей в радиационных технологиях |
| topic_facet |
Применение ускорителей в радиационных технологиях |
| publishDate |
2006 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Article |
| title_alt |
Предложения по экспериментальному исследованию кильватерно-полевого ондуляторного излучения Пропозиції, що до експериментального дослідження кільватерно- польового ондуляторного випромінювання |
| description |
The possibility of detection of a wake-field undulator radiation generated by short bunches of relativistic charged
particles, moving through a periodic rf structure, is estimated.
Проведена оценка возможности регистрации кильватерно-полевого ондуляторного излучения, генерируемого короткими сгустками релятивистских заряженных частиц, движущихся в периодической резонансной структуре.
Проведено оцінку можливості реєстрації кільватерно-польового ондуляторного випромінювання, що
генерується короткими згустками релятивістських заряджених частинок, що рухаються в періодичній
резонансній структурі.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/79876 |
| citation_txt |
Proposals for experimental study of wakefield undulator radiation / A.N. Opanasenko // Вопросы атомной науки и техники. — 2006. — № 3. — С. 151-153. — Бібліогр.: 11 назв. — англ. |
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| first_indexed |
2025-11-26T20:09:30Z |
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2025-11-26T20:09:30Z |
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1850772666377568256 |
| fulltext |
PROPOSALS FOR EXPERIMENTAL STUDY OF WAKEFIELD UNDULA-
TOR RADIATION
A.N. Opanasenko
NSC KIPT, Kharkiv, Ukraine
E-mail: Opanasenko@kipt.kharkov.ua
The possibility of detection of a wake-field undulator radiation generated by short bunches of relativistic charged
particles, moving through a periodic rf structure, is estimated.
PACS: 29.27, 41.60.A, 41.60.B, 41.60.C
1. INTRODUCTION
Recent research [1-5] into a novel wake-field undu-
lator (WFU) radiation mechanism has specified new po-
tential opportunities for generating an ultra-short wave-
length light. The mechanism consists in photon emission
by a short bunch of relativistic charged particles undu-
lating at nonsynchronous harmonics of a wake-field
(WF) induced by the bunch moving through a periodic
corrugated waveguide without external fields. The basic
theoretical results of studies into the WFU radiation in-
clude the following.
• In a relatively long-wave spectral region of the
periodic structure (where diffraction of generated
waves is essential) the radiation manifests itself in
a coherent interference of the WF and WFU radi-
ation. The pure WFU radiation takes place only
within the relatively ultra-short wave range, where
the wave diffraction of the WFU radiation can be
neglected [1, 2].
• The power of the coherent WFU radiation emitted
by the bunch of N particles is proportional to N 4
[1].
• The power of the incoherent WFU radiation is
proportional to N 3 [2].
• Since the WFU radiation power is proportional to
the electron energy squared, it can become com-
parable with the WF power or even exceed it [2,
3].
• The creation of the WF undulator with sub-mil-
limeter periods may open up the possibilities of
generation the hard X-rays employing the relative-
ly low electron energies without external alterna-
tive fields [4, 5].
On ground of above-mentioned we can conclude that
experimental studies into the WFU radiation predicted
are of great benefit. The goal of the present paper is to
estimate the possibilities of carrying out proof-of-princi-
ple experiments on observing the WFU radiation.
2. WFU RADIATION CHARACTERISTICS
The WFU radiation has a line spectrum with reso-
nant wavelengths
( ) ( )22p D pλ γ≈ , (1)
where p =1, 2,… is a non-synchronous spatial harmon-
ic’s number, D is the rf structure period, γ is the Lorentz
factor (γ>>1).
Let (p) be a spectral flux (photons/s) into a small
bandwidth ∆ω of the р-th harmonics. Then, by analogy
with Ref. [6,7], the spectral-angular flux density emitted
non-coherently by the bunch in a forward direction is
given by
( )
( )
( )
22 2
p
p
u aver p
d N Nf K
d
ωα γ
ω
∆=
Ω
F
, (2)
where Ω is the solid angle, α is the fine-structure con-
stant, Nu is the number of the rf structure periods, ( )pK
r
is the WF undulator parameter [4,5,8], faver is the average
bunch repetition frequency, 〈…〉 denotes an averaging.
The formula for the full flux of the p-th harmonics in
a central cone 22 rπ σ ў∆ Ω = (with an angular rms width
( )1r uNσ γў = ) into a FWHM bandwidth
( )
u
p N1≅∆ ωω [7] is very useful for experimental es-
timations and given by
( ) ( ) 2
2
p p
full averNf Kπ α=F . (3)
2.1. WFU RADIATION FROM AN S-BAND
WAVEGUIDE
Let us consider the possibilities of detection the
WFU radiation from the WF undulator being an axisym-
metric disk loaded waveguide (DLW) schematically de-
picted in Fig.1.
ρ b
NuD
r b a
θ
b
d
D
u
r b
axis
bunch
d
Fig.1. DLW as WF undulator
In this figure: a is the aperture radius, D-d is the disk
thickness, b is the cell radius, rb is the bunch distance
from the DLW axis, ρb is the bunch radius, θ is the max-
imum possible angular spread of the bunch.
At first we will perform an under-estimation of the
full fluxes of the WFU radiation out of both a conven-
tional SLAC-type rf section [9] and a STRUM90 section
designed and fabricated at the NSC KIPT (Ukraine)
[10]. The dimensions of these sections are shown in Ta-
ble 1.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.151-153.
151
mailto:A.Author@ifbd.net
Table 1. The DLW parameters
DLW D d a b Nu
STRUM90 7.1 6.7 1.5 4.1 24
SLAC-type 36 3 1.3…0.1 4.2…4.1 85
Note: the dimensions are given in cm
Let us look at the wavelengths of the WFU radiation,
obtained at the above-mentioned rf structures, as a func-
tion of the electron energy (the dependence is presented
in Fig.2). It shows that for the S-band rf structures the
electron bunches with the energies not less than
100 MeV are required for generating the well-detectable
WFU radiation (below infrared light).
10 100 1 .103 1 .104 1 .105
0.01
0.1
1
10
100
1 .103
1 .104
1 .105
1 .106
STRUM90 (4pi/3) (KIPT)
2pi/3 (SLAC)
770 nm - the upper limit of visible spectrum
Electron energy (MeV)
W
av
el
en
gt
h
(
an
gs
tr
om
)
Fig.2. The wavelength of WF undulator radiation
versus electron energy
In order to estimate the magnitudes of the photon
fluxes emitted by the bunch in the DLW, we have used
analytical relations for the WFU parameter derived in
Ref.[8] for the wake-fields excited in the lowest pass-
band (TM01-type mode). The full fluxes in the central
cone into the FWHM bandwidth as functions of the
bunch charge are shown in Fig.3. Here we consider the
ultra-relativistic single bunches with a 6D phase volume
typical for the SLAC beams that follow through the giv-
en rf sections at a distance equal rb=0.75a from the axis
(see Fig.4) with a repetition rate 120 Hz. It is easy to no-
tice that the full flux under-estimated, 104…105 ph/sec,
can be achieved at the bunch charge about 10 nC.
0.1 1 10
0.01
0.1
1
10
100
1 .103
1 .104
1 .105
1 .106
STRUM90 (4pi/3) (KIPT)
2pi/3 DLW (SLAC)
faver =120 Hz
Charge of a bunch ( nC )
Fu
ll
Fl
ux
in
C
en
tr
al
C
on
e
(
ph
/s
)
Fig.3. The full flux of the WFU radiation in the central
cone into the FWHM bandwidth versus bunch charge
Let us consider the upper estimation of a beam trans-
verse phase dimension required for the experiments. Let
us assume that there are none of additional focusing ele-
ments along the rf structure, and there is a bunch
crossover at the structure half-length. Then, supposing ρ
b=2σr and θ=2σθ (where σr and σθ are the rms radius
and angular spread of the bunch, respectively), see
Fig.1, the maximum normalized rms emittance can be
estimated as
22 b r
n r r
u
a r
N Dθ
σε γ σ σ γ σ − −= = , (4)
with the maximum magnitude
( ) 2
,max , at
4 4
b b
n r
u
a r a r
N D
ε γ σ
− −= = . (5)
So, for the STRUM90 section Eq.(5) results in εn,max
≈400 mm·mrad at σr ≈1 mm, whereas for the SLAC sec-
tion we have εn,max≈150 mm·mrad at σr≈0.7 mm. In the
given section the bunch is moving at rb= 0.75a.
2.2 WFU RADIATION FROM SUB-MM PERI-
ODIC WAVEGUIDE
Further, we will analyze conditions, under which the
WFU radiation emitted by the ultra short bunches ob-
tained at the so-called table-top accelerators, could be
detected. As an example we consider a photo-injector
developed at Eindhoven Technical University [11]. The
parameters of the photo-injector are given in Table 2.
Table 2. The parameters of TU/E photo-injector
Energy 10 MeV
Emittance 1 mm mrad
Length 100 fs
Charge 0.1 nC
As follows from Eq.(1), the rf structure periods re-
quired for photon generation, by 10 MeV electron
bunches, in the visible spectrum that can be detected
easily by multiplier phototubes, lie within 0.3…0.6 mm.
To obtain the under-estimated value for the photon
flux generated at the rf structures with sub-millimeter
periods, we have carried out optimization of the rf struc-
ture geometry. The mean-square of the WFU parameter
modulus [8] was used as an efficiency function. First,
we have found an optimal set for the dimensions of the
S-band DLW by varying the appropriate sizes. Then, us-
ing a scaling approach we have determined the optimal
dimensions for the rf structure with the sub-millimeter
period required. The optimal DLW dimensions are pre-
sented in Table 3.
Table 3. The optimal dimensions for the DLW
n mode D' d' a' b'
1 4π/3 71.45 39.46 20 41.2
150 4π/3 0.476 0.263 0.133 0.275
200 4π/3 0.357 0.197 0.100 0.206
Note: n=D/D'=d/d'=a/a'=b/b' is the reduction ratio, all
the dimensions are given in mm
Further, let us compare the photon flux emitted by a
single bunch at two optimal rf structures having different
reduction ratio n=150 and 200, respectively. We sup-
pose that in the each section the bunch moves at
r'b=rb/n=0.75a'. The dependences of photon numbers in
the central cone into the FWHM bandwidth per bunch
transit through the section (see Eq.(3)) on the bunch
charge are presented in Fig.4.
Fig.4 shows that the single 0.1 nC bunch can emit
not less than 44…80 photons per one transit through the
152
sub-mm structures with n=150 and 200; each structure
consists only of 10 periods. Substituting the data from
Table 3 into Eq.(5), we can obtain the upper-estimations
for the normalized emittance ε'n,max≈1.2…0.9 mm·mrad
at σ'r ≈8…6 µm corresponding to the structure with
n=150 and 200, respectively. As follows from Eq.(5), to
rise significantly the normalized emittance and bunch ra-
dius it is necessary to increase the transverse dimension
of the waveguide in several times. Besides, considerable
increase in the WFU radiation flux may be provided by
both solving the repetition rate step-up problem and
raising the bunch charge in several times.
0.01 0.1 1 100.01
0.1
1
10
100
1 .103
1 .104
1 .105
1 .106
1 .107
1 .108
Scaling - n=200
Scaling - n=150
Charge of a bunch ( nC )
N
u
m
b
er
o
f
P
h
o
to
n
s
in
C
o
n
e
p
er
S
h
o
rt
Fig.4. The photon number of the WFU radiation in the
central cone into the FWHM bandwidth emitted by a
single bunch versus the bunch charge
3. CONCLUSION
Because well-detectable wavelengths are located be-
low infrared light, the electron energies not less than
100 MeV are required for observation of the WFU radi-
ation from the S-band accelerator structures. The under-
estimation of the full flux, 104…105 ph/sec, emitted by
the single bunches at a repetition rate 120 Hz from the
S-band accelerator structures can be achieved at the
bunch charge about 10 nC.
For observation of the WFU radiation emitted by the
ultra-short electron bunches from the TU/E photo-injec-
tor it is necessary to solve the problems of increase in
the repetition rate and/or the bunch charge.
REFERENCES
1. A. Opanasenko. Radiation by self-oscillating rel-
ativistic charged particle moving along periodic
structure. Proc. of MMET2002, Kiev, Ukraine. 2002,
v.2, p.642-643;
2. A. Opanasenko. Radiation of charged particles
in self-wakefield. Proc. of RUPAC2002, Obninsk,
Russia. 2002, v.1, p.264-270;
3. A. Opanasenko. Characteristics of undulator-type
radiation emitted by bunch of charged particles in
wakefield // Problems of Atomic Science and Technol-
ogy. Series: Nuclear Physics Investigations. 2004,
№2(43), p.138-140.
4. A. Opanasenko. Conception of X-ray Source
Based on Compact Wakefield Undulator. Proc. of
EPAC 2004, Lucerne, Switzerland. p.2412-2414.
5. A. Opanasenko. Wakefield undulator for gener-
ating X-rays. Proc. of RUPAC’04, Dubna, Russia.
2004, p.278-280.
6. I.V. Basarov. Possibilities of Coherent X-ray
Production with ERL. ERL 02-05. 2002, p.1-12.
7. K.J. Kim. Characteristics of synchrotron radia-
tion. AIP Conf. Proc. 1989, v.189(1), p.565-632.
8. A. Opanasenko. Analytical formulas for alternat-
ing wake force of corrugated waveguides // Problems
of Atomic Science and Technology. Series: Nuclear
Physics Investigations. 2006, №8(46), p.148-150.
9. G.A. Loew and R.B. Neal. Accelerating struc-
tures. Linear Accelerator, ed.: by P.M. Lapostolle and
A.L. Septier. Amsterdam, 1970.
10. M.I. Ayzatsky, Е.Z. Biller, V.V. Volobuev et al.
Accelerating section for short-pulsed of linac opera-
tion mode // Problems of Atomic Science and Tech-
nology. Series: Nuclear Physics Investigations. 1991,
№3(21), p.16-18.
11. G.J.H. Brussaard, M.J. Van der Wiel. Ultra-
high Gradient Compact Accelerator Developments.
Proc. of EPAC 2004, Lucerne, Switzerland, p.74.
ПРЕДЛОЖЕНИЯ ПО ЭКСПЕРИМЕНТАЛЬНОМУ ИССЛЕДОВАНИЮ КИЛЬВАТЕРНО-ПОЛЕВО-
ГО ОНДУЛЯТОРНОГО ИЗЛУЧЕНИЯ
А.Н.Опанасенко
Проведена оценка возможности регистрации кильватерно-полевого ондуляторного излучения, генерируе-
мого короткими сгустками релятивистских заряженных частиц, движущихся в периодической резонансной
структуре.
ПРОПОЗИЦІЇ, ЩО ДО ЕКСПЕРИМЕНТАЛЬНОГО ДОСЛІДЖЕННЯ КІЛЬВАТЕРНО-
ПОЛЬОВОГО ОНДУЛЯТОРНОГО ВИПРОМІНЮВАННЯ
А.М.Опанасенко
Проведено оцінку можливості реєстрації кільватерно-польового ондуляторного випромінювання, що
генерується короткими згустками релятивістських заряджених частинок, що рухаються в періодичній
резонансній структурі.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.151-153.
153
1. INTRODUCTION
2. WFU RADIATION CHARACTERISTICS
2.1. WFU radiation from AN S-band waveguide
2.2 WFU radiation from SUB-MM PERIODIC waveguide
3. CONCLUSION
REFERENCES
ПРЕДЛОЖЕНИЯ ПО ЭКСПЕРИМЕНТАЛЬНОМУ ИССЛЕДОВАНИЮ КИЛЬВАТЕРНО-ПОЛЕВОГО ОНДУЛЯТОРНОГО ИЗЛУЧЕНИЯ
Пропозиції, що до експериментального дослідження кільватерно- польового ондуляторного випромінювання
|