The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering
The feasibility of the development of intense X-ray sources based on Compton scattering in laser-electron storage rings is discussed. The results of the electron beam dynamics simulation involving Compton and intrabeam scattering are presented.
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Zitieren: | The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering / The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering // Вопросы атомной науки и техники. — 2002. — № 2. — С. 78-80. — Бібліогр.: 14 назв. — англ. |
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Gladkikh, P.I. Karnaukhov, I.M. Telegin, Yu.N. Zelinsky, A.Yu. 2015-04-12T06:37:37Z 2015-04-12T06:37:37Z 2002 The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering / The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering // Вопросы атомной науки и техники. — 2002. — № 2. — С. 78-80. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 29.20.Dh, 29.27.Bd https://nasplib.isofts.kiev.ua/handle/123456789/80122 The feasibility of the development of intense X-ray sources based on Compton scattering in laser-electron storage rings is discussed. The results of the electron beam dynamics simulation involving Compton and intrabeam scattering are presented. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Theory and technics of particle acceleration The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering Моделирование динамики электронного пучка в лазер-электронном накопительном кольце с учетом комптоновского и внутрипучкового рассеяния Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering |
| spellingShingle |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering Gladkikh, P.I. Karnaukhov, I.M. Telegin, Yu.N. Zelinsky, A.Yu. Theory and technics of particle acceleration |
| title_short |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering |
| title_full |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering |
| title_fullStr |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering |
| title_full_unstemmed |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering |
| title_sort |
electron beam dynamics simulation in the laser-electron storage ring involving compton and intrabeam scattering |
| author |
Gladkikh, P.I. Karnaukhov, I.M. Telegin, Yu.N. Zelinsky, A.Yu. |
| author_facet |
Gladkikh, P.I. Karnaukhov, I.M. Telegin, Yu.N. Zelinsky, A.Yu. |
| topic |
Theory and technics of particle acceleration |
| topic_facet |
Theory and technics of particle acceleration |
| publishDate |
2002 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Моделирование динамики электронного пучка в лазер-электронном накопительном кольце с учетом комптоновского и внутрипучкового рассеяния |
| description |
The feasibility of the development of intense X-ray sources based on Compton scattering in laser-electron storage rings is discussed. The results of the electron beam dynamics simulation involving Compton and intrabeam scattering are presented.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/80122 |
| citation_txt |
The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering / The electron beam dynamics simulation in the laser-electron storage ring involving Compton and intrabeam scattering // Вопросы атомной науки и техники. — 2002. — № 2. — С. 78-80. — Бібліогр.: 14 назв. — англ. |
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| first_indexed |
2025-11-27T09:12:31Z |
| last_indexed |
2025-11-27T09:12:31Z |
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| fulltext |
THE ELECTRON BEAM DYNAMICS SIMULATION IN THE LASER-
ELECTRON STORAGE RING INVOLVING COMPTON AND
INTRABEAM SCATTERING
P.I. Gladkikh, I.M. Karnaukhov, Yu.N. Telegin, A.Yu. Zelinsky
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: zelinsky@kipt.kharkov.ua
The feasibility of the development of intense X-ray sources based on Compton scattering in laser-electron storage
rings is discussed. The results of the electron beam dynamics simulation involving Compton and intrabeam scattering
are presented.
PACS: 29.20.Dh, 29.27.Bd
1. INTRODUCTION
In recent years several schemes of using the laser
electron interaction for establishing the compact X-ray
sources have been proposed [1-6]. The background for
producing hard photons by scattering laser photons on
relativistic electrons seems quite clear and efficient. It
appears that for producing the X-ray beams with high
intensity the increasing of the initial laser beam intensity
will be enough. Abilities of the modern laser equipments
with the laser flash energies up to 10 J allow the laser-
electron storage rings (LESR) to have bright prospects.
The experiments that have been carried out [7, 8]
proved the applicability of the proposed schemes.
However, the electron beam dynamics in the LESR
under conditions of interaction with the dense photon
beam is essentially different from that in a commonly
used storage rings. Such differences originate from
increasing of the quantum fluctuation effects and, hence,
from increasing of the energy spread in the beam. It
leads to the increasing of the chromatic aberrations
effect onto the particle motion. This effect is so crucial
that leads to the beam blow-up and, finally, to its loss.
On the other hand, in the case of total suppression of the
chromatic effects in the ring, the effect of laser cooling
leads to the decreasing of transverse beam size, and
intrabeam scattering has to be taken into account.
Z.Huang has investigated the beam dynamics in the
LESR analytically using undulator approach and has
obtained expressions for the steady state beam
parameters [9]. We carried out the numerical simulation
of the longitudinal dynamics of the electron beam
interacting with the dense laser target by using the
Monte-Carlo method and the kinematic approach for
description of the process of photon-electron interaction.
The results of calculations for the steady state energy
spread and bunch length in the LESR were in a good
agreement with the estimations obtained by using
Z.Huang’s expressions [10,11]. But undulator approach
doesn’t permit to investigate the transverse beam
dynamics taking into account chromatic aberrations in
the beam with large value of the energy spread and
intrabeam scattering.
In this paper the approach is described that allowed
us to create the computer code for the full-scale 3-D
simulation of particle motion in the storage ring taking
into account photon-electron interactions and intrabeam
scattering. The first results of calculations are shown
and discussed. Algorithm had been realized within the
pack of DeCA codes [12].
2. THE KINEMATIC APPROACH
The photon-electron interactions in the LESR can be
described with the quantum theory where the Compton
scattering is considered as a process of elastic collision
of a photon with a free electron.
In a collision of a laser photon with energy εγ0 and a
relativistic electron with energy E0 at a small collision
angle α0, the photon is scattered in a solid angle of about
1/γ , where γ = E0 / mc2, mc2 is the rest energy of the
electron.
The energy spectrum of scattered photons is
determined by differential cross section of Compton
scattering [13]:
( ) ( )( ) ;2212141
1
12
d
d 0
−−+−−−+
−
= yrrxPrry
yxy ce
c λ
σσ
(1)
where
10 +
=≤=
x
xy
E
y m
γε
;
( ) 1
1
≤
−
=
yx
yr ;
( )
42
0
0
2
00 2cos4
cm
E
x
αε γ= ;
;10*5.2 229
2
2
0 m
mc
e −=
= πσ
λe, Pc - polarization direction of electron and photon
beams (
2
1≤eλ ; 1≤cP );
;2 1σλσσ cecc P+= +
( )
( )
;
12
18
2
11ln841
2
22
0
+
−+++
−−=+
xx
x
xxxc
σ
σ
78 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 78-80.
( )
( )
+
−
+
+−+
+=
2
0
1
12
1
1
1
2
51ln21
2
xx
x
xx
σ
σ .
The differential cross-section for various electron
energies and for the fixed photon energy has essential
differences even if electron energy is changed within
some percents. For this reason, for obtaining the
accurate results in our calculations for electrons with
different energies we have to use the various branches of
curve (1).
One can write the photon scattering angle in the
interaction plane as a function of the photon energy as
follows:
( ) 10 −=
y
yy mθθ γ , (2)
where 1
0
2
0 += x
E
mcθ . The electron scattering angle is
given by:
( ) ( )
y
yyye −
=
1γθθ . (3)
3. THE MONTE-CARLO PROCEDURE
The simulation of the photon - electron interaction
by the Monte-Carlo method, realized in the DeCA code
is based on the follow theorem:
If the variate ξ is specified with the distribution
function ( )xFξ and ξ satisfies the equation:
( ) α
ξ
ξ =∫
∞−
tFd , (4)
where α is variate which is uniformly distributed within
[0,1], then ξ is distributed according to ( )xFξ .
So, by integrating y
c
d
dσ
from - to εI with fixed
electron beam energy E0i and normalizing this integral
with total Compton cross section: cσ , one receives the
correspondence between the variate uniformly
distributed within [0,1] and the scattered photon energy.
By setting the electron beam energy and the scattered
photon energy one can build a two-dimensional table of
correspondence of these values to the number within
interval [0,1]. Thus, if we know the recoiled electron
energy it will be enough to generate the variate which
uniformly distributed within [0,1] and to find in the
correspondence table which scattered photon energy this
one corresponds to.
We accepted the following model for simulation: an
electron with coordinates (x,x’,z,z’,s,∆E/E0) interacts
with a laser flash, the laser flash is assumed to be a
cylinder with the length Llf and the radius Rlf , the photon
density has uniform distribution along cylinder axes and
Gaussian distribution in transverse directions:
( )
+
−= 2
22
0 2
1exp,,
lf
lflf
lflflflflf
R
zx
sIszxI , (5)
where I0 is maximum value of laser intensity.
In the case of laser flash rotation around reference
trajectory with the angles αlf, βlf in horizontal and
vertical planes, correspondingly, one can express the
photons coordinates in the laser flash by the matrix of
rotary transformation:
−
−=
s
z
x
s
z
x
lflflflflf
lflflflflf
lflf
lf
lf
lf
ββαβα
ββααβ
αα
cossincossinsin
sincoscossincos
0sincos
The algorithm of the interaction simulation includes
the follow steps:
1. The electron free path length sx, inside a photon
flash is determined by the expression:
( )
c
s
s
lflflf sszxI
x
σ
αlnd,,
1
−=∫ ,
where α is variate distributed uniformly within [0,1].
If sx is larger then flash length, an interaction takes
no place and the electron coordinates don’t change. The
algorithm passes to the simulation of the particle motion
in the next lattice element.
2. In another case, according to the procedure
described above the process of photon scattering
is simulated.
3. According to (3) the angle of the electron
scattering is determined.
4. INTRABEAM SCATTERING
SIMULATION
The formalism of intrabeam scattering was
developed by J. Bjorken and S.K. Mtingwa [14]. We
have used this formalism to calculate the emittance
growth rate due to intrabeam scattering and emittance
increment. Then matrix of emittance transformation is
formed. Such procedure is repeated every several
thousand turns for estimation of emittance growth rate.
5. RESULTS OF CALCULATION
We have carried out the simulation of electron-
photon interaction for the variant of LESR-N100 storage
ring lattice. The simulations were performed with
following parameters: electron energy E0=225 MeV,
number of electrons per bunch 3*109, incident photon
energy 1.17 eV, (Nd:YAG laser), laser flash energy – 10
mJ, laser flash waist – 50 µ.. We simulated electron –
photon interactions with zero collision angle. Such
parameters provide the scattered radiation intensity up
to 1014 phot/s. The main results are shown in Fig. 1-4.
One can see that electron motion is stable. The steady
state horizontal size of the electron beam, in our
opinion, is caused by the chromatic effects (Fig. 1). The
vertical size decreases due to both synchrotron radiation
damping and laser cooling (Fig. 2). The steady state
energy spread is about 1.2 % (Fig. 3), and it is in a good
agreement with the analytical estimates [11].
79
The obtained spectrum of the scattered photons is
shown in Fig. 4.
0.0 0.5 1.0 1.5 2.0
0.10
0.12
0.14
0.16
0.18
0.20
n * 106
σ x , mm
Fig. 1. Horizontal electron beam size versus turn
number
0.0 0.5 1.0 1.5 2.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
n * 106
σ z , mm
Fig. 2. Vertical electron beam size versus turn
number
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
n * 106
δ , %
Fig. 3. Energy spread versus turn number
0 100 200 300 400 500 600 700 800
0.0
0.2
0.4
0.6
0.8
1.0
f
ε γ , keV
Fig. 4. Normalized scattered photon spectrum for
electron beam energy 200 MeV
6. CONCLUSION
The code for 3-D simulation of laser-electron
interaction by the Monte-Carlo method was developed.
The algorithm of the intrabeam scattering calculation in
single-particle tracking was developed too. These
algorithms were realized in the DeCA code and permit
to investigate the beam dynamics in the LESR through
the periods of time that exceed the real damping times
(millions of turns).
REFERENCES
1. P. Sprangle, A. Ting, E. Esarey et al. Tunable,
short pulse hard X-rays from a compact laser
synchrotron source // J. Appl. Phys. 1992, № 72,
p. 5032-5038.
2. Z. Chen et al. Development of a compact high
brightness X-ray source // Nucl. Instr. & Meth. In
Phys. Res. 1994, A 341, p. 346-350.
3. K.-J. Kim, S. Chattopadhyay, C.V. Shank.
Generation of femtosecond X-rays by 90O
Thompson scattering // Nucl. Instr. & Meth. In
Phys. Res. 1994, A 341, p. 351-354.
4. A.A. Zholents, M.S. Zolotarev. A proposal
for the generation of ultra-short X-ray pulses //
Nucl. Instr. & Meth. In Phys. Res. 1995, A 358,
p. 455-458.
5. Z. Huang, R.D. Ruth. Laser-electron-storage
ring // Phys. Rev. Lett. 1998, № 80, p. 976-979.
6. E. Bulyak, P. Gladkikh, I. Karnaukhov et al.
Source of X-ray radiation based on Compton
scattering // Nucl. Instr. & Meth. In Phys. Res. 2000,
A 448, p. 48-50.
7. V. Balakin et al. Focusing of submicro beams
for TeV-scale e+e- linear colliders // Phys. Rev.
Lett. 1995, № 74, p. 2479-2482.
8. R.W. Schoenlein et al. Femtosecond X-ray
pulses at 0.4 A generated by 90o Thompson
scattering: tool for probing the structural dynamics
of materials // Science. 1997, № 274, p. 236-238.
9. Z. Huang. Radiative cooling of relativistic
electron beams. SLAC-R-527, 1998, 141 p.
10. P. Gladkikh, I. Karnaukhov, Yu. Telegin,
A. Zelinsky, A. Shcherbakov. Beam dynamic
simulation in the storage ring N-100 with electron
photon interaction. Proc. of EPAC - 2000, 2000,
v. 2, p. 1199-1201.
11. I. Karnaukhov, Yu. Telegin, A. Zelinsky.
Investigation of longitudinal dynamic in laser-
electron storage ring // Nucl. Instr. & Meth. In
Phys. Res. 2001, A 470, p. 23-28.
12. P Gladkikh, M. Strelkov, A. Zelinsky. The
application package DECA for calculating cyclic
accelerators. Proc. of the IIIth National Conf. on
Particle Accelerator, 1993, p. 194-196.
13. V. Telnov. Laser cooling of electron beams
for linear colliders // Nuclear Instruments and
Methods in Physics Research. 1995, A 355, p. 3-
18.
80
14. J. Bjorken, S.K. Mtingwa. Intrabeam
scattering // Particle Accelerators. 1983, № 13,
p. 115-119.
81
PACS: 29.20.Dh, 29.27.Bd
REFERENCES
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