Synchrotron radiation losses in laser-plasma accelerators
Like in conventional accelerators, a synchrotron radiation can significantly suppress an acceleration in a bubble. The dynamics of accelerating electron in the bubble with consideration of the synchrotron radiation reaction force is studied. The total suppression of electron acceleration by the ra...
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| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2006 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Цитувати: | Synchrotron radiation losses in laser-plasma accelerators / I.Yu. Kostyukov , E.N. Nerush , A. Pukhov // Вопросы атомной науки и техники. — 2006. — № 2. — С. 169-171. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859584838447661056 |
|---|---|
| author | Kostyukov, I.Yu. Nerush, E.N. Pukhov, A. |
| author_facet | Kostyukov, I.Yu. Nerush, E.N. Pukhov, A. |
| citation_txt | Synchrotron radiation losses in laser-plasma accelerators / I.Yu. Kostyukov , E.N. Nerush , A. Pukhov // Вопросы атомной науки и техники. — 2006. — № 2. — С. 169-171. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Like in conventional accelerators, a synchrotron radiation can significantly suppress an acceleration in a bubble.
The dynamics of accelerating electron in the bubble with consideration of the synchrotron radiation reaction force is
studied. The total suppression of electron acceleration by the radiation losses is discussed.
Как и в случае традиционных ускорителей, потери, связанные с синхротронным излучением, могут существенно снизить эффективность ускорения. В работе исследована динамика электрона в ионной полости с учетом действия силы реакции синхротронного излучения. Обсуждается полное подавление ускорения электронов радиационными потерями.
Як й у випадку традиційних прискорювачів, втрати, пов'язані із синхротронним випромінюванням,
можуть істотно знизити ефективність прискорення. У роботі досліджена динаміка електрона в іонній
порожнині з урахуванням дії сили реакції синхротронного випромінювання. Обговорюється повне
придушення прискорення електронів радіаційними втратами.
|
| first_indexed | 2025-11-27T09:12:04Z |
| format | Article |
| fulltext |
SYNCHROTRON RADIATION LOSSES IN LASER-PLASMA ACCELER-
ATORS
I.Yu. Kostyukov1, E.N. Nerush2, A. Pukhov3
1Institute of Applied Physics RAS, Nizhny Novgorod, 603950, Russia
2Nizhny Novgorod University, Nizhny Novgorod, 603950, Russia
3Heinrich-Heine-Universitat Dusseldorf, 40225, Dusseldorf, Germany
E-mail: kost@appl.sci-nnov.ru
Like in conventional accelerators, a synchrotron radiation can significantly suppress an acceleration in a bubble.
The dynamics of accelerating electron in the bubble with consideration of the synchrotron radiation reaction force is
studied. The total suppression of electron acceleration by the radiation losses is discussed.
PACS: 41.60.Ap, 52.40.Mj
1. INTRODUCTION
A mechanism, based on the acceleration of charged
particles in strongly nonlinear plasma wave generated
by an ultrahigh intensity short laser pulse, is one of the
perspective candidates for the accelerators of the future.
The low acceleration rate leads to the huge-scale accel-
eration facility, which poses a serious limit for conven-
tional accelerators to increase the energy of the acceler-
ated particle, while the laser-plasma acceleration
scheme can provide much higher acceleration gradient.
Recently, an impressive progress in the generation of
short quasi-monoenergetic bunch of ultra relativistic
electrons in laser plasma was achieved [1].
One of the models [2], describing the generation of a
quasi-monoenergetic bunch of ultra relativistic elec-
trons, assumes that the generation is caused by a transi-
tion to a strongly nonlinear regime of laser-plasma inter-
action. A periodic plasma wave mutates to the solitary
ionic cavity – “bubble”, which is free from plasma elec-
trons and moving behind the laser pulse. The back-
ground plasma electrons as well as external electron
bunch can be trapped in the bubble and can be accelerat-
ed up to very high energy. Acceleration is accompanied
by the electron betatron oscillations because of the ultra-
high intense transversal field in the bubble. As a result
of betatron wiggling the trapped electrons radiate elec-
tromagnetic waves. The radiation spectrum of the ultra
relativistic electrons lies in the X-ray range because of
the Doppler effect [3]. Like in conventional accelera-
tors, the radiation losses can significantly suppress the
acceleration in the bubble.
2. ELECTRON DYNAMICS UNDER ACTION
OF RADIATION REACTION FORCE
The space-time distribution of the electromagnetic
fields in the bubble can be approximated by a linear
function of the coordinates and time [4]
,2/)( txEx −= ,4/yBE zy =−= ,4/zBE yz == (1)
where we use dimensionless units, normalizing the time
to pω/1 , the velocity to the speed of light c , the lengths
to pc ω/ , the electromagnetic fields to emc p /ω , and the
electron density n to the background density 0n ;
( ) 2/1
0
2 /4 mnep πω = is the electron plasma frequency,
e and m are the electron charge and electron mass, re-
spectively. It is assumed that laser pulse propagates
along x-axis. Then, the Lorentz force acting on a rela-
tivistic electron with 1≈xv inside the cavity is
,2/)( txFx −−= ,2/yFy −= 2/zFz −= . (2)
We assume that the electron trajectory is confined in xy
plane; the electron is slowly accelerated in x direction
and 1> >> > yx pp , where xp is the longitudinal momen-
tum of the electron and yp is the transversal momentum
of the electron. In this case we can neglect the action of
the longitudinal force ( 0=xE ). Thus, the electron tra-
jectory is given by the relation [5]
),2sin(
84
1)( 0
2
trttx bωνν −
−= ),sin()( 0 trty bω= (3)
where γω 2/1=b is the betatron frequency of the elec-
tron oscillations in the bubble, ,2// 0 γν rpp xy == γ
is the relativistic electron gamma-factor, 0r is the ampli-
tude of the electron betatron oscillations. The electron
trajectory in the ion channel is similar to the trajectory
of an electron moving in the homogeneous magnetic
field. In the latter case, the electron trajectory is spiral-
like. As a result, the radiation spectrum of the relativis-
tic electron undergoing betatron oscillations in the ion
channel is close to the spectrum of synchrotron radiation
[5].
The relativistic equations of the electron motion with
radiation reaction force is given by the relation [6]
,i
k
ik
i
guF
ds
du µ+= (4)
( )( ) i
m
kml
kl
k
kl
ill
kl
ik
i uuFuFuFFuu
x
Fg +−
∂
∂= , (5)
where ikF is the tensor of the electromagnetic field, ku
is the 4-velocity of the electron, )3/(2 32 mce pωµ = . Sub-
stituting Eqs.(1) and (3) into Eq.(4), we can calculate
the radiation reaction force on the relativistic electron
undergoing betatron oscillations in the ion channel. As a
result, the equation describing the evolution of the elec-
tron energy can be derived
22
08
1 γµγ r
dt
d −≈ . (6)
__________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.169-171.
169
The energy loss of an electron per unit distance is
[ ] [ ]
cm
MeVmrcmnQ e
2
0
345105.1
×= −− γµ . (7)
It is seen from Eq.(7) that the radiated power is propor-
tional to the square of gamma-factor.
It is known [7] that the longitudinal velocity is in-
variant of motion for the electron dynamics in homoge-
neous magnetic field under action of the synchrotron ra-
diation reaction force. It is not the case for the electron
undergoing betatron oscillations. Making of use Eq.(4),
the equation for longitudinal velocity of the electron can
be derived
γ
µ 12
0rdt
dvx ∝ . (8)
It follows from Eq.(7) that the characteristic time, dur-
ing which the longitudinal velocity is significantly
changed, is much more than the time, during which the
electron energy is converted into the radiation. So, we
can consider the longitudinal velocity of the electron as
invariant of motion, too. Moreover, the conservation of
the longitudinal velocity becomes more accurate as the
electron energy increases. Making of use the invariant
,constvx ≈ the final momentum components of the
electron can be predicted in the limit ∞→t . Let at
0=t the electron momentum be 0xp p= and 1yp p= ,
then ( ) 2/12
1
2
01 pp ++=γ , ( ) 2/.12
1
2
00 1// ppppv xx ++== γ .
Thus, the final momentum components of the electron
are ( ) 2/12
10 1/ pppx += and 0=yp at ∞→t , that is the
transversal energy of the electron is converted into the
radiation energy.
3. NUMERICAL SIMULATION RESULTS
Equations of motion (4) with fields (2) are numeri-
cally integrated for the electron with the initial condi-
tions 510xp = , 0=yp , 80 −=x , 20 =r at 0=t and
plasma density 19
0 10=n cm-3.
Fig.1. γ as a function of time without radiation reac-
tion force (line 1) and with radiation reaction force
(line 2)
The electron energy as a function of time with and with-
out consideration of a photon recoil is shown in Fig.1. It
is seen from Fig.1 that the electron is accelerated in the
bubble fields if radiation reaction is not taken into ac-
count while it is significantly decelerated if the effect of
radiation is taken into account. Therefore, the radiation
reaction force can strongly suppress the acceleration of
the ultra relativistic electrons in the bubble.
The effect of the radiation on electron acceleration is
also studied by a two-dimensional relativistic particle-
in-cell hybrid code in cylindrical geometry. The qua-
sistatic approximation (the plasma wake is assumed to
be slowly changed in the laser pulse frame) is used to
accelerate the computation. The code includes the emis-
sion of electromagnetic field by the relativistic elec-
trons. The emitted radiation exerts recoil on the electron
and the recoil force is included in the code.
Fig.2. Density plot of electron beam acceleration in the
bubble with radiation reaction force (a) and without of
that (b). The darker is the gray color, the higher is the
electron density
The incident laser pulse is circularly polarized, has
the Gaussian envelope ( )2222
0 //exp ll Lrraa ξ−−= , and
the wavelength 82.0=λ μm. The parameters of the
laser pulse are 5=lr , 2=lL , 100 =a . The pulse propa-
gates in plasma with the density 19
0 10−=n cm-3. This
laser pulse generates the bubble. We simulate the X-ray
emission from the external electron bunch with 410=γ ,
__________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.169-171.
9∙104
1
2
105
0 2000 ω
p
t
γ
0 x-t 20
0
18
r
a)
beam
0 x-t 20
0
18
r
b)
beam
laser
pulse
laser
pulse
169
radius 2=br and density 1710−=bn cm-3, propagating
in the bubble. The density plot is shown in Fig.2 with
consideration of the radiation reaction force (Fig.2,a)
and without consideration of that (Fig.2,b). The bunch
electron distribution function is shown in Fig.3. The
bunch is monoenergetic at the beginning of interaction
(line 1 in Fig.3). The radiation reaction force decelerates
the part of the bunch electrons with large amplitude of
the betatron oscillations, while the electrons with small
amplitude are accelerated by the longitudinal electric
field (see line 1 in Fig.3). The bunch electrons are accel-
erated if photon recoil is not taken into account (line 3
in Fig.3). The bubble forces focus the bunch (Fig.2,a.).
The deceleration by the radiation losses leads to the
bunch focusing at earlier moment of time (see Fig.2,b.)
than that without radiation reaction.
Fig.3. The electron distribution function of the bunch in
the bubble: initial distribution function (1), final distri-
bution function with radiation reaction force (2) and
without radiation reaction force (3)
4. CONCLUSIONS
It follows from Eq.(6) that the radiation reaction
force increases as square of the electron energy while
the accelerating force determined by the longitudinal
electric field does not depend on the electron energy.
Therefore, the radiation reaction can totally suppress the
electron acceleration in the bubble. The energy thresh-
old can be estimated from the balance of the radiation
reaction force and the accelerating force.
This work has been supported by Russian Founda-
tion for Basic Research (Grant No. 04-02-16684).
REFERENCES
1. T. Catsoleas. Electrons hang ten on laser wake //
Nature. 2004, v.431, №9, p.515-516.
2. A. Pukhov and J. Meyer-ter-Vehn. Laser wake field
acceleration: the highly non-linear broken-wave
regime // Applied Physics. 2002, v.B74, №3, p.355-
361.
3. S. Kiselev, A. Pukhov, and I. Kostyukov. X-ray
generation in strongly nonlinear plasma waves //
Phys. Rev. Lett. 2004, №13, p.135004-1-135004-4.
4. I. Kostyukov, A. Pukhov, and S. Kiselev. X-ray
generation in an ion channel // Physics of Plasmas.
2003, №10, p.4818-4828.
5. I. Kostyukov, A. Pukhov, and S. Kiselev. Phe-
nomenological theory of laser-plasma interaction in
bubble regime // Physics of Plasmas. 2004, №14,
p.5256-5264.
6. L.D. Landau and E.M. Lifshitz. The classical theo-
ry of field. M.: “Nauka”, 1988, p.268-277.
7. V.L. Ginzburg. Theoretical physics and astro-
physics. M.: “Nauka”, 1988, p.58-74.
ПОТЕРИ, СВЯЗАННЫЕ С СИНХРОТРОННЫМ ИЗЛУЧЕНИЕМ, В ПЛАЗМЕННЫХ УСКОРИТЕ-
ЛЯХ
И.Ю. Костюков, Е.Н. Неруш, А. Пухов
Как и в случае традиционных ускорителей, потери, связанные с синхротронным излучением, могут су-
щественно снизить эффективность ускорения. В работе исследована динамика электрона в ионной полости с
учетом действия силы реакции синхротронного излучения. Обсуждается полное подавление ускорения элек-
тронов радиационными потерями.
ВТРАТИ, ПОВ'ЯЗАНІ ІЗ СИНХРОТРОННИМ ВИПРОМІНЮВАННЯМ, У ПЛАЗМОВИХ
ПРИСКОРЮВАЧАХ
І.Ю. Костюков, Є.Н. Неруш, А. Пухов
Як й у випадку традиційних прискорювачів, втрати, пов'язані із синхротронним випромінюванням,
можуть істотно знизити ефективність прискорення. У роботі досліджена динаміка електрона в іонній
порожнині з урахуванням дії сили реакції синхротронного випромінювання. Обговорюється повне
придушення прискорення електронів радіаційними втратами.
1
2
3
104 1.02∙1049.66∙103
γ
N
e
(a
.u
.)
162
Потери, связанные с синхротронным излучением, в плазменных ускорителях
|
| id | nasplib_isofts_kiev_ua-123456789-78874 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-27T09:12:04Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kostyukov, I.Yu. Nerush, E.N. Pukhov, A. 2015-03-22T09:10:08Z 2015-03-22T09:10:08Z 2006 Synchrotron radiation losses in laser-plasma accelerators / I.Yu. Kostyukov , E.N. Nerush , A. Pukhov // Вопросы атомной науки и техники. — 2006. — № 2. — С. 169-171. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 41.60.Ap, 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/78874 Like in conventional accelerators, a synchrotron radiation can significantly suppress an acceleration in a bubble. The dynamics of accelerating electron in the bubble with consideration of the synchrotron radiation reaction force is studied. The total suppression of electron acceleration by the radiation losses is discussed. Как и в случае традиционных ускорителей, потери, связанные с синхротронным излучением, могут существенно снизить эффективность ускорения. В работе исследована динамика электрона в ионной полости с учетом действия силы реакции синхротронного излучения. Обсуждается полное подавление ускорения электронов радиационными потерями. Як й у випадку традиційних прискорювачів, втрати, пов'язані із синхротронним випромінюванням, можуть істотно знизити ефективність прискорення. У роботі досліджена динаміка електрона в іонній порожнині з урахуванням дії сили реакції синхротронного випромінювання. Обговорюється повне придушення прискорення електронів радіаційними втратами. This work has been supported by Russian Foundation for Basic Research (Grant No. 04-02-16684). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Применение ускорителей в радиационных технологиях Synchrotron radiation losses in laser-plasma accelerators Потери, связанные с синхротронным излучением, в плазменных ускорителях Втрати, пов'язані із синхротронним випромінюванням, у плазмових прискорювачах Article published earlier |
| spellingShingle | Synchrotron radiation losses in laser-plasma accelerators Kostyukov, I.Yu. Nerush, E.N. Pukhov, A. Применение ускорителей в радиационных технологиях |
| title | Synchrotron radiation losses in laser-plasma accelerators |
| title_alt | Потери, связанные с синхротронным излучением, в плазменных ускорителях Втрати, пов'язані із синхротронним випромінюванням, у плазмових прискорювачах |
| title_full | Synchrotron radiation losses in laser-plasma accelerators |
| title_fullStr | Synchrotron radiation losses in laser-plasma accelerators |
| title_full_unstemmed | Synchrotron radiation losses in laser-plasma accelerators |
| title_short | Synchrotron radiation losses in laser-plasma accelerators |
| title_sort | synchrotron radiation losses in laser-plasma accelerators |
| topic | Применение ускорителей в радиационных технологиях |
| topic_facet | Применение ускорителей в радиационных технологиях |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78874 |
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