Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code
A 2D axially symmetrical hybrid PIC code is developed to study transformation of the laser energy into x-rays in plasma. A quasistatic approximation (the plasma wake is assumed to be slowly changed in a laser pulse frame) is used to accelerate computation. A comparison with simulation results obta...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Цитувати: | Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code / I. Kostyukov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 154-156. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-798772015-04-07T03:02:08Z Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code Kostyukov, I. Применение ускорителей в радиационных технологиях A 2D axially symmetrical hybrid PIC code is developed to study transformation of the laser energy into x-rays in plasma. A quasistatic approximation (the plasma wake is assumed to be slowly changed in a laser pulse frame) is used to accelerate computation. A comparison with simulation results obtained with a fully 3D electromagnetic PIC code is performed Для моделирования трансформации лазерного излучения разработан двухмерный аксиально-симметричный гибридный численный код, использующий метод частиц в ячейках. В качестве упрощающего предположения использовалось "квазистатическое" приближение (плазменная волна медленно меняется в системе отсчета, связанной с лазерным импульсом). Проведено сравнение с результатами моделирования с помощью полностью трехмерного, электромагнитного кода, использующего метод частиц в ячейках. Для моделювання трансформації лазерного випромінювання розроблено двомірний аксіально- симетричний гібридний чисельний код, що використовує метод часток в осередках. Як припущення, що спрощує, використано "квазістатичне" наближення (плазмова хвиля повільно міняється в системі відліку, пов'язаної з лазерним імпульсом). Проведено порівняння з результатами моделювання за допомогою повністю тривимірного, електромагнітного коду, що використає метод часток в осередках. 2006 Article Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code / I. Kostyukov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 154-156. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 41.60.Ap, 52.40.Mj http://dspace.nbuv.gov.ua/handle/123456789/79877 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Применение ускорителей в радиационных технологиях Применение ускорителей в радиационных технологиях |
| spellingShingle |
Применение ускорителей в радиационных технологиях Применение ускорителей в радиационных технологиях Kostyukov, I. Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code Вопросы атомной науки и техники |
| description |
A 2D axially symmetrical hybrid PIC code is developed to study transformation of the laser energy into x-rays in
plasma. A quasistatic approximation (the plasma wake is assumed to be slowly changed in a laser pulse frame) is
used to accelerate computation. A comparison with simulation results obtained with a fully 3D electromagnetic PIC
code is performed |
| format |
Article |
| author |
Kostyukov, I. |
| author_facet |
Kostyukov, I. |
| author_sort |
Kostyukov, I. |
| title |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| title_short |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| title_full |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| title_fullStr |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| title_full_unstemmed |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| title_sort |
simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2006 |
| topic_facet |
Применение ускорителей в радиационных технологиях |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/79877 |
| citation_txt |
Simulation of laser-plasma synchrotron radiation source by a relativistic hybrid code / I. Kostyukov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 154-156. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kostyukovi simulationoflaserplasmasynchrotronradiationsourcebyarelativistichybridcode |
| first_indexed |
2025-07-06T03:49:46Z |
| last_indexed |
2025-07-06T03:49:46Z |
| _version_ |
1836867950392377344 |
| fulltext |
SIMULATION OF LASER-PLASMA SYNCHROTRON RADIATION
SOURCE BY A RELATIVISTIC HYBRID CODE
I. Kostyukov
Institute of Applied Physics RAS, Nizhny Novgorod, 603950, Russia
E-mail: kost@appl.sci-nnov.ru
A 2D axially symmetrical hybrid PIC code is developed to study transformation of the laser energy into x-rays in
plasma. A quasistatic approximation (the plasma wake is assumed to be slowly changed in a laser pulse frame) is
used to accelerate computation. A comparison with simulation results obtained with a fully 3D electromagnetic PIC
code is performed.
PACS: 41.60.Ap, 52.40.Mj
The generation and application of high-brightness
X-rays is a fast developing area of science and technolo-
gy [1]. Diverse demands of multidisciplinary research
(fast process probing, biology object imaging, investiga-
tion of chemical reactions, etc.), as well as industrial
and medical applications, drive the quest for intense and
compact x-ray sources. Contemporary synchrotrons
equipped with wiggler magnets are the most intense
X-ray sources available now. High cost and large-scale
significantly suppress the wide use of those sources.
It has been recently predicted that part of the cold
plasma electrons can be trapped by plasma wake and ac-
celerated up to very high energy [2, 3]. Later this mech-
anism, called Bubble acceleration, has been observed
experimentally [4]. In Bubble regime, the plasma wake
is the solitary plasma cavity (Bubble), which is free
from cold plasma electrons, behind the laser pulse. The
trapped plasma electrons or external electron beam is
accelerated and simultaneously undergoes betatron os-
cillations in the Bubble. They efficiently radiate X-rays
due to the betatron wiggling.
Therefore, the laser-plasma X-ray source combines
the acceleration and wiggling processes. Moreover, it
dramatically downsizes the radiation source. The laser-
plasma acceleration system is very compact (several
meters) compared with that of conventional syn-
chrotrons or free electron lasers (hundreds meters) while
the effective plasma wiggler is also small (several cen-
timeters) compared to the magnet wiggler (tens meters).
Since the ultrahigh intensity laser-plasma interaction
is strongly nonlinear phenomenon, which is rich in com-
plex processes, the theoretical analysis of this phe-
nomenon is very difficult. The numerical simulation is
still very important and powerful tool for the interaction
investigation as well as the interpretation of the laser-
plasma experiments. The most efficient numerical meth-
od for simulation of laser-plasma interaction among
various numerical schemes is particle in cell (PIC)
method [5]. However, this method requires a lot of com-
puter resources for simulation of full-scale experiments.
Several quick PIC codes with so-called quasistatic ap-
proximation [6] have been developed [7, 8] to accelerate
computer simulations. In this paper we present a quick
PIC code with quasistatic approximation for simulation
of laser-plasma synchrotron radiation.
Let a laser pulse propagates along x -axis, and two-
dimensional axially symmetrical geometry is adopted.
The ions are considered to be immobile. It is assumed in
the framework of quasistatic approximation that the
plasma quickly responds on laser field, and plasma
fields are the functions of r and ctx −=ξ , where c is
the speed of light. The characteristic times of the laser
pulse and the bunch of the trapped electrons are much
longer than the plasma response time. Fist, plasma re-
sponse is calculated, then the evolution of the laser
pulse and bunch is found in the plasma field distribu-
tion, and then again plasma response is calculated for
the new shape of the bunch and the pulse.
Like in PIC codes plasma is modelled by macro-
particles. Each plasma macroparticle is determined by a
longitudinal coordinate, ξ , a transverse coordinate, r ,
momentum components, rp and xp , a mass m , and a
charge q . All particle parameters are functions of ξ ,
thus, ξ plays a role of time. Unlike PIC technique, the
plasma macroparticles are the Langragian particles,
which move along trajectory line determined by the ini-
tial value of transversal coordinate, 0r . Information
propagates from the head of laser pulse ( 0=ζ ) to nega-
tive values of ζ within the light speed frame. Accord-
ingly, we integrate equation of motion slice by slice
from 0=ζ to L−=ζ , where L is the length of the
simulation region. The plasma is assumed to be cold
that is 0=rp and 0=xp at 0=ζ .
Introducing a plasma wake potential xA−=Φ ϕ , the
equations for the wake potentials and magnetic filed in
quasistatic approximations in axially symmetrical ge-
ometry (no dependence on azimuthal angle θ ) are
ρ−=Φ∆ ⊥ xj , (1)
,1
2
2
xjrB
rr
+Φ
∂
∂=
∂
∂
ξ
θ , (2)
where the gauge xA−=ϕ is used, ϕ is the scalar poten-
tial, A is the vector potential, θB is the azimuthal mag-
netic filed, j is the density of electron current, ρ is the
electron density. We use dimensionless units, normaliz-
ing the time by pω/1 , the velocity by the speed of light c
, the lengths by pc ω/ , the electromagnetic fields by
qmc p /ω− , the electron density n by the background
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p. 154-156.154
density 0n , ( ) 2/1
0
2 /4 mnqp πω = is the plasma frequen-
cy. The obtained equations are similar to that in Ref. [7].
In quasistatic approximations
1=Φ+−= xpH γ , (3)
is the integral of motion [3], where
( ) 2/12221 app rx +++=γ is the relativistic gamma-
factor of the electron, 2a is the ponderomotive po-
tential of the laser pulse [7]. xp and γ can be found as
functions of ξ , r , rp and 2
la from Eq. (3). The equa-
tions of plasma macroparticle motion are [7]
θγ
ξ
B
r
a
rd
dpr −
∂
∂
−
∂
Φ∂
Φ+
=
2
2
1
1
1
, (4)
Φ+
=
1
rp
d
dr
ξ
. (5)
Making the use of Eqs. (4) and (5), the current den-
sity and the electron density can be found by the way
adopted in PIC methods [5]. Eqs. (1)-(5) are solved using
a finite difference scheme, in which a grid is set up in
both the axial coordinate ξ and the radial coordinate r .
The evolution of the laser fired is described by a
parabolic equation (see in more detail Ref. [7]). A parti-
cle is considered to be trapped if longitudinal velocity of
the particle is more than the bubble velocity bx vv > .
The bubble velocity is calculated from the solution of
equation for dynamics of the laser pulse. The dynamics
of the particle trapped is described by equations
[ ]( ) radv
q
dt
d FBvEp +×+
−
=
1
, (6)
γ
rp
dt
dr = , b
x v
p
dt
d −=
γ
ξ
, (7)
where radF is the radiation reaction force [9]. The
emission of electromagnetic fields by the trapped elec-
trons is included into the code. The emitted radiation ex-
erts recoil on the electron. The recoil force is also in-
cluded. The radiation generation and recoil force are
taken into account only for the trapped particle because
they are only the highly relativistic particles given the
main contribution into the radiated power. The reversal
effect of trapped electrons on the plasma wake is taken
into account as well.
We verified that the code developed gave the results,
which were similar to that obtained by a fully 3D rela-
tivistic PIC code [5] in a strongly nonlinear regime. For
simplicity, we consider the laser-plasma interaction ne-
glecting the trapped particle and the evolution of laser
pulse. This regime corresponds to the beginning of the
interaction when a laser pulse changes insignificantly
and number of the particles trapped is small. The inci-
dent laser pulse is circularly polarized, has the Gaussian
envelope ( )2222
0 //exp ll Lrraa ξ−−= , and the wave-
length 82.0=λ μm. The parameters of the laser pulse
are 5=lr , 2=lL , 100 =a . The pulse propagates in plas-
ma with the density 19
0 10−=n cm-3. The result of simu-
lation is shown in Fig.1. It presents the density plot of
the short, ultrahigh intensity laser pulse propagating in
plasma, calculated by (a) the axially symmetrical 2D
PIC hybrid code; (b) the fully 3D PIC code [5]. The
darker is gray color, the higher is the electron density. It
is seen from Fig.1 that the results obtained are in a good
agreement with the simulation results obtained by the
fully 3D PIC code.
Fig.1. The density plot of short, ultrahigh intensity laser
pulse propagating in plasma, calculated by (a) axially
symmetrical 2D PIC hybrid (b) by fully 3D PIC code
[5]. The darker is gray color, the higher is electron
density
To simulate the X-ray generation we assume that the
electron radiation spectrum is synchrotron like at any
given moment of time. The spectrum integrated over a
solid angle is defined by a universal function )/( cS ωω ,
where ∫
∞
=
x
dyyKxxS )()( 3/5 , cω is the critical frequency
[9]. The critical frequency is given by the relation
( ) ⊥= Fc
22/3 γω ; ⊥F is the transversal to the electron
momentum force. In our code, we follow trajectories of
each electron and calculate the emission during the in-
teraction.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p. 154-156.155
190
-20
20
-20
20
0 19
r
x-t
x-t
a)
b)
las
er
pulse
laser
pulse
laser
pulse
We simulate the X-ray emission from an external
electron bunch with 310=γ , length 40=bL , radius
3=br with total charge 4=bQ nC, propagating in the
bubble. The photon flux, XF , (photon number per sec-
ond in 0.1% bandwidth) from the bunch as a function of
the photon energy is shown in Fig.2. The photon flux
obtained is in a good agreement with estimations for the
flux [1].
Fig.2. The photon flux as function of the photon energy
CONCLUSION
The X-ray generation from a relativistic electron
bunch propagating in the laser plasma is modeled by the
2D axially symmetrical hybrid PIC code. The quasistat-
ic approximation is used to accelerate the computation.
The code includes the emission of electromagnetic field
by the relativistic electrons. The emitted radiation exerts
recoil on the electron and the recoil force is included
into the code. The results obtained are in a good agree-
ment with that obtained by the fully 3D electromagnetic
PIC [5].
This work has been supported by Russian Founda-
tion for Basic Research (Grant No. 04-02-16684).
REFERENCES
1. S. Kiselev, A. Pukhov and I. Kostyukov. X-ray
generation in strongly nonlinear plasma waves //
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3. I. Kostyukov, A. Pukhov and S. Kiselev. Phe-
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№14, p.5256-5264.
4. J. Faure, Y. Glinek, A. Pukhov et al. A laser-plasma
accelerator producing monoenergetic electron beam
// Nature. 2004, v.431, №9, p.541-544.
5. A. Pukhov. VLPL // Journal of Plasma Physics.
1999, v.61, №10, p. 425-428.
6. P. Sprangle, E. Esarey, and A. Ting. Nonlinear in-
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cal Review A. 1990, v.41, №8, p.4463-4469.
7. P. Mora and T.M. Antonsen. Kinetic modeling of
intense, short laser pulses propagating in tenious
plasmas // Physics of Plasmas. 1997, v.4, №1,
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8. K.V. Lotov. Fine wakefield structure in the blowout
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МОДЕЛИРОВАНИЕ ИСТОЧНИКА СИНХРОТРОННОГО ИЗЛУЧЕНИЯ, ОСНОВАННО-
ГО НА ПРЕОБРАЗОВАНИИ ЛАЗЕРНОГО ИЗЛУЧЕНИЯ В ПЛАЗМЕ, ДВУХМЕРНЫМ
РЕЛЯТИВИСТСКИМ ГИБРИДНЫМ КОДОМ
И.Ю. Костюков
Для моделирования трансформации лазерного излучения разработан двухмерный аксиально-симметрич-
ный гибридный численный код, использующий метод частиц в ячейках. В качестве упрощающего предполо-
жения использовалось "квазистатическое" приближение (плазменная волна медленно меняется в системе от-
счета, связанной с лазерным импульсом). Проведено сравнение с результатами моделирования с помощью
полностью трехмерного, электромагнитного кода, использующего метод частиц в ячейках.
МОДЕЛЮВАННЯ ДЖЕРЕЛА СИНХРОТРОННОГО ВИПРОМІНЮВАННЯ,
ЗАСНОВАНОГО НА ПЕРЕТВОРЕННІ ЛАЗЕРНОГО ВИПРОМІНЮВАННЯ В ПЛАЗМІ,
ДВОМІРНИМ РЕЛЯТИВІСТСЬКИМ ГІБРИДНИМ КОДОМ
І.Ю. Костюков
Для моделювання трансформації лазерного випромінювання розроблено двомірний аксіально-
симетричний гібридний чисельний код, що використовує метод часток в осередках. Як припущення, що
спрощує, використано "квазістатичне" наближення (плазмова хвиля повільно міняється в системі відліку,
пов'язаної з лазерним імпульсом). Проведено порівняння з результатами моделювання за допомогою
повністю тривимірного, електромагнітного коду, що використає метод часток в осередках.
102
2
1
, eV
F x, (
10
15
·с
-1
)
0
104
156
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p. 154-156.157
Моделирование источника синхротронного излучения, основанного на преобразовании лазерного излучения в плазме, двухмерным релятивистским гибридным кодом
МОДЕЛЮВАННЯ ДЖЕРЕЛА СИНХРОТРОННОГО ВИПРОМІНЮВАННЯ, ЗАСНОВАНОГО НА ПЕРЕТВОРЕННІ ЛАЗЕРНОГО ВИПРОМІНЮВАННЯ В ПЛАЗМІ, ДВОМІРНИМ РЕЛЯТИВІСТСЬКИМ ГІБРИДНИМ КОДОМ
|