Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma
Acceleration in a plasma wake field is simulated with 2D axially symmetric hybrid PIC code. The dependence of the parameters of the accelerated electrons on the laser pulse duration (at a given pulse energy) is studied and the range of pulse duration values for efficient electron acceleration is f...
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| Zitieren: | Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma / I.Yu. Kostyukov, N.V. Vvedenskii // Вопросы атомной науки и техники. — 2006. — № 2. — С. 70-72. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-787692015-03-21T03:02:02Z Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma Kostyukov, I.Yu. Vvedenskii, N.V. Линейные ускорители заряженных частиц Acceleration in a plasma wake field is simulated with 2D axially symmetric hybrid PIC code. The dependence of the parameters of the accelerated electrons on the laser pulse duration (at a given pulse energy) is studied and the range of pulse duration values for efficient electron acceleration is found. В настоящей работе процессы ускорения электронов в кильватерной волне моделируются с помощью двумерного аксиально-симметричного гибридного численного кода, использующего метод частиц в ячейках. На основании проведенных численных расчетов определены зависимости параметров ускоренных электронов от длительности лазерного импульса (при заданной его энергии) и найдены области оптимальных значений длительности импульса, отвечающие наиболее эффективной генерации ускоренных электронов. У дійсній роботі процеси прискорення електронів у кільватерній хвилі моделюються за допомогою двовимірного аксіально-симетричного гібридного чисельного коду, що використає метод часток в осередках. На підставі проведених чисельних розрахунків визначені залежності параметрів прискорених електронів від тривалості лазерного імпульсу (при заданій його енергії) і знайдені області оптимальних значень тривалості імпульсу, що відповідають найбільш ефективної генерації прискорених електронів. 2006 Article Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma / I.Yu. Kostyukov, N.V. Vvedenskii // Вопросы атомной науки и техники. — 2006. — № 2. — С. 70-72. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 41.60.Ap, 52.40.Mj http://dspace.nbuv.gov.ua/handle/123456789/78769 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Линейные ускорители заряженных частиц Линейные ускорители заряженных частиц |
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Линейные ускорители заряженных частиц Линейные ускорители заряженных частиц Kostyukov, I.Yu. Vvedenskii, N.V. Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma Вопросы атомной науки и техники |
| description |
Acceleration in a plasma wake field is simulated with 2D axially symmetric hybrid PIC code. The dependence of
the parameters of the accelerated electrons on the laser pulse duration (at a given pulse energy) is studied and the
range of pulse duration values for efficient electron acceleration is found. |
| format |
Article |
| author |
Kostyukov, I.Yu. Vvedenskii, N.V. |
| author_facet |
Kostyukov, I.Yu. Vvedenskii, N.V. |
| author_sort |
Kostyukov, I.Yu. |
| title |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| title_short |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| title_full |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| title_fullStr |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| title_full_unstemmed |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| title_sort |
pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2006 |
| topic_facet |
Линейные ускорители заряженных частиц |
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http://dspace.nbuv.gov.ua/handle/123456789/78769 |
| citation_txt |
Pic simulation of electron acceleration in a wake field generated by a high-power laser pulse in plasma / I.Yu. Kostyukov, N.V. Vvedenskii // Вопросы атомной науки и техники. — 2006. — № 2. — С. 70-72. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kostyukoviyu picsimulationofelectronaccelerationinawakefieldgeneratedbyahighpowerlaserpulseinplasma AT vvedenskiinv picsimulationofelectronaccelerationinawakefieldgeneratedbyahighpowerlaserpulseinplasma |
| first_indexed |
2025-07-06T02:49:26Z |
| last_indexed |
2025-07-06T02:49:26Z |
| _version_ |
1836864154242121728 |
| fulltext |
PIC SIMULATION OF ELECTRON ACCELERATION IN A WAKE
FIELD GENERATED BY A HIGH-POWER LASER PULSE IN PLASMA
I.Yu. Kostyukov, N.V. Vvedenskii
Institute of Applied Physics RAS, Nizhny Novgorod, 603950, Russia
E-mail: kost@appl.sci-nnov.ru
Acceleration in a plasma wake field is simulated with 2D axially symmetric hybrid PIC code. The dependence of
the parameters of the accelerated electrons on the laser pulse duration (at a given pulse energy) is studied and the
range of pulse duration values for efficient electron acceleration is found.
PACS: 41.60.Ap, 52.40.Mj
1. INTRODUCTION
When focused, petawatt laser pulses reach intensities
up to I=1021 W/cm2 and an electric field is E=1014 V/m
[1]. An appealing application for these laser fields is the
high-gradient acceleration of charged particles. Indeed,
would it be possible to use the petawatt laser field effi-
ciently, a TeV accelerator may have length of a few cen-
timeters only. T. Tajima and J. Dawson [2] have pro-
posed to convert the transverse laser field into the longi-
tudinal one of a plasma wave. The terawatt laser pulses
exert Gigabar pressures on plasma electrons, separating
them from ions and generating electric wake fields in
the order of TV/m. It appears that the most attractive for
wake field acceleration are laser pulses shorter than the
plasma wavelength.
Recently, impressive progress in the generation of
short quasi-monoenergetic bunch of ultra relativistic
electrons in laser plasma has been achieved [3]. One of
the models [4,5], describing generation of quasi-mo-
noenergetic bunch of ultra relativistic electrons, as-
sumes that the generation is caused by transition to
strongly nonlinear regime of laser-plasma interaction.
The fast plasma wave breaking occurs at this regime. As
a result, 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 can be trapped in the bubble.
The external electron bunch and the trapped electrons
can be accelerated up to very high energy.
Recent dramatic progress in laser pulse compression
makes generation of ultrashort ultrahigh intensity laser
pulses possible [6]. Therefore, it is important to study
the effect of the laser pulse duration on the acceleration
rate. The laser pulse energy is assumed to be un-
changed.
2. ACCELERATION THEORY
The one-dimensional electron dynamics in electro-
magnetic fields is governed by Hamiltonian
,)(1 2 ϕ−++= xx APH (1)
where xP is the canonical electron momentum, xA is
the vector potential, ϕ is the scalar potential. 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 pω , the electron densi-
ty n to the background density 0n ,
( ) 2/1
0
2 /4 mnep πω = is the plasma frequency, e and
m are the electron charge and electron mass, respective-
ly.
We consider the electron acceleration in the electro-
magnetic field of plasma wake generated by the laser
pulse. The electromagnetic potentials are the function of
tvx 0−=ξ , where 0v is the group velocity of the laser
pulse. If potentials are the function of ξ then Hamiltoni-
an (1) is not invariant of motion. We can change vari-
ables in the Hamiltonian from x and xP to ξ and
xPP =ξ by a canonical transformation with generating
function
( ) ( ) ξξ PtvxtxPS 0,, −= . (2)
The Hamiltonian in the new variables takes the form
transformation
( )[ ] ( ) xxx PvAPH 0
21 −−++= ξϕξ . (3)
Hamiltonian (3) does not depend on time and it is in-
variant of motion. It can be rewritten in the form
( ) constpvH x =−Φ−= 0ξγ , (4)
where 21 xp+=γ is the relativistic gamma-factor,
( ) xx AAv −≈−=Φ ϕϕξ 0 is the wake potential,
xxx APp += is the kinetic momentum. The gauge
xA−=ϕ (5)
is used.
The change in the electron energy in the ultrarela-
tivistic limit 1> >γ , when the electron passes the dis-
tance corresponding the change in the wake potential
∆ Φ , is
∆ Φ≈∆ 2
02γγ , (6)
where ( ) 2/12
00 1
−
−= vγ is the gamma-factor of the laser
pulse. It is seen from Eq. (5) that the electron energy
gain is proportional to the change in the wake potential
and to the square of the gamma-factor of the laser pulse.
3. SIMULATION RESULTS
We simulate the bubble generation by two-dimen-
sional relativistic particle-in-sell hybrid code in cyl-
indrical geometry. The quasistatic approximation (the
plasma wake is assumed to be slowly changed in the
laser pulse frame) is used to accelerate computation. It
___________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.70-72.70
follows from fully three-dimensional particle-in-cell
simulations [7] that the laser pulse change is not signifi-
cantly and the number of the trapped electrons is very
small when the electrons stay in accelerating phase. In
present simulation the dynamics of the laser pulse and
the effect of the trapped electrons on the bubble are ne-
glected.
Fig.1. Density plot of bubble generation by the laser
pulse with 1=lL , 1.140 =a (a); 2=lL , 100 =a (b);
5=lL , 3.60 =a (c). It is assumed constaLl =2
0
The incident laser pulse is circularly polarized, has
the Gaussian envelope ( )2 2 2 2
0 exp / /l la a r r Lξ= − − , and
the wavelength 82.0=λ μm. The parameter of the laser
pulse 5=lr . The pulse propagates in plasma with the
density 19
0 10=n cm-3. This laser pulse generates the
bubble. It is assumed constaLl =2
0 .
The density plot of bubble generated by the laser
pulse is shown in Fig.1, where 1=lL , 1.140 =a
(Fig.1,a); 2=lL , 100 =a (Fig.1,b); 5=lL , 3.60 =a
(Fig.1,c). It is seen from Fig.1 that the shortest laser
pulse generates the largest bubble. The simulation re-
sults is similar to that [4,5] obtained by fully three di-
mensional relativistic particle in cell code [8].
The wake potential peaks at the axis 0=r ( 0=Φ is
assumed at infinity) [5]. Therefore, the maximal change
in Φ is achieved if the electron moves along the axis
0=r . The wake potential of the bubbles at the axis
0=r shown in Fig.1 is presented in Fig.2.
Fig.2. Φ as function of ξ at the axis 0=r for the laser
pulse with 5=lL , 3.60 =a (line 1); 2=lL , 100 =a
(line 2); 1=lL , 1.140 =a (line 3)
It is seen from Fig.2 that the largest ∆ Φ is achieved
for shortest laser pulse. Thus, the electron energy gain
due to laser wake field acceleration is highest for the
shortest laser pulse.
4. CONCLUSIONS
It conclusions we study the effect of the laser pulse
duration on the laser wake field acceleration. The elec-
tron energy gain due to laser wake field acceleration is
highest for the shortest laser pulse.
It can be explained as follows. Inside the bubble the
electrons are absent while the ions are uniformly dis-
tributed. As a result the electric field is a linear function
of ξ while the wake potential is proportional to 2ξ [5].
The maximum of the accelerating field (in the bubble
boundary) as well as the maximum of the wake poten-
tial (in the bubble center) are proportional to the bubble
size. Therefore, high acceleration rate can be achieved
in the large bubble.
The shorter is the laser pulse the larger radius, where
the laser intensity is still high, and the bigger is the gen-
erated bubble (for given laser pulse energy). So, the
wake field acceleration is more efficient with laser pulse
as short as possible.
___________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.70-72.
25
0
0 20x-t
Φ
1
2
3
70
200
-20
20
r
x-t
b)
laser
pulse
200
-20
20
r
x-t
a)
laser
pulse
laser
pulse
200
-20
20
r
x-t
c)
The ponderomotive force concept is used to study
laser pulse duration effect. This concept is based on the
averaging over laser field periods. Therefore, our results
are valid not for very short pulses. The laser pulse
should contain many laser periods. More accurate analy-
sis is needed to study the interactions with ultrashort
laser pulse with a few laser periods.
Our results are obtained under assumptions that the
group velocity of the laser pulse does not depend on the
pulse duration. However, further investigations are
needed to study the effect of the pulse duration on the
group velocity.
This work has been supported in part by Russian
Foundation for Basic Research (Grant No. 04-02-16684,
No. 05-02-17367) and by Russian Science Support
Foundation.
REFERENCES
1. Gérard A. Mourou, Christopher P.J. Barty, and
Michael D. Perry. Ultrahigh-Intensity Lasers:
Physics of the Extreme on a Tabletop // Physics To-
day. 1998, №1, p.22-26.
2. A.T. Tajima and J. Dawson. Laser Electron Accel-
erators // Phys. Rev. Lett. 1979, v.43, №4, p.267-
270.
3. T. Catsoleas. Electrons hang ten on laser wake //
Nature. 2004, v.431, №9, p.515-516.
4. 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.
5. I. Kostyukov, A. Pukhov, and S. Kiselev. Phe-
nomenological theory of laser-plasma interaction in
bubble regime // Physics of Plasmas. 2004, v.11,
№14, p.5256-5264.
6. O. Shorokhov, A. Pukhov, and I. Kostyukov. Self-
Compression of Laser Pulses in Plasma // Phys.
Rev. Lett. 2004, v.91, №26, p.265002-1-265002-4.
7. S. Kiselev, A. Pukhov, and I. Kostyukov. X-ray
generation in strongly nonlinear plasma waves //
Phys. Rev. Lett. 2004, v.93, №13, p.135004-1-
135004-4.
8. A. Pukhov. Three-dimensional electromagnetic rel-
ativistic particle-in-cell code VLPL (Virtual Laser
Plasma Lab) // Journal of Plasma Physics. 1999,
v.61, №10, p.425-428.
МОДЕЛИРОВАНИЕ МЕТОДОМ ЧАСТИЦ В ЯЧЕЙКАХ УСКОРЕНИЯ ЭЛЕКТРОНОВ В КИЛЬВА-
ТЕРНОЙ ВОЛНЕ, ГЕНЕРИРУЕМОЙ МОЩНЫМ ЛАЗЕРНЫМ ИМПУЛЬСОМ В ПЛАЗМЕ
И.Ю. Костюков, Н.В. Введенский
В настоящей работе процессы ускорения электронов в кильватерной волне моделируются с помощью
двумерного аксиально-симметричного гибридного численного кода, использующего метод частиц в ячей-
ках. На основании проведенных численных расчетов определены зависимости параметров ускоренных элек-
тронов от длительности лазерного импульса (при заданной его энергии) и найдены области оптимальных
значений длительности импульса, отвечающие наиболее эффективной генерации ускоренных электронов.
МОДЕЛЮВАННЯ МЕТОДОМ ЧАСТОК В ОСЕРЕДКАХ ПРИСКОРЕННЯ ЕЛЕКТРОНІВ У
КІЛЬВАТЕРНІЙ ХВИЛІ, ГЕНЕРИРУЕМОЙ ПОТУЖНИМ ЛАЗЕРНИМ ІМПУЛЬСОМ У ПЛАЗМІ
І.Ю. Костюков, Н.В. Введенський
У дійсній роботі процеси прискорення електронів у кільватерній хвилі моделюються за допомогою
двовимірного аксіально-симетричного гібридного чисельного коду, що використає метод часток в
осередках. На підставі проведених чисельних розрахунків визначені залежності параметрів прискорених
електронів від тривалості лазерного імпульсу (при заданій його енергії) і знайдені області оптимальних
значень тривалості імпульсу, що відповідають найбільш ефективної генерації прискорених електронів.
62
Моделирование методом частиц в ячейках ускорения электронов в кильватерной волне, генерируемой мощным лазерным импульсом в плазме
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