About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator
An analysis of the dependence of the acceleration rate of charged particles by a surface wave arising when a laser pulse/(plane wave) is incident on the interface between two dielectric media on the phase velocity of the excited wave is carried out. It is shown that at resonance acceleration this de...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1956372023-12-05T19:33:56Z About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator Bolshov, O.O. Vasiliev, A.V. Povrozin, A.I. Sotnikov, G.V. Novel and non-standard acceleration technologies An analysis of the dependence of the acceleration rate of charged particles by a surface wave arising when a laser pulse/(plane wave) is incident on the interface between two dielectric media on the phase velocity of the excited wave is carried out. It is shown that at resonance acceleration this dependence has a maximum, for ultra-relativistic particles the acceleration rate tends to zero. The dependences of the acceleration rate on the phase velocity of the excited wave for various refractive indices (dielectric permittivities) of optically transparent medias are investigated analytically and numerically. Проведено аналіз залежності темпу прискорення заряджених частинок поверхневої хвилею, що виникає при падінні лазерного імпульсу/(плоскої хвилі) на межу розділу двох середовищ, від фазової швидкості хвилі, що збуджується. Показано, що при резонансному прискоренні ця залежність має максимум, для ультрарелятивістських частинок темп прискорення прагне до нуля. Аналітично та чисельно досліджено залежності темпу прискорення від фазової швидкості хвилі, що збуджується, для різних показників заломлення (діелектричної проникності) оптично прозорих матеріалів. Проведен анализ зависимости темпа ускорения заряженных частиц поверхностной волной, возникающей при падении лазерного импульса/(плоской волны) на границу раздела двух сред, от фазовой скорости возбуждаемой волны. Показано, что при резонансном ускорении эта зависимость имеет максимум, для ультрарелятивистских частиц темп ускорения стремится к нулю. Аналитически и численно исследованы зависимости темпа ускорения от фазовой скорости возбуждаемой волны для различных показателей преломления (диэлектрических проницаемостей) оптически прозрачных материалов. 2021 Article About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator / O.O. Bolshov, A.V. Vasiliev, A.I. Povrozin, G.V. Sotnikov // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 57-60. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 41.75.Lx, 41.60.-m, 41.75.Ht, 41.85.Ar DOI: https://doi.org/10.46813/2021-136-057 http://dspace.nbuv.gov.ua/handle/123456789/195637 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Novel and non-standard acceleration technologies Novel and non-standard acceleration technologies |
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Novel and non-standard acceleration technologies Novel and non-standard acceleration technologies Bolshov, O.O. Vasiliev, A.V. Povrozin, A.I. Sotnikov, G.V. About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator Вопросы атомной науки и техники |
| description |
An analysis of the dependence of the acceleration rate of charged particles by a surface wave arising when a laser pulse/(plane wave) is incident on the interface between two dielectric media on the phase velocity of the excited wave is carried out. It is shown that at resonance acceleration this dependence has a maximum, for ultra-relativistic particles the acceleration rate tends to zero. The dependences of the acceleration rate on the phase velocity of the excited wave for various refractive indices (dielectric permittivities) of optically transparent medias are investigated analytically and numerically. |
| format |
Article |
| author |
Bolshov, O.O. Vasiliev, A.V. Povrozin, A.I. Sotnikov, G.V. |
| author_facet |
Bolshov, O.O. Vasiliev, A.V. Povrozin, A.I. Sotnikov, G.V. |
| author_sort |
Bolshov, O.O. |
| title |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| title_short |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| title_full |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| title_fullStr |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| title_full_unstemmed |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| title_sort |
about the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2021 |
| topic_facet |
Novel and non-standard acceleration technologies |
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http://dspace.nbuv.gov.ua/handle/123456789/195637 |
| citation_txt |
About the acceleration rate of relativistic beams by a surface wave in a dielectric laser accelerator / O.O. Bolshov, A.V. Vasiliev, A.I. Povrozin, G.V. Sotnikov // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 57-60. — Бібліогр.: 18 назв. — англ. |
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Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2021. № 6(136) 57
https://doi.org/10.46813/2021-136-057
ABOUT THE ACCELERATION RATE OF RELATIVISTIC BEAMS
BY A SURFACE WAVE IN A DIELECTRIC LASER ACCELERATOR
O.O. Bolshov, A.V. Vasiliev, A.I. Povrozin, G.V. Sotnikov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: sotnikov@kipt.kharkov.ua
An analysis of the dependence of the acceleration rate of charged particles by a surface wave arising when a la-
ser pulse/(plane wave) is incident on the interface between two dielectric media on the phase velocity of the excited
wave is carried out. It is shown that at resonance acceleration this dependence has a maximum, for ultra-relativistic
particles the acceleration rate tends to zero. The dependences of the acceleration rate on the phase velocity of the
excited wave for various refractive indices (dielectric permittivities) of optically transparent medias are investigated
analytically and numerically.
PACS: 41.75.Lx, 41.60.-m, 41.75.Ht, 41.85.Ar
INTRODUCTION
The idea of dielectric laser accelerators (DLA), to
use dielectric structures for acceleration by waves aris-
ing from their illumination with laser beams, arose in
the last century [1 - 2]. Subsequent investigations
showed the possibility of creating on the basis of this
idea compact accelerators with aacceleration rate of
~ 1 GeV/m [3 - 8]. Interest in the use of laser beams to
accelerate charged particles has renewed in the last dec-
ade due to the widespread use of lasers at the TW level
of the micron wavelength and pulse durations 100fs and
less. Progress in laser technology has made it possible to
proceed to experimental verification and implementa-
tion of the basic principles of accelerators based on die-
lectric structures (see [9 - 12] and reference there).
The existing in NSC KIPT the TW laser system [13]
also makes it possible to carry out research on laser ac-
celeration in dielectric or chip structures. Due to the
phase mismatch between the accelerated beam and the
laser-excited wave, the creation of an operating acceler-
ator will inevitably require its sectioning with different
input beam energies. Our numerical simulation of the
acceleration of beams in chip structures did not reveal a
significant difference in the acceleration rates as a func-
tion of the initial beam energy [14, 15]. At the same
time, it was stated in paper [2], and it was theoretically
shown in paper [3] that for ultra-relativistic electrons the
acceleration rate tends to zero,
2
0 01 1/accE ,
0 is a phase velocity of incident wave. Similar de-
pendence on relativistic factor
0 is also given in [16,
17] when studying DLA based on chip or grating struc-
tures.
The pointed out dependence strongly limits the pos-
sibilities of using the DLA scheme in the relativistic
region of energies of the accelerated beams. In order to
study the exact dependence of the acceleration rate on
the beam energy and mitigate the limitations in the rela-
tivistic region, we, following the statement of problem
[3], will obtain the amplitude of the transmitted wave
when the plane wave is incident on the dielectric-
vacuum interface and will investigate it dependence on
the beam velocity and dielectric material.
1. STATEMENT OF THE PROBLEM
AND BASE EQUATIONS
Let an elliptically polarized plane wave falls from a
optically transparent medium with refractive index
n1= n under an angle onto the boundary between the
vacuum and this medium. Geometry of the problem and
the coordinate system is given in Fig. 1. For simplicity
of perception in Fig. 1 are depicted only electromagnet-
ic fields components corresponding to the case of p-
polarized plane wave. The boundary surface is the plane
y = 0, the incident plane is xz-plane, and the x-axis is
directed along the propagation of accelerated beam. In
such a frame the components of the electric vector of
the incident arbitrary elliptical wave will be of the form
Fig. 1. Geometry of the problem and coordinate system.
Here is shown the case of p-polarized plane wave
is incident from dielectric medium ( 0y , refractive
index 1n n ) on the dielectric-vacuum interface (y=0).
The accelerated electron beam moves parallel
to the dielectric-vacuum boundary
0 2 || 2
0 2 || 2
1
exp[ ( )] cos exp[ ( )];
exp[ ( )] sin exp[ ( )];
exp[ ( )],
i i
x x
i i
y y
i
z
E E i E i
E E i E i
E E i
(1)
where 1 1 2 12x y xk x k y t k x k y t , ||E and
E are amplitudes of p- and s-polarized waves and 1
and 2 are their arbitrary phases.
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 58
If sin 1/ n the incident electromagnetic wave un-
dergoes total internal reflection and sin sin 1n .
Then the analytical continuation of Snell's law to the
complex plane provides for the wave vector of the
transmitted wave
2 2
2 2
2 2
sin , sin 1x yk n k i n
, (2)
is the vacuum wavelength.
Having used the Fresnel formulae for the transmis-
sion coefficients separately for p-polarized, s-polarized
wave obtain their expressions for the case total internal
reflection
||
||
2 2 2 2
2 cos( )
1 sin cos ( )
in
T e
n n
, (3)
2
2 cos( )
1
in
T e
n
. (4)
Here
2 2
||
sin 1
( )
cos( )
n n
tg
,
2 2sin 1
( )
cos( )
n
tg
n
.
Using equations (1), (3), (4) the components of the
electric field can be written as
|| || 2 ||
|| || 2 ||
1
cos( )exp[ ( )],
sin( )exp[ ( )],
exp[ ( )],
t
x
t
y
t
z
E T E i
E T E i
E E T i
(5)
where 2 2sin( ) sin 1n x i n t
с с
.
Separating the real part from expressions (5), we ob-
tain the final expressions for the components of the
electric field of transmitted wave
2
|| 2 0 2
|| 2 2 1 1
1 sin( ),
cos( ), cos( ),
t
x
t t
y z
E E F
E E F E E F
(6)
and for components of the magnetic field
21
0 1
0
1
1 || 2 0 2
0
1 sin( ),
cos( ), cos( ).
t
x
t t
y z
F
H E
F
H E H E F
(7)
In equations (6), (7)
2 2
1
2
2
2
2 2 2 2
2 2
1 1
2 2 || 0
2 cos( ) 2
exp sin ( ) 1 ,
1
2 sin( )cos( )
1 sin ( ) cos
2
exp sin ( ) 1 ,
2
[ sin( ) ] ,
2 1
[ sin( ) ] , .
sin( )
n
F n y
n
n
F
n n
n y
n x ct
n x ct
n
. (8)
The equations give the possibility to investigate the
dependence of amplitude of transmitted wave on phase
velocity surface wave 0 arising when plane wave is
incident to dielectric boundary interface undergoing the
total internal reflection. It should be pointed that the
expressions for the components of the electromagnetic
fields of transmitted wave (6)-(8) coincide in form with
given in [3]. More general case, when the angle between
incident wave and direction of beam propagation is arbi-
trary, considered in [8]. However in the limiting case of
zeroth this angle (this case correspond to the highest
acceleration rate) the expressions [8] go to equations
(6)-(8).
2. NUMERICAL ANALYSIS
As stated above, we will be interested in the depend-
ence of the acceleration rate on the phase velocity of the
synchronous wave, or on the initial beam energy. For
beams propagating parallel to the dielectric-vacuum
interface in the x-axis direction, this acceleration rate
Gmax is determined by the amplitude of the longitudinal
electric field component
2
max || 2 0 0 ||( ) 1 acG qE F qE F . (9)
In Fig. 2 are shown the dependencies of the ampli-
tude of transverse component F2 and longitudinal com-
ponent Fac of transmitted wave from phase velocity of
the excited wave at the boundary surface y = 0
for the
dielectric material of fused silica 1.453n .
Fig. 2. Amplitude of transverse component F2
(at the
top) and longitudinal component Fac (at the bottom)
of transmitted wave at the boundary surface versus
phase velocity of the excited surface wave.
Permittivity of dielectric is = 2.112 (fused silica)
From Fig. 2 follows that the transverse component
amplitude of transmitted wave monotonically increases
over entire interval of permitted 0
when increase the
phase velocity of excited surface wave. At the same
time the longitudinal electric field increases from
0 1/ 0.7n to 0 0.858 (this corresponds electron
beam energy Wb 0.5 MeV) and then falls quickly to
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 59
zero
1
. When Wb 2.1 MeV
(
0 0.858 ) acceleration
rate decreases twice.
If we chose a different distance over the dielectric
plane the then dependencies of transverse component F2
and longitudinal component Fac remain qualitatively the
same (Fig. 3 for y = /2). The maximum of accelerated
field is shifted to greater beam energies (compare with
Fig. 2) and corresponds to beam energy Wb 1.6 MeV
(0 = 0.97). At Wb 50 MeV acceleration rate falls by
10 times in comparison with the maximum.
Fig. 3. Amplitude of transverse component F2 (at the
top) and longitudinal component Fac (at the bottom)
of transmitted wave at y = /2
versus phase velocity
of the excited surface wave. Permittivity of dielectric
is = 2.112 (fused silica)
Now let us study the behavior of the longitudinal
component of the electric field with a change in the die-
lectric medium. In Fig. 4 are shown the dependencies
Fac on the phase velocity of excited surface wave for
some optically transparent material: fused silica, sap-
phire, diamond, schott-IG, gallium indium arsenide and
silicon-germanium. With an increase in the dielectric
constant, the acceleration rate increases over the entire
range of permitted phase velocities of the wave (the top
graph), and its maximum shifts towards higher values of
the phase velocity (the bottom graph). The latter result
is especially important when accelerating more energet-
ic electron beams. For case of silicon-germanium medi-
um at Wb 50 MeV acceleration rate falls by 8 times in
comparison with the maximum.
Let us estimate the value of acceleration rate (9) in
the best case from the presented in Fig. 4, the case of
use for DLA of silicon-germanium medium.
1
While writing this paper we found that alike plotsare
given in the paper [18].
Fig. 4. Amplitude longitudinal component Fac (at the
bottom) of transmitted wave at y = /2
versus phase
velocity of the excited surface wave: 1 – fused silica
= 2.112 red line; 2 – sapphire = 3.1329 blue
dotted line; 3 – diamond = 5.76 green dashed line;
4 – schott-IG = 6.7081 violet dot-dash line; 5 – gal-
lium indium arsenide = 11.05496 cyan line; 6 – sili-
con-germanium = 20.196036 brown dotted line
Let the amplitude of incident wave is 1.82 GeV/m (this
corresponds the vacuum power density of 4.410
11
W/cm
2
).
In the maximum of acceleration rate (beam energy is
2.4 MeV) the acceleration rate is 1.3 GeV/m. At Wb
50 MeV acceleration rate is 160 MeV/m.
CONCLUSIONS
I this paper the dependence of the acceleration rate
of charged particles by a surface wave arising when a
laser pulse/(plane wave) is incident on the interface be-
tween two dielectric media on the phase velocity of the
excited wave is studied.
The dependences of the acceleration rate on the
phase velocity of the excited wave for various refractive
indices (dielectric permittivities) of optically transparent
medias are investigated analytically and numerically.
At resonance acceleration these dependencies have
the maximum, for ultra-relativistic particles the acceler-
ation rate tends to zero. Maximum of acceleration rate
increases when refractive index increases.
Maximum of acceleration rate shifts to higher initial
energy of electrons when refractive index increases.
This result is very important for DLA using for beam
acceleraton the surface wave arising when laser beam is
incident onto dielectric-vacuum boundary under the
angle of total internal reflection.
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 60
The applicability of the conclusion about a decrease
in the acceleration rate when using ultra-relativistic
electronic beams to accelerators using a chip or grating
structures requires a separate study.
ACKNOWLEDGEMENTS
The study is supported by the National Research Foun-
dation of Ukraine under the program "Leading and Young
Scientists Research Support" (project # 2020.02/0299), by
NAS of Ukraine program "Perspective investigations on
plasma physics, controlled thermonuclear fusion and
plasma technologies", project P-1/63-2020.
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Article received 09.10.2021
О ТЕМПЕ УСКОРЕНИЯ РЕЛЯТИВИСТСКИХ ПУЧКОВ ПОВЕРХНОСТНОЙ ВОЛНОЙ
В ДИЭЛЕКТРИЧЕСКОМ ЛАЗЕРНОМ УСКОРИТЕЛЕ
А.О. Большов, А.В. Васильев, А.И. Поврозин, Г.В. Сотников
Проведен анализ зависимости темпа ускорения заряженных частиц поверхностной волной, возникающей
при падении лазерного импульса/(плоской волны) на границу раздела двух сред, от фазовой скорости воз-
буждаемой волны. Показано, что при резонансном ускорении эта зависимость имеет максимум, для ультра-
релятивистских частиц темп ускорения стремится к нулю. Аналитически и численно исследованы зависимо-
сти темпа ускорения от фазовой скорости возбуждаемой волны для различных показателей преломления
(диэлектрических проницаемостей) оптически прозрачных материалов.
ПРО ТЕМП ПРИСКОРЕННЯ РЕЛЯТИВІСТСЬКИХ ПУЧКІВ ПОВЕРХНЕВОЮ ХВИЛЕЮ
У ДІЕЛЕКТРИЧНОМУ ЛАЗЕРНОМУ ПРИСКОРЮВАЧІ
О.О. Большов, А.В. Васильєв, А.І. Поврозін, Г.В. Сотніков
Проведено аналіз залежності темпу прискорення заряджених частинок поверхневої хвилею, що виникає
при падінні лазерного імпульсу/(плоскої хвилі) на межу розділу двох середовищ, від фазової швидкості хви-
лі, що збуджується. Показано, що при резонансному прискоренні ця залежність має максимум, для ультра-
релятивістських частинок темп прискорення прагне до нуля. Аналітично та чисельно досліджено залежності
темпу прискорення від фазової швидкості хвилі, що збуджується, для різних показників заломлення (діелек-
тричної проникності) оптично прозорих матеріалів.
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