Comparative analysis of acceleration gradients for chip structures with different refractive indices
The results of numerical studies of accelerating gradients in accelerators based on dielectric chip structures with different refractive indices, excited by a titanium-sapphire laser pulse, are presented. A comparative analysis of the influence of the refractive index on the rate of acceleration of...
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| Cite this: | Comparative analysis of acceleration gradients for chip structures with different refractive indices / A.V. Vasyliev, O.O. Bolshov, O.O. Svistunov, A.I. Povrozin, V.P. Zaitcev, V.P. Leshchenko, G.V. Sotnikov // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 75-79. — Бібліогр.: 25 назв. — англ. |
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Vasyliev, A.V. Bolshov, O.O. Svistunov, O.O. Povrozin, A.I. Zaitcev, V.P. Leshchenko, V.P. Sotnikov, G.V. 2023-12-05T17:39:08Z 2023-12-05T17:39:08Z 2021 Comparative analysis of acceleration gradients for chip structures with different refractive indices / A.V. Vasyliev, O.O. Bolshov, O.O. Svistunov, A.I. Povrozin, V.P. Zaitcev, V.P. Leshchenko, G.V. Sotnikov // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 75-79. — Бібліогр.: 25 назв. — англ. 1562-6016 PACS: 41.75.Jv, 41.75.Ht, 42.25.Bs DOI: https://doi.org/10.46813/2021-136-075 https://nasplib.isofts.kiev.ua/handle/123456789/195642 The results of numerical studies of accelerating gradients in accelerators based on dielectric chip structures with different refractive indices, excited by a titanium-sapphire laser pulse, are presented. A comparative analysis of the influence of the refractive index on the rate of acceleration of electron bunches is carried out. Promising materials for the manufacture of dielectric laser accelerators are proposed. Представлені результати чисельних досліджень прискорюючих градієнтів у прискорювачах на основі діелектричних ЧІП-структур з різними показниками заломлення, збуджуваних титан-сапфіровим лазерним імпульсом. Проведено порівняльний аналіз впливу показника заломлення на темп прискорення електронних згустків. Запропоновано перспективні матеріали для виготовлення діелектричних лазерних прискорювачів. Представлены результаты численных исследований ускоряющих градиентов в ускорителях на основе диэлектрических ЧИП-структур с различными показателями преломления, возбуждаемых титан-сапфировым лазерным импульсом. Проведен сравнительный анализ влияния показателя преломления на темп ускорения электронных сгустков. Предложены перспективные материалы для изготовления диэлектрических лазерных ускорителей. Work supported by The National Research Foundation of Ukraine, program "Leading and Young Scientists Research Support" (project # 2020.02/0299). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Novel and non-standard acceleration technologies Comparative analysis of acceleration gradients for chip structures with different refractive indices Порівняльний аналіз градієнтів прискорення для ЧІП-структур з різними показниками заломлення Сравнительный анализ градиентов ускорения для ЧИП-структур с различными показателями преломления Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Comparative analysis of acceleration gradients for chip structures with different refractive indices |
| spellingShingle |
Comparative analysis of acceleration gradients for chip structures with different refractive indices Vasyliev, A.V. Bolshov, O.O. Svistunov, O.O. Povrozin, A.I. Zaitcev, V.P. Leshchenko, V.P. Sotnikov, G.V. Novel and non-standard acceleration technologies |
| title_short |
Comparative analysis of acceleration gradients for chip structures with different refractive indices |
| title_full |
Comparative analysis of acceleration gradients for chip structures with different refractive indices |
| title_fullStr |
Comparative analysis of acceleration gradients for chip structures with different refractive indices |
| title_full_unstemmed |
Comparative analysis of acceleration gradients for chip structures with different refractive indices |
| title_sort |
comparative analysis of acceleration gradients for chip structures with different refractive indices |
| author |
Vasyliev, A.V. Bolshov, O.O. Svistunov, O.O. Povrozin, A.I. Zaitcev, V.P. Leshchenko, V.P. Sotnikov, G.V. |
| author_facet |
Vasyliev, A.V. Bolshov, O.O. Svistunov, O.O. Povrozin, A.I. Zaitcev, V.P. Leshchenko, V.P. Sotnikov, G.V. |
| topic |
Novel and non-standard acceleration technologies |
| topic_facet |
Novel and non-standard acceleration technologies |
| publishDate |
2021 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Порівняльний аналіз градієнтів прискорення для ЧІП-структур з різними показниками заломлення Сравнительный анализ градиентов ускорения для ЧИП-структур с различными показателями преломления |
| description |
The results of numerical studies of accelerating gradients in accelerators based on dielectric chip structures with different refractive indices, excited by a titanium-sapphire laser pulse, are presented. A comparative analysis of the influence of the refractive index on the rate of acceleration of electron bunches is carried out. Promising materials for the manufacture of dielectric laser accelerators are proposed.
Представлені результати чисельних досліджень прискорюючих градієнтів у прискорювачах на основі діелектричних ЧІП-структур з різними показниками заломлення, збуджуваних титан-сапфіровим лазерним імпульсом. Проведено порівняльний аналіз впливу показника заломлення на темп прискорення електронних згустків. Запропоновано перспективні матеріали для виготовлення діелектричних лазерних прискорювачів.
Представлены результаты численных исследований ускоряющих градиентов в ускорителях на основе диэлектрических ЧИП-структур с различными показателями преломления, возбуждаемых титан-сапфировым лазерным импульсом. Проведен сравнительный анализ влияния показателя преломления на темп ускорения электронных сгустков. Предложены перспективные материалы для изготовления диэлектрических лазерных ускорителей.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195642 |
| citation_txt |
Comparative analysis of acceleration gradients for chip structures with different refractive indices / A.V. Vasyliev, O.O. Bolshov, O.O. Svistunov, A.I. Povrozin, V.P. Zaitcev, V.P. Leshchenko, G.V. Sotnikov // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 75-79. — Бібліогр.: 25 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2021. № 6(136) 75
https://doi.org/10.46813/2021-136-075
COMPARATIVE ANALYSIS OF ACCELERATION GRADIENTS
FOR CHIP STRUCTURES WITH DIFFERENT REFRACTIVE INDICES
A.V. Vasyliev, O.O. Bolshov, O.O. Svistunov, A.I. Povrozin, V.P. Zaitsev, V.P. Leshchenko
G.V. Sotnikov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: o.bolshov@student.csn.khai.edu
The results of numerical studies of accelerating gradients in accelerators based on dielectric chip structures with
different refractive indices, excited by a titanium-sapphire laser pulse, are presented. A comparative analysis of the
influence of the refractive index on the rate of acceleration of electron bunches is carried out. Promising materials
for the manufacture of dielectric laser accelerators are proposed.
PACS: 41.75.Jv, 41.75.Ht, 42.25.Bs
INTRODUCTION
Particle accelerators are an important tool in basic
scientific research, industry and medicine. Traditional
RF accelerators are often expensive and too large,
which hinders their to be widespread, and their accelera-
tion gradients are limited by the low breakdown thresh-
old of the materials used and are usually equal to
20…30 MeV/m. In this regard, it became necessary to
develop more compact and cheaper accelerators, which,
in this case, would provide greater efficiency. One of
such options is the concept of dielectric wakefield ac-
celerators driven by a long sequence of electron bunches
[1]. Another proposed by us turned out to be dielectric
laser accelerators (DLA) based on chip structures,
which will be considered in this work.
The dielectric structures used in such accelerators
have a high damage threshold when operating in the
optical range. Dielectrics have higher gradients due to
the fact that they withstand fields exceeding 1 GV/m
[2]. Due to advanced nanomanufacturing techniques, it
has become possible to create precise and low-cost
nanostructures from a variety of dielectric materials. In
addition, they are transparent to the operating wave-
lengths of high-power and commercially available
femtosecond laser systems. Thus, DLAs exhibit larger
acceleration gradients than RF accelerators, are smaller
and less expensive.
1. ACCELERATION GRADIENT
Following [2] give the expression for the accelera-
tion gradient depending on the refractive index. To
quantify DLA efficiency, an indicator such as the accel-
eration gradient Gacc is used, which is usually written as:
0
1
( ( ), )
g
acc z
g
G E z t t dz
, (1)
where g is the grating period of the structure, z is the
direction of propagation of electrons, Ez(z(t), t) is the
longitudinal electric field. The acceleration gradient
shows the electron energy gain per unit length and is
usually measured in MeV/m.
Two other important indicators are:
1. The acceleration factor fA:
0
acc
A
G
f
E
, (2)
where E0 is the input electric field inside the structure
after Fresnel reflection at the interface between the two
media. The acceleration coefficient is a dimensionless
quantity that shows the efficiency of converting an inci-
dent electric field into an acceleration gradient.
2. The field enhancement factor :
max
0
E
E
, (3)
where Emax is the maximum electric field in the struc-
ture. This coefficient determines the ability of the struc-
ture to enhance the input field.
From equation:
2 2
0 0 0 0
1 1
2 2
inc
inc r
E
E E E
n
, (4)
where Einc is the input electric field outside the struc-
ture, n =
r is the refractive index of the material; it
follows that the acceleration gradient can be written as:
0
2 incA A
acc inc
p
Ff f
G E
n n c
, (5)
where Finc is the power density of laser radiation, p is
the pulse duration.
In Section 5, we will compare Eqs. (4) and (5) with
the results of numerical simulation.
2. MATERIAL SELECTION CRITERIA
The material of the structure is an important compo-
nent of the DLA and therefore some criteria should be
followed when choosing it:
1. Transparency. The dielectric material must be
transparent in the selected region of the laser spectrum.
This is necessary to transfer maximum power to the
accelerator and reduce material heating. Most dielectric
materials are transparent to infrared radiation, so this
criterion is not essential for the creation of DLA.
2. Laser-induced damage threshold (LIDT). From
Eqn. (5) it follows that the acceleration gradient is pro-
portional to the square root of the laser pulse power and,
therefore, the maximum acceleration gradient is limited
by the breakdown of the dielectric material. Thus, to
obtain large acceleration gradients, materials should be
used that will withstand high electric field strengths. It
should also be taken into account that grating structures
will be less durable than the bulk material [3].
mailto:o.bolshov@student.csn.khai.edu
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 76
3. Refractive index. DLA is an optical phase mask
that modulates the amplitude and phase shift of electro-
magnetic waves when laser radiation is incident on the
chip structure. Higher refractive indices give greater
limiting of the electric field and create greater phase
contrast.
It should be noted that since DLA operates in the re-
verse mode of Cherenkov radiation, for greater energy
modulation, it is necessary to adhere to the rule that the
electron velocity c should be greater than the phase
velocity of light in the material c/n, which means
1/n .
4. Simplicity of production. One of the conditions for
synchronization between the first spatial harmonic and
the electron bunch is that the period of the
electrodynamic structure of the accelerator must satisfy
the relation
g [4], where is the wavelength of
laser radiation. That is, the grating period of the chip
structure must be equal to the operating wavelength for
relativistic electrons. Moreover, the production of such
structures should be relatively quick and cheap.
5. Resistance to radiation of relativistic electrons.
Materials such as Fused Silica, YAG, Lithium niobate
and Sapphire are not damaged by relativistic electrons,
while borosilicate glass (BK7) is.
3. MATERIALS OVERVIEW
Fused Silica was used in the first DLA demonstra-
tions [2, 5]. The material has a relatively high LIDT –
2.1 J/cm
2
(at a wavelength 800 nm, with a pulse dura-
tion of 30 fs [6]), and the methods of producing
nanostructures from it are well studied [7 - 10]. In addi-
tion, as mentioned above, Fused Silica is resistant to
electrons. One of the disadvantages of Fused Silica is its
low refractive index 1.45.
Recently, the production of DLA from Sapphire and
Gallium Oxide has been demonstrated [11]. Both mate-
rials outperform Fused Silica in terms of LIDT and re-
fractive index. Sapphire has a LIDT of 11 J/cm
2
(800 nm, 100 fs) [12] and a refractive index of 1.76.
Gallium Oxide has, respectively, 2.6 J/cm
2
(760 nm,
9 fs) and a refractive index of 1.9 [13]. The main disad-
vantage of these materials is the complexity of manufac-
turing chip structures from them.
One of the materials mentioned that can withstand
the high energies of relativistic electrons is Lithium nio-
bate. This material is also interesting because it has the
highest refractive index among those considered in this
work, it is equal to 2.26. However, its LIDT is lower
than that of the previous two materials, it is equal to
2.0 J/cm
2
[14].
The last material reviewed is the commercially
available BK7 optical glass. In terms of refractive index,
it is close to Fused Silica, it is equal to 1.51. But it has
the lowest LIDT, only 2.55 J/cm
2
(760 nm, 200 fs) [15].
At the same time, as already noted, BK7 is destroyed by
the radiation of relativistic electrons. Nevertheless, such
material can be used in research in a number of cases,
due to its availability.
Based on the works [16 - 18], for clarity, we intro-
duce an equation for approximating the available data of
LIDT of materials and reduce all values to the parame-
ters of laser radiation equal to 800 nm wavelength and
120 fs pulse duration:
2 2
2 2 1 1
1 1
( , ) ( , )LIDT LIDT
, (6)
where 1 and 1 are the wavelength and duration of the
pulse for the known LIDT, 2 and 2 are the values of
the determined LIDT (in our case, 800 nm and 120 fs).
All of these materials are transparent for a wave-
length of 800 nm and have a low absorption index
(~10
-8
…10
-7
) [19 - 24]. For this reason, dielectric losses
were not taken into account in the simulation.
The materials considered and their parameters are
shown in Table 1.
Table 1
DLA materials and their characteristics:
Material
LIDT
(J/cm
2
)
Approx.
LIDT
(J/cm
2
)
Refractive
index, n
Trans-
mittance
Fused
Silica
2.10 4.20 1.45 0.90
BK7 2.55 2.07 1.51 0.90
Sapphire 11.00 12.05 1.76 0.85
Gallium
oxide
2.60 9.99 1.90 0.80
Lithium
niobate
2.00 3.43 2.26 0.75
4. SIMULATION AND RESULTS
We used the particle-in-cell method to simulate
DLA. A structure with a single grating was irradiated
perpendicularly for transmission with a Gaussian pulse.
The electron source was located at a height /2 above
the surface of the structure and emitted one electron
bunch. The parameters of the chip structure, Gaussian
pulse, and electron bunch are given in Table 2.
Table 2
Parameters of the chip structure, Gaussian pulse,
and electron bunch used in the numerical simulation
Chip structure
Period, g 800 nm
Pillars height, h 400 nm
Grooves width, w 400 nm
Gaussian pulse
Center wavelength, 800 nm
Pulse duration, p 120 fs
Beam waist, w0 14 um
Electric field intensity, Einc 1 GV/m
Electron bunch
Bunch width 100 nm
Electron energy 50 MeV
Bunch length 0.35 fs
From the previously investigated profiles of chip
structures [25], the profile of the “grooves” type was
chosen as the main one for this work. The geometric
image of the profile is shown in Fig. 1. Numerical mod-
eling was carried out for all materials listed in Table 1.
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 77
Fig. 1. Geometric image of profile of the used structure
Fig. 2 shows energy gain of the electrons depending
on the longitudinal coordinate of electron propagation z
for different materials of chip structures. The figure
shows that energy gain is proportional to the refractive
index of the material.
Fig. 2. Energy gain of the electrons for different
materials of the accelerator
Fig. 3,a-c show the dependence of the electric field
strength along the z coordinate (accelerating channel).
The blue curve indicates the distribution of the electric
field at the time of the maximum intensity of the accel-
erating field when the electron is above the pillars of the
chip structure, the red curve indicates the distribution of
the field strength after half the optical period, during
which the electron passes half the grating period and
will be above the grooves. With an increase in the re-
fractive index, the difference in intensity decreases.
Thus, in the case of Fused Silica, although electrons
experience a stronger accelerating field, they also expe-
rience a strong decelerating field after a time equal to
the phase change in the /2 interval. Whereas for Lithi-
um niobate, due to the higher refractive index, the am-
plitude of the fields in the channel is less [see eqs. (4)
and (5)], but the electron is in the accelerating phase
throughout the entire path. As a result, Lithium niobate
gives greater acceleration and a smoother curve in Fig. 2
(compared to Fused Silica curve). It follows from this
that a more uniform electric field acts on the electron.
Fig. 3,b shows an intermediate case that corresponds to
the average refractive index of the selected materials
(for Sapphire). In this case, the maximum intensity of
the accelerating field is less than for the case with Fused
Silica. However, when the phase changes by /2, the
electron is still affected by the decelerating field, which
is why the total acceleration gradient is lower than for
the case with Lithium niobate.
Fig. 3,d-f show the distribution of the longitudinal
electric field at the moment of maximum intensity at the
height of the flight of electrons. Red color corresponds
to the accelerating field, blue one to the decelerating.
The presented figures clearly show how the refractive
index of the structure affects the formation of the longi-
tudinal accelerating component of the electric field in
space. In Fig. 3,d field has a more uniform distribution
throughout the entire flight of electrons. It can be seen
that for materials with a higher refractive index
(Fig. 3,e,f), the field modulation becomes more pro-
nounced. When the wave phase changes in the /2 in-
terval, the field will change to a decelerating one and
the electrons located above the grooves will be affected
by the decelerating field, the stronger the lower the re-
fractive index of the material. Consequently, the most
advantageous in this case will be a material that, due to
its refractive index, makes it possible to change the field
to an accelerating one.
Fig. 3. Electric field intensity along the propagation of electrons for various materials (a-c);
distribution of electric fields formed by the chip structure in accordance with a-c (d-f).
The dotted line indicates the height of the flight of electrons /2
Table 3 shows the acceleration gradients obtained at
modeling for various materials, as well as the ratio of
refractive indices and acceleration gradients with those
of Fused Silica, the main material used in DLA.
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 78
Table 3
Refractive indices and acceleration gradients of various
materials, and the ratio of these parameters to those
of Fused Silica
Material
Refrac-
tive
index
Acceleration
gradient,
(MeV/m)
Fused
Silica
refractive
index ratio
Fused
Silica
gradient
ratio
Fused
Silica
1.45 73.7 1.00 1.00
BK7 1.51 92.5 1.04 1.26
Sapphire 1.76 102.9 1.21 1.40
Gallium
oxide
1.90 113.3 1.31 1.54
Lithium
niobate
2.26 140.4 1.56 1.91
Simulation results and material characterization in-
dicate that Sapphire, Gallium oxide and Lithium niobate
are promising candidates as primary materials for DLA
research.
CONCLUSIONS
In this paper, various criteria that are desirable to
consider when choosing a material for DLA were de-
scribed, and materials common in research were consid-
ered, as well as those that have more preferred charac-
teristics.
Simulation of the acceleration of electrons was car-
ried out using the considered materials as the material of
the dielectric structure.
The results obtained showed the increase of the en-
ergy gain of the accelerated electron bunch with an in-
crease in the refractive index. At the same time, as fol-
lows from expressions (4) and (5), the amplitude of the
longitudinal electric field decreases with an increase in
the refractive index. But the integral effect during the
motion of the accelerated bunch along the structure con-
sists in an increase in its energy gain, since for half the
period of the structure, the bunch is in a weaker deceler-
ating field with an increase in the refractive index.
Moreover, for some materials, the bunch can be in the
accelerating phase throughout the entire period of the
structure, which can lead to an even greater energy gain.
Sapphire, Gallium oxide and Lithium niobate have
been identified as promising materials for future DLA
research.
ACKNOWLEDGEMENTS
Work supported by The National Research Founda-
tion of Ukraine, program "Leading and Young Scien-
tists Research Support" (project # 2020.02/0299).
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Article received 07.10.2021
СРАВНИТЕЛЬНЫЙ АНАЛИЗ ГРАДИЕНТОВ УСКОРЕНИЯ ДЛЯ ЧИП-СТРУКТУР
С РАЗЛИЧНЫМИ ПОКАЗАТЕЛЯМИ ПРЕЛОМЛЕНИЯ
А.В. Васильев, А.О. Большов, О.А. Свистунов, А.И. Поврозин, В.П. Зайцев, В.П. Лещенко, Г.В. Сотников
Представлены результаты численных исследований ускоряющих градиентов в ускорителях на основе ди-
электрических ЧИП-структур с различными показателями преломления, возбуждаемых титан-сапфировым
лазерным импульсом. Проведен сравнительный анализ влияния показателя преломления на темп ускорения
электронных сгустков. Предложены перспективные материалы для изготовления диэлектрических лазерных
ускорителей.
ПОРІВНЯЛЬНИЙ АНАЛІЗ ГРАДІЄНТІВ ПРИСКОРЕННЯ ДЛЯ ЧІП-СТРУКТУР З РІЗНИМИ
ПОКАЗНИКАМИ ЗАЛОМЛЕННЯ
А.В. Васильєв, О.О. Большов, О.О. Свістунов, А.І. Поврозін, В.П. Зайцев, В.П. Лещенко, Г.В. Сотніков
Представлені результати чисельних досліджень прискорюючих градієнтів у прискорювачах на основі ді-
електричних ЧІП-структур з різними показниками заломлення, збуджуваних титан-сапфіровим лазерним
імпульсом. Проведено порівняльний аналіз впливу показника заломлення на темп прискорення електронних
згустків. Запропоновано перспективні матеріали для виготовлення діелектричних лазерних прискорювачів.
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