A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma
The paper considers the process of excitation of a wakefield in a plasma by a laser pulse. The plasma density corresponds to the density of free electrons in the metal. A method is demonstrated for keeping self-injected bunch in the accelerating phase of the wakefield as laser pulse and bunch move i...
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| Zitieren: | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma / D.S. Bondar, V.I. Maslov, I.N. Onishchenko // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 67-70. — Бібліогр.: 17 назв. — англ. |
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| citation_txt | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma / D.S. Bondar, V.I. Maslov, I.N. Onishchenko // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 67-70. — Бібліогр.: 17 назв. — англ. |
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| description | The paper considers the process of excitation of a wakefield in a plasma by a laser pulse. The plasma density corresponds to the density of free electrons in the metal. A method is demonstrated for keeping self-injected bunch in the accelerating phase of the wakefield as laser pulse and bunch move in plasma with an increasing density gradient. Thus, the rate of acceleration of self-injected bunch is maintained and enhanced.
Розглянуто процес збудження кільватерного поля в плазмі лазерним імпульсом. Густина плазми відповідає густині вільних електронів у металі. Продемонстровано метод утримання самоінжектованого згусткa у фазі прискорення кільватерного поля, коли лазерний імпульс і згусток рухаються в плазмі зі зростаючим градієнтом щільності. Таким чином, темп прискорення самоінжектованого згусткa зберігається.
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ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 67
https://doi.org/10.46813/2023-146-067
A METHOD FOR MAINTAINING THE ACCELERATION RATE
AND INCREASING THE ENERGY OF SELF-INJECTED BUNCH DUE
TO THE USE OF INHOMOGENEOUS PLASMA
D.S. Bondar
1,2
, V.I. Maslov
1,2
, I.N. Onishchenko
1
1
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine;
2
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: bondar.ds@yahoo.com
The paper considers the process of excitation of a wakefield in a plasma by a laser pulse. The plasma density
corresponds to the density of free electrons in the metal. A method is demonstrated for keeping self-injected bunch
in the accelerating phase of the wakefield as laser pulse and bunch move in plasma with an increasing density gradi-
ent. Thus, the rate of acceleration of self-injected bunch is maintained and enhanced.
PACS: 29.17.+w; 41.75.Lx
INTRODUCTION
Wakefield acceleration has been a subject of intense
research due to its potential to revolutionize particle
acceleration technology. This method of particle accel-
eration utilizes the electric fields generated in the wake
of a driving pulse, typically a laser or a particle beam,
propagating through a plasma [1 - 5]. The advantages of
wakefield acceleration are numerous and have been
explored in various contexts, including solid-state plas-
mas and longitudinally inhomogeneous plasmas.
One of the primary advantages of wakefield acceler-
ation is its ability to achieve extremely high accelerating
gradients, several orders of magnitude higher than those
achievable with conventional accelerator technology.
This high gradient allows for the production of high-
energy particles over short distances, potentially leading
to more compact and cost-effective accelerators [6 - 8].
In the context of solid-state plasmas, wakefield ac-
celeration can be particularly advantageous. Solid-state
plasmas are dense electron plasmas in solid-state mate-
rials, such as metals, semiconductors etc. The high den-
sity of these plasmas allows for the generation of strong
wakefield and, consequently, high accelerating gradi-
ents. Moreover, solid-state plasmas can be more easily
manipulated and controlled than gaseous plasmas, al-
lowing for more precise control over the acceleration
process [9 - 11].
Wakefield acceleration in longitudinally inhomoge-
neous plasmas also presents unique advantages. Longi-
tudinal inhomogeneity refers to variations in the plasma
density along the direction of propagation of the driving
pulse. These variations can be exploited to enhance the
efficiency of energy transfer from the driving pulse to
the wakefield, thereby increasing the accelerating gradi-
ent. Furthermore, by carefully designing the longitudi-
nal density profile, it is possible to optimize the acceler-
ation of particles [12, 13].
Wakefield acceleration in longitudinally inhomoge-
neous plasmas also presents unique advantages. Longi-
tudinal inhomogeneity refers to variations in the plasma
density along the direction of propagation of the driving
pulse. These variations can be exploited to enhance the
efficiency of energy transfer from the driving pulse to
the wakefield, thereby increasing the accelerating gradi-
ent. Furthermore, by carefully designing the longitudi-
nal density profile, it is possible to optimize the acceler-
ation of particles [14 - 17].
In conclusion, wakefield acceleration offers a prom-
ising avenue for advancing particle acceleration tech-
nology. Its potential for achieving high accelerating
gradients in a compact setup, coupled with its versatility
and applicability in various contexts, makes it a compel-
ling subject for further research and development.
The excitation of the wakefield and the motion of
bunch in an inhomogeneous plasma were studied. The
motion of bunch was considered at the beginning of the
simulation process, not far from the injection point. In
particular, the fields acting on the bunch and the longi-
tudinal momentum of the bunch are investigated.
1. STATEMENT OF THE PROBLEM
With the help of numerical simulation, excitation by
a laser pulse of a wakefield in a plasma is considered.
The plasma density is considered, which is close to the
density of free electrons in metals. Profiled pulse is con-
sidered. Profiling is achieved by using “semi-cosine”
pulse with a cosine intensity distribution ranging from
0 to π/2.
The main parameters of the system were as follows:
the plasma electron density (unperturbed), to which the
density on the graph is normalized is n0e=10
23
cm
-3
, the
ratio of the plasma frequency to the laser frequency is
ωpe/ω0=0.1008, where ω0 is the laser frequency, ωpe is
the plasma frequency. The laser wavelength was
λl=10.6 nm. All lengths, distances and coordinates were
normalized to the laser wavelength λl. The laser pulse
propagated along the axis of the system. The length of
the simulation window was 800, the width 50. The laser
amplitude a=EE0
-1
was normalized to the overturning
field E0=mecω0(2πe)
-1
. Force normalization, respective-
ly, F0=mecω0/2π. The mass ratio of ions and electrons
was 1836. Time was normalized to the period of the
electromagnetic wave T0. A laser pulse with the follow-
ing parameters is considered: amplitude a=5, half-length
equal to 3, half-width at half-height equal to 4. The spa-
tial dimensions are indicated for a cosine pulse, for a
half-cosine pulse it is half as much. It is known that a
self-injected bunch, moving along the wake bubble,
enters the deceleration phase of the wake wave. The
68 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146)
process begins after the self-injected bunch reaches the
middle of the wake bubble. This leads to the stop of the
acceleration process and the loss of energy by the self-
injected bunch. The main idea of inhomogeneity is that
during the time until the self-injected bunch from the
injection point reaches the middle of the wake bubble in
homogeneous case, the plasma density will increase by
4 times. This will lead to a twofold decrease in the
plasma wave length and, as a consequence, to stabiliza-
tion of the position of the self-injected bunch in the re-
gion of the accelerating phase of the wakefield.
2. RESULTS OF SIMULATION
At first, let us consider how the bunch energy
changes in the inhomogeneous case. The condition for
the Cherenkov resonance of a laser pulse with a wake
plasma wave:
KVg=pe (1)
or
Vg=vph=pe/K, (2)
K=2/; vph – wave vector and phase velocity of the
Langmuir wave. Vg, , k – group velocity, frequency
and wave vector of the laser pulse.
=(pe
2
+c
2
k
2
)
1/2
, (3)
k=(
2
-pe
2
)
1/2
/c . (4)
From (3) it can be obtained:
Vg=d/dk=c
2
k/(pe
2
+c
2
k
2
)
1/2
=c
2
k/=
=c(1-pe
2
/
2
)
1/2
c(1-pe
2
/2
2
). (5)
From (2) it can be obtained:
=2Vg/pe=2(c/pe)(1-pe
2
/
2
)
1/2
2(c/pe)(1-pe
2
/2
2
). (6)
Both factors c/pe and (1-pe
2
/2
2
) decrease as
ne(x) increases. But the 1
st
multiplier reduces more.
In order for the accelerated bunch to stay in the re-
gion of the maximum accelerating field all the time, the
bunch shear rate relative to the bubble Vb(t)-Vg(x)
should be equal to the plasma wave length contraction
rate d/dt.
Vb(t)-Vg(x)=d/dt=(d/dz)(dz/dt), (7)
dz/dt=Vg .
In the ultrarelativistic bunch approximation Vbc.
And neglecting the change in Vg in an inhomogeneous
plasma, we obtain:
c/Vg-1=d/dz. (8)
At times (c-Vg)=/2 shift by (c-Vg)=/2 in the
case of a homogeneous plasma and in the approximation
that in an inhomogeneous plasma the bunch accelerates
to Exmax and in the approximation that Ex is distributed
Ex=Exmax(1-2x/) in the case of a homogeneous plasma
the bunch accelerates to
dεb/dt=eEv, (9)
εb=ecExdx/(c-Vg)=
=ecExmax(/4)(1-2x/)
2
/(c-Vg)0
/2
=
=ecExmax(/4)/(c-Vg). (10)
In an inhomogeneous plasma with a constant Exmax
and with acceleration over an interval of almost 2 times
greater, since it accelerates until the bubble almost
completely collapses.
εb=ecExmax(/2)2/(c-Vg)=
=ecExmax/(c-Vg). (11)
In the inhomogeneous case, the energy acquired by a
self-injected bunch is theoretically 4 times higher than
the energy in the homogeneous case. In fact in the in-
homogeneous case the accelerating wakefield grows and
the energy of accelerated electrons increases even more.
Let us perform numerical simulation to verify the effi-
ciency of using inhomogeneous plasma.
Obviously, when simulating a real case, taking into
account all factors, including the nonlinearity and loca-
tion of the bunch relative to the accelerating phase of
the wake wave, we will observe a smaller value of the
energy increase but, nevertheless, an increase in energy
will be observed.
Fig. 1 shows a graph of the density during the pro-
cess of excitation of the wakefield in the plasma by a
laser pulse. The pattern of simulation in the homogene-
ous and inhomogeneous cases is the same. One can ob-
serve a self-injected bunch, which has just formed and
begins its movement along the wake bubble (t=60T0).
Fig. 1. Plasma electron density distribution ne(x, y)
and longitudinal accelerating field Ex(x), t=60T0.
Semi-cosine distribution of laser pulse both
in the homogeneous and inhomogeneous case
Fig. 2 characterizes the simulation pattern in the
homogeneous case at the moment when the self-injected
bunch approaches the point when the accelerating wake-
field Ex=0.
Comparison of Figs. 2 and 3, homogeneous and in-
homogeneous cases at the same time points, indicates
that due to the use of longitudinally inhomogeneous
plasma, it is possible to keep the self-injected bunch in
the acceleration phase, almost at the injection point.
Fig. 2. Plasma electron density distribution ne(x, y)
and longitudinal accelerating field Ex(x), t=140T0.
Semi-cosine distribution in the homogeneous case
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 69
At the same time, when the self-injected bunch hits
zero field in the homogeneous case, and later in the de-
celeration phase of the wake wave.
Fig. 3. Plasma electron density distribution ne(x, y)
and longitudinal accelerating field Ex(x), t=140T0.
Semi-cosine distribution in the inhomogeneous case
Fig. 4 shows the case of a full cosine laser intensity
distribution (non-profiled case). Obviously, the ad-
vantage of using profiling, due to which stabilization of
bunches is observed, their transverse expansion is re-
duced.
Fig. 4. Plasma electron density distribution ne(x, y)
and longitudinal accelerating field Ex(x), t=140T0.
Full-cosine distribution in the homogeneous case
Fig. 5 shows the distribution of the longitudinal
component of the pulse of a self-injected bunch simul-
taneously in the homogeneous and inhomogeneous cas-
es, when the effect of inhomogeneity is not yet felt in
the case of a half-cosine laser. A stable bunch can be
observed, but small momentum values.
Comparing Figs. 5 and 6, we can conclude that in
the inhomogeneous case, when the self-injected bunch
reaches the middle of the wake bubble, there is an in-
crease in the longitudinal momentum by a factor of 2.2
if we compare the bunch momenta at moments t=60T0
and t=140T0. The average momentum in the main re-
gion of the bunch was taken as the momentum based on
the graphic dependences. It has been studied that the
increase in energy in the inhomogeneous case as com-
pared to the homogeneous case reaches 3. In the homo-
geneous case, due to the motion of the self-injected
bunch along the wake bubble, at the moment 140 the
longitudinal field in the bunch region in normalized
units reaches approximately 0.0354. In the inhomoge-
neous case, due to the confinement of the bunch near
the injection point, at the same time in the bunch region,
the value of the longitudinal acceleration field is 0.2681.
Thus, an increase in the bunch acceleration field by a
factor of approximately 7.6 is observed due to the use of
plasma inhomogeneity.
Fig. 5. Distribution of the longitudinal component
of the momentum Px(x, y) in the electrons of a self-
injected bunch, t=60T0. Semi-cosine distribution
both in the homogeneous and inhomogeneous case
Fig. 6. Distribution of the longitudinal component
of the momentum Px(x, y) in the electrons of a self-
injected bunch, t=140T0. Semi-cosine distribution
both in the inhomogeneous case
In the case of a semi-cosine intensity distribution,
when the plasma is inhomogeneous, at time t=140T0,
the formation of self-injected bunches with a minimum
spatial distribution in the transverse direction is ob-
served. This contrasts with the homogeneous case of an
unshaped laser pulse. In this case, the decay of the self-
injected bunch into 3 parts is observed, the transverse
size of the bunch is much larger than the bunch in the
case when the driver is semi-cosine and the plasma is
inhomogeneous.
CONCLUSIONS
In the course of the study, the use of inhomogeneous
plasma was considered in the study of self-injected
bunches, which were formed when the wake field was
excited by a profiled laser pulse.
It was shown that the use of profiled pulse and in-
homogeneous plasma has a positive effect on the quality
of self-injected bunch and leads to the retention of
70 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146)
bunch in the acceleration field, which contributes to an
increase in the energy gain and an increase in the longi-
tudinal acceleration field in the bunch region.
In addition, the advantage of using shaped pulse in
an inhomogeneous case is the increased longitudinal
momentum of the bunch, which provides more efficient
acceleration.
ACKNOWLEDGEMENTS
This work is supported by National Research Founda-
tion of Ukraine “Leading and Young Scientists Re-
search Support”, grant agreement № 2020.02/0299.
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Article received 29.07.2023
СПОСІБ ПІДТРИМАННЯ ТЕМПУ ПРИСКОРЕННЯ ТА ЗБІЛЬШЕННЯ ЕНЕРГІЇ
САМОІНЖЕКТОВАНОГО ЗГУСТКA ШЛЯХОМ ВИКОРИСТАННЯ НЕОДНОРІДНОЇ ПЛАЗМИ
Д.С. Бондар, В.І. Маслов, І.М. Оніщенко
Розглянуто процес збудження кільватерного поля в плазмі лазерним імпульсом. Густина плазми відпові-
дає густині вільних електронів у металі. Продемонстровано метод утримання самоінжектованого згусткa у
фазі прискорення кільватерного поля, коли лазерний імпульс і згусток рухаються в плазмі зі зростаючим
градієнтом щільності. Таким чином, темп прискорення самоінжектованого згусткa зберігається.
|
| id | nasplib_isofts_kiev_ua-123456789-196176 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:13:39Z |
| publishDate | 2023 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bondar, D.S. Maslov, V.I. Onishchenko, I.N. 2023-12-11T11:52:11Z 2023-12-11T11:52:11Z 2023 A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma / D.S. Bondar, V.I. Maslov, I.N. Onishchenko // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 67-70. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 29.17.+w; 41.75.Lx DOI: https://doi.org/10.46813/2023-146-067 https://nasplib.isofts.kiev.ua/handle/123456789/196176 The paper considers the process of excitation of a wakefield in a plasma by a laser pulse. The plasma density corresponds to the density of free electrons in the metal. A method is demonstrated for keeping self-injected bunch in the accelerating phase of the wakefield as laser pulse and bunch move in plasma with an increasing density gradient. Thus, the rate of acceleration of self-injected bunch is maintained and enhanced. Розглянуто процес збудження кільватерного поля в плазмі лазерним імпульсом. Густина плазми відповідає густині вільних електронів у металі. Продемонстровано метод утримання самоінжектованого згусткa у фазі прискорення кільватерного поля, коли лазерний імпульс і згусток рухаються в плазмі зі зростаючим градієнтом щільності. Таким чином, темп прискорення самоінжектованого згусткa зберігається. This work is supported by National Research Foundation of Ukraine “Leading and Young Scientists Research Support”, grant agreement № 2020.02/0299. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology New methods of charged particles acceleration A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma Спосіб підтримання темпу прискорення та збільшення енергії самоінжектованого згусткa шляхом використання неоднорідної плазми Article published earlier |
| spellingShingle | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma Bondar, D.S. Maslov, V.I. Onishchenko, I.N. New methods of charged particles acceleration |
| title | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| title_alt | Спосіб підтримання темпу прискорення та збільшення енергії самоінжектованого згусткa шляхом використання неоднорідної плазми |
| title_full | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| title_fullStr | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| title_full_unstemmed | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| title_short | A method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| title_sort | method for maintaining the acceleration rate and increasing the energy of self-injected bunch due to the use of inhomogeneous plasma |
| topic | New methods of charged particles acceleration |
| topic_facet | New methods of charged particles acceleration |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/196176 |
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