Effective acceptance evaluation of linear resonance accelerator
One of the most important challenges for accelerators is to match an accelerating beam with an accelerator acceptance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF focusing is carried out with no taking into account a beam space charge...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
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| Cite this: | Effective acceptance evaluation of linear resonance accelerator / V.S. Dyubkov,. E.S. Masunov // Вопросы атомной науки и техники. — 2010. — № 3. — С. 94-97. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859946615999037440 |
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| author | Dyubkov, V.S. Masunov, E.S. |
| author_facet | Dyubkov, V.S. Masunov, E.S. |
| citation_txt | Effective acceptance evaluation of linear resonance accelerator / V.S. Dyubkov,. E.S. Masunov // Вопросы атомной науки и техники. — 2010. — № 3. — С. 94-97. — Бібліогр.: 5 назв. — англ. |
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| description | One of the most important challenges for accelerators is to match an accelerating beam with an accelerator acceptance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF focusing is carried out with no taking into account a beam space charge; a model taking into account non-coherent bunch particle oscillations is considered with the use of an averaging technique over rapid oscillations. Analytical results obtained are verified. Computer simulations of self-consistent low-energy ion beam dynamics are performed.
Одной из наиболее важных задач для ускорителей является задача согласования ускоряемого пучка с аксептансом ускорителя, решение которой позволяет снизить потери частиц пучка. Производится оценка эффективного аксептанса (области захвата) линейного резонансного ускорителя с ВЧ-фокусировкой без учёта поля собственного пространственного заряда пучка; рассматривается модель, учитывающая некогерентные колебания частиц сгустка, с использованием метода усреднения по быстрым осцилляциям. Полученные аналитические результаты проверяются. Проводятся численные моделирования самосогласованной динамики низкоэнергетического ионного пучка.
Одним із найбільш важливих завдань для прискорювачів є завдання узгодження прискорюючого пучка з аксептансом прискорювача, рішення якого дозволяє знизити втрати частинок пучка. Проводиться оцінка ефективного аксептанса (області захоплення) резонансного лінійного прискорювача з ВЧ-фокусуванням без урахування поля власного просторового заряду пучка; розглядається модель, що враховує некогерентні коливання частинок згустку, з використанням методу усереднення по швидким осциляціям. Отримані аналітичні результати перевіряються. Проводяться чисельні моделювання самоузгодженої динаміки низькоенергетичного іонного пучка.
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EFFECTIVE ACCEPTANCE EVALUATION
OF LINEAR RESONANCE ACCELERATOR
V.S. Dyubkov,. É.S. Masunov
Chair of Electrophysical Facilities, National Research Nuclear University (MEPhI),
Moscow, Russia
E-mail: vsdyubkov@mephi.ru
One of the most important challenges for accelerators is to match an accelerating beam with an accelerator accep-
tance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF
focusing is carried out with no taking into account a beam space charge; a model taking into account non-coherent
bunch particle oscillations is considered with the use of an averaging technique over rapid oscillations. Analytical
results obtained are verified. Computer simulations of self-consistent low-energy ion beam dynamics are performed.
PACS: 02.30.Em; 41.75.Lx
1. INTRODUCTION
One of the most urgent problems of accelerator en-
gineering to date is a design and development of high-
performance high-current systems for an injection and
acceleration of low-velocity heavy-ion beams. This
problem as well as others cannot be solved without tak-
ing into account problem solution on beam emittance
matching with an acceptance of an accelerator channel.
Effective acceptance evaluation for the resonance accel-
erator channel depends on a mathematical model used
for describing a beam dynamics. Effective acceptance
evaluation of the resonance accelerator channel was
performed previously on basis of charged particle beam
oscillation as a whole [1-4], that is under the assumption
of coherent oscillations of individual particles. It is evi-
dent that this model does not correspond to real condi-
tions in the beam given completely but it allows one
make some important estimation. It is of particular in-
terest to consider a model, which is taking into account
non-coherent particle oscillations in the beam, and ana-
lyze results based on it.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 3.
Series: Nuclear Physics Investigations (54), p.94-97.
94
2. ACCEPTANCE EVALUATION
It is difficult to analyze a beam dynamics in a high
frequency polyharmonic field. Therefore, we will use
one of methods of an averaging over a rapid oscillations
period, following the formalism presented in Ref. [1–4].
The first to use an averaging method was P.L. Kapitsa
[5]. One first expresses RF field in an axisymmetric peri-
odic resonant structure as Fourier’s representation by
spatial harmonics of a standing wave assuming that the
structure period is a slowly varying function of a longi-
tudinal coordinate z
(1)
( ) ( )
( ) ( ) ,cossin
;coscos
0
1
0
0||
tzdkrkIEE
tzdkrkIEE
n
nnn
n
nnn
ω∫=
ω∫=
∑
∑
∞
=
⊥
∞
=
where En is the nth harmonic amplitude of RF field on
the axis; ( ) Dnkn π+θ= 2 is the propagation wave
number for the nth RF field spatial harmonic; D is the
resonant structure geometric period; θ is the phase ad-
vance per D period; ω is the circular frequency; I0, I1 are
modified Bessel functions of the first kind.
As it was stated above, we will take into account
non-coherent particle oscillations in the beam being
accelerated. To this end, one introduces a notion of a
reference particle, i.e. a particle moving on the channel
axis. This particle is at the point with coordinates (zr; 0)
at given moment of time (subscript “r” means a value
for the reference particle). A magnetic force can be ne-
glected for low-energy ions. We will assume that
dz/dr << 1. Then, one passes into the reference particle
rest frame. There is a differentiation over longitudinal
coordinate in the beam motion equation. Thus, the mo-
tion equation together with an equation of particle phase
variation can be presented in a view of a system of the
first order differential equations as follows
( ) ( )
( )
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
β
−
β
=
ξ
ψ
β
=
ξ
β
−=
ξ
Θ
⊥⊥
.11
;,,
;,0,,0,
r||||
||
||r||
d
d
trze
d
d
tzetze
d
d
(2)
Here we introduced the following dimensionless va-
riables: ,r γ−γ=Θ γ is the Lorentz’s factor; ,2 λπ=ξ z
,2 2
0||,||, cmZeEe πλ= ⊥⊥ e is the elementary charge, Z is
a charge state of an ion, λ is a wave length of RF field,
m0 is an ion rest mass, c is the light velocity in free
space; ,||,||, c⊥⊥ υ=β ( ).rtt −ω=ψ Note, it can be as-
sumed that ( ),||r|| β−ββ≈Θ s where is the equilib-
rium particle velocity and s is a number of the synchro-
nous harmonic, provided
sβ
1|| <<β−β s is satisfied.
Therefore, we can write ( ) 2
||r|| sdd ββ−β≈ξψ for the
last equation of the system (2). Now the first and the
third equations of the system (2) can be united as fol-
lows
( ) ,13
32
2
ξ
Θ
β
=
ξ
ψ
ξκ+
ξ
ψ
d
d
d
d
d
d
s
(3)
and the second equation of the system (2) can be rewrit-
ten in the form
( ) ,
32
2
s
e
d
d
d
d
β
=
ξ
δ
ξκ+
ξ
δ ⊥ (4)
where λβπ=δ sr2 is the dimensionless transverse va-
riable and κ = (ln β s)′ξ . On averaging over rapid oscilla-
tion period one can present the motion equation in the
smooth approximation with the restrictions mentioned
above in the following matrix form
, (5) efLU−=ΥΛ+Υ &&&
where the dot above stands for differentiation with re-
spect to the independent ξ variable. Hereafter ψ and δ
mean its averaged values and
95
.L,0
03, ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟
⎠
⎞⎜
⎝
⎛
κ
κ=Λ⎟
⎠
⎞⎜
⎝
⎛
δ
ψ=Υ
δ∂
∂
ψ∂
∂
(6)
efU is an effective potential function (EPF) describ-
ing a two-dimensional low-energy beam interaction
with the polyharmonical field of the system subject to
the incoherent particle oscillations. EPF allows the
beam dynamics to be investigated carefully. For the Wi-
deröe type structure EPF can be expressed as
; (7)
4
0
ef ∑
=
=
i
iUU
( ) ( )[ ]
( ) ( ) ( ) ( )
( )[ ] ( )[ ]
( ) ( )[ ] ( ){ } ( ) ( )[ ]
( ) ( ) ( )[ ] ( ) ( ) ( )[ ]∑∑
∑∑
∑∑
∑∑
∞
=+
≠
∞
=−
≠
∞
=+
≠
∞
=−
≠
∞
=
∞
≠
∞
=
∞
≠
φ−φ+ψδ
ν
+φ−φ+ψδ
ν
=
φ−φ+ψδι
ν
−φ−φ+ψδι+δι
ν
−=
−ψδι
μ
−−ψδι
ν
−=
δ
μ
+δ
ν
=
φ−φψ−φ+ψδ
β
=
spnspn
spnspn
kkk
sn
psn
ns
pn
kkk
sn
psn
ns
pn
sn
kkk
sn ns
pn
spsn
kkk
sn ns
pn
sn
n ns
n
sn
sn ns
n
sn
n ns
n
sn
sn ns
n
s
s
w
ee
w
ee
U
I
ee
II
ee
U
IeIeU
weweU
IeU
2
rr
2
,,2
,
2
rr
1
,,2
,
4
rr,0
2
2
,
rr,0,0
2
2
,
3
,0
0
2
,
2
,02
,
2
2
0
,
0
2
,
2
0
,2
,
2
1
rrr00
.2cos22cos
16
12cos22cos
8
1
;2cos2cos
8
12cos22cos
8
1
;1cos
8
11cos
8
1
;
16
1
16
1
;sincossin
2
(8)
Here ;2 2
0
2 cmZeEe snn πβλ= φr is the reference par-
ticle phase; ( ) ,, snsns kkk −=ν ( ) ,, snsns kkk +=μ
,, snsn kk=ι s, n, p = 0, 1, 2, … and the functions of the
dimensionless transverse coordinate are defined as
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ).
;
;1
,1,1,0,0
2
,,
,1,1,0,0
1
,,
,
2
1,
2
0
0
,
διδι−διδι=
διδι+διδι=
−δι+δι=
spsnspsnpsn
spsnspsnpsn
snsnsn
IIIIw
IIIIw
IIw
(9)
From these expressions, we can see that the term
of EPF is responsible for both the beam acceleration and
0U
its transverse defocusing. The term influences only
the transverse motion, always focusing the beam in the
transverse direction. The terms have an
influence not only on the longitudinal motion but also
on the transverse one.
1U
432 ,, UUU
To define eigenfrequencies of small system vibra-
tions, EPF is expanded in Maclaurin’s series
( ,
22
T
22
0
22
0
ef ΥΥ+
δΩ
+
ψΩ
= δψ oU ) (10)
and the coefficients in which are given by
.2cos
32
12cos
16
1
32
1
32
1sin
4
;2cos
8
12cos
4
1
8
1
8
1sin
2
r
2
2
,
,,
2
,
2
,
r
2
2
,
,,2
0
2
,
2
,2
2
,
2
,
r
2
0
r
2
2
,
r
2
2
,0
2
,
2
2
,
2
r
2
0
φ
ν
ιι−ι−ι
+φ
ν
ιι
+
μ
ι
+
ν
ι
+φ
β
=Ω
φ
ν
−φ
ν
−
μ
+
ν
+φ
β
−=Ω
∑∑∑∑
∑∑∑∑
∞
=+
≠
∞
=−
≠
∞
=
∞
≠
δ
∞
=+
≠
∞
=−
≠
∞
=
∞
≠
ψ
spnspn
spnspn
kkk
sn
pn
ns
spsnsnsp
pn
kkk
sn ns
spsn
n
n ns
sn
sn
n
ns
sn
s
s
kkk
sn ns
pn
kkk
sn ns
pn
n ns
n
sn ns
n
s
s
eeeeeee
eeeeeee
(11)
A character of the vibrations will depend on ratio be-
tween the dissipative coefficient κ and eigenfrequencies. It
is necessary that for the vibration process. ,02
0 >Ω ψ 02
0 >Ω δ
Changing the total mechanical energy E, that is
is defined by the following equation ,5.0 ef
T UE +ΥΥ= &&
,2Φ−=
ξd
dE
(12)
where is Rayleigh-Onsager function. ΥΛΥ=Φ && T5.0
A capture region allows for the fact of an explicit
dependence of system Hamiltonian on ξ variable is cal-
culated numerically.
3. COMPUTER SIMULATION RESULTS
The analytical results obtained above were used to
investigate the beam matching possibility at the linac
output. The beam was the unbunched 2.5 keV/u lead
ions Pb25+ with charge-to-mass ratio is equal to 0.12. We
consider there are two spatial harmonics at the linac.
One of it is the synchronous harmonic with s = 0, and
another one is the nonsynchronous (focusing) with
n = 1. Self-consistent beam dynamics simulations were
conducted by means of a modified version of the spe-
cialized computer code BEAMDULAC–ARF3 based on CIC
technique to calculate beam self-space-charge field. At
the beginning, computer simulations were made for the
linac structure under the following parameters:
λ = 8.88 m; system length L = 2.44 m; bunching length
(Lb) and field increasing one (Lf) are the same and the
former being equal to 1.75 m; channel aperture
a = 5 mm; input/output value of the equilibrium particle
phase ϕs = −0.5π/−0.125π; synchronous harmonic max-
imal value at the axis is equal to 42.67 kV/cm; ratio of
the harmonic amplitudes χ = e1/e0 is equal to 4. The
equilibrium particle phase linearly increases at the
bunching length and plateaus further. Note that the vari-
ation of the synchronous harmonic amplitude against
longitudinal coordinate (at the length Lf) was calculated
by using the technique described in [1]. Initial beam
radius and current were 1 mm and 5 μA respectively.
The output beam energy and current transmission coef-
ficient were 260 keV/u and 85% in this case. 4D beam
phase volume projections onto phase plane to-
gether with phase paths at linac input and output are
shown in Fig.1 and Fig.2 correspondingly. The projec-
tions of the beam phase volume onto phase plane
),( ψψ &
),( δδ &
together with RMS emittances are shown in Fig.3. Ei-
genfrequencies variations along the linac as well as dissi-
pative coefficient are shown in Fig.4. Fig.2 illustrates
rather fine beam bunching at the output, but Fig.4 shows
that all along. Due to this fact, the output beam
radius is nearly 5 times as high as the input one.
02
0 ≤Ω δ
96
Fig.1. Initial beam distribution in the plane )ψ,(ψ &
Fig.2. Resulting beam distribution in the plane )ψ,(ψ &
Fig.3. 4D beam phase volume projection onto
“•” and “+” correspond to the input and output one
):δ,(δ &
Fig.4. Normalized eigenfrequencies and dissipative
coefficient versus longitudinal coordinate
It is worth pointing out that the parameters presented
were chosen to ensure the necessary output energy and
the beam matching question was not taken into account.
To fulfill beam matching at the linac output, i.e. out-
put beam radius should be equal to input one or so, we
decided to reduce acceleration rate so as to guarantee a
positivity of the eigenfrequency of the small transverse
tunes at least near the output.
Thus, the all previous parameters were kept the same
except for the following ones: the synchronous har-
monic maximal value at the axis was changed to
16.08 kV/cm, output value of the equilibrium particle
phase to −π ⁄6 and the ratio of the harmonic amplitudes
to 9. Under this conditions the output beam energy and
current transmission coefficient are 103 keV/u and 85%
respectively. The particle loss is observed in longitudi-
nal direction in both cases.
4D beam phase volume projections onto ),( ψψ &
phase plane together with phase paths calculated in
keeping with Eq. (5) at linac input and output are shown
in Fig.5 and Fig.6 for this case.
Fig.5. Initial beam distribution in the plane )ψ,(ψ &
Fig.6. 4D beam phase volume projection
onto phase plane and phase paths )ψ,(ψ &
The projections of the beam phase volume onto
phase plane together with RMS emittances are
shown in Fig.7. Variations of the eigenfrequencies and
dissipative coefficient throughout the linac are shown in
Fig.8. Fig.8 shows that
),( δδ &
02
0 >Ω ψ and starting 02
0 >Ω δ
from ξ = 0.9. The output beam radius is nearly 1.5 times
greater than the input one because of this fact. This re-
sult is acceptable.
Fig.7. 4D beam phase volume projection onto
“•” and “+” correspond to the input and output one
):δ,(δ &
Fig.8. Reduced eigenfrequencies and dissipative
coefficient vs longitudinal coordinate
It is worth-while to compare phase capture regions
on level at the linac output for conservative and
nonconservative approximations in both cases. For the
former one, capture region in nonconservative approxi-
mation is about 38% more than that for conservative
approximation. For the latter, capture region in noncon-
servative approximation is about 21% more as com-
pared with conservative one.
0=ψ&
SUMMARY
Beam dynamics model with regard for particles non-
coherent oscillations was made. Effective acceptance
evaluation in terms of this model was evaluated. The
necessary restrictions on the linac parameters were im-
posed to make beam matching at the output. The nu-
merical simulations of the self-consistent low-velocity
heavy-ion beam dynamics confirmed the analytical re-
sults obtained.
ACKNOWLEDGEMENTS
On behalf of friends and colleagues, author pays re-
spect to Prof. Eduard Sergeevich Masunov’s family in
connection with his sudden decease.
REFERENCES
1. V.S. Dyubkov, E.S. Masunov. Investigation and
optimization of low-energy heavy-ion beam dynam-
ics in periodic axisymmetrical structures with dc fo-
cusing // International Journal of Modern Physics A.
2009, v.24, №5, p.843-856.
2. E.S. Masunov, N.E. Vinogradov. RF focusing of ion
beams in the axisymmetric periodic structure of a li-
near accelerator // Zhurnal Tekhnicheskoi Fiziki.
2001, v.71, №9, p.79-87 (in Russian).
3. E.S. Masunov, S.M. Polozov. Ion beam acceleration
and focusing in RF structures with undulators //
Zhurnal Tekhnicheskoi Fiziki. 2005, v.75, №7,
p.112-118 (in Russian).
4. E.S. Masunov, V.S. Dyubkov. Comparison of two
focusing methods in low-energy ion linac with elec-
tric undulator fields // Problems of Atomic Science
and Technology. Series “Nuclear Physics Investiga-
tions” (49). 2008, №3, p.166-170.
5. P.L. Kapitsa. Dynamic stability of a pendulum with
an oscillating suspension point // Zhurnal Eksperi-
mental'noi i Teoreticheskoi Fiziki. 1951, v.21, №.5,
p.588-597 (in Russian).
Статья поступила в редакцию 07.09.2009 г.
ОЦЕНКА ЭФФЕКТИВНОГО АКСЕПТАНСА ЛИНЕЙНОГО РЕЗОНАНСНОГО УСКОРИТЕЛЯ
B.C. Дюбков, Э.С. Масунов
Одной из наиболее важных задач для ускорителей является задача согласования ускоряемого пучка с
аксептансом ускорителя, решение которой позволяет снизить потери частиц пучка. Производится оценка
эффективного аксептанса (области захвата) линейного резонансного ускорителя с ВЧ-фокусировкой без
учёта поля собственного пространственного заряда пучка; рассматривается модель, учитывающая некоге-
рентные колебания частиц сгустка, с использованием метода усреднения по быстрым осцилляциям. Полу-
ченные аналитические результаты проверяются. Проводятся численные моделирования самосогласованной
динамики низкоэнергетического ионного пучка.
ОЦІНКА ЕФЕКТИВНОГО АКСЕПТАНСУ ЛІНІЙНОГО РЕЗОНАНСНОГО ПРИСКОРЮВАЧА
B.C. Дюбков, Е.С. Масунов
Одним із найбільш важливих завдань для прискорювачів є завдання узгодження прискорюючого пучка з
аксептансом прискорювача, рішення якого дозволяє знизити втрати частинок пучка. Проводиться оцінка
ефективного аксептанса (області захоплення) резонансного лінійного прискорювача з ВЧ-фокусуванням без
урахування поля власного просторового заряду пучка; розглядається модель, що враховує некогерентні ко-
ливання частинок згустку, з використанням методу усереднення по швидким осциляціям. Отримані аналіти-
чні результати перевіряються. Проводяться чисельні моделювання самоузгодженої динаміки низькоенерге-
тичного іонного пучка.
97
ОЦЕНКА ЭФФЕКТИВНОГО АКСЕПТАНСА ЛИНЕЙНОГО РЕЗОНАНСНОГО УСКОРИТЕЛЯ
|
| id | nasplib_isofts_kiev_ua-123456789-17023 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:14:49Z |
| publishDate | 2010 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Dyubkov, V.S. Masunov, E.S. 2011-02-18T11:36:54Z 2011-02-18T11:36:54Z 2010 Effective acceptance evaluation of linear resonance accelerator / V.S. Dyubkov,. E.S. Masunov // Вопросы атомной науки и техники. — 2010. — № 3. — С. 94-97. — Бібліогр.: 5 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17023 One of the most important challenges for accelerators is to match an accelerating beam with an accelerator acceptance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF focusing is carried out with no taking into account a beam space charge; a model taking into account non-coherent bunch particle oscillations is considered with the use of an averaging technique over rapid oscillations. Analytical results obtained are verified. Computer simulations of self-consistent low-energy ion beam dynamics are performed. Одной из наиболее важных задач для ускорителей является задача согласования ускоряемого пучка с аксептансом ускорителя, решение которой позволяет снизить потери частиц пучка. Производится оценка эффективного аксептанса (области захвата) линейного резонансного ускорителя с ВЧ-фокусировкой без учёта поля собственного пространственного заряда пучка; рассматривается модель, учитывающая некогерентные колебания частиц сгустка, с использованием метода усреднения по быстрым осцилляциям. Полученные аналитические результаты проверяются. Проводятся численные моделирования самосогласованной динамики низкоэнергетического ионного пучка. Одним із найбільш важливих завдань для прискорювачів є завдання узгодження прискорюючого пучка з аксептансом прискорювача, рішення якого дозволяє знизити втрати частинок пучка. Проводиться оцінка ефективного аксептанса (області захоплення) резонансного лінійного прискорювача з ВЧ-фокусуванням без урахування поля власного просторового заряду пучка; розглядається модель, що враховує некогерентні коливання частинок згустку, з використанням методу усереднення по швидким осциляціям. Отримані аналітичні результати перевіряються. Проводяться чисельні моделювання самоузгодженої динаміки низькоенергетичного іонного пучка. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Новые методы ускорения, сильноточные пучки Effective acceptance evaluation of linear resonance accelerator Оценка эффективного аксептанса линейного резонансного ускорителя Оцінка ефективного аксептансу лінійного резонансного прискорювача Article published earlier |
| spellingShingle | Effective acceptance evaluation of linear resonance accelerator Dyubkov, V.S. Masunov, E.S. Новые методы ускорения, сильноточные пучки |
| title | Effective acceptance evaluation of linear resonance accelerator |
| title_alt | Оценка эффективного аксептанса линейного резонансного ускорителя Оцінка ефективного аксептансу лінійного резонансного прискорювача |
| title_full | Effective acceptance evaluation of linear resonance accelerator |
| title_fullStr | Effective acceptance evaluation of linear resonance accelerator |
| title_full_unstemmed | Effective acceptance evaluation of linear resonance accelerator |
| title_short | Effective acceptance evaluation of linear resonance accelerator |
| title_sort | effective acceptance evaluation of linear resonance accelerator |
| topic | Новые методы ускорения, сильноточные пучки |
| topic_facet | Новые методы ускорения, сильноточные пучки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/17023 |
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