Ion beam acceleration in system from periodic sequence of independetly phased cavities
Ion superconducting linac is based on periodic system consisting of the identical niobium cavities. By specific
 phasing of the RF cavities one can provide a stable particle motion in the whole accelerator. In this paper the beam
 stability conditions are founded. The matrix calculat...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2008 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Цитувати: | Ion beam acceleration in system from periodic sequence of independetly phased cavities / E.S. Masunov, A.V. Samoshin // Вопросы атомной науки и техники. — 2008. — № 3. — С. 158-162. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859993538298642432 |
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| author | Masunov, E.S. Samoshin, A.V. |
| author_facet | Masunov, E.S. Samoshin, A.V. |
| citation_txt | Ion beam acceleration in system from periodic sequence of independetly phased cavities / E.S. Masunov, A.V. Samoshin // Вопросы атомной науки и техники. — 2008. — № 3. — С. 158-162. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Ion superconducting linac is based on periodic system consisting of the identical niobium cavities. By specific
phasing of the RF cavities one can provide a stable particle motion in the whole accelerator. In this paper the beam
stability conditions are founded. The matrix calculation and motion equation in the smooth approximation are used
for alternating phase focusing analysis in superconducting linac.
Надпровідний лінійний прискорювач іонів заснований на використанні періодичної системи, що складається з ідентичних ніобієвих резонаторів. За допомогою спеціального фазування ВЧ-резонаторів можна забезпечити стійкий рух часток у всьому прискорювачі. У статті знайдено умови стійкості руху пучка іонів. Для аналізу фазозмінного фокусування пучка у надпровідному прискорювачі використано матричний метод розрахунку і рівняння руху у гладкому наближенні.
Сверхпроводящий линейный ускоритель ионов основан на использовании периодической системы, состоящей из идентичных ниобиевых резонаторов. Посредством специального фазирования ВЧ-резонаторов можно обеспечить устойчивое движение частиц во всем ускорителе. В этой статье найдены условия устойчивости движения пучка ионов. Матричный метод расчета и уравнение движения в гладком приближении используются для анализа фазопеременной фокусировки пучка в сверхпроводящем ускорителе.
|
| first_indexed | 2025-12-07T16:33:15Z |
| format | Article |
| fulltext |
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PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 3.
Series: Nuclear Physics Investigations (49), p.158-162. 158
ION BEAM ACCELERATION IN SYSTEM FROM PERIODIC
SEQUENCE OF INDEPENDETLY PHASED CAVITIES
E.S. Masunov, A.V. Samoshin
Moscow Engineering Physics Institute (State University), Moscow, 115409, Russia
E-mail: ESMasunov@mephi.ru
Ion superconducting linac is based on periodic system consisting of the identical niobium cavities. By specific
phasing of the RF cavities one can provide a stable particle motion in the whole accelerator. In this paper the beam
stability conditions are founded. The matrix calculation and motion equation in the smooth approximation are used
for alternating phase focusing analysis in superconducting linac.
PACS: 29.27.-A, 29.27.Bd
1. INTRODUCTION
Ion superconducting linac is usually based on the
superconducting (SC) interdigital cavities. This linac
consists of the niobium cavities which can provide typi-
cally 1 MV of accelerating potential per cavity. Such
structures can be used for ion acceleration with different
mass-charge ratio in the low energy region [1] and for
proton linac in the high-energy region (SNS, JHF, ESS
project). It is desirable to have a constant geometry of
the accelerating cavity in order to simplify manufactur-
ing. Such geometry leads to a non-synchronism but a
stable longitudinal particle motion can be provided by
proper phasing of the RF cavities. The ions are accele-
rated and slipping relative to the RF wave in depen-
dence of the ratio between the particle velocity β and
the phase velocity of the wave βG. The geometrical ve-
locity βG of the RF wave is constant for cavities. The
geometric size of a cavity and a wave velocity βG must
be changed step by step from one class to other class.
The optimum number of cavity in each class determines
the number of classes in SC linac. The identical cavities
operate at the some initial drive phase φ. By controlling
the driven phase of the accelerating structure and the
distance between the cavities, the beam can be both lon-
gitudinally stable and accelerated in the whole system.
In this paper two methods of the beam dynamics inves-
tigation are compared for low ion velocities and for the
charge-to-mass ratio Z/A = 1/66. This comparison can
be demonstrated with an example a post-accelerator of
radioactive ion beams (RIB) linac, where beam velocity
increases from β = 0.01 to β = 0.06 [1].
Beam focusing can be provided with help of SC so-
lenoid lenses, following each cavity and with help of
special RF fields. A schematic plot of one period of the
accelerator structure is shown in Fig.1. The low-charge-
state beams and the low velocity require stronger trans-
verse focusing than one is used in existing SC ion linac.
The large radial variation of the axial accelerating field
induces a beam energy spread, which will accumulate as
the beam passes through successive resonators. Early
investigation of beam dynamics shown that for the ini-
tial normalized transverse emittance εT = 0.1π⋅mm⋅mrad
and the longitudinal emittance εV = 0.3π⋅keV/u⋅nsec the
connection between the longitudinal and transverse mo-
tion can be neglected if maximum beam envelop
Xm < 3-4 mm and inner radius of accelerating drift tubes
a = 15 mm.
2. BEAM STABILITY ANALISYS BY
TRANSFER MATRICES
The general axisymmetric equations of motion for
ion moving inside an accelerator can be written as
( )
( )( ) .2
γ2
2
ββ1,
d
dγ
d
d
,2
γ2
2
,
d
dγ
d
d
ϕ
ϕ
A
rm
q
GtrrqE
t
rm
t
A
zm
qtrzqE
t
zm
t
∂
∂
−−=
∂
∂
−=
⎟
⎠
⎞⎜
⎝
⎛
⎟
⎠
⎞⎜
⎝
⎛
r
r
. (1)
In every cavity the acceleration RF field of periodic
H-cavity is represented as an expansion in spatial har-
monics
( ) ( )( ) ( )
( ) ( )( ) ( ) ⎪⎭
⎪
⎬
⎫
−=
−=
∑
∑
tzzhrhEE
tzzhrhEE
innr
innz
ωcossinI
ωcoscosI
10
00
, (2)
where E0 is amplitude of RF field at the axis (E0 ≠ 0 if
–Lr/2 < z–zi < Lr/2), hn = π/D + 2πn/D, n = 0, 1, 2, …,
D is the period length of the cavity, Lr is the cavity
length, zi is the coordinate of the i-th cavity center. I0, I1
are modified Bessel function. In our case the reference
particle velocity βc and the geometrical velocity βG are
closely in each class of the identical cavities. Retaining
in (2) only zeroth harmonic we can use the traveling
wave system. In this system ωt can be replaced by
h0(z–zi) + φ0i, where φ0i is the RF phase when the refer-
ence particle traverses the cavity center. In equation (1)
the value Aφ is the azimuthal vector-potential of the
magnetic field in every solenoid (B = rotA).
Fig.1. Layout of structure period
2.1. SOLENOID FOCUSING
From the motion equations (1) it can find the cavity,
solenoid and drift space matrices Mres, Msol and Mdr, if
RF field and magnetic field amplitudes are approx-
imated by the step function [2]. The transfer matrix for
one period, Mz and Mr, are obtained by multiplying
these matrices. The transfer matrices Mz and Mr allow to
find the phase advances per period:
159
( )11 22
1μ arccos ,
2z z zM M⎛ ⎞= +⎜ ⎟
⎝ ⎠
(3)
( )11 22
1μ arccos .
2r r rM M⎛ ⎞= +⎜ ⎟
⎝ ⎠
(4)
The longitudinal and transverse beam dynamics are sta-
ble if
1μcos ≤z , 1μcos ≤r . (5)
From these inequalities it can compute the necessary
magnetic field value В for a considered interval of beam
velocity 0.01 ≤ β ≤ 0.06. The choice of μz and μr is li-
mited by the bunch size. In our case, the solenoid mag-
netic field B determines μr, the beta function and the
extreme values of the beam envelope. For a charge-to-
mass ratio Z/A = 1/66 and beam velocity range
0.01 < βc < 0.02 a proper focusing can be reached with
magnetic fields up to 15 T, if μr < 250. For beam veloci-
ties between 0.05 − 0.06c, the solenoid magnetic field B
must be increased to obtain μr ≈ 250.
The final choice of the focusing magnetic field and
the parameter μr can be made if the normalized trans-
verse emittance Vr and maximum size of beam envelope
Xm are fixed. In our case
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= 2
12
βγ
arcsinμ
m
rr
r X
MV
, (6)
where Mr12 is non-diagonal element of the transfer ma-
trix. We can find the value of the focusing magnetic
field Bmin as function of the ion velocity β if the envelop
Xm is the constant along the linac. The system of two
equations (4) and (6) can be solved for Xm = const in the
accelerator structure which consists of the periodic se-
quence of the solenoids and the resonators. For the acce-
leration phase φc=−20°, when the beam velocity in-
creases from 0.01 to 0.06, the functions Bmin(β) decreas-
es from 16 T to 10.5 T if the beam envelop Xm = 3 mm
and from 14 T to 8 T if Xm = 4 mm.
Fig.2. The beam stability area for different values of B
It is interesting to investigate the common stability
area for longitudinal and transverse dynamics on the
plane of variables α and φ, where the interaction para-
meter α = LŪ/4Lv, Ū = qU/mic2 is a dimensionless am-
plitude of accelerating potential per cavity, mi = Amp,
Lv = λβ3γ3/2π, L = Lres + 2Ld + Lsol is a period length, φc
is reference particle phase. The borders of stability area
between μz = 0 and μr = 0 are shown in Fig.2 for differ-
ent values of magnetic field B, when Lr/L = 1/4. In our
case the longitudinal dynamics is stable only if φc < 0.
For B = 0 and φc < 0 the radial dynamics is instability.
In this case the common area of beam stability is absent.
This area appears and extends when magnetic field B
increases. The minimum value of focusing field Bmin can
be founded from the condition μr = 0. It’s value depends
on α and φc. When the beam velocity βc increases the
value of interaction parameter α (defocusing factor)
quickly decreases (α ~ 1/βc
3). In this case the magnetic
field B can be smaller for the same φc.
2.2. APF AND SOLENOID FOCUSING
The RF defocusing factor and required solenoid field
are very large in the SC resonators. Another method of
RF focusing is the alternating phase focusing (APF) [3].
Using transfer matrix calculations, we can study an al-
ternating phase focusing structure in the superconduct-
ing linac by changing the sign of the reference phase
value at each cavity [2]. Let’s consider a simple case of
the focusing period containing two SC cavities. By ad-
justing the phases ϕ1 and ϕ2 of each cavity individually,
we can provide both acceleration and focusing. The
phase advances per period, μz and μr, can be found from
two transfer matrices Mz and Mr.
a)
b)
c)
Fig.3. The beam stability area for APF
The borders of common stability area between μz = 0
and μr = 0 are shown in Fig.3 by black lines for deferent
values of α, when Lr/L = 1/4. In this figure the new no-
tations ϕc and Δ are used instead of ϕ1,2 = ϕc ± Δ. For
the charge-to-mass ratio Z/A = 1/66 the parameter α ≈ 1,
when the beam velocity 0.01< βc < 0.02. In this case a
large area of the stability on a plane (ϕc,Δ) is available.
If the beam velocity βc > 0.03, the parameter α becomes
less than 0.1. For small α, the area of stability tapers
160
abruptly and the phase advances per period, μz and μr,
quickly decrease. In this case the working point is lo-
cated near stability borders.
The area of stability can be extended by adding a so-
lenoid focusing which will also provide a separate con-
trol of transverse and longitudinal beam dynamics. For
accelerator with SC solenoids this method was devel-
oped and studied both analytically [2] and with the help
of the three-dimensional code TRACK [4]. It was
shown that a combined focusing structure with solenoid
and APF has obvious advantages compared to the refer-
ence design and can significantly reduce the cost of the
linac. In our case for a beam velocity range of
0.03 < βc < 0.04 when α = 0.1 it is sufficient to add one
SC solenoid per accelerating period. If one solenoid
with magnetic field B = 9 T is added, there is a large
area of stability and a wide range of Δ and ϕc is possi-
ble. The stability diagram for B = 9 T is shown in
Fig.3,a by the hatching.
3. BEAM STABILITY ANALISYS
BY SMOOTH APPROXIMATION
In SC linac design, it is very important to know the
bucket size since it relates to the longitudinal RF focus-
ing. In this case the longitudinal acceptance cannot be
obtained by matrix method because of the assumption
that the particles have small longitudinal oscillation
amplitude. In order to investigate the nonlinear ion
beam dynamics in such accelerated structure and to cal-
culate the longitudinal and transverse acceptances it can
be used smooth approximation [5,6]. In periodical struc-
ture, which was shown in Fig.1, RF field can be ex-
panded into a Fourier series as
( )
( )
⎭
⎬
⎫
⎩
⎨
⎧
++=
⎭
⎬
⎫
⎩
⎨
⎧
++=
∑
∑
∞
∞
1
,,0.01
1
,,0.00
sincosI
sincosI
zkfzkffrk
L
UE
zkfzkffrk
L
UE
n
s
nrn
c
nrrr
n
s
nzn
c
nzzz
(7)
Here )ψφcos(00, += cz Sf , )ψφsin(00, +−= cr Sf ,
( ) ( )ψφcos1, +−= +
cn
nc
nz Tf , ( ) ( )ψφsin1 1
, +−= −+
cn
ns
nz Tf
( ) ( )ψφsin1 1
, +−= ++
cn
nc
nr Tf , ( ) ( )ψφcos1, +−= −
cn
ns
nr Tf
−+± ±= nnn SST , Sn
± = sin(Yn
±)/Yn
±, Yn
± = (kc ± kn)Lr/2.
In this expressions: E = 2U/Lr, U is the cavity vol-
tage amplitude; kn = 2πn/L, n = 0, 1, 2, …; kc is slip-
ping factor, kc = (2π/λ)(1/βc – 1/βG). In the coefficients
fn
c,s the phase relative to the reference particle ψ de-
fined by ψ = ω(t – tc), tc is the flight time of the
reference particle.
In the simple case the vector-potential of the mag-
netic field Aφ = Br/2 can be approximated by the step
function at every solenoid. If Ls is effective solenoid
length and L is a lattice period, the external solenoid
magnetic field can be represented as an expansion into
spatial harmonics too.
3.1. SOLENOID FOCUSING
Let us consider particle acceleration in the polyhar-
monic fields of the cavities and solenoids. In general,
individual particle motion is complicated but can be
represented as the sum of a slow smooth motion (ψ and
ρ = h0r) and a fast oscillation ( ψ~ and ρ~ ). The force driv-
ing the ion motion can be separated into two parts cor-
responding to the fast and slow motion. Following
Ref. [6] one can apply averaging over the fast oscilla-
tions and obtain the phase and radial motion equations
in smooth approximation.
( )
( )
ρdξ
dρβγln
dξ
d
dξ
ρd
ψdξ
dψβγln
dξ
d3
dξ
ψd
2
2
2
2
∂
∂
−=⎥
⎦
⎤
⎢
⎣
⎡
+
∂
∂
−=⎥
⎦
⎤
⎢
⎣
⎡
+
eff
eff
U
U
, (8)
where Ueff = U0 + U1 + U2 is effective potential function.
We use the following designations:
( )[ ] 2
000 ρ
2
1φsinφcosψ)ψφsin(ρIα4
L
LbSU c
ccc +−−+=
( )
( )
( ) ( )
( )
( )∑
∞
⎥
⎦
⎤
⎢
⎣
⎡
+++=
1
2
,
2
,2
2
12
,
2
,2
2
02
1 π2
ρI
π2
ρIα s
nr
c
nr
s
nz
c
nz ff
n
ff
n
U , (9)
( )
( ) ( )∑∑ ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+−= 2
2
2
2
2
,
12 ρ
sin
π2
1sin
π2
ρρIα4
n
n
n
n
c
nrs
X
X
n
b
X
X
n
f
L
L
bU
Here b = (qBL/2mcβcγc)2, Xn = πnLs/L.
The effective potential Ueff provides the full descrip-
tion of the ion dynamics in the smooth one-particle ap-
proximation. In Ref. [7] the longitudinal smooth ap-
proximation with acceleration in SC linac was investi-
gated by the numerical simulation. In our case the anal-
ysis of the effective potential (9) makes it possible to
study the condition at which the radial and phase stabili-
ty of the beam is achieved. We begin our analysis with
expanding Ueff in the vicinity of its minimum (ψ = 0,
ρ = 0):
( ) ...ρ
2
1ψ
2
10,0 2222 +Ω+Ω+= rzeffeff UU (10)
The expansion coefficients here depend on the pa-
rameter of interaction α, the values of Lr/L, Ls/L and the
slipping factor kc. The radial and phase stability of the
beam will be provided when Ωz
2 > 0, Ωr
2 > 0, where Ωz,
Ωr are dimensionless frequencies of small longitudinal
and transverse oscillations.
In the simplest case when the phase velocity βG
changes from cavity to cavity and kc = 0
( ) ( )
( ) ( )( )
L
Lb s
r
z
+++−−=Ω
−−=Ω
c
22
c
c
2
c
φcos1χαφαsin2
φ2cosχαφαsin2 (11)
Here the value of χ depends on the ratio of Lr/L. For
some of Lr/L the value of χ is listed in Table 1.
Table 1
Lr/L 0 1/4 1/2 1
χ 1/3 3/16 1/12 0
In single wave approximation when Lr/L = 1 and fast
oscillation terms are absent, the value of χ = 0. In this
case, the dimensionless frequencies Ωz, Ωr are close to
the longitudinal and transverse phase advances per a
cavity μz and μr which were founded by transfer matrix
calculation. But the conditions of focusing are changed
if the parameter α is large and the fast oscillations are
161
considered. The functions Ωz(α) and Ωr(α) for different
values of φc are shown in Fig.4. The phase advances
should be less than about π/2 for stable beam mo-
tion [8]. In this case, the smooth approximation is ex-
pected to be almost accurate and dimensionless fre-
quencies Ωz, Ωr are close to the phase advances per a
period μz and μr.
Fig.4. The frequencies of longitudinal (solid lines) and
transverse (dot lines) oscillations for B = 12 T
(1 – φc = –10°, 2 – φc = –20° and 3 – φc = –30°)
As it can see from Fig.4, the longitudinal oscillation
will be stability for –π/4 < φc < 0 if the interaction pa-
rameter α is limited, α < αmax = sin(–φc)/χcos(2φc). In
this case the frequency of longitudinal oscillation has
maximum value in α = αmax/2. If the magnetic field is
absent the radial stability of the beam is achieved, if the
interaction parameter α > αmin = 2sin(–φc)/χ(1+ cos2φc)
The borders of stability area between Ωz = 0 and
Ωr = 0 are shown in Fig.5 for deferent values of magnet-
ic field, B, when Lr/L = 1/4.
The value α on stability diagram moves down quick-
ly on the α = 0 axis when the beam velocity increases.
For B = 0, the area of stability exists but it tapers abrupt-
ly and the radial stability is absent when the beam ve-
locity increases. The common area of stability can be
extended by a solenoid focusing which will also provide
a separate control of transverse and longitudinal beam
dynamics. For beam velocity β ≥ 0.1, α ≈ 2 it is suffi-
cient to increase the solenoid field B = 12T if the refer-
ence particle phase φc > −20°.
Fig.5. Stability area for different values of the magnetic
field B
3.2. APF AND SOLENOID FOCUSING
The smooth approximation has been applied to the
study of APF in RIB linac. New effective potential Ueff
must be find for this accelerating structure. The analysis
of the effective potential makes it possible to study the
condition at which the radial and phase stability of the
beam is achieved. In the simplest case when a slipping
factor kc = 0 it can find the dimensionless frequencies of
the small oscillations:
{
( )}
2
2 2
1 2
8α cos sinφ
α χ cos -χ sin cos 2φ ,
z c
c
Ω = − Δ +
⎡ ⎤+ Δ Δ⎣ ⎦
(12)
( ) ( )[ ] .φsin1sinχφcos1cosχ
2
α
sinφcosα4
22
2
22
1
2
ρ
⎭
⎬
⎫+Δ++Δ+
⎩
⎨
⎧ +Δ=Ω
cc
c
(13)
In this expressions ϕ1,2 = ϕc ± Δ are reference par-
ticle phases in the neighbour cavities, the values of χ1,2
depend on the ratio of Lr/L (see Table 2). The common
area of the beam stability is shown in Fig.3 by the fill-
ing. This area is located between the borders where
Ωz = 0 and Ωr = 0.
Table 2
Lres 0 L/4 L/2 L
χ1 1/6 1/24 0 0
χ2 1/2 1/3 1/6 0
The analysis of APF for the charge-to-mass ratio
Z/A = 1/66 shows that the effective focusing and accele-
ration are realized, when the beam velocity
0.01< βc < 0.02 and the cavity length is small
(Lr/L < 1/4). The longitudinal and transverse stabilities
are realized simultaneously only for a small asymmetry
at the choice of the reference particle phases (φc = −5°)
and for large value Δ . If the value of Δ increases the
rate of energy gain reduces. The working point is lo-
cated near right side of beam stability border where
Ωz = 0 for symmetric choice of the reference particle
phases (φc = 0). In this case the longitudinal acceptance
is very small.
Fig.6. Separatrixes for φc = –5°, Δ = 45° and ρ = 0 for
different parameter α:
1 – α = 2, 2 – α = 1 and 3 – α = 0.1
It is interesting to investigate the nonlinear ion beam
dynamics in such accelerated structure. Using of the
162
effective potential Ueff we can calculate the longitudinal
acceptance. In Fig.6 it is shown the separatrixes for
φc = −5°, Δ = 45° and ρ = 0 when the beam velocity
increases and the parameter α decreases from 2 to 0.1.
The energy spread of the separatrix, Δγ = (LV/L)(dψ/dξ),
decreases in 10 times and the phase length Ψ of separa-
trix decreases in 3 times. In this case longitudinal accep-
tance decreases in 15 times. If the value of the cavity
voltage amplitude U is preset the separatrix area de-
pends on the value of Lr/L ratio. The smooth approxima-
tion gives a weaker effective RF bucket, i.e. smaller
phase acceptance and potential well depth, compared
with the single wave approximation when the fast oscil-
lations are not considered.
For small α the value of longitudinal acceptance
quickly decreases and size of beam envelope Xm in-
creases. These disadvantages of APF can be removed by
adding a focusing solenoid into focusing period which
will also allow separate control of the transverse and
longitudinal beam dynamics. The combination of low-
field SC solenoids and APF is very effectively at all
range of beam velocity 0.02 ≤ β ≤ 0.06. The combined
focusing structure includes both SC solenoid and APF
in every focusing period. The transverse focusing can be
realized in the magnetic field B ≤ 6 Т for maximum
value of beam envelop Xm=4 mm and B ≤ 9 Т for beam
envelop Xm=3 mm. But in this case the longitudinal fo-
cusing will become worse because the longitudinal os-
cillation frequency Ωz will be small.
CONCLUSION
Two methods of the focusing analysis are compared
for low ion velocities. The low charge state beams re-
quire stronger transverse focusing in RIB linac. In order
to reduce the cost of the SC solenoids it can be used
APF or the combination of low-field SC solenoids and
ARF. By the smooth approximation it is studied more
detailed nonlinear ion beam dynamics and found the
borders of the beam stability area. It is done the recom-
mendation for choice of the reference particle phases
and the value of solenoid magnetic field B.
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p.145.
УСКОРЕНИЕ ИОННОГО ПУЧКА В СИСТЕМЕ ИЗ ПЕРИОДИЧЕСКОЙ
ПОСЛЕДОВАТЕЛЬНОСТИ НЕЗАВИСИМО ФАЗИРУЕМЫХ РЕЗОНАТОРОВ
Э.С. Масунов, А.В. Самошин
Сверхпроводящий линейный ускоритель ионов основан на использовании периодической системы, со-
стоящей из идентичных ниобиевых резонаторов. Посредством специального фазирования ВЧ-резонаторов
можно обеспечить устойчивое движение частиц во всем ускорителе. В этой статье найдены условия устой-
чивости движения пучка ионов. Матричный метод расчета и уравнение движения в гладком приближении
используются для анализа фазопеременной фокусировки пучка в сверхпроводящем ускорителе.
ПРИСКОРЕННЯ ІОННОГО ПУЧКУ У СИСТЕМІ З ПЕРІОДИЧНОЮ ПОСЛІДОВНІСТЮ
НЕЗАЛЕЖНО ФАЗУЄМИХ РЕЗОНАТОРІВ
Е.С. Масунов, А.В. Самошин
Надпровідний лінійний прискорювач іонів заснований на використанні періодичної системи, що склада-
ється з ідентичних ніобієвих резонаторів. За допомогою спеціального фазування ВЧ-резонаторів можна за-
безпечити стійкий рух часток у всьому прискорювачі. У статті знайдено умови стійкості руху пучка іонів.
Для аналізу фазозмінного фокусування пучка у надпровідному прискорювачі використано матричний метод
розрахунку і рівняння руху у гладкому наближенні.
|
| id | nasplib_isofts_kiev_ua-123456789-111403 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:33:15Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Masunov, E.S. Samoshin, A.V. 2017-01-09T18:56:57Z 2017-01-09T18:56:57Z 2008 Ion beam acceleration in system from periodic sequence of independetly phased cavities / E.S. Masunov, A.V. Samoshin // Вопросы атомной науки и техники. — 2008. — № 3. — С. 158-162. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 29.27.-A, 29.27.Bd https://nasplib.isofts.kiev.ua/handle/123456789/111403 Ion superconducting linac is based on periodic system consisting of the identical niobium cavities. By specific
 phasing of the RF cavities one can provide a stable particle motion in the whole accelerator. In this paper the beam
 stability conditions are founded. The matrix calculation and motion equation in the smooth approximation are used
 for alternating phase focusing analysis in superconducting linac. Надпровідний лінійний прискорювач іонів заснований на використанні періодичної системи, що складається з ідентичних ніобієвих резонаторів. За допомогою спеціального фазування ВЧ-резонаторів можна забезпечити стійкий рух часток у всьому прискорювачі. У статті знайдено умови стійкості руху пучка іонів. Для аналізу фазозмінного фокусування пучка у надпровідному прискорювачі використано матричний метод розрахунку і рівняння руху у гладкому наближенні. Сверхпроводящий линейный ускоритель ионов основан на использовании периодической системы, состоящей из идентичных ниобиевых резонаторов. Посредством специального фазирования ВЧ-резонаторов можно обеспечить устойчивое движение частиц во всем ускорителе. В этой статье найдены условия устойчивости движения пучка ионов. Матричный метод расчета и уравнение движения в гладком приближении используются для анализа фазопеременной фокусировки пучка в сверхпроводящем ускорителе. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения, сильноточные пучки Ion beam acceleration in system from periodic sequence of independetly phased cavities Прискорення іонного пучку у системі з періодичною послідовністю незалежно фазуємих резонаторів Ускорение ионного пучка в системе из периодической последовательности независимо фазируемых резонаторов Article published earlier |
| spellingShingle | Ion beam acceleration in system from periodic sequence of independetly phased cavities Masunov, E.S. Samoshin, A.V. Новые методы ускорения, сильноточные пучки |
| title | Ion beam acceleration in system from periodic sequence of independetly phased cavities |
| title_alt | Прискорення іонного пучку у системі з періодичною послідовністю незалежно фазуємих резонаторів Ускорение ионного пучка в системе из периодической последовательности независимо фазируемых резонаторов |
| title_full | Ion beam acceleration in system from periodic sequence of independetly phased cavities |
| title_fullStr | Ion beam acceleration in system from periodic sequence of independetly phased cavities |
| title_full_unstemmed | Ion beam acceleration in system from periodic sequence of independetly phased cavities |
| title_short | Ion beam acceleration in system from periodic sequence of independetly phased cavities |
| title_sort | ion beam acceleration in system from periodic sequence of independetly phased cavities |
| topic | Новые методы ускорения, сильноточные пучки |
| topic_facet | Новые методы ускорения, сильноточные пучки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111403 |
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