Comparison of two focusing methods in low-energy ion linac with electric undulator fields
It is well known that nonsynchronous harmonics of RF field (RF undulator) are focusing the particles [1, 2].
 In low-energy linear accelerators the periodic sequence of electrostatic lenses (electrostatic undulator) can be used for
 the ion beams focusing too. The conditions of the b...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Cite this: | Comparison of two focusing methods in low-energy ion linac with electric undulator fields / E.S. Masunov, V.S. Dyubkov // Вопросы атомной науки и техники. — 2008. — № 3. — С. 166-170. — Бібліогр.: 10 назв. — англ. |
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| author | Masunov, E.S. Dyubkov, V.S. |
| author_facet | Masunov, E.S. Dyubkov, V.S. |
| citation_txt | Comparison of two focusing methods in low-energy ion linac with electric undulator fields / E.S. Masunov, V.S. Dyubkov // Вопросы атомной науки и техники. — 2008. — № 3. — С. 166-170. — Бібліогр.: 10 назв. — англ. |
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| description | It is well known that nonsynchronous harmonics of RF field (RF undulator) are focusing the particles [1, 2].
In low-energy linear accelerators the periodic sequence of electrostatic lenses (electrostatic undulator) can be used for
the ion beams focusing too. The conditions of the beam stability were found and analyzed for two undulator types.
Відомо, що несинхронні гармоніки високочастотного поля (ВЧ-ондулятор) фокусують частинки. У лінійних прискорювачах на малу енергію періодична послідовність електростатичних лінз (електростатичний ондулятор) теж може використатися для фокусування іонних пучків. Умови стійкості пучка знайдені і проаналізовані для двох типів ондулятора.
Известно, что несинхронные гармоники высокочастотного поля (ВЧ-ондулятор) фокусируют частицы. В линейных ускорителях на малую энергию периодическая последовательность электростатических линз (электростатический ондулятор) тоже может использоваться для фокусировки ионных пучков. Условия устойчивости пучка найдены и проанализированы для двух типов ондулятора.
|
| first_indexed | 2025-12-07T16:58:04Z |
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COMPARISON OF TWO FOCUSING METHODS IN LOW-ENERGY
ION LINAC WITH ELECTRIC UNDULATOR FIELDS
E.S. Masunov, V.S. Dyubkov
Department of Electrophysical Installations, Moscow Engineering Physics Institute (State
University), Kashirskoe shosse 31, Moscow 115409, Russian Federation, +7(495)323-9292
E-mail: ESMasunov@mephi.ru
It is well known that nonsynchronous harmonics of RF field (RF undulator) are focusing the particles [1, 2].
In low-energy linear accelerators the periodic sequence of electrostatic lenses (electrostatic undulator) can be used for
the ion beams focusing too. The conditions of the beam stability were found and analyzed for two undulator types.
PACS: 41.75.Lx; 41.85.Ne
1. INTRODUCTION
The problem of the effective low-energy linac de-
sign is of interest to many fields of science, industry and
medicine (e.g. nuclear physics, surface hardening, ion
implantation, hadron therapy). The most significant
problem for low-energy high-current beams of charged
particles is the question of the transverse stability
through Coulomb repelling forces influence. Low-ener-
gy heavy-ion beams transport is known to be realized by
means of the periodic sequence of electrostatic lenses
(electrostatic undulator) [3]. It offers to constructively
join a periodic RF cavity and the electrostatic undulator
(ESU) in the same device. To accelerate the low-energy
ion beams one of the following RF focusing types can
be used: alternating phase focusing (APF), radio fre-
quency quadrupoles (RFQ), focusing by means of the
nonsynchronous wave field as well as the undulator RF
focusing. The main principles of APF were described in
Refs. [4, 5]. The modification of APF was suggested in
later studies [6]. A reached threshold beam current in
RFQ [7] is about 100…150 mA and the further current
rise leads to severe difficulties. A particle focusing with
the use of the nonsynchronous wave in the two-wave
approach was considered in Ref. [8]. The methods were
used to describe RF focusing in reference mentioned
above have a number of shortcomings. For example,
there is no correct relationship between longitudinal and
transverse beam motion, the averaging method which
was used is not quite valid. Detailed analysis of the fo-
cusing by means of nonsynchronous waves of RF field
shows that the focusing by the slow harmonic field in
periodical ordinary Wideröe type and Alvarez type
structures is not effective since the acceleration rate is
very small. Increasing the fast harmonic amplitude leads
to appearance of the longitudinal beam instability,
which quickly disrupts the resonant conditions. The RF
focusing by the nonsynchronous harmonics was studied
in [2] particularly.
Alternatively, the acceleration and the focusing can
be realized by means of the electromagnetic waves
which are nonsynchronous with beam (the so-called un-
dulator focusing) [9]. Systems without synchronous
wave are effective only for the light ion beams. For the
low-energy heavy-ion beams to be accelerated it is nec-
essary to have the synchronous wave with the particles.
In the case of RF focusing, in the bunch frame the slow
wave affects the particles similar to the electrostatic un-
dulator. The goal of this work is the analysis and the
comparison of the RF focusing and the electrostatic one.
2. MOTION EQUATION
The analytical investigation of the beam dynamics in
a polyharmonical field is a difficult problem. The rapid
longitudinal and transverse oscillations as well as the
strong dependence of the field components on the trans-
verse coordinates does not allow us to use the linear ap-
proximation in the paraxial region for a field series. Af-
ter all, the analytical beam dynamics investigation can
be carried out by means of the averaging method over
the rapid oscillations period (the so-called smooth ap-
proximation) in the oscillating fields, which was sug-
gested by P.L. Kapitsa [10] for the first time. Let us ex-
press RF field in an axisymmetric periodic resonant
structure and ESU field as an expansion by the standing
wave spatial harmonics assuming that the structure peri-
od is a slowly varying function of the longitudinal coor-
dinate z
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ,sin
;cos
;cossin
;coscos
0
1
0
0
0
1
0
0
∑ ∫
∑ ∫
∑ ∫
∑ ∫
∞
=
∞
=
∞
=
∞
=
=
=
ω=
ω=
n
u
n
u
n
u
n
u
r
n
u
n
u
n
u
n
u
z
n
nnnr
n
nnnz
dzkrkIEE
dzkrkIEE
tdzkrkIEE
tdzkrkIEE
(1)
where nE , u
nE are the nth RF and ESU fields harmonic
amplitude on the axis; ( ) Dnkn π+θ= 2 is the propaga-
tion wave number for the nth RF field spatial harmonic,
( ) uuu
n Dnk π+θ= 2 is the factor of the nth ESU field
harmonic; D, Du are the geometric periods of the reso-
nant structure and ESU; θ, θu are the phase advances per
period D, Du respectively; ω is the angular frequency;
I0, I1 are modified Bessel functions of the first kind.
We shall assume the beam velocity (the one-particle
approximation) υ does not equal one of the spatial har-
monic phase-velocities υn = ω/kn except the synchronous
harmonic of RF field, the geometric period of RF struc-
ture being defined as ( )πθ+λβ= 2sD s , where s is the
synchronous harmonic number, βs is the relative veloci-
ty of the synchronous particle, λ denotes RF wave-
length. Thus, the solution of the motion equation (the
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 3.
Series: Nuclear Physics Investigations (49), p.166-170.
166
particle path) in the rapidly oscillating field (1) we shall
search as a sum of a slowly varying beam radius-vector
component and a rapidly oscillating one. We assume
that the amplitude of the rapid velocity oscillations is
much smaller than the slowly varying velocity compo-
nent for the smooth approximation to be employed.
With the aid of the averaging over the rapid oscillations
(as it was done in Ref. [1]) we obtain the motion equa-
tion, in the bunch frame, in the form
,grad22
effUdtRd
−= (2)
where ( )rzzR s ,−=
, effU
is the effective potential
function (EPF) which describes the tridimensional low-
energy beam interaction with the polyharmonical field
of the system and determines the beam-wave system
Hamiltonian ( ) effUdtRdH
+=
2
5.0 . The EPF depends
only on the slowly varying (in comparison with the
rapid oscillation period) transverse coordinate r and
the phase difference of the particle in the synchronous
harmonic wave tzdk s ω−=ϕ ∫ and the quasi-equilibri-
um (synchronous) particle φs.
3. EPF FOR DIFFERENT STRUCTURES
3.1. WIDERÖE TYPE STRUCTURE
If we put θu = θ = π, Du = D and take point ζ = ρ = 0
as the reference point of normalized EPF (
2
seffeff UU β=
), then EPF for Wideröe type structure
can be written as WWWW
eff UUUU 210 ++= , where
( ) ( ) ( ) ( )[ ]
( ) ( )
( )
( ) ( )[
( ) ( ) ]
( ) ( ) ( )[
( ) ] .2cos
2sin222cos
8
12cos2sin2
22cos
16
1
;
4
1
16
1
16
1
;sincossin
2
1
,,
2
2
2
,
2
,,
12
,
2
,
0
2
,
02
,
2
,
02
,
2
1
00
s
ss
psn
kkk
sn sn
pn
ss
kkk
sn
s
psn
sn
pnW
sn
n sn
u
n
sn
n sn
nsn
sn sn
nW
ssss
W
f
ee
f
ee
U
f
kk
e
f
e
f
e
U
IeU
spn
spn
ϕ−
−ϕζ+ϕ+ζρ×
×
ν
+ϕ−ϕζ+
+ϕ+ζρ
ν
=
ρ
+
+ρ
µ
+ρ
ν
=
ϕ−ϕζ−ϕ+ζρ−=
∑
∑
∑
∑∑
=−
≠
=+
≠
≠
(3)
Here 22 mceEe snn π βλ= , 22 mceEe s
u
n
u
n π βλ= ,
sz λ βπ=ξ 2 , sξ−ξ=ζ , sr λ βπ=ρ 2 , tω=τ are
the normalized values; s, n, p = 0, 1, 2 …,
( ) ( ) ssnsnssnsn kkkkkk +=µ−=ν ,, , and the func-
tions of the dimensionless transverse coordinate are de-
fined as
( )
( ) ;
;1
1100
,,
1
2
1
2
0
,
0
ρ
ρ−
ρ
ρ=ρ
−
ρ+
ρ=ρ
s
p
s
n
s
p
s
npsn
s
n
s
nsn
k
k
I
k
k
I
k
k
I
k
k
If
k
k
I
k
k
If
( ) .1100
,,
2
ρ
ρ+
ρ
ρ=ρ
s
p
s
n
s
p
s
npsn
k
k
I
k
k
I
k
k
I
k
k
If
From these expressions we can see that the term
WU 0 of EPF is responsible for both the beam accelera-
tion and its transverse defocusing. The term WU1 influ-
ences only on the transverse motion, always focusing
the beam in the transverse direction. The term WU 2 has
an influence not only on the longitudinal motion but on
the transverse one. The extreme point of WU 2 as well as
WU 0 is a saddle point. Therefore, the necessary condi-
tion for simultaneous transverse and longitudinal focus-
ing is the existence of the total minimum of EPF. If
ESU is absent (i.e. 0=u
ne ) the term WU1 is reduced. In
this case the transverse stability is achieved only by us-
ing nonsynchronous harmonics of RF field. For the am-
plitudes of the nonsynchronous harmonics to be in-
creased we should include additional electrodes. There-
by, the utilization of ESU allows us to achieve the trans-
verse stability without the complication channel geome-
try if the equal in absolute value d-c potentials are sup-
plied on the same electrodes which are used to excite
RF field, i.e. we can constructively join the periodic RF
system and ESU in the same device.
At first we analyze EPF in the paraxial region. The
EPF W
effU is expanded in Maclaurin’s series
( ) ,6222 4322222 α+δ ζ+ε ζ ρ+ρω+ζω= ρζ oU W
eff
(4)
where the expansion coefficients are given by
( ) ( )
( )
( )
( )
( )
( )
( ) ( ) .;
;2cos
16
1
2cos
32
1
8
3
32
3
32
3sin
4
1
;2cos
2
1
2cos
4
1sin
2
1
22
2
2
22
2
,
2
2
22
2
,
2
2
2
,
2
2
2
,
2
2
2
2
,
2
2
,
2
ss
kkk
sn
s
s
pnpn
sn
pn
kkk
sn
s
s
pnpn
sn
pn
n
u
n
n s
n
sn
n
sn s
n
sn
n
ss
kkk
sn
s
sn
pn
kkk
sn
s
sn
pn
ss
spn
spn
spn
spn
k
kkkkee
k
kkkkee
e
k
ke
k
ke
e
ee
ee
e
ϕ∂ω∂=δϕ∂ω∂=ε
ϕ
++
ν
+
+ϕ
−+
ν
+
++
µ
+
+
ν
+ϕ−=ω
ϕ
ν
−
−ϕ
ν
−ϕ=ω
ζρ
=−
≠
=+
≠
≠
ρ
=−
≠
=+
≠
ζ
∑
∑
∑∑
∑
∑
∑
(5)
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 3.
Series: Nuclear Physics Investigations (49), p.166-170.
167
It is necessary that the parameters of the channel will
be chosen in terms of the conditions 0,0 22 >ω>ω ρζ
(for the simultaneous transverse and longitudinal focus-
ing). Furthermore, if we take into account the third-or-
der terms in the anharmonic potential (4) it may lead to
appearance of internal parametric resonances. It can de-
stroy the stable beam dynamics due to beam-wave sys-
tem energy transfer between two degrees of freedom. In
this case the small oscillations frequencies satisfy the re-
lation ωρ/ωζ = l/2, where l = 1, 2, 3 … . Another impor-
tant restriction on the choice of the spatial harmonic am-
plitudes can be obtained from the condition of nonover-
lapping for different waves resonances in the phase
space ( )ζζ , . On the one hand, this restriction defines
limits of the applicability of the averaging method. On
the other hand, it is the necessary condition of the longi-
tudinal (phase) stability.
The effective separatrix for the axial particles can be
found analytically in terms of the system Hamiltonian.
For the saddle point to be defined we are using the
equation 0234 =++++ dcxgxqxx , where the coeffi-
cients are certain functions of the harmonic amplitudes
and φs. Using Decartes – Euler or Ferrari’s solution we
have ( ) sileft x ϕ−=ζ arctg2 , where xi is a real root of the
quartic equation, which is chosen so that ζleft < 0. Know-
ing the position of the effective separatrix saddle point
the bucket boundary is determined by the equation
( ) ( )( ) 21
0,20,2 ζ−ζ±=ζ W
effleft
W
eff UU . (6)
The capture region of ESU in approach of the basic
harmonic can be expressed as:
( )( )[ ] 21
0 sin12 ψ+ϕ+=ββ uu
s
u e , (7)
where ψ = 0, if 00 >ue or ψ = π, if 00 <ue .
As it was said the condition which determines the
bottom limit of the spatial harmonic amplitudes is the
existence of the absolute minimum of EPF. When we
are using the channel with a simple period (one elec-
trode per period D) we can take into account only
uee 00 , in W
effU because the higher harmonics are smaller
than written above. Therefore, the condition 02 >ω ρ
may be represented as
( ) ( ) .1613sin2 0
2
00 −ϕ> eee s
u (8)
3.2. ALVAREZ TYPE STRUCTURE
The EPF for Alvarez type structure A
effU
(θ = 0, θu = π; Du = D) has a view similar to W
effU . The
most important feature is the existence of an additional
term in AU 2 , where superscript A denotes values of the
structure at hand. Thus, the additional term in AU 2 and
the term AU1 become
( ) ( ) ( ) ( )[ ]ssss Iee ϕ−ϕζ+ϕ+ζρ 2cos2sin222cos2
4
1
020 ;
( ) ( )
,1
4
1
16
1
16
1
2
1
2
0
2
,
02
,
2
,
02
,
2
1
−
ρ+
ρ⋅
+
+ρ
µ
+ρ
ν
=
∑
∑∑
≠
s
u
m
s
u
m
m s
u
m
u
m
sn
n sn
nsn
sn sn
nA
k
k
I
k
k
I
kk
e
f
e
f
e
U
(9)
where s, n, p > 0 and m ≥ 0 unlike the system consid-
ered above. The harmonic amplitude of RF field en for
Alvarez type structure is not equal to Wideröe type
structure one. Moreover, in this case the basic harmonic
is e1, and e0 is the dimensionless average field value.
The existence of the additional term in AU 2 leads to the
next serious result. The additional term may be compa-
rable with AU 0 and essentially increases the acceleration
rate since the average field value is large. One can as-
sume that an Alvarez type structure, which is commonly
used for acceleration of medium-beta particles, may be
used for the low-energy beam acceleration. In this case
the transverse stability can be achieved by using ESU in
view of the period smallness. The resume made about
the each term of W
effU in previous subsection is valid for
A
effU in this subsection too.
4. NUMERICAL SIMULATION
The computer simulation of high-intensity proton
beam dynamics in the discussed Wideröe type structure
with the basic spatial harmonic (e0) of the RF field was
carried out by means of the specialized computer code
BEAMDULAC – ARF3 [2]. In the case of RF focusing
only the first nonsynchronous harmonic was taken into
account. We examined only the basic spatial harmonic
of ESU (i.e. ue0 ) studying the electrostatic focusing.
Simulation parameters are the following: beam injection
energy Win is 80 keV; input current Iin = 0.1 A; beam ra-
dius rb = 2 mm; ψ = π; longitudinal/transverse input
beam emittance εφ/ερ = 3.2π keV·rad/20π mm·mrad; RF
wave-length λ = 1.5 m; input (Ein) and output (Eout) val-
ues of the synchronous harmonic field strength are
1.7 kV/cm and 18.4 kV/cm respectively. The lengths of
the accelerator (L), amplitude rise (Le) and the equilibri-
um phase decay (Lgr) are 2.5 m, 2.325 m and 1.8 m;
channel aperture a = 4 mm; relative energy spread is
2%; longitudinal/transverse input channel acceptance
Aφ/Aρ = 33π keV·rad/40π mm·mrad. The amplitude ratio
is e1/e0 = e0
u/e0 ≈ 10, the law of the synchronous har-
monic amplitude variation along Le is given by
π+=
e
out L
zEE
19
5sin676.1093.0 2
0 . (10)
The synchronous harmonic amplitude equals to Eout
for z ≥ Le. The quasi-equilibrium particle phase is linear-
ly reduced from value π/2 to π/4 at the length Lgr and
equals to π/4 for z ≥ Lgr.
The output longitudinal and transverse phase spaces
are shown in Fig.1 (for the RF focusing) and Fig.2 (for
the electrostatic focusing). As we can see in Fig.1,a the
beam has uniform phase and velocity distributions in-
side the effective separatrix at the end of structure. In
Fig.2,a it is shown that the beam has nonuniform phase
168
and velocity distributions. Moreover, beam periodically
traverses the synchronous harmonic separatrix boundary
because the strong ESU field has an effect on the longi-
tudinal particle motion. Particles remain inside of the
separatrix in the case of the averaged motion. The out-
put transmission, energy, longitudinal and transverse
emittances are about 66%, 0.71 MeV, 100π keV·rad,
54π mm∙mrad for two structure types respectively. The
particle loss is observed in the longitudinal direction in
both cases. It is the result of an interaction with the non-
synchronous harmonic which leads to increase of the
beam amplitude oscillations. Note that the law of the
synchronous harmonic amplitude variation (10) is not
optimal to obtain the maximal output energy under the
high transmission. The numerical simulation results
confirmed similarity between RF focusing and the elec-
trostatic one. All results obtained in the smooth approxi-
mation coincide up to 10%.
Fig.1. The output beam emittances for RF focusing:
a – longitudinal; b – transverse
Fig.2. The output beam emittances for ESU focusing:
a – longitudinal; b – transverse
5. CHANNEL GEOMETRY CHOICE
For Wideröe type structures with a simple period the
spatial harmonic amplitudes are a rapidly decreasing
function of its number which proportional to
( ) ( ) 11
0 sin −−
nnnmax YYakIE , where Emax is the maximal
field strength at the aperture a in the electrode-gap,
Yn = πng/D, g – the inter-electrode gap width. For the
amplitude e1 to be increased up to 10e0 it is necessary to
set three electrodes on the period D and either provide
the adjacent electrodes (which have equal apertures)
with different potentials or periodically vary the internal
radius of the adjacent electrodes. Only the latter way
can be practically realized in the RF cavity. In this case
the additional electrodes with internal radius b must be
shifted to the position D/3 + ∆ and 2D/3 – ∆ respective-
ly, where 10 32 eDe π=∆ . By varying the length and
corner radii of electrodes one can depress the higher
harmonics and obtain only two waves in the structure.
The ratio between internal radii b/a versus a/D for dif-
ferent values of e1/e0 is shown in Fig.3.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 3.
Series: Nuclear Physics Investigations (49), p.166-170.
169
Fig.3. Values of b/a vs a/D for different ratio e1/e0
Note, if the beam injection energy is about 100 keV
and λ = 1.5 m the electrodes lengths are about 3 mm.
Thus, the significant amplitude e1 may lead to RF dis-
charge; also it is difficult to produce such small con-
struction units.
As it was mentioned above, the additional d-c voltage
generator can be used for the transverse focusing in the
structure with the simple period. However, in this case
we face difficulties which are that the desired value ue0
must be held along the channel. The question of high-
voltage input into RF cavity should be investigated too.
CONCLUSION
The comparison of two undulator types was done.
The possibility of the electrostatic undulator application
to focusing the low-energy high-intensity heavy ions
was studied. The computer simulation of the high-inten-
sity ion beam dynamics in Wideröe type structure with
RF undulator as well as with ESU was carried out. It
was shown that the electrostatic undulator can be a sub-
stitution for RF one. Using Alvarez type structure for
low-energy beam acceleration was discussed. It is inter-
esting to study a structure realization possibility with
ESU operating at 0-mode for further increasing the ac-
celeration rate. Thus, the discussed structures need the
next deep research.
REFERENCES
1. É.S. Masunov. Particle dynamics in a linear undula-
tor accelerator // Zhurnal Tekhnicheskoi Fiziki.
1990, v.60, №.8, p.152-157 (in Russian).
2. É.S. Masunov, N.E. Vinogradov. RF focusing of
ion beams in the axisymmetric periodic structure of
a linear accelerator // Zhurnal Tekhnicheskoi Fiziki.
2001, v.71, №9, p.79-87 (in Russian).
3. É.S. Masunov, S.M. Polozov, T.V. Kulevoy,
V.I. Pershin. Low energy ribbon ion beam source
and transport system // Problems of Atomic Science
and Technology, Series “Nuclear Physics Investi-
gations” (46), 2006, №2, p.123-125.
4. Ya.B. Fainberg. Phase-alternating focusing in linear
accelerators // Zhurnal Tekhnicheskoi Fiziki. 1959,
v.29, №5, p.568-579 (in Russian).
5. M.L. Good. Phase-reversal focusing in linear accel-
erators // The Physical Review. Second Series.
1953, v.92, №2, p.538.
6. V.V. Kushin. On increasing of efficiency of alter-
nating-phase focusing in linear accelerators //
Atomnaya Énergiya. 1970, v.29, №2, p.123-124 (in
Russian).
7. I.M. Kapchinskij, V.A. Teplyakov. Linear ion ac-
celerator with spatially homogeneous strong focus-
ing // Pribory i Tekhnika Éksperimenta. 1970, №2,
p.19-22 (in Russian).
8. V.K. Baev, S.A. Minaev. Efficiency of the ion fo-
cusing by field of traveling wave in linear accelera-
tor // Zhurnal Tekhnicheskoi Fiziki. 1981, v.51,
№11, p.2310-2314 (in Russian).
9. É.S. Masunov, S.M. Polozov. Ion beam accelera-
tion and focusing in RF structures with undulators
// Zhurnal Tekhnicheskoi Fiziki. 2005, v.75, №7,
p.112-118 (in Russian).
10. P.L. Kapitsa. Dynamic stability of a pendulum with
an oscillating suspension point // Zhurnal Éksperi-
mental'noi i Teoreticheskoi Fiziki. 1951, v.21, №5,
p.588-597 (in Russian).
СРАВНЕНИЕ ДВУХ СПОСОБОВ ФОКУСИРОВКИ ИОНОВ В ЛИНЕЙНОМ УСКОРИТЕЛЕ
НА МАЛУЮ ЭНЕРГИЮ С ПОМОЩЬЮ ЭЛЕКТРИЧЕСКИХ ПОЛЕЙ ОНДУЛЯТОРОВ
Э.С. Масунов, B.C. Дюбков
Известно, что несинхронные гармоники высокочастотного поля (ВЧ-ондулятор) фокусируют частицы. В
линейных ускорителях на малую энергию периодическая последовательность электростатических линз
(электростатический ондулятор) тоже может использоваться для фокусировки ионных пучков. Условия
устойчивости пучка найдены и проанализированы для двух типов ондулятора.
ПОРІВНЯННЯ ДВОХ СПОСОБІВ ФОКУСУВАННЯ ІОНІВ У ЛІНІЙНОМУ ПРИСКОРЮВАЧІ
НА МАЛУ ЕНЕРГІЮ ЗА ДОПОМОГОЮ ЕЛЕКТРИЧНИХ ПОЛІВ ОНДУЛЯТОРІВ
Е.С. Масунов, B.C. Дюбков
Відомо, що несинхронні гармоніки високочастотного поля (ВЧ-ондулятор) фокусують частинки. У
лінійних прискорювачах на малу енергію періодична послідовність електростатичних лінз
(електростатичний ондулятор) теж може використатися для фокусування іонних пучків. Умови стійкості
пучка знайдені і проаналізовані для двох типів ондулятора.
170
СРАВНЕНИЕ ДВУХ СПОСОБОВ ФОКУСИРОВКИ ИОНОВ В ЛИНЕЙНОМ УСКОРИТЕЛЕ
НА МАЛУЮ ЭНЕРГИЮ С ПОМОЩЬЮ ЭЛЕКТРИЧЕСКИХ ПОЛЕЙ ОНДУЛЯТОРОВ
ПОРІВНЯННЯ ДВОХ СПОСОБІВ ФОКУСУВАННЯ ІОНІВ У ЛІНІЙНОМУ ПРИСКОРЮВАЧІ
НА МАЛУ ЕНЕРГІЮ ЗА ДОПОМОГОЮ ЕЛЕКТРИЧНИХ ПОЛІВ ОНДУЛЯТОРІВ
|
| id | nasplib_isofts_kiev_ua-123456789-111428 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:58:04Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Masunov, E.S. Dyubkov, V.S. 2017-01-09T20:15:32Z 2017-01-09T20:15:32Z 2008 Comparison of two focusing methods in low-energy ion linac with electric undulator fields / E.S. Masunov, V.S. Dyubkov // Вопросы атомной науки и техники. — 2008. — № 3. — С. 166-170. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 41.75.Lx; 41.85.Ne https://nasplib.isofts.kiev.ua/handle/123456789/111428 It is well known that nonsynchronous harmonics of RF field (RF undulator) are focusing the particles [1, 2].
 In low-energy linear accelerators the periodic sequence of electrostatic lenses (electrostatic undulator) can be used for
 the ion beams focusing too. The conditions of the beam stability were found and analyzed for two undulator types. Відомо, що несинхронні гармоніки високочастотного поля (ВЧ-ондулятор) фокусують частинки. У лінійних прискорювачах на малу енергію періодична послідовність електростатичних лінз (електростатичний ондулятор) теж може використатися для фокусування іонних пучків. Умови стійкості пучка знайдені і проаналізовані для двох типів ондулятора. Известно, что несинхронные гармоники высокочастотного поля (ВЧ-ондулятор) фокусируют частицы. В линейных ускорителях на малую энергию периодическая последовательность электростатических линз (электростатический ондулятор) тоже может использоваться для фокусировки ионных пучков. Условия устойчивости пучка найдены и проанализированы для двух типов ондулятора. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения, сильноточные пучки Comparison of two focusing methods in low-energy ion linac with electric undulator fields Порівняння двох способів фокусування іонів у лінійному прискорювачі на малу енергію за допомогою електричних полів ондуляторів Сравнение двух способов фокусировки ионов в линейном ускорителе на малую энергию с помощью электрических полей ондуляторов Article published earlier |
| spellingShingle | Comparison of two focusing methods in low-energy ion linac with electric undulator fields Masunov, E.S. Dyubkov, V.S. Новые методы ускорения, сильноточные пучки |
| title | Comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| title_alt | Порівняння двох способів фокусування іонів у лінійному прискорювачі на малу енергію за допомогою електричних полів ондуляторів Сравнение двух способов фокусировки ионов в линейном ускорителе на малую энергию с помощью электрических полей ондуляторов |
| title_full | Comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| title_fullStr | Comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| title_full_unstemmed | Comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| title_short | Comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| title_sort | comparison of two focusing methods in low-energy ion linac with electric undulator fields |
| topic | Новые методы ускорения, сильноточные пучки |
| topic_facet | Новые методы ускорения, сильноточные пучки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111428 |
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