Space charge effects and RF focusing of ribbon beam in ion linac
Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and acceleration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing influence (RF focusing concept). Investigation of intensive ribbon beam dyna...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | Space charge effects and RF focusing of ribbon beam in ion linac / E.S. Masunov, N.E. Vinogradov, S.M. Polozov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 71-73. — Бібліогр.: 3 назв. — англ. |
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irk-123456789-789892015-03-25T03:01:47Z Space charge effects and RF focusing of ribbon beam in ion linac Masunov, E.S. Vinogradov, N.E. Polozov, S.M. Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and acceleration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing influence (RF focusing concept). Investigation of intensive ribbon beam dynamics features is carried out. The space charge effects are studied numerically by means of "super particles" approach. The proposal of 80% transmission 1 A limit current ribbon beam accelerator for the ITER neutral injection system and some another applications is presented. 2001 Article Space charge effects and RF focusing of ribbon beam in ion linac / E.S. Masunov, N.E. Vinogradov, S.M. Polozov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 71-73. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS numbers: 41.75.L, 41.85.E, 29.27.F http://dspace.nbuv.gov.ua/handle/123456789/78989 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and acceleration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing influence (RF focusing concept). Investigation of intensive ribbon beam dynamics features is carried out. The space charge effects are studied numerically by means of "super particles" approach. The proposal of 80% transmission 1 A limit current ribbon beam accelerator for the ITER neutral injection system and some another applications is presented. |
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Article |
| author |
Masunov, E.S. Vinogradov, N.E. Polozov, S.M. |
| spellingShingle |
Masunov, E.S. Vinogradov, N.E. Polozov, S.M. Space charge effects and RF focusing of ribbon beam in ion linac Вопросы атомной науки и техники |
| author_facet |
Masunov, E.S. Vinogradov, N.E. Polozov, S.M. |
| author_sort |
Masunov, E.S. |
| title |
Space charge effects and RF focusing of ribbon beam in ion linac |
| title_short |
Space charge effects and RF focusing of ribbon beam in ion linac |
| title_full |
Space charge effects and RF focusing of ribbon beam in ion linac |
| title_fullStr |
Space charge effects and RF focusing of ribbon beam in ion linac |
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Space charge effects and RF focusing of ribbon beam in ion linac |
| title_sort |
space charge effects and rf focusing of ribbon beam in ion linac |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/78989 |
| citation_txt |
Space charge effects and RF focusing of ribbon beam in ion linac / E.S. Masunov, N.E. Vinogradov, S.M. Polozov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 71-73. — Бібліогр.: 3 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-06T03:07:04Z |
| last_indexed |
2025-07-06T03:07:04Z |
| _version_ |
1836865264172400640 |
| fulltext |
SPACE CHARGE EFFECTS AND RF FOCUSING
OF RIBBON BEAM IN ION LINAC
E.S. Masunov, N.E. Vinogradov, S.M. Polozov
Moscow State Engineering Physics Institute,
115409, Kashirskoe Shosse 31, box 14, Moscow, Russia
masunov@dinus.mephi.ru.
Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and ac-
celeration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing in-
fluence (RF focusing concept). Investigation of intensive ribbon beam dynamics features is carried out. The space
charge effects are studied numerically by means of ″super particles″ approach. The proposal of 80% transmission 1
A limit current ribbon beam accelerator for the ITER neutral injection system and some another applications is pre-
sented.
PACS numbers: 41.75.L, 41.85.E, 29.27.F
1 INTRODUCTION
Using of a neutral injection system (NIS) is known
to be effective way to heat thermonuclear plasmas. It
can be realized as a combination of a high intensive ion
beam linac with funneling and stripping systems. Ap-
plying of the well-known RFQ linac is not suitable for
this purpose because of the insufficient output beam
current. Early in [1] it was suggested to use the undula-
tor linear accelerator of a ribbon D − beam. Applying of
plane structures with ribbon beams has the following
specific features: 1) large value of bunch cross-section
allows to increase greatly the output current; 2) large
beam surface is convenient for effective neutralization;
3) it is suitable to combine the plane channel and high-
intensity ion source. The most of aspects of the undula-
tor accelerator design was investigated in [1]. In the pa-
per [2] studying intensive ribbon beam dynamics was
carried out in the 2D model. In this paper concept of the
RF focusing intensive ribbon beam accelerator is dis-
cussed. Space charge effects are investigated in 3D
model. Differences between this kind of accelerator and
the undulator accelerator are considered.
2 PARTICLE MOTION EQUATION
The acceleration system discussed is supposed to be
realize as an interdigital H-type structure. It consists of a
cavity, some vanes inside it and a number of electrodes
alternatively connected to the vanes. Usually only the
ribbon beam thickness keeping is investigated To create
the RF field components which can provide the trans-
verse focusing along the ribbon width it is suggested [1]
to apply the curved electrodes of a special form (see
Fig. 1). Let us assume the beam to interact with only
two space harmonics of the RF field. Then the field po-
tential can be presented as
U U k x k y h dz tp x
p
y
p
p
p s n
= ∫∑
=
ch( ) ch( ) sin( ) cos( )
,
ω . (1)
Here s, n are numbers of synchronous and nonsyn-
chronous harmonics respectively; U p are harmonic am-
plitudes; k x
p , k y
p , hp are wave numbers;
h p Dp = +( ) /µ π2 , µ is the phase advance per period
of the structure D . Formula (1) determines the RF field
of the structure considered. The motion equation in this
field in a smooth approximation can be obtained using
the averaging method [1]. In the single particle ap-
proach does not taking into account the space charge
field it gives
d
d
U eff
2
2
R
Rτ
∂
∂
= − , (2)
where U eff is the effective potential function which can
be expressed as
U U Ueff = +0 1 ,
[ ]U ez
s
0
1
2= − + −ch( ) ch( ) sin( ) cosρ η ψ χ χ ψ , (3)
U
e en
s n
p
s pp s n
1
2
2
2
2
1
16
1 1
16
1
=
−
+
−
− +
=
∑
∆ ∆, ,,
.
Here [ ]R = ρ η χ, , ,
e
e k X k Y
e k X k Y
e k X k Y
p
x
p
x
p
y
p
y
p
x
p
y
p
x
p
x
p
y
p
=
sh( ) ch( )
ch( ) sh( )
ch( ) ch( )
, e
e E
mcx y z
p x y z
p
c
, ,
, ,=
λ
π β2 2 are
the dimensionless field harmonic amplitudes,
ρ π
λ β
= 2
c
X , η π
λ β
= 2
c
Y , χ ω ψ= − −∫ h dZ ts , X, Y, Z
are the slowly varying coordinates, ψ and β c are the
synchronous particle phase and velocity respectively,
∆ s p
p s
s
h h
h,
± =
±
.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 71-73.
71
Fig. 1. The plane structure.
Effective potential function (3) determines the 3D
beam motion completely. Term U 0 describes interac-
tion of particle with synchronous harmonic accelerating
and defocusing the beam. Summand U1 evaluates only
the transverse focusing and is being independent of the
synchronous particle phase. The form of equation (2) al-
lows the Hamilton analysis to be used. Existence of a
total minimum of the function U eff is the necessary
condition of simultaneous transverse and longitudinal
focusing. Expanding the U eff near the synchronous par-
ticle coordinate one can formulate this condition in the
form
ω χ
2 0> , ω ρ
2 0> , ω η
2 0> , (4)
where ω χ , ω ρ , ω η are frequencies of small longitudi-
nal and transverse oscillations. If the condition (4) is
satisfied, the effective potential function U eff is the 3D
potential well in the bunch frame. Therefore, in the RF
focusing ribbon beam accelerator discussed the particle
energy gain is achieved by affecting the synchronous
wave field. The ribbon transverse stability is achieved
using the focusing influence of a nonsynchronous field
harmonic (RF focusing concept).
3 CHOICE OF CAVITY PARAMETERS
3.1 RF field harmonic structure
So, for the plane structure k kx
p
y
p< < , one can as-
sume e e ey
p
z
p
p≅ ≡ , p=s, n. Because of the shielding
effect (i.e. interaction between bunch space charge and
channel walls) the defocusing influence of Coulomb
field along the ribbon width is weak. The focusing in
this direction is provided using the curved electrodes.
The focusing condition ω η
2 0> can be presented in the
form
α ψ χ αsin( )
, ,
+ < +
+
− +
1
2
1 1 1
2 4
2
2 2
2 2
e h
h
en
s n s n
n
s
n
∆ ∆
, (5)
where α ≡ e es n/ . Formula (5) defines the value of the
parameter α which allows the transverse stability to be
achieved for all values of particle phase. It can be seen
from condition (5) that a large phase capture under a
good transverse focusing may be obtained if α < < 1 .
On the other hand, this parameter is bounded below be-
cause the acceleration gradient dW dz En/ . cos= 0 5α ψ
is proportional to α. Parameter en also defines the value
of the frequency ω η . The value of en is bounded above
by a sparking criteria. Formula (5) also gives that the
RF focusing is more effective in the case of low beam
velocity. One can optimize the set {s, n, µ} calculating
value of ω η at fixed α, en , ψ. The system providing
the most strong transverse focusing is to be chosen. It
should be noted that structures with a large harmonic
number are not effective. Firstly, realization of systems
with p>2, p=s, n is hardly possible since it is necessary
to set many electrodes per structure period. Secondly,
the value of the field amplitude which corresponds to
separatrices overlapping decreases fast versus growth of
harmonic number. It may lead to longitudinal instabili-
ty. One can see from (5) that if the inequality α < < 1 is
satisfied, systems with s>n are ineligible because of in-
sufficient transverse focusing. For the cavity parameters
we consider (see below) the acceleration structure {s=0,
n=1, µ=π} is to be regarded as the best. The optimum
ratio k kx
p
y
p/ can be obtained using a computer simula-
tion of beam dynamics. For the cavity parameters of ac-
celerator discussed (see below), the transmission coeffi-
cient is maximal if k kx
p
y
p/ =1/23. In this case the trans-
verse frequency ω ρ is very small. Actually, the beam
particles do not have time to complete even one oscilla-
tion along the ribbon width. It means that such a plane
structure can be considered as an analogy of multibeam
system.
3.2 Acceleration channel parameters
Let the acceleration cavity consists of two subsec-
tions: the gentle buncher subsection and the acceleration
one. In the gentle buncher the synchronous particle
phase decreases linearly from ψ=π/2 to some nominal
value and the RF field amplitude increases as a fair-
curve. Here the beam is being bunched carefully and ac-
celerated insignificantly. In the acceleration subsection
these parameters are fixed making the bunch to gain the
necessary energy. The approach described allows to en-
large the transmission coefficient greatly. During the
bunching process the averaged separatrix is slowly de-
formed. In the undulator ribbon beam accelerator [1] RF
field inside the channel is primary transversal. So fast
oscillation amplitudes of a longitudinal coordinate and
velocity are very small, and difference between the lon-
gitudinal motion in phase space and its smooth approxi-
mation is insignificant. Therefore the phase motion is
not very sensitive to the slow changing of cavity param-
eters. In the accelerator of this type to achieve a large
transmission the field amplitude versus longitudinal co-
ordinate in the gentle buncher can be chosen as any
growing function (for instance, it may be proportional to
sine). In the RF focusing ribbon beam accelerator dis-
cussed here the RF field in the interaction area is prima-
ry longitudinal. In this case fast oscillation amplitudes
of a longitudinal coordinate and velocity are not small,
and transmission is very sensitive to the choice of the
field amplitude as a function of the longitudinal coordi-
nate. The reason is loosing of bunch particles with ve-
locities of large fast oscillation amplitudes from within
the deforming separatrix. In paper [3] a special method
of gentle buncher parameter choice for the acceleration
system with a primary longitudinal RF field was sug-
gested. It is based on the concept of longitudinal limit
current nondecreasing. Value of this characteristic is ap-
proximately proportional to longitudinal acceptance. To
provide a high transmission the longitudinal acceptance
should be increasing function. This statement defines
the relationship between the field amplitude, syn-
chronous particle phase and beam velocity in the gentle
72
bunching subsection. Such approach can be used for
cavity parameter choice in the RF ribbon beam accelera-
tor described. The electrode form depends on the equi-
librium particle velocity and is defined by relationship
( ) ( ) ( )k k hx
p
y
p
p
2 2 2+ = , p=s, n, which can be derived
from Maxwell’s equations. The ratio k kx
p
y
p/ =const is
the system parameter. Construction of the structure peri-
od is defined by the phase advance µ and harmonics
number s, n. The form and size of electrode cross-sec-
tions should provide the necessary harmonic spectrum
of the RF field. It can be obtained by computer simula-
tion in the 2D model.
4 NUMERICAL SIMULATION
The computer simulation of high-intensity ribbon
beam dynamics in the plane structure described was car-
ried out by means of the ″superparticles″ method. The
Coulomb field is calculated using the Cloud-in-Cell
method. Here the space charge density is computed on
the grid which is set into the bunch area. The Poisson
equation on the grid is solved using the fast Fourier
transform. Gentle buncher parameters (see Fig. 2) were
optimized numerically by means of the component-wise
descent method. The starting parameters for computer
optimization were calculated by the approach described
in previous chapter.
Fig. 2. Gentle bunching subsection parameters.
Fig.3. Dimensionless space-charge filled potential
without taking into account (1) and with taking into
account (2) the shielding effect.
It was shown that for acceleration of a high-intensity
beam the shielding effect is significant. This circum-
stance is very important for large transmission obtain-
ing. Fig. 3 shows the difference between the space
charge field potential with and without shielding effect.
Table 1 contains results of computer simulation. It can
be seen that the RF focusing ribbon beam accelerator
which is suggested in this paper provides a high trans-
mission under a large input current. Fig. 4 shows the
transmission coefficient versus input current. It proofs
the efficiency of the plane structure using for high-in-
tensity beam acceleration. To test the averaging method
applicability the computer simulation was carried out
for both RF field and averaged one. All results obtained
in a smooth approximation and for the RF field coincide
up to 5-10%.
Fig. 4. Transmission versus input current, A.
Table 1. Numerical simulation results.
Parameter Value
Operating frequency, MHz 150
Parameter α 0.1
Maximum field amplitude Emax , kV/cm 280
Input/Output Energy, MeV 0.1/2.0
Total length, m 3
x-aperture, cm 0.2
y-aperture, cm 5
5 CONCLUSION
The RF focusing ribbon beam accelerator concept is
discussed. Methods of transmission coefficient increas-
ing are suggested. High intensity ribbon beam 3D dy-
namics is studied by means of computer simulations. It
is shown that applying of RF focusing plane structure
for intensive ion beam acceleration allows to realize a
1 A output current under more than 80% transmission.
REFERENCES
1. E.S.Masunov // Sov. Phys. – Tech. Phys. 1990,
v. 35, № 8, p. 962-965.
2. E.S.Masunov, A.S.Roshal. // Proc. of the 1997 Par-
ticle Accelerator Conference, Vancouver, BC,
Canada, May 1997, v. 3, p. 2835-2837
3. E.S.Masunov, N.E.Vinogradov. // Phys. Rev. ST
Accel. Beams. 2001, No 7, 070101.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 73-73.
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