High intensity proton beam dynamics simulation in the initial part of ADS LINAC
One of the most important scientific and technical challenges is the design and development of a new type power reactor, which has a higher nuclear safety. At present several projects related to the so-called hybrid (subcritical) reactors, based on high power proton accelerators, are realized worldw...
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irk-123456789-1118812017-01-16T03:03:09Z High intensity proton beam dynamics simulation in the initial part of ADS LINAC Dyubkov, V.S. Динамика пучков One of the most important scientific and technical challenges is the design and development of a new type power reactor, which has a higher nuclear safety. At present several projects related to the so-called hybrid (subcritical) reactors, based on high power proton accelerators, are realized worldwide. Accelerator-driver, as a part of hybrid system (ADS), must meet a number of requirements, among which small losses of the accelerated particles. To fulfill this requirement, it is necessary to ensure small beam emittance at the injector output, exact alignment and work stability of all accelerator parts, a careful study of the beam halo formation and envelope control. On the basis of the developed beam envelope control method main parameters of the linear accelerator-driver initial part which provide high acceleration rate under small particle losses are chosen. Numerical simulation of self-consistent high intensity proton beam dynamics in the initial part of the accelerator-driver is performed. Одним з актуальних науково-технічних завдань є розробка і створення нового типу енергетичного реактора, що має підвищену ядерну безпеку. В даний час у світі реалізується кілька проектів, пов'язаних з так званими гібридними (підкритичними) реакторами, що будуються на базі протонних прискорювачів великої потужності. До прискорювача-драйвера протонних пучків, що входить до складу гібридної системи, пред'являється ряд досить жорстких вимог, серед яких забезпечення щонайменших втрат прискорених частинок. Для виконання цієї вимоги необхідно забезпечити мале значення еміттансу пучка на виході інжектора, точне узгодження і стабільність роботи всіх частин прискорювача, ретельне дослідження утворення ореола пучка і контроль його огинаючої. У цій роботі на підставі розробленого методу контролю за огинаючою пучка вибираються основні параметри початкової частини лінійного прискорювача-драйвера, що забезпечують високий темп прискорення за малих втрат частинок. Проводиться чисельне моделювання самоузгодженого потужнострумового протонного пучка в початковій частині прискорювача-драйвера. Одной из актуальных научно-технических задач является разработка и создание нового типа энергетического реактора, обладающего повышенной ядерной безопасностью. В настоящее время в мире реализуется несколько проектов, связанных с так называемыми гибридными (подкритическими) реакторами, строящимися на базе протонных ускорителей большой мощности. К ускорителю-драйверу протонных пучков, входящему в состав гибридной системы, предъявляется ряд достаточно жестких требований, среди которых обеспечение сверхмалых потерь ускоряемых частиц. Для выполнения этого требования необходимо обеспечить малое значение эмиттанса пучка на выходе инжектора, точное согласование и стабильность работы всех частей ускорителя, тщательное исследование образования ореола пучка и контроль его огибающей. В данной работе на основании разработанного метода контроля за огибающей пучка выбираются основные параметры начальной части линейного ускорителя-драйвера, обеспечивающие высокий темп ускорения при малых потерях частиц. Проводится численное моделирование самосогласованного сильноточного протонного пучка в начальной части ускорителя-драйвера. 2013 Article High intensity proton beam dynamics simulation in the initial part of ADS LINAC / V.S. Dyubkov // Вопросы атомной науки и техники. — 2013. — № 6. — С. 141-144. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 02.30.Em; 41.75.Lx http://dspace.nbuv.gov.ua/handle/123456789/111881 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика пучков Динамика пучков |
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Динамика пучков Динамика пучков Dyubkov, V.S. High intensity proton beam dynamics simulation in the initial part of ADS LINAC Вопросы атомной науки и техники |
| description |
One of the most important scientific and technical challenges is the design and development of a new type power reactor, which has a higher nuclear safety. At present several projects related to the so-called hybrid (subcritical) reactors, based on high power proton accelerators, are realized worldwide. Accelerator-driver, as a part of hybrid system (ADS), must meet a number of requirements, among which small losses of the accelerated particles. To fulfill this requirement, it is necessary to ensure small beam emittance at the injector output, exact alignment and work stability of all accelerator parts, a careful study of the beam halo formation and envelope control. On the basis of the developed beam envelope control method main parameters of the linear accelerator-driver initial part which provide high acceleration rate under small particle losses are chosen. Numerical simulation of self-consistent high intensity proton beam dynamics in the initial part of the accelerator-driver is performed. |
| format |
Article |
| author |
Dyubkov, V.S. |
| author_facet |
Dyubkov, V.S. |
| author_sort |
Dyubkov, V.S. |
| title |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC |
| title_short |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC |
| title_full |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC |
| title_fullStr |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC |
| title_full_unstemmed |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC |
| title_sort |
high intensity proton beam dynamics simulation in the initial part of ads linac |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2013 |
| topic_facet |
Динамика пучков |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/111881 |
| citation_txt |
High intensity proton beam dynamics simulation in the initial part of ADS LINAC / V.S. Dyubkov // Вопросы атомной науки и техники. — 2013. — № 6. — С. 141-144. — Бібліогр.: 5 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2013. №6(88) 141
HIGH INTENSITY PROTON BEAM DYNAMICS SIMULATION
IN THE INITIAL PART OF ADS LINAC
V.S. Dyubkov
National Research Nuclear University “MEPhI”, Moscow, Russian Federation
E-mail: vsdyubkov@mephi.ru
One of the most important scientific and technical challenges is the design and development of a new type power
reactor, which has a higher nuclear safety. At present several projects related to the so-called hybrid (subcritical) reac-
tors, based on high power proton accelerators, are realized worldwide. Accelerator-driver, as a part of hybrid system
(ADS), must meet a number of requirements, among which small losses of the accelerated particles. To fulfill this
requirement, it is necessary to ensure small beam emittance at the injector output, exact alignment and work stability
of all accelerator parts, a careful study of the beam halo formation and envelope control. On the basis of the devel-
oped beam envelope control method main parameters of the linear accelerator-driver initial part which provide high
acceleration rate under small particle losses are chosen. Numerical simulation of self-consistent high intensity proton
beam dynamics in the initial part of the accelerator-driver is performed.
PACS: 02.30.Em; 41.75.Lx
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 proton and ion beams. In
particular, 18 countries of the World declared the design
and development of systems on the basis of the acceler-
ator drivers (ADS) to date. The most developed projects
of these systems, which based on linear accelerators, are
MYRRHA (Belgium), ESS (Sweden), IFMIF (Italy) [1 -
3]. In order to ensure the safety and stability of this
systems it is used well-tried and proven engineering
solutions. The initial part of a linear accelerator-driver is
a section with spatially homogeneous quadrupole focus-
ing (RFQ), as a general rule. However, a grave draw-
back of classical RFQ structures is the relatively low
acceleration rate that often leads to an increase of the
accelerator driver total length. Structures with RF focus-
ing by means of spatial harmonics (an acceleration rate
of which can reach up to 1.5…2 MeV/m under high
current transmission) can be used as an alternative to
channels with RFQ. In addition, main losses of the par-
ticles typically occur in initial parts of the RFQ sections
due to Coulomb interaction. Therefore it is necessary to
develop an analytical method to control the beam enve-
lope and halo formation. The goals of this work are to
present beam dynamics investigation method, which
allows one to perform optimization of linac parameters
in order to realize beam envelope control, and to define
main parameters of structure with RF focusing by
means of nonsynchronous spatial harmonic which guar-
antee high acceleration rate under high current transmis-
sion (over 90 %) and halo formation decrease.
1. ANALYTICAL RESULTS
It is difficult to investigate a beam dynamics in a
high frequency polyharmonic field. Therefore, one can
use a method of an averaging over a rapid oscillations
period, following the formalism presented in Ref. [4].
One first expresses RF field in an axisymmetric periodic
resonant structure as Fourier’s representation by spatial
harmonics of a standing wave assuming that the struc-
ture period is a slowly varying function of a longitudinal
coordinate z
,cossin
;coscos
0
1
0
0||
tzdkrkIEE
tzdkrkIEE
n
nnn
n
nnn
(1)
where En is the nth harmonic amplitude of RF field on
the axis; Dnkn 2 is the propagation wave
number for the n-th RF field spatial harmonic; D is the
resonant structure geometric period; is the phase ad-
vance per D period; is the circular frequency; I0, I1 are
modified Bessel functions of the first kind.
One has to 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 par-
ticle). A magnetic force can be neglected for low-energy
ions. Assuming that dr/dz << 1 one passes into the ref-
erence particle rest frame. There is a differentiation over
longitudinal coordinate in the beam motion equation.
Thus, the motion 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
.
11
;
,,ˆ
;,0,ˆ,0,ˆ
r| || |
| |
| |r| |
d
d
trze
d
d
tzetze
d
d
(2)
The following dimensionless variables were intro-
duced here: ,r is the Lorentz’s factor;
,2 z ,2ˆ 2
0| | ,| | , cmeEe e is the elementary
charge, λ is a wave length of RF field, m0 is proton rest
mass, c is the light velocity in free space; ,||,||, c
.rtt Note, it can be assumed that
,||r||s
where s is the equilibrium particle
velocity and s is a number of the synchronous harmonic,
provided 1|| s is satisfied. Therefore, we can
write 2
||r|| sdd for the last equation of
ISSN 1562-6016. ВАНТ. 2013. №6(88) 142
the system (2). Now the first and the third equations of
the system (2) can be united as follows
,
1
3
32
2
d
d
d
d
d
d
s
(3)
and the second equation of the system (2) can be rewrit-
ten in the form
,
ˆ
32
2
s
e
d
d
d
d (4)
where sr2 is the dimensionless transverse var-
iable and = (ln 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
efLU , (5)
where the dot above stands for differentiation with re-
spect to the independent variable. Hereafter and
mean its averaged values and
.L,
0
03
, (6)
efU is an effective potential function (EPF) describ-
ing a two-dimensional low-energy beam interaction
with the polyharmonical field of the system. For Wid-
eroe type structure in the case of two spatial harmonics
(one of it is the synchronous harmonic with n = 0, and
another one is the nonsynchronous with n = 1) efU can
be expressed as
.2cos2cos33
32
2cos22cos3
32
1cos3
128
5
1cos
32
133
256
5
1
64
sincossin
2
rr1100
10
rr00
10
0
2
0
0
2
0
2
1
2
0
2
12
1
2
0
2
0
rrr0
0
ef
IIII
ee
II
ee
I
e
I
e
II
e
II
e
I
e
U
s
(7)
Here ;2 2
0
2 cmeEe snn r is the reference par-
ticle phase.
To define eigenfrequencies of small system vibra-
tions, EPF is expanded in Maclaurin’s series
,
22
T
22
0
22
0
ef oU (8)
and the coefficients in which are given by
.
512
45
128
2cos
64
3
sin
4
,
128
5
32
2cos
16
sin
2
2
1
2
0
r
10
r
02
0
2
1
2
0
r
10
r
02
0
eeeee
eeeee
s
s (9)
A character of the vibrations will depend on ratio be-
tween the dissipative coefficient and eigenfrequencies.
It is necessary that ,02
0 02
0 for the beam
envelope has no increase.
2. NUMERICAL RESULTS
Linac parameters with RF focusing by means of one
nonsynchronous spatial harmonic were optimized by
using numerical self-consistent low-energy proton beam
dynamics simulation after beam dynamics optimization
in one particle approximation on the basis of obtained
analytical results was carried out. Self-consistent beam
dynamics simulations were performed by using a modi-
fied version of the specialized computer code
BEAMDULAC-ARF3 based on CIC technique to calcu-
late beam self-space-charge field. To ensure high cur-
rent transmission (over 90%) special optimization of the
field change law was done. It was based on the supposi-
tion that channel acceptance is a nondecreasing function
of the longitudinal beam coordinate. Therefore, taking
into account the equation of motion for the equilibrium
particle, the law of the synchronous harmonic amplitude
variation at a field increasing length can be written as
3
0 0 0 0
0
1.5
0
1.5 1.5 8
0
ˆ ˆ ˆ ˆ cos
ˆ 0 0 0
ˆsin2
,
ˆ8 0 0 0
s
s
s
s
de e d e d e
d d d e
e
e
(10)
where ℓ is a certain function of ξ, ς is a longitudinal
acceptance phase width, φs is the equilibrium particle
phase in the synchronous harmonic field, χ is the ampli-
tude ratio (e1∕e0).
Main linac parameters are listed in Table 1. A varia-
tion of the linac parameters are shown in Fig. 1.
Table 1
Main linac parameters
Parameter Value
Operational frequency, MHz 176.105
Total linac length, m 2
Bunching length, m 1.7
Input equilibrium particle phase −90°
Output equilibrium particle phase −22.5°
Input synchronous harmonic amplitude,
kV/cm
0.5
Amplitude ratio 7.4
Linac half-aperture, mm 5
For example, summarized in Table 2 beam parameters
were used for simulation. It is clearly that input transversal
emittance for ADS linac (about 0.2π mm·mrad) much
smaller that presented in Table 2, but latter one was
used to illustrate an effectiveness of the linac with RF
focusing by means of nonsynchronous spatial harmon-
ics.
Table 2
Input beam parameters
Parameter Value
Particle p
Input energy, keV 65
Input energy spread, % 1
Input radius, mm 2,5
Input transversal emittance,
π·mm·mrad
18
Input beam current, mA 10
The output beam particles phase portraits are shown
in Fig. 2,a (color indicates particle density) and Fig. 2,b
(color indicates particles in corresponding scattering
ellipses). From this Figures one can see that beam has
rather good quality.
ISSN 1562-6016. ВАНТ. 2013. №6(88) 143
Fig. 1. Main linac parameters
Fig. 2,a. Output longitudinal beam particles distribution
Fig. 2,b. Output transversal beam particles distribution
1 – RMS emittance; 2 – Floquet ellipse; 3 – histogram
of particles distribution by radii; 4 – histogram of parti-
cles distribution by transverse velocity components
Beam maximal radius variation along linac is shown
in Fig. 3,a. As one can see there is no beam radius in-
crease as well as transversal emittance one at the linac
output. Main particle losses arise from not quite adia-
batic bunching process and it is observed in longitudinal
phase space mainly (Fig. 3,b).
Halo is an intrinsic property of the beam as it was
stated in [5]. To estimate the halo one can use results
presented in [5] by supposing that the motion is uncou-
pled between phase planes (that is right for axial re-
gion). Thus halo parameter has the next form
,2
22
1293
2
1,10,22,0
1,33,1
2
2,20,44,0
H (11)
where μn,k is the central moment of the order n, s in
dzdrr, system.
Fig. 3,a. Beam envelope
Fig. 3,b. Transmission vs longitudinal coordinate
The behavior of the halo parameter is illustrated in
Fig. 4. Significant halo formation in the 2D phase-space
corresponds to H > 1 as it is showed by carried out sim-
ulations.
Output beam parameters are listed in Table 3.
Table 3
Output beam parameters
Parameter Value
Output energy, MeV 2
Ouput radius, mm 2,5
Output transversal emittance,
π·mm·mrad
18
Current transmission, % 91
Fig. 4. Halo parameter vs longitudinal coordinate
Variation of the linac current transmission coeffi-
cient under different input beam currents is shown in
Fig. 5.
ISSN 1562-6016. ВАНТ. 2013. №6(88) 144
Fig. 5. Current transmission coefficient vs initial proton
beam current
SUMMARY
The necessary requirements to ensure beam enve-
lope preservation were formulated. The main parameters
of linear accelerator-driver front-end part were chosen.
There are no beam envelope overgrowth and significant
halo formation under chosen parameters at the linac
output. Numerical simulation of self-consistent beam
dynamics confirmed the analytical results.
ACKNOWLEDGEMENTS
This work is supported in part by the Ministry of
Science and Education of Russian Federation under
contracts No. 14.A18.21.1568 and 14.516.11.0084.
REFERENCES
1. H. Aït Abderrahim. Multi-purpose hYbrid Research
Reactor for High-tech Applications a multipurpose
fast spectrum research reactor // International Jour-
nal of Energy Research. 2012, v. 36, p. 1331-1337.
2. End to end beam dynamics of the ESS linac / M.
Eshraqi et al. // Proceedings of IPAC2012, p. 3933-
3935.
3. K. Shinto. Present Status of the Accelerator System
in the IFMIF/EVEDA Project // Journal of Plasma
and Fusion Research SERIES. 2010, v. 9, p. 174-179.
4. 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).
5. C.K. Allen, T.P. Wangler. Beam halo definitions
based upon moments of the particle distribution //
Physical Review Special Topics – Accelerators and
Beams. 2002, v. 5, p. 124202.
Article received 06.09.2013
МОДЕЛИРОВАНИЕ ДИНАМИКИ СИЛЬНОТОЧНОГО ПРОТОННОГО ПУЧКА В НАЧАЛЬНОЙ
ЧАСТИ УСКОРИТЕЛЯ-ДРАЙВЕРА ДЛЯ ГИБРИДНЫХ СИСТЕМ
В.С. Дюбков
Одной из актуальных научно-технических задач является разработка и создание нового типа энергетиче-
ского реактора, обладающего повышенной ядерной безопасностью. В настоящее время в мире реализуется
несколько проектов, связанных с так называемыми гибридными (подкритическими) реакторами, строящи-
мися на базе протонных ускорителей большой мощности. К ускорителю-драйверу протонных пучков, вхо-
дящему в состав гибридной системы, предъявляется ряд достаточно жестких требований, среди которых
обеспечение сверхмалых потерь ускоряемых частиц. Для выполнения этого требования необходимо обеспе-
чить малое значение эмиттанса пучка на выходе инжектора, точное согласование и стабильность работы
всех частей ускорителя, тщательное исследование образования ореола пучка и контроль его огибающей. В
данной работе на основании разработанного метода контроля за огибающей пучка выбираются основные
параметры начальной части линейного ускорителя-драйвера, обеспечивающие высокий темп ускорения при
малых потерях частиц. Проводится численное моделирование самосогласованного сильноточного протон-
ного пучка в начальной части ускорителя-драйвера.
МОДЕЛЮВАННЯ ДИНАМІКИ ПОТУЖНОСТРУМОВОГО ПРОТОННОГО ПУЧКА
В ПОЧАТКОВІЙ ЧАСТИНИ ПРИСКОРЮВАЧА-ДРАЙВЕРА ДЛЯ ГІБРИДНИХ СИСТЕМ
В.С. Дюбков
Одним з актуальних науково-технічних завдань є розробка і створення нового типу енергетичного реак-
тора, що має підвищену ядерну безпеку. В даний час у світі реалізується кілька проектів, пов'язаних з так
званими гібридними (підкритичними) реакторами, що будуються на базі протонних прискорювачів великої
потужності. До прискорювача-драйвера протонних пучків, що входить до складу гібридної системи, пред'я-
вляється ряд досить жорстких вимог, серед яких забезпечення щонайменших втрат прискорених частинок.
Для виконання цієї вимоги необхідно забезпечити мале значення еміттансу пучка на виході інжектора, точне
узгодження і стабільність роботи всіх частин прискорювача, ретельне дослідження утворення ореола пучка і
контроль його огинаючої. У цій роботі на підставі розробленого методу контролю за огинаючою пучка ви-
бираються основні параметри початкової частини лінійного прискорювача-драйвера, що забезпечують висо-
кий темп прискорення за малих втрат частинок. Проводиться чисельне моделювання самоузгодженого по-
тужнострумового протонного пучка в початковій частині прискорювача-драйвера.
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