Effective acceptance evaluation of linear resonance accelerator

One of the most important challenges for accelerators is to match an accelerating beam with an accelerator acceptance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF focusing is carried out with no taking into account a beam space charge...

Full description

Saved in:
Bibliographic Details
Date:2010
Main Authors: Dyubkov, V.S., Masunov, E.S.
Format: Article
Language:English
Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2010
Subjects:
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/17023
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Effective acceptance evaluation of linear resonance accelerator / V.S. Dyubkov,. E.S. Masunov // Вопросы атомной науки и техники. — 2010. — № 3. — С. 94-97. — Бібліогр.: 5 назв. — англ.

Institution

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