Characteristics of inhomogeneous accelerating structures

Characteristics of inhomogeneous accelerating structures

We present the results of investigations of accelerating structures consisting of a segment of an inhomogeneous disk-loaded waveguide, input and output couplers. The sizes of the apertures inside the waveguide take random values in the interval 1.2< a <1.3 cm. The cavity radii and the paramet...

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Datum:2004
Hauptverfasser: Ayzatsky, M.I., Kramarenko, K.Yu.
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Sprache:English
Veröffentlicht: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2004
Schriftenreihe:Вопросы атомной науки и техники
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Элементы ускорителей
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/79333
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Zitieren:НазваниеCharacteristics of inhomogeneous accelerating structures / M.I. Ayzatsky, K.Yu. Kramarenko // Вопросы атомной науки и техники. — 2004. — № 2. — С. 69-71. — Бібліогр.: 5 назв. — англ.

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spelling irk-123456789-793332015-04-01T03:02:09Z Characteristics of inhomogeneous accelerating structures Ayzatsky, M.I. Kramarenko, K.Yu. Элементы ускорителей We present the results of investigations of accelerating structures consisting of a segment of an inhomogeneous disk-loaded waveguide, input and output couplers. The sizes of the apertures inside the waveguide take random values in the interval 1.2< a <1.3 cm. The cavity radii and the parameters of the couplers are tuned depending on the iris apertures and the operating frequency. At the operating frequency (2797.2 MHz) the phase shift per cell is 2pi/3. Ми приводимо результати дослідження прискорюючих структур, які складаються з відрізку неоднорідного хвилеводу, вхідного та вихідного трансформаторів типу хвилі. Розміри отворів зв’язку у середині хвилеводу приймають випадкові значення в інтервалі 1.2< a <1.3 см. Радіуси ячійок і параметри трансформаторів типу хвилі налагоджуються в залежності від розмірів отворів зв’язку та робочої частоти. На робочій частоті (2797.2 МГц) набіг фази поля на комірці складає 2π/3. Мы представляем результаты исследования ускоряющих структур, состоящих из отрезка неоднородного диафрагмированного волновода, входного и выходного трансформаторов типа волны. Размеры радиусов отверстий связи внутри волновода принимают случайные значения в интервале 1.2< a <1.3 см. Радиусы ячеек и параметры трансформаторов типа волны настраиваются в зависимости от размеров пролетных отверстий и значения рабочей частоты. На рабочей частоте (2797.2 МГц) набег фазы поля на ячейке составляет 2π/3. 2004 Article НазваниеCharacteristics of inhomogeneous accelerating structures / M.I. Ayzatsky, K.Yu. Kramarenko // Вопросы атомной науки и техники. — 2004. — № 2. — С. 69-71. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/79333 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Элементы ускорителей
Элементы ускорителей
spellingShingle Элементы ускорителей
Элементы ускорителей
Ayzatsky, M.I.
Kramarenko, K.Yu.
Characteristics of inhomogeneous accelerating structures
Вопросы атомной науки и техники
description We present the results of investigations of accelerating structures consisting of a segment of an inhomogeneous disk-loaded waveguide, input and output couplers. The sizes of the apertures inside the waveguide take random values in the interval 1.2< a <1.3 cm. The cavity radii and the parameters of the couplers are tuned depending on the iris apertures and the operating frequency. At the operating frequency (2797.2 MHz) the phase shift per cell is 2pi/3.
format Article
author Ayzatsky, M.I.
Kramarenko, K.Yu.
author_facet Ayzatsky, M.I.
Kramarenko, K.Yu.
author_sort Ayzatsky, M.I.
title Characteristics of inhomogeneous accelerating structures
title_short Characteristics of inhomogeneous accelerating structures
title_full Characteristics of inhomogeneous accelerating structures
title_fullStr Characteristics of inhomogeneous accelerating structures
title_full_unstemmed Characteristics of inhomogeneous accelerating structures
title_sort characteristics of inhomogeneous accelerating structures
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate 2004
topic_facet Элементы ускорителей
url http://dspace.nbuv.gov.ua/handle/123456789/79333
citation_txt НазваниеCharacteristics of inhomogeneous accelerating structures / M.I. Ayzatsky, K.Yu. Kramarenko // Вопросы атомной науки и техники. — 2004. — № 2. — С. 69-71. — Бібліогр.: 5 назв. — англ.
series Вопросы атомной науки и техники
work_keys_str_mv AT ayzatskymi characteristicsofinhomogeneousacceleratingstructures
AT kramarenkokyu characteristicsofinhomogeneousacceleratingstructures
first_indexed 2025-07-06T03:24:50Z
last_indexed 2025-07-06T03:24:50Z
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fulltext CHARACTERISTICS OF INHOMOGENEOUS ACCELERATING STRUC- TURES M.I. Ayzatsky, K.Yu. Kramarenko National Science Center “Kharkov Institute of Physics & Technology”, Ukraine E-mail: kramer@kipt.kharkov.ua We present the results of investigations of accelerating structures consisting of a segment of an inhomogeneous disk-loaded waveguide, input and output couplers. The sizes of the apertures inside the waveguide take random val- ues in the interval 1.2< a <1.3 cm. The cavity radii and the parameters of the couplers are tuned depending on the iris apertures and the operating frequency. At the operating frequency (2797.2 MHz) the phase shift per cell is 2pi/3. PACS: 29.17.+w 1. INTRODUCTION The transverse instability in linear accelerators is due to the dipole modes excited by the beam. There are different methods of beam break-up suppression: quality factor decreasing, reduction of the effective length of coherent interaction, using of external focusing. The so- called detuned structure is designed to be an approxi- mately constant gradient with the dipole mode frequen- cies adjusted to have a Gaussian density distribution by varying the iris radius and the disk thickness. For evacu- ation of dipole modes the damped detuned structure has four rounded rectangular damping manifolds arranged at 90 degree intervals in azimuth around the accelerator cells. Another way to decrease the quality factor of dipole mode is making the radial cuttings on the disks. In the constant gradient and quasi-constant gradient structures the accelerating mode properties are essential- ly unchanged but the beam breakup passband is per- turbed in frequency. Existence of passbands in the structure is the conse- quence of its periodicity. It is possible to suppress the transverse instability by the use of non-periodic acceler- ating structures. From other hand, acceleration is possi- ble only in the case when the synchronism condition be- tween particles and electromagnetic field is fulfilled. On the base of the method [1] the tuning method was developed for adjusting elements of disk-loaded structures, in which the sizes of apertures are arbitrary [2]. The radii of the cells are tuned in dependence on the sizes of the apertures so that at the operating frequency the phase shift per cell equals the transit angle of the rel- ativistic particle. The consecutive tuning is used in the case of small coupling coefficients between cells, when only the adjacent coupling plays the important role. The cells are consecutively tuned in the special cavity stack. The negligence of the “remote” coupling produces er- rors during tuning of about ∆ϕ ≤ +0.5° [3] which agree in value and sign with the obtained deviation of the op- erating frequency of about 150-200 kHz [2]. 2. METHOD OF CONSECUTIVE TUNING Under small coupling disk-loaded waveguides can be described with a definite accuracy as a chain of oscil- lators, every of which is coupled only with adjacent ones: ( )[ ] , 1 1 )(2 1 )(2 22 + + − − Γ+Γ =−Γ+ nnnnnn nnn UU U ωω ωω (1) where Un is the amplitude of E010-mode in the n-th cavi- ty, ωn the eigenfrequency of E010-mode in the n-th cavi- ty. In general, coefficients Γn, Γn (-) and Γn (+) for the n-th cavity depend on the iris radii an and an+1, the dimen- sions of the n-1, n, n+1 cavities, and the frequency [3]. In the most simple case of coupling through the small aperture in the infinitely thin wall coefficients Γn, Γn (-) and Γn (+) have been obtained in the following form [4]: , )(3 2 )(3 2 2 3 1 01 2 1 2 3 01 2 1 )0( 1, )0( 1, db a Jdb a J n n n n nnnnn + +− ⋅+⋅ =+→Γ λπλπ αα (2.1) , )(3 2 1 3 01 2 1 )0( 1, )( dbb a J nn n nnn − − − ⋅=→Γ λπ β (2.2) , )(3 2 1 3 1 01 2 1 )0( 1, )( dbb a J nn n nnn + + + + ⋅=→Γ λπ β (2.3) where λ01 is the first root of the zero order Bessel func- tion J0, b and d are the radius and length of the cavity. The coupling coefficients of two cavities, without any assumptions on the cavity dimensions, are given in [5]: ,1, )0( 1,1, )0( 1, ++−− Λ⋅+Λ⋅→Γ nnnnnnnnn αα (3.1) ,~ 1, )0( 1, )( −− − Λ⋅→Γ nnnnn β (3.2) .~ 1, )0( 1, )( ++ + Λ⋅→Γ nnnnn β (3.3) Coefficients Λ and Λ~ depend not only on the geomet- rical dimensions of the cells, but on the frequency as well. However, it was shown that the dependence of these coefficients on the iris radius and wall thickness is the most efficient. For the wall thickness t = 0.4 cm the dependence of the coefficients Λ and Λ~ on а can be approximated by the following expressions: ,5242.17078.01633.0 2 +−=Λ aa (4.1) .0799.06541.01966.0~ 2 −+−=Λ aa (4.2) ___________________________________________________________ PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2. Series: Nuclear Physics Investigations (43), p.69-71. 69 We find the condition when the set of equations (1) at the operating frequency ω = ω* have the solution of the following form: )exp(0, ϕinUU nn = , (5) where Un,0 is the real value. To obtain the solution of the set of equations (1) of such a form, the following condi- tion is to be fulfilled: 0,1 )( 0,1 )( + + − − Γ=Γ nnnn UU . (6) Under this condition the equations for the n-th and n-1- th cavities can be written in the form: ( )[ ] 0,1 )(2 0, 2 * 2 cos2 1 − −Γ⋅ =−Γ+ nnn nnn U U ωϕ ωω (7.1) ( )[ ] ,cos2 1 0, )( 1 2 1 0,1 2 *1 2 1 nnn nnn U U + −− −−− Γ⋅ =−Γ+ ωϕ ωω (7.2) hence ( )( ) ( )( ) .cos4 11 )( 1 )(2 1 22 2 *1 2 1 2 * 2 + − − − −− ΓΓ⋅ =−Γ+−Γ+ nnnn nnnn ωωϕ ωωωω (8) So, if the values of bn-1, an-1, an, an+1, d are already known, the value of bn can be obtained from this equa- tion. We suppose that all cells have an equal length D = d + t, which is determined by the synchronism con- dition between the electromagnetic field and the parti- cle. If bn has been obtained, and an, an+1, an+2 are known, then one can obtain bn+1 from equation (8), and so on. So, the whole accelerating structure can be consecutive- ly tuned. At the first step two identical cells (a1 = a2 = a3 = a0, b1 = b2 = b0) are to be tuned on the fixed phase shift per cell ϕ. Then, using disks with arbi- trary values of a, all the radii of the cells b can be deter- mined. Any segment of the structure tuned by such a way can be considered as an independent structure. 3. CHARACTERISTICS OF INHOMOGE- NEOUS STRUCTURES Smooth variation of the iris radius is used in con- stant gradient and quasi-constant gradient structures. The method of consecutive tuning makes it possible to tune the structures not only with the smooth low of aperture variation, but with the abrupt one as well. Ran- dom distribution of the iris aperture can be considered as an example of this variation. Consider the structure in which the value of the iris radius deviates from the constant value of a0 on some random quantity rn: nn raa += 0 . (9) Lets the quantity rn is uniformly distributed in the in- terval ±0.05 cm. The iris and cell radii in the “random” constant impedance structure are shown in Fig. 1. The structure is 3.036 meters long with 85 cells (including the couplers). Frequency of the accelerating mode is f* = 2797.2 MHz. Phase shift per cell is ϕ = 2π /3. 0 15 30 45 60 75 90 1.2 1.25 1.3 a, c m 0 15 30 45 60 75 90 4.2 4.22 4.24 4.26 4.28 n b, c m Fig. 1 Iris radii - a and cell radii – b in the “random” constant impedance structure The iris radius in the constant impedance structure is a0 = 1.25 cm. In Fig. 2 we have shown the amplitude distribution and the phase shift per cell in the “random” constant impedance structure and in the usual constant impedance structure. 0 15 30 45 60 75 90 10 20 30 U 0 15 30 45 60 75 90 119.8 120 120.2 φ 0 15 30 45 60 75 90 118.7 120 121.3 n φ Fig. 2 Field amplitude distribution U MV/m and phase shift per cell φ° in the “random” structure (*) and in the constant- impedance structure (о) The energy gain, rate of acceleration and the power attenuation in the constant-impedance and in the “ran- dom” constant-impedance structure are shown in Ta- ble 1. The length of the input (output) coupler is equal to that of the structure cell. The frequencies of the couplers and the coupling values are determined from the condi- tion of reflected wave absence at the operating frequen- cy. Table 1. Characteristics of constant-impedance and “random” constant-impedance sections Input power 13 MW Constant- impedance “random” structure Energy gain, MeV 36.76 36.96 Rate of accel., MeV/m 12.11 12.17 3 70 Attenuation, nep. 0.69 0.79 Amplitude distribution and phase shift per cell in the constant gradient and “random” constant gradient struc- tures are shown in Fig. 3. In Table 2 we have shown characteristics of these sections. 0 15 30 45 60 75 90 10 20 30 U 0 15 30 45 60 75 90 119.5 120 120.5 φ 0 15 30 45 60 75 90 118 120 122 φ n Fig. 3 Field amplitude distribution U MV/m and phase shift per cell φ° in the “random” structure (*) and in the constant gradient structure (о) Table 2. Characteristics of constant-gradient and “random” constant-gradient sections Input power 13 MW Constant- gradient “random” structure Energy gain, MeV 43.23 42.92 Rate of accel., MeV/m 14.23 14.13 Attenuation, nep. 1.107 1.23 The values of the energy gain and the rate of accel- eration in Tables 1, 2 are higher than one can expect in reality. It is caused by the fact that the influence of high- er modes on the field distribution in the cell is not con- sidered in the using model. However, these values can be used for the comparison of different structures. The characteristics of “random” structures are com- parable with the characteristics of constant impedance and constant gradient ones. Despite the fact that there would be some worry about field breakdown, we as- sume that the “random” structure can be used for the suppression of beam blow-up instability. REFERENCES 1. G. Bienvenu, J.C. Bourdon, P. Brunet et al. Accel- erating structure developments for the LEP injector linac // Proc. of the LAC. GSI-84-11. 1984. 2. M.I. Ayzatsky, E.Z. Biller. Development of inho- mogeneous disk-loaded accelerating waveguides and RF-coupling // Proc of the 25th ILAC. 1996, v.1, p. 119-122. 3. M.I. Ayzatsky. New mathematical model of an infi- nite cavity chai // Proc of the 5th EPAC. 1996, v.3, p. 2026-2028. 4. V.V. Vladimirsky. Coupling of electromagnetic cavities through the small hole // Journal of Techni- cal Physics. 1947, v.17, №11, p.1277-1282 (in Rus- sian). 5. M.I. Ayzatsky. For two cavity coupling // Journal of Technical Physics. 1996, v.66, №9, p.137-147 (in Russian). ХАРАКТЕРИСТИКИ НЕОДНОРОДНЫХ УСКОРЯЮЩИХ СТРУКТУР Н.И. Айзацкий, Е.Ю. Крамаренко Мы представляем результаты исследования ускоряющих структур, состоящих из отрезка неоднородного диафрагмированного волновода, входного и выходного трансформаторов типа волны. Размеры радиусов от- верстий связи внутри волновода принимают случайные значения в интервале 1.2< a <1.3 см. Радиусы ячеек и параметры трансформаторов типа волны настраиваются в зависимости от размеров пролетных отверстий и значения рабочей частоты. На рабочей частоте (2797.2 МГц) набег фазы поля на ячейке составляет 2π/3. ХАРАКТЕРИСТИКИ НЕОДНОРІДНИХ ПРИСКОРЮЮЧИХ СТРУКТУР М.І. Айзацький, К.Ю. Крамаренко Ми приводимо результати дослідження прискорюючих структур, які складаються з відрізку неоднорідного хвилеводу, вхідного та вихідного трансформаторів типу хвилі. Розміри отворів зв’язку у середині хвилеводу приймають випадкові значення в інтервалі 1.2< a <1.3 см. Радіуси ячійок і параметри трансформаторів типу хвилі налагоджуються в залежності від розмірів отворів зв’язку та робочої частоти. На робочій частоті (2797.2 МГц) набіг фази поля на комірці складає 2π/3. ___________________________________________________________ PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2. Series: Nuclear Physics Investigations (43), p.69-71. 71 PACS: 29.17.+w REFERENCES Н.И. Айзацкий, Е.Ю. Крамаренко М.І. Айзацький, К.Ю. Крамаренко

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