Accelerating structure for high-gradient accelerator
The conventional TW-mode accelerating structures are usually used for high gradient linacs. But these structures grow old quickly during running. It is very serious problem for creation next linear colliders [1]. In this article brief review of defects TW-mode accelerators is presented, and circuit...
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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: | Accelerating structure for high-gradient accelerator / O.N. Brezhnev, V.M. Pavlov, O.V. Pirogov, Ju.D. Chernousov // Вопросы атомной науки и техники. — 2001. — № 3. — С. 65-67. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-792382015-03-31T03:02:46Z Accelerating structure for high-gradient accelerator Brezhnev, O.N. Pavlov, V.M. Pirogov, O.V. Chernousov, Ju.D. The conventional TW-mode accelerating structures are usually used for high gradient linacs. But these structures grow old quickly during running. It is very serious problem for creation next linear colliders [1]. In this article brief review of defects TW-mode accelerators is presented, and circuit of an accelerator on the basis of a parallel coupled cavity structure, in which accelerating resonators fed parallel from a few waveguides, is offered. 2001 Article Accelerating structure for high-gradient accelerator / O.N. Brezhnev, V.M. Pavlov, O.V. Pirogov, Ju.D. Chernousov // Вопросы атомной науки и техники. — 2001. — № 3. — С. 65-67. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS numbers: 29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/79238 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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The conventional TW-mode accelerating structures are usually used for high gradient linacs. But these structures grow old quickly during running. It is very serious problem for creation next linear colliders [1]. In this article brief review of defects TW-mode accelerators is presented, and circuit of an accelerator on the basis of a parallel coupled cavity structure, in which accelerating resonators fed parallel from a few waveguides, is offered. |
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Article |
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Brezhnev, O.N. Pavlov, V.M. Pirogov, O.V. Chernousov, Ju.D. |
| spellingShingle |
Brezhnev, O.N. Pavlov, V.M. Pirogov, O.V. Chernousov, Ju.D. Accelerating structure for high-gradient accelerator Вопросы атомной науки и техники |
| author_facet |
Brezhnev, O.N. Pavlov, V.M. Pirogov, O.V. Chernousov, Ju.D. |
| author_sort |
Brezhnev, O.N. |
| title |
Accelerating structure for high-gradient accelerator |
| title_short |
Accelerating structure for high-gradient accelerator |
| title_full |
Accelerating structure for high-gradient accelerator |
| title_fullStr |
Accelerating structure for high-gradient accelerator |
| title_full_unstemmed |
Accelerating structure for high-gradient accelerator |
| title_sort |
accelerating structure for high-gradient accelerator |
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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/123456789/79238 |
| citation_txt |
Accelerating structure for high-gradient accelerator / O.N. Brezhnev, V.M. Pavlov, O.V. Pirogov, Ju.D. Chernousov // Вопросы атомной науки и техники. — 2001. — № 3. — С. 65-67. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT brezhnevon acceleratingstructureforhighgradientaccelerator AT pavlovvm acceleratingstructureforhighgradientaccelerator AT pirogovov acceleratingstructureforhighgradientaccelerator AT chernousovjud acceleratingstructureforhighgradientaccelerator |
| first_indexed |
2025-07-06T03:17:12Z |
| last_indexed |
2025-07-06T03:17:12Z |
| _version_ |
1836865901611188224 |
| fulltext |
ACCELERATING STRUCTURE FOR HIGH-GRADIENT
ACCELERATOR
O.N. Brezhnev, V.M. Pavlov, O.V. Pirogov, Ju.D. Chernousov1
Budker Institute of Nuclear Physics,
Siberian Branch of Academy of Science, 630090 Novosibirsk, Russia, Lavrentiev Ave., 11,
e-mail: Pavlov@inp.nsk.su
1Institute of Chemical Kinetic and Combustion,
Siberian Branch of Academy of Science, 630090 Novosibirsk, Russia, Institutskaya Str., 3,
e-mail: Chern@catalysis.nsk.su
The conventional TW-mode accelerating structures are usually used for high gradient linacs. But these structures
grow old quickly during running. It is very serious problem for creation next linear colliders [1].
In this article brief review of defects TW-mode accelerators is presented, and circuit of an accelerator on the basis of
a parallel coupled cavity structure, in which accelerating resonators fed parallel from a few waveguides, is offered.
PACS numbers: 29.17.+w
1 INTRODUCTION
We are seen a few inconveniences of TW-mode
accelerating structures:
1. Breakdown development from RF point of view:
The place of RF breakdown advances to a genera-
tor for standard TW-mode operated structure. Each
breakdown leads allocation of all accumulated energy
form power input up to a place of initial point RF
breakdown. Whole structure damaged up to a place
of initial point, and the upstream part of the structure
has more damages then downstream cells.
One way for overcoming this is to transit onto the
SW-operate mode.
2. Breakdown consequences:
2.1. The surface damages occur more often on the
nose cone, where the structure has the maximum
electric field. When the damage nose cone is hap-
pened and the pits and volcano-like mountains are ap-
peared, the change resonant frequency of the E010-
mode cavity is proportional to
cavity
in)pit(mounta
0
0 ~
V
V
f
f ∆∆
.
But the main frequency of cell is changed a little, be-
cause the number and size of pits and mountains into
one cavity are approximately equal, and general
in)pit(mountaV∆ is approximately equal to zero.
But the coupled coefficient between cells in case
of the small iris aperture 2a and thickness of di-
aphragm d is proportional to [3] deeak α−⋅3~ . Aver-
age changes of “a” will result in shift of phase be-
tween cells θ , affecting the detuning characteristics.
One way for overcoming this is the transition on
outside coupling slots like biperiodic structure.
2.2. Products of destroy surface (which spoils
vacuum condition in structure) in standard TW-struc-
tures are removed out through the whole channel of
an accelerator (diameter of an aperture approximately
of 9-10 mm at a length of accelerating structure of order 1
m by operate frequency 11÷ 14 GHz).
All of enumerated possible decisions are included in
the parallel-coupled cavity structures.
2 PARALLEL COUPLED CAVITY ACCELER-
ATING STUCTURES
Parallel-coupled accelerating structures have been used
earlier [2]. But inasmuch as standard rectangular waveg-
uides have the phase velocity more then c the coaxial feed-
er was used. Unfortunately, the coaxial line can not be
used for feeding the high gradient colliders with a high in-
put RF power.
If we do not take into account the coaxial feed line,
such kind of a structure has a lot of advantages:
The RF breakdown takes place only into a single cavity
and does not provoke a breakdown in the other cavities.
Only 1/N fraction of full RF stored energy is involved in
the process of damage (N is the number of cavities).
The coupling cavity slot is placed on the flank edge of
cavity. It is not a place with a strong electric field. But the
damage of an aperture is not so catastrophic.
In the parallel coupled cavity structure the products of
destroied surface are removing out quickly from the cavi-
ties into a waveguide feeder, which has a large cross size
(when waveguide feeder has a standard rectangular form).
There is a very simple HOM problem solution: it is
possible to make the damping HOM slot with a higher
mode load along waveguide feeder or at the end of the
waveguide.
The parallel coupled accelerating structure with rectan-
gular waveguide feeder are shown on Fig. 1.
The Fig. 1(a) shows single-waveguide-feeder accelera-
tor like that of [4]. It has 3-cell π -operate accelerating
mode cavities.
The Fig. 1(b, c, d) shows multiwaveguide structures [5]
in which as a resonant elements E010 cylindrical cavities are
used.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.
Серия: Ядерно-физические исследования (38), с. 65-67.
65
Fig. 1. Parallel coupled cavity accelerating structures with rectangular feeding waveguides.
In case of two feed waveguiges (Fig. 1 (b)) one can
use the travelling wave regime in feed waveguides. The
equality of accelerating particles velocity and phase ve-
locity is valid in case of opposing motion accelerating
particles and power in waveguide. The operating mode
in this case may be πθπ <<2/ and the wavelength of
a waveguide is equal to ( ) 1/ −
=Λ
θπ
λβ
. In Fig. 1(b)
shown is the case when 4/3πθ = ( 1=β ) and the dis-
tance between cavities equals to 4/2 Λp = ( λ3=Λ ).
This corresponds to minimum waveguide reflection. But
this structure is very difficult to tuning.
Fig. 1(c) shows a three-waveguide-feed of cavities.
For 1=β the operating mode is πθ = and λ3=Λ .
All variants (a), (b) and (c) have the rectangular
waveguide with the wavelength λ3=Λ . Such waveg-
uide has large wave resistance (threefold for conserva-
tion of waveguide high resistance) and small group ve-
locity 0.33⋅c
The most attractive is the case (d): four feed waveg-
uides. For the operating mode πθ = waveguides with
λ2=Λ must be used. They have not a so-large wave re-
sistance and the group velocity equals to 0.5⋅c. Such ac-
celerator can be fed by two RF klystron with a double
RF output.
Fig. 2 shows the rectangular waveguide coupled in
common wide wall with cavity (a), its full equivalent
circuit (b) and equivalent circuit of one period (c). In
Fig. 2(b, c) shown are: 0Y - the wave admittance, the
ideal transformer coefficients Wm , Sm and suscep-
tances WjB and gjB - are determined by sizes of the
waveguide, cavity and coupling aperture.
CSgW
W
YmjBjB
mZ 2
2
++
= , ( )k jQZ
QYC δ⋅+⋅
=
00
0
21 ,
ck /ω= , ( ) 00 / kkkk −≈δ , π Z 1200 = Ω, 0Q is the
quality factor. The cavity exciting current is equal to
( ) 0
00
00
00
0
21 km
YmZj
j
m
m
k jQk
Qj
jI
W
CS
W
S ⋅−=⋅
⋅+
⋅
⋅−=
δ ,
( ) ( ) ( ) ( )∫∫ ⋅⋅=+⋅⋅=⋅=
z
CCzC
V
c IntIdz t zIdV jj ϕϕωεε cos2cos20
ε
is normalized cavity distribution function of the elec-
tric field ( ( ) 1=⋅∫ dV
V
εε
), CI is the average beam cur-
rent, ϕ is the angle between accelerating current and
cavity oscillations.
For πθ =Λ at the resonance frequency the reflected
power is equal to
( ) 2
1
cos2
1
1
+
⋅⋅
−⋅
+
−=
N 2
IlZ N
P
N 2
N 2 P Ce
Inpref β
ϕβ
β
β ,
where:
N - number of single cavities per one waveguide,
β - single cavity coupling coefficient,
InpP - input power,
eZ - effective cavity shunt impedance per length unit,
l - length of a single cavity.
66
Fig. 2. (a) waveguide-cavity aperture coupling, (b) its
equivalent circuit, (c) equivalent circuit of one period.
Distribution of n-th cavity electric field is
ε
⋅= nn uE , where nu is the amplitude that equals to
( )
( )
( )
( )
( )
⋅
+
−⋅
+
⋅−= −
00
0
00
01 2
12
cos2
12
24
1
ωεβ
ϕ
ωεβ
β
CCInpn
n
IntQ
N
IQ
N
P
u
Energy gain per single cavity is equal to
( )
( ) ( ) ( ) ( )ϕ
β
ϕ
β
β
2cos
12
cos
12
24
⋅
+
−⋅
+
=
N
lZI
N
lZP
U eCeInp
n ,
but the total energy gain is equal to
( )
( ) ( ) ( ) ( )ϕ
β
ϕ
β
β 2cos
12
cos
12
24
⋅
+
⋅
−⋅
+
⋅=⋅=
N
lZIN
N
lZP
NUNU eCeInp
n
The charm of such kind cavities powering and oper-
ating on π -mode is the equal increment of accelerating
particle energy in all cavities (constant gradient acceler-
ating regime) with equal sizes of all cavities and cou-
pling slots.
For a matched regime (reflected power is equal to
zero) without current load 0 Pref = ⇒ N/12 =β and
then
( ) ( )
⋅⋅−⋅⋅−= −
0
00
0
001 2
2
cos2
/1
k
IntQZI
k
QZ
NPu CC
Inp
n
n
ϕ
( ) ( ) ( )ϕϕ 2cos
2
cos/ ⋅−⋅=
lZIlZNPU eC
eInpn ,
( ) ( )ϕϕ 2cos
2
cos ⋅
⋅
−⋅⋅=⋅=
lZIN
lZPNUNU eC
eInpn .
The simple case is 0=CI and 0=ϕ :
the amplitude of electric field in the n-th cavity is equal
to
( ) ( ) 0
00
01
0
001 2
1
2
/1 n
Inpn
Inp
n
n u
N
QP
k
QZNPu =⋅−=⋅−= −−
ωε
,
the energy gain per one cavity is equal to
0n
eInp
n U
N
lZP
U == ,
and the total energy gain is equal to
0UlZPNUNU eInpn =⋅=⋅= .
If m of N cavities are shorted (size of coupling slot is
equal to zero) for example in case of breakdown, then
we must to replace N by N-m. In this case the reflected
power is increased up to
( )
P
m-2N
mP Inp
2
ref ⋅= 2 , Nm ,...,1,0= ,
n0n u
m-2N
2Nu ⋅= , ( )mNn −= ,...,1 ,
n0n U
m-2N
2NU ⋅= , ( ) ( )
02
2 U
mN
mNUmNU n ⋅
−
−=⋅−= .
All the above is related only to a single waveguide
feeder. One can see that unlike the travelling wave
mode accelerator, the increase of the amplitude of elec-
tric field in a parallel coupled cavity accelerator is
small, when one cavity is breakdown.
Example:
Operating frequency MHz11424 ,
Input power MW150MW752 PInp =×= ,
Nb. of waveguides 4 ,
Nb. of cavities per single feeding waveguide 45,
Effective shunt impedance /mM90 Ω= Z e ,
Energy gain MV/m75 Eacc = ,
Input power for single cavity MW83.01 P ≅ ,
Total length of accelerating section m37.2 L ≅ ,
Energy gain per section MeV178 U ≅ .
If only 1 from 45 cavities of single feeding waveg-
uide is shorted in case of breakdown, the amplitude of
electric field in the other cavities concerned to this
waveguide is increased only up to
000 011.1
89
90
nnnn uuu
m-2N
2Nu ⋅=⋅=⋅= .
REFERENCES
1. J.W.Wang and G.A.Loew. Field Emission and RF
Breakdown in High-Gradient Room-Temperature
Linac Structures. SLAC-PUB-7684, October 1997.
2. R.M.Sundelin, J.L.Kirchgessner, and M.Tiger. Par-
allel Coupled Structure // IEEE Trans. on Nuc. Sci-
ence. June 1977, v. NS-24, No. 3, p. 1686-1688.
3. J.Gao. Analytical approach and scaling laws in the
design of disk-loaded travelling wave accelerating
structures // Particle Accelerators. 1994, v. 43 (4),
p. 235-257.
4. G.Shaffer High power UHF components for DESY
// IEEE Transaction on Nuclear Science. 1995,
NS-12, No.3, p. 208-212.
5. V.M.Pavlov, A.S.Bogomolov, A.S.Sharkhov. Mul-
tisptep decelerating system, Licence SU
№ 1295466 А1, 1985.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.
Серия: Ядерно-физические исследования (38), с. 67-67.
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