Approximations of operating characteristics of the elliptic cross-section beam position monitors
In the specialized storage rings it is necessary to measure a position of a beam with an absolute accuracy up to 10 µm that corresponds to a relative accuracy about 10⁻³ for the central region of a monitor. The position of a beam is usually measured with the help of electrostatic button monitors....
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2004 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Approximations of operating characteristics of the elliptic cross-section beam position monitors / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 108-110. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859904825957810176 |
|---|---|
| author | Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. |
| author_facet | Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. |
| citation_txt | Approximations of operating characteristics of the elliptic cross-section beam position monitors / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 108-110. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In the specialized storage rings it is necessary to measure a position of a beam with an absolute accuracy up to
10 µm that corresponds to a relative accuracy about 10⁻³ for the central region of a monitor. The position of a beam
is usually measured with the help of electrostatic button monitors. Operating characteristics of a beam position
monitor are individual for each copy, are measured on precision benches and approximated by analytical functions.
In the paper the various methods of approximation of operating characteristics are considered and the variant
allowing one to reduce an error of approximation in tens times in comparison with a traditional method is found.
В спеціалізованих нагромаджувачах необхідно виміряти положення пучку з абсолютною точністю до 10 мкм, що
відповідає відносній точності біля 10⁻³ для центральної області датчика. Положення пучку вимірюються за допомогою
електростатичних кнопкових датчиків. Робочі характеристики датчиків положення пучку є індивідуальними для
кожного екземпляру, одержуються на прецизійних стендах та аппроксимуються аналітичними функціями. В роботі розглянуто різні методи апроксимації робочих характеристик та знайдено варіант, що дозволяє зменшити похибку
апроксимації в десятки разів в зрівнянні с традиційним методом.
В специализированных накопителях необходимо измерять положение пучка с абсолютной точностью до 10 мкм, что
соответствует относительной точности около 10⁻³ для центральной области датчика. Положение пучка обычно
измеряется с помощью электростатических кнопочных датчиков. Рабочие характеристики датчиков положения пучка
являются индивидуальными для каждого экземпляра, снимаются на прецизионных стендах и аппроксимируются
аналитическими функциями. В работе рассмотрены различные методы аппроксимации рабочих характеристик и найден
вариант, позволяющий уменьшить погрешность аппроксимации в десятки раз по сравнению с традиционным методом.
|
| first_indexed | 2025-12-07T15:58:57Z |
| format | Article |
| fulltext |
APPROXIMATIONS OF OPERATING CHARACTERISTICS
OF THE ELLIPTIC CROSS-SECTION BEAM POSITION MONITORS
V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov
National Science Center “Kharkov Institute of Physics and Technology”
Akademicheskaya St, 1, Kharkov, UA-61108, Ukraine
E-mail: shcherbakov@kipt.kharkov.ua
In the specialized storage rings it is necessary to measure a position of a beam with an absolute accuracy up to
10 µm that corresponds to a relative accuracy about 10-3 for the central region of a monitor. The position of a beam
is usually measured with the help of electrostatic button monitors. Operating characteristics of a beam position
monitor are individual for each copy, are measured on precision benches and approximated by analytical functions.
In the paper the various methods of approximation of operating characteristics are considered and the variant
allowing one to reduce an error of approximation in tens times in comparison with a traditional method is found.
PACS: 29.20.-c, 29.27.Fh, 02.30.Mw
The operating characteristics (OC) of a four-
electrode beam position monitor (BPM) (Figure)
measured on the bench look like:
),,,( 43211 kkkkbk uuuufx = , (1)
),,,( 43212 kkkkbk uuuufy = , (2)
where xbk, ybk are the coordinates of the beam imitator;
kkkk uuuu 4321 ,,, are the signals measured on the
appropriate electrodes; k is the number of the measured
point in the selected region of the BPM aperture. The
set data obtained allows to approximate OC of BPM
power polynomials or empirically picked out
elementary functions.
The position of a beam defined with the help of
approximating functions will have an error containing
an error of work of a mechanical drive of the bench, an
error of measurement of signals on electrodes, an error
of a method of approximation of operating
characteristics.
U1U2
U3U4
Beam
Y
X
yb
xb
imit.
The layout of the BPM cross-section
In this work the possibility of discovering of
functions that would have minimum errors of
approximation of OC of BPM is studied. The study is
carried out by simulation of bench measurement of OC
of BPM. The model of a monitor for the storage ring N-
100M [1] in the form of an ellipse was considered. Its
geometrical parameters: major axis - 100 mm, minor
axis - 30 mm, coordinates of the center of electrodes xe=
±14.4 mm, ye=±14.36 mm, size of electrodes - 5 mm,
electric capacity of an electrode - 4 pF. The values of
monitor signals were calculated with the help of the
formulas defined in [2].
The signals on BPM electrodes in the elliptical
coordinates are:
]};sin
sinh
sinsinh
cos
cosh
coscosh
[sin2{2 200
1
d
d
bb
d
d
bb
n
bd
n
n
nnn
n
nn
n
n
cC
liu
ν
µ
νµν
µ
νµψψ
π
+
×+= ∑
=
(3)
where d=1,2,3,4 - number of an electrode, ib – current of
a beam imitator, 2l - longitudinal size of an electrode,
c – velocity of light, C – capacity of an electrode, µb
-radial coordinate of beam imitator, νb - angular
coordinate of beam imitator, 2ψ - angular size of
electrodes, µd – radial coordinate of an electrode, νd -
angular coordinate of an electrode.
Elliptic coordinates are expressed through the
Cartesian coordinates as follows:
2
222222222
2
4)(
arccos
a
axyxayxa
h
−+++++
=µ
(4)
2
222222222
2
4)(
arccos
a
axyxayxa −++−++
=ν
(5)
where 2a is the distance between focuses. Formulas are
true for |x|<a.
To optimize the functions approximating OC, they
are found as:
( ),,1 ggb VHx Φ= (6)
( ).,2 ggb VHy Φ= (7)
Arguments Hg and Vg represent the normalized linear
combinations of the measured signals of BPM. Research
was carried out for four variants of definition of
arguments Hg and Vg (g=1,2,3,4):
4321
4321
1
4321
4231
1 ,
uuuu
uuuu
V
uuuu
uuuu
H
+++
−−+
=
+++
−−+
= (8)
+
−
+
+
−
=
+
−
+
+
−
=
32
32
41
41
2
23
23
41
41
2 2
1,
2
1
uu
uu
uu
uu
V
uu
uu
uu
uu
H
(9)
+
−
+
+
−
=
+
−
+
+
−
=
42
42
31
31
3
43
43
21
21
3 2
1,
2
1
uu
uu
uu
uu
V
uu
uu
uu
uu
H
(10)
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.108-110. 108
mailto:shcherbakov@kipt.kharkov.ua
+
−
+
+
−
=
+
−
+
+
−
=
42
42
31
31
4
23
23
41
41
4 2
1,
2
1
uu
uu
uu
uu
V
uu
uu
uu
uu
H
(11)
The first variant (traditional) has obtained rather
wide application in practice [3,4], the second one was
proposed in [5], but the propagation was not found, the
third and the fourth ones are considered for the first
time.
Research was carried out in the assumption of an
ideally symmetric BPM. It has allowed obtaining the
simplified form of approximating functions.
Approximation of operating characteristics (6), (7) was
carried out by polynomials up to 7-th order
∑ ∑
= =
+−
+−=
M
m
m
n
n
g
nm
gnnmb VHAx
0 0
2122
2,122 , (12)
∑ ∑
= =
+−
+−=
M
m
m
n
n
g
nm
gnnmb HVBy
0 0
2122
2,122 , (13)
and by the empirically picked out expression
][
][
0 0
2122
2,122∑ ∑
= =
+−
+−⋅+
+⋅=
M
m
m
n
n
g
nm
gnnm
gb
VHESinhD
HArcTanhCx
, (14)
for which М=3. Coefficients A, B, C, D, E were
calculated with the fitting carried out by the method of
least squares.
Since the accuracy of approximation depends on the
distance from the beam up to the center of BPM, the
simulation was carried out for two monitor regions: 1
(central) region with dimensions |x|≤10mm, |y|≤5), and
II (far) region with dimensions |x|≤40mm, |y|≤7mm.
In each region of BPM the coefficients of
expressions (12), (13), (14) were calculated for 4
variants of definition of arguments (8), (9), (10), (11).
The data set was calculated with 1 mm step for both
regions.
Results of simulation were estimated by the relative
root-mean-square errors of approximation averaged on
fixed region as follows:
′
′−
= ∑
=
n
k bk
bkbk
x n
x
xx
0
2
/σ , (15)
′
′−
= ∑
=
n
k bk
bkbk
y n
y
yy
0
2
/σ , (16)
where bkx , bky - true values of beam coordinates
assigned in the calculation of signals by formulas (3),
(4), (5); bkx ′ , bky ′ - beam coordinates calculated by
formulas (12),(13),(14) for the corresponding true Hgk
and Vgk, k – number of the point for which the error was
calculated, n – quantity of the calculated points.
Calculations were carried out with a 0.9 mm step on
both coordinates.
Results of calculations are given in Table 1. From
the results obtained it is seen that for the central region
of BPM the best approximation of OC (6) is provided
with expressions (14), (11) and the best approximation
of OC (7) is provided with expressions (13), (11). The
corresponding errors of the approximation are equal to
σx=1.2×10-5, σy=1.9×10-4 while the traditional
approximation method (the formulas (12), (13) (8)) has
greater errors σx=1.7×10-3, σy=7.8×10-4. In the far region
of BPM the best results is obtained with using formulas
(14), (10) - σx=5.2×10-2 and formulas (13), (9) - σy=0.4.
The traditional approximation method has greater errors
σx=0.3, σy=0.45.
One can see, that the error of approximation of OC
(7) less σy=0.4 cannot be obtained for the far region of
BPM. Presumably, it is caused by the form of the
monitor that is very extended along the axis X. To be
convinced of this supposition the approximation of OC
of BPM for the storage ring ISI-800 [6] was carried out.
The BPM of ISI-800 has the following geometrical
parameters: cross-section - elliptic, the big axis -
60 mm, a small axis - 36 mm, distance between of
centers of electrodes along X axis - 22.86 mm and along
Y axis - 32.86 mm, diameter of electrodes - 5 mm. The
results of calculations are given in Table 2 with the
indication of used formulas.
Approximations of OC of the ISI-800 monitor in
region 1 have errors comparable with the corresponding
errors of the N-100M monitor. Approximations of OC
(7) by expression (13) in region II have errors σ
y=(5.2...6.2)×10-2, that confirms the supposition
expressed above about a negative influence of the very
extended form of a monitor on the accuracy of
approximation.
The method of estimation of errors of approximating
functions also allows analyzing a possibility to lower an
order of polynomials being used. Calculations of errors
for the central region of N-100М BPM are brought
together in Table 3 at approximation of OC by
polynomials up to 7-th, 5-th, 3-rd and 1-st orders.
Traditionally used formulas (12), (13), (8) and the
formulas giving the best results (13), (14), (11) are
considered for comparison. From Table 3 the obvious
advantage of the method of approximation of OC (6)
and (7) by expressions (13), (14), (11) is visible in
comparison with the traditional method at equal orders
of polynomials. Use of this method of approximation
enables one to apply into practice the polynomials of
lower orders (5-th or even 3-rd) with a required error
about 10-3.
The carried out simulation and the analysis of the
obtained results have shown that the approximation of
operating characteristics of elliptic cross-section BPM is
fulfilled most precisely by the method using expressions
(13), (14), (11) for the central region of a monitor and
for optimal chosen far region of a monitor. The above-
mentioned method allows fulfilling precision
measurements in the center of the monitor using the
approximation of OC by polynomials of 5-th order. The
form of the monitor very much extended along the axis
X increases the errors of approximation of OC,
especially the error of characteristic of a beam
displacement along the axis Y in the far region.
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.108-110.109
In conclusion the authors thank Dr. A. Mytsykov for
useful advises and the discussion of results of this work.
Table 1. Average errors of different approximation methods of OC of N-100M BPM
Region of cross-section BPM Number of formula σx (12) σy (13) σx (14)
1
-10≤x≤10
-5≤y≤5
(8) 0.001696 0.000788 0.000264
(9) 0.001057 0.001542 0.000015
(10) 0.001173 0.000226 0.000145
(11) 0.001044 0.000195 0.000012
II
-40≤x≤40
-7≤y≤7
(8) 0.304776 0.451419 0.181716
(9) 0.420346 0.406421 0.074058
(10) 0.298039 0.478659 0.052067
(11) 0.285599 0.476832 0.063378
Table 2. Average errors of different approximation methods of OC of ISI-800 BPM
Region of cross-section BPM Number of formula σx (12) σy (13) σx (14)
1
-10≤x≤10
-5≤y≤5
(8) 0.000646 0.000385 0.000511
(9) 0.000431 0.000522 0.000021
(10) 0.000469 0.000195 0.000111
(11) 0.000390 0.000186 0.000015
II
-23≤x≤23
-10≤y≤10
(8) 0.100030 0.059887 0.042760
(9) 0.062090 0.062081 0.010127
(10) 0.079737 0.059247 0.021223
(11) 0.062902 0.052716 0.009328
Table 3. Average errors of approximation of OC for central region of N -100М BPM
Order of polynomials Number of formula σx (12) σy (13) σx (14)
7–order, M=3 (11) - 0.000195 0.000012
5–order, M=2 (11) - 0.000876 0.000087
3–order, M=1 (11) - 0.004655 0.000766
1-order, M=0 (11) - 0.075856 0.002039
7–order, M=3 (8) 0.001696 0.000788 -
5–order, M=2 (8) 0.006095 0.001869 -
3–order, M=1 (8) 0.034405 0.021693 -
1-order, M=0 (8) 0.140973 0.208716 -
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Electron Storage Ring // VANT. Series: Nuclear
Physics Research (40). 2002, №2, p.72-74.
2. A. Zelinsky, I. Karnaukhov, V. Lyashchenko,
V. Trotsenko // VANT. Series: Nuclear Physics
Research. 1999, №1, p.73-79 (in Russian).
3. Eva S. Bozoki. Determination of Beam Position from
Induced Electric Signals // Nuclear Instruments and
Methods in Physics Research. A 307. 1991, p. 195-206.
4. K.Ye, L. Ma and H. Huang. The Calibration of BEPC
Beam Position Monitors. // Proceedings of 8-th Beam
Instrumentation Workshop, May 4-7, 1998, SLAC,
Stanford, CA.
5. J. Borer and C. Bovet. Diagnostics // CERN/LEP-
BI/84-14, Geneva, October 1984.
6. I. Karnaukhov, E. Bulyak, S. Kononenko,
A. Shcherbakov, A. Tarasenko, A. Zelinsky. Progress
of the ISI-800 Project. // Particle Accelerator
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Energy Accelerators, 1-5 May 1995; Dallas, Texas,
USA.
АППРОКСИМАЦИИ РАБОЧИХ ХАРАКТЕРИСТИК ДАТЧИКОВ ПОЛОЖЕНИЯ ПУЧКА
ЭЛЛИПТИЧЕСКОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ
В.Е. Иващенко, И. M. Карнаухов, В.И. Троценко, A.A. Щербаков
В специализированных накопителях необходимо измерять положение пучка с абсолютной точностью до 10 мкм, что
соответствует относительной точности около 10-3 для центральной области датчика. Положение пучка обычно
измеряется с помощью электростатических кнопочных датчиков. Рабочие характеристики датчиков положения пучка
являются индивидуальными для каждого экземпляра, снимаются на прецизионных стендах и аппроксимируются
аналитическими функциями. В работе рассмотрены различные методы аппроксимации рабочих характеристик и найден
вариант, позволяющий уменьшить погрешность аппроксимации в десятки раз по сравнению с традиционным методом.
АППРОКСИМАЦІЯ РОБОЧИХ ХАРАКТЕРИСТИК ДАТЧИКІВ ПОЛОЖЕННЯ ПУЧКУ
ЕЛІПТИЧНОГО ПОПЕРЕЧНОГО ПЕРЕРІЗУ
В.Є. Іващенко, І. M. Карнаухов, В.І. Троценко, О.О. Щербаков
В спеціалізованих нагромаджувачах необхідно виміряти положення пучку з абсолютною точністю до 10 мкм, що
відповідає відносній точності біля 10-3 для центральної області датчика. Положення пучку вимірюються за допомогою
електростатичних кнопкових датчиків. Робочі характеристики датчиків положення пучку є індивідуальними для
кожного екземпляру, одержуються на прецизійних стендах та аппроксимуються аналітичними функціями. В роботі
110
розглянуто різні методи апроксимації робочих характеристик та знайдено варіант, що дозволяє зменшити похибку
апроксимації в десятки разів в зрівнянні с традиційним методом.
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.108-110.111
V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov
1
II
1
II
В.Е. Иващенко, И. M. Карнаухов, В.И. Троценко, A.A. Щербаков
В.Є. Іващенко, І. M. Карнаухов, В.І. Троценко, О.О. Щербаков
|
| id | nasplib_isofts_kiev_ua-123456789-79360 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:58:57Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. 2015-03-31T14:39:33Z 2015-03-31T14:39:33Z 2004 Approximations of operating characteristics of the elliptic cross-section beam position monitors / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 108-110. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 29.20.-c, 29.27.Fh, 02.30.Mw https://nasplib.isofts.kiev.ua/handle/123456789/79360 In the specialized storage rings it is necessary to measure a position of a beam with an absolute accuracy up to 10 µm that corresponds to a relative accuracy about 10⁻³ for the central region of a monitor. The position of a beam is usually measured with the help of electrostatic button monitors. Operating characteristics of a beam position monitor are individual for each copy, are measured on precision benches and approximated by analytical functions. In the paper the various methods of approximation of operating characteristics are considered and the variant allowing one to reduce an error of approximation in tens times in comparison with a traditional method is found. В спеціалізованих нагромаджувачах необхідно виміряти положення пучку з абсолютною точністю до 10 мкм, що відповідає відносній точності біля 10⁻³ для центральної області датчика. Положення пучку вимірюються за допомогою електростатичних кнопкових датчиків. Робочі характеристики датчиків положення пучку є індивідуальними для кожного екземпляру, одержуються на прецизійних стендах та аппроксимуються аналітичними функціями. В роботі розглянуто різні методи апроксимації робочих характеристик та знайдено варіант, що дозволяє зменшити похибку апроксимації в десятки разів в зрівнянні с традиційним методом. В специализированных накопителях необходимо измерять положение пучка с абсолютной точностью до 10 мкм, что соответствует относительной точности около 10⁻³ для центральной области датчика. Положение пучка обычно измеряется с помощью электростатических кнопочных датчиков. Рабочие характеристики датчиков положения пучка являются индивидуальными для каждого экземпляра, снимаются на прецизионных стендах и аппроксимируются аналитическими функциями. В работе рассмотрены различные методы аппроксимации рабочих характеристик и найден вариант, позволяющий уменьшить погрешность аппроксимации в десятки раз по сравнению с традиционным методом. In conclusion the authors thank Dr. A. Mytsykov for useful advises and the discussion of results of this work. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Элементы ускорителей Approximations of operating characteristics of the elliptic cross-section beam position monitors Аппроксимація робочих характеристик датчиків положення пучку еліптичного поперечного перерізу Аппроксимации рабочих характеристик датчиков положения пучка эллиптического поперечного сечения Article published earlier |
| spellingShingle | Approximations of operating characteristics of the elliptic cross-section beam position monitors Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. Элементы ускорителей |
| title | Approximations of operating characteristics of the elliptic cross-section beam position monitors |
| title_alt | Аппроксимація робочих характеристик датчиків положення пучку еліптичного поперечного перерізу Аппроксимации рабочих характеристик датчиков положения пучка эллиптического поперечного сечения |
| title_full | Approximations of operating characteristics of the elliptic cross-section beam position monitors |
| title_fullStr | Approximations of operating characteristics of the elliptic cross-section beam position monitors |
| title_full_unstemmed | Approximations of operating characteristics of the elliptic cross-section beam position monitors |
| title_short | Approximations of operating characteristics of the elliptic cross-section beam position monitors |
| title_sort | approximations of operating characteristics of the elliptic cross-section beam position monitors |
| topic | Элементы ускорителей |
| topic_facet | Элементы ускорителей |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79360 |
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