Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section
The various methods of approximation of operating characteristics of electrostatic beam position monitors were investigated. The new method that allows on order to increase the precision of approximation of horizontal coordinate is found. The simulation of measurement of frequencies of betatron osc...
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| Zitieren: | Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 5. — С. 142-144. — Бібліогр.: 4 назв. — англ. |
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Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. 2015-04-19T17:05:54Z 2015-04-19T17:05:54Z 2004 Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 5. — С. 142-144. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 29.20.-c, 29.27.Fh, 02.30.Mw https://nasplib.isofts.kiev.ua/handle/123456789/80612 The various methods of approximation of operating characteristics of electrostatic beam position monitors were investigated. The new method that allows on order to increase the precision of approximation of horizontal coordinate is found. The simulation of measurement of frequencies of betatron oscillations is carried out. Досліджено різні методи апроксимації робочих характеристик електростатичних датчиків положення пучка. Знайдено новий метод, що дозволяє на порядок підвищити точність апроксимації горизонтальної координати. Виконано моделювання вимірювання частот бетатронних коливань. Исследованы различные методы аппроксимации рабочих характеристик электростатических датчиков положения пучка. Найден новый метод, позволяющий на порядок повысить точность аппроксимации гори- зонтальной координаты. Выполнено моделирование измерения частот бетатронных колебаний. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Теория и техника ускорения частиц Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section Робочі характеристики електростатичних датчиків еліптичного, прямокутного та круглого поперечного перетину Рабочие характеристики электростатических датчиков эллиптического, прямоугольного и круглого поперечного сечения Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| spellingShingle |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section Ivashchenko, V.E. Karnaukhov, I.M. Trotsenko, V.I. Shcherbakov, A.A. Теория и техника ускорения частиц |
| title_short |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| title_full |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| title_fullStr |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| title_full_unstemmed |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| title_sort |
operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section |
| 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. |
| topic |
Теория и техника ускорения частиц |
| topic_facet |
Теория и техника ускорения частиц |
| publishDate |
2004 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Робочі характеристики електростатичних датчиків еліптичного, прямокутного та круглого поперечного перетину Рабочие характеристики электростатических датчиков эллиптического, прямоугольного и круглого поперечного сечения |
| description |
The various methods of approximation of operating characteristics of electrostatic beam position monitors were
investigated. The new method that allows on order to increase the precision of approximation of horizontal coordinate is found. The simulation of measurement of frequencies of betatron oscillations is carried out.
Досліджено різні методи апроксимації робочих характеристик електростатичних датчиків положення
пучка. Знайдено новий метод, що дозволяє на порядок підвищити точність апроксимації горизонтальної
координати. Виконано моделювання вимірювання частот бетатронних коливань.
Исследованы различные методы аппроксимации рабочих характеристик электростатических датчиков
положения пучка. Найден новый метод, позволяющий на порядок повысить точность аппроксимации гори-
зонтальной координаты. Выполнено моделирование измерения частот бетатронных колебаний.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/80612 |
| citation_txt |
Operating characteristics of the electrostatic monitors of elliptic, rectangular and circular cross-section / V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov // Вопросы атомной науки и техники. — 2004. — № 5. — С. 142-144. — Бібліогр.: 4 назв. — англ. |
| work_keys_str_mv |
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| first_indexed |
2025-11-24T03:46:14Z |
| last_indexed |
2025-11-24T03:46:14Z |
| _version_ |
1850839728225517568 |
| fulltext |
OPERATING CHARACTERISTICS OF THE ELECTROSTATIC MONITORS
OF ELLIPTIC, RECTANGULAR AND CIRCULAR CROSS-SECTION
V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko, A.A. Shcherbakov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: v.ivashchenko@kipt.kharkov.ua
The various methods of approximation of operating characteristics of electrostatic beam position monitors were
investigated. The new method that allows on order to increase the precision of approximation of horizontal coordi-
nate is found. The simulation of measurement of frequencies of betatron oscillations is carried out.
PACS: 29.20.-c, 29.27.Fh, 02.30.Mw
1. INTRODUCTION
For measurement of the parameters of betatron tune
and coordinates of closed orbit (CO) of electron beam in
storage rings (SR) usually apply four-electrode electro-
static monitors (EM). On their basis create betatron tune
monitors (BTM) and beam position monitors (BPM)
with using corresponding combinations of four mea-
sured signals. The measurement accuracy of BPM
should be much higher, than precision of positioning of
magnetic elements of SR (<<100 µm).
In the articles [1,2] were shown that nonlinearity of
operating characteristics (OC) of the EM of elliptic
cross-section leads to errors of measured parameters of
a beam. One of the sources of measurement errors of
beam coordinates is the approximation error of monitors
operating characteristics. The traditional methods of the
approximation allow to execute the measurement with
high accuracy only in very small region near the center
of the monitor. In the article [3] the new method of ap-
proximation of OC of BPM that allows on the order to
increase measurement accuracy in comparison with a
traditional method was offered.
Because in practice are widely applied BPM of rect-
angular and circular cross-section, in the given paper of
possibility of approximating of their operating charac-
teristics by methods described in [2] for BPM of an el-
liptic cross-section were researched. The measurement
simulation of spectrums of betatron oscillations and
transverse beam coordinates by the EM of storage ring
N-100M (NESTOR) is carried out also.
2. SIMULATION OF BPM CROSS-SECTION
Coordinates of a closed orbit of a beam versus the
signals of the BPM (Figure) in the Cartesian frame are
defined as:
)V,H()u,u,u,u(fx ck,ktck,tkkkkkbk 143211 Φ== , (1)
)V,H()u,u,u,u(fy ck,ktck,ktkkkkbk 243212 Φ== , (2)
here: k – is ordinal number of measurement point, Htk, ck,
Vtk, ck – are the normalized differential linear combina-
tions of the measured signals:
kkkk
kkkk
tk
kkkk
kkkk
tk
uuuu
uuuuV
uuuu
uuuuH
4321
4321
4321
4231
+++
−−+
=
+++
−−+
=
, (traditional) (3)
+
−
+
+
−
=
+
−
+
+
−
=
kk
kk
kk
kk
ck
kk
kk
kk
kk
ck
uu
uu
uu
uuV
uu
uu
uu
uuH
42
42
31
31
23
23
41
41
2
1
2
1
, (combined) (4)
The expressions (1), (2) are operating characteristics
of BPMs. They are measured on precision test bench
and traditionally approximated by degree polynomials:
∑ ∑
= =
+−
+−=
K
m
m
n
n
c,t
nm
c,tn,nmb VHAx
0 0
2122
2122 , (5)
∑ ∑
= =
+−
+−=
K
m
m
n
n
c,t
nm
c,tn,nmb HVBy
0 0
2122
2122 . (6)
Approximation of OC (1) by new empirical function
]VHE[shD
]H[acthCx
K
m
m
n
n
c,t
nm
c,tn,nm
c,tb
∑ ∑
= =
+−
+−⋅+
+⋅=
0 0
2122
2122
, (7)
was considered in work [3].
The electrostatic monitor layouts of elliptic, rectangular and circular cross-section,
u1, u2, u3, u4 is signals of monitor electrodes
142 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2004, № 5.
Series: Nuclear Physics Investigations (44), p. 142-144.
Table 1. Average errors of an approximation calculated by various methods for the operation characteristics of
the elliptic BPM (N-100M). The size of BPM: the big axis is 79 mm, a small axis is 28.7 mm, the coordinates of the
electrode centers is Xe=±10 mm, Ye=±13.89 mm, the size of the electrodes is 5 mm
Region of BPM, mm Error→
↓ Formula→
σx
(5) – polynomial
σx
(7) – empirical
σy
(6) –polynomial
-8<x<8
-4<y<4
(3) - traditional 0.002662 0.001351 0.001756
(4) - combined 0.001995 0.000102 0.000789
Table 2. Average errors of an approximation calculated by various methods for the operation characteristics of
the rectangular BPM. The size of BPM is 100 mm× 30 mm, the coordinates of the electrode centers is Xe =14.4 mm,
Ye=15 mm, the size of the electrodes is 5 mm
Region of BPM, mm Error→
↓ Formula→
σx
(5) – polynomial
σx
(7) – empirical
σy
(6) –polynomial
-10<x<10
-5<y<5
(3) - traditional 0.005730 0.001255 0.001711
(4) - combined 0.004874 0.000037 0.000835
Table 3. Average errors of an approximation calculated by various methods for the operation characteristics of
the circular BPM. Diameter of BPM is 41 mm, the coordinates of the electrode centers is Xe=14.49 mm,
Ye=14.49 mm, the size of the electrodes is 5 mm
Region of BPM, mm Error→
↓ Formula→
σx
(5) – polynomial
σx
(7) – empirical
σy
(6) –polynomial
-9.5<x<9.5
-5.5<y<5.5
(3) - traditional 0.003305 0.002940 0.003738
(4) - combined 0.001877 0.000558 0.000501
Table 4. The amplitudes of harmonics of signal Hβ [µV]
Harmonics
Coordin. of CO
ω0 (k±qx) ω0 (k±qy) ω0 (k±2qx) ω0 (k±2qy) ω0 (k±qx±qy) ω0
xb =9 mm, yb =7 mm 1637 33.6 91.1 5 4.5 1.3
xb =4 mm, yb =3 mm 627 71.8 19.7 1.3 1.7 2.2
xb =0 mm, yb =0 mm 0 74 0 0 0 0
Table 5. The amplitudes of harmonics of signal Vβ [µV]
Harmonics
Coordin. of CO
ω0 (k±qy) ω0 (k±qx) ω0 (k±2qx) ω0 (k±2qy) ω0 (k±qx±qy) ω0
xb =14 mm, yb =7 mm 983 112 132 12.9 4.7 6
xb =9 mm, yb =7 mm 1364 111 26.4 3.6 1.7 4
xb =4 mm, yb =3 mm 415 68.4 14.6 0.6 0.2 2.6
xb =0 mm, yb =0 mm 0 59.4 0 0 0 0
The simulation of bench measuring of operating
characteristics (1), (2) of rectangular and round cross-
section BPM were carried out and their approximations
by expressions (5), (6), (7) for two variants of argu-
ments (3), (4) are obtained, by methods described in [2].
The geometrical parameters of the said monitors were
chosen similar to monitor of an elliptic cross-section
considered in [2]. BPM designed for N100-M is investi-
gated also. In all cases the approximation of OC was
carried out by polynomials of 5-th order for which K=2.
The results of calculations are brought together in Ta-
bles 1-3 as relative root-mean-square errors of approximation
averaged on fixed region of BPMs - σx and σy.
One can see, for all forms of a cross-section of the
monitors the error of approximation σx of coordinate xb
by empirical expression (7) with the combined argu-
ments Hc, Vc about ten times is less than at approxima-
tion by the polynomial (5) with traditional arguments
Ht, Vt (3).
Use of combined arguments Hc, Vc at approximation
of OC (2) by the polynomial (6) too reduces in some
times error of approximation σy in comparison with the
use traditional arguments Ht, Vt.
Thus, the approximation of operation characteristics
(1), (2) by expressions (6), (7) with use of arguments (4)
gives considerably smaller general error of measuring of
coordinates of the beam for any shape of cross section
of monitors in comparison with traditionally used ap-
proximations. Use of empirical expression (7) and the
combined arguments Ht, Vt will allow to fulfill precision
measurements of the beam coordinates of SR N-100М
with accuracy up to ±10 µm (≤±10-3).
3. SIMULATION OF OC OF THE STORAGE
RING N-100М BTM
Operating characteristics of BTM are frequency
spectrum of horizontal and vertical signals of beam de-
viation. In practice these signals are extracted with the
help of the corresponding differential combinations of
four EM signals.
Signals of horizontal Hβ and vertical Vβ beam devia-
tion are:
143
( ) ( ) ,),,(
1
0
,,,,,4,2,3,1 ∑
−
=
=+−+=
M
n
nbnbnHnbnnnn YXGZiuuuuH β
( ) ( ) ,),,(
1
0
,,,,,4,3,2,1 ∑
−
=
=+−+=
M
n
nbnbnVnbnnnn YXGZiuuuuVβ
( ) ( )∑
∞
=
−+=
1
0,,0, ],/2cos[2/
k
nknnb MntkIIi πω
j
n,b
m
n,b
j,m
j,mn,H YXSZ ∑
∞
=
=
0
,
j
n,b
m
n,b
j,m
j,mn,V XYDZ ∑
∞
=
=
0
,
nbn,b xxX += , nbn,b yyY += ,
)]/2([cos 0, Mntqax xnxn πω −= ,
)]/2(cos[ 0, Mntqay ynyn πω −= ,
n,bi is a current of corresponding n-th bunch of beam; ω0 is
rotation frequency of bunch in storage ring; n,HZ , n,VZ
are coupling impedances; G is geometric parameters of the
BTM; bx , by are CO coordinates; nx , ny are horizontal
and vertical components of beam deviation from the CO;
xq , yq are fractional parts of horizontal and vertical beta-
tron tune, M is quantity of the bunches.
As a result of calculations we obtain a series of harmonics
with frequencies ( ) 0ωyx dqrqk ±± , where k, r, d
=0,1,2…- are coefficients of harmonics measured by BTM.
In ideal case BTM should extracted only harmonics
( ) 0ωxqk ± or ( ) 0ωyqk ± , 0ωk . But really always
will be present higher and combination parasitic har-
monics. As shown in [2], the contribution to measured
signal of parasitic harmonics strongly depends on beam
closed orbit coordinates in the aperture of the monitor.
Calculations of the spectrums of the signals Hβ, Vβ of
BTM of N-100M were carried out for electron beam
with parameters М=1, Ik=2 mA, ax=ay=1 mm, qx=0.155,
qy=0.082 and the results are brought together in Tables 4,5.
One can see from Tables 4, 5 in both cases the spec-
trum of the measured signals are enriched by parasitic
harmonics with increase of coordinates of the closed or-
bit. For example, at xb =9 mm, yb =7 mm the amplitude
of the parasitic harmonics ( ) 0ωyqk ± of the signal Hβ
exceeds amplitude of measured harmonics ( ) 0ωxqk ± , that
will not allow correctly to execute measuring.
Similar situation arises at measuring the signal Vβ at
coordinates of the closed orbit xb =14 mm, yb=7 mm.
4. CONCLUSIONS
Thus, the approximation of operation characteristics
(1), (2) by expressions (6), (7) with use of arguments (4)
gives considerably smaller general error of measuring of
coordinates of the beam for any shapes of cross section
of monitors in comparison with traditionally used ap-
proximations. Use of empirical expression (7) and the
combined arguments Ht, Vt will allow to fulfill precision
measurements of the beam coordinates of SR N-100М
with accuracy up to ±10 µm (≤±10-3).
As the result of the carried out calculations it is visi-
ble that region about xb =±4 mm, yb =±3 mm for the
monitor of storage ring N-100M is optimal for reliable
measurements of betatron tune signals.
REFERENCES
1. V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko,
A.A. Shcherbakov. Study of Spectrum Signals of
Electrostatic Beam Monitors // Journal of Kharkiv
University, physical series “Nuclei, Particles,
Fields”. 2002, issue 4, №574, p. 102-106.
2. V.E. Ivashchenko, I.M. Karnaukhov, V.I. Trotsenko,
A.A. Shcherbakov. Approximations of Operating
Characteristics of the Elliptic Cross-Section Beam
Position Monitors // Problems of Atomic Science
and Technology, series: Nuclear Physics Investiga-
tions (43). 2004, №2, p. 108-110.
3. R. Biscardi, J.W. Bittner. Switched Detector for
Beam Position Monitor. Proceedings of the 1989
IEEE Particle Accelerator Conference, March 20-23,
1989, Chicago, IL, v. 3 of 3, p. 1516-1518.
4. A. Stella, A. Drago, A. Ghigo et all. Beam Position
Monitor System of DAФNE. Proceedings of 8-th
Beam Instrumentation Workshop, May 4-7, 1998,
SLAC, Stanford, CA.
.
РАБОЧИЕ ХАРАКТЕРИСТИКИ ЭЛЕКТРОСТАТИЧЕСКИХ ДАТЧИКОВ ЭЛЛИПТИЧЕСКОГО,
ПРЯМОУГОЛЬНОГО И КРУГЛОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ
В.Е. Иващенко, И.M. Карнаухов, В.И. Троценко, A.A. Щербаков
Исследованы различные методы аппроксимации рабочих характеристик электростатических датчиков
положения пучка. Найден новый метод, позволяющий на порядок повысить точность аппроксимации гори-
зонтальной координаты. Выполнено моделирование измерения частот бетатронных колебаний.
РОБОЧІ ХАРАКТЕРИСТИКИ ЕЛЕКТРОСТАТИЧНИХ ДАТЧИКІВ ЕЛІПТИЧНОГО,
ПРЯМОКУТНОГО ТА КРУГЛОГО ПОПЕРЕЧНОГО ПЕРЕТИНУ
В.Є. Іващенко, І.M. Карнаухов, В.І. Троценко, О.О. Щербаков
Досліджено різні методи апроксимації робочих характеристик електростатичних датчиків положення
пучка. Знайдено новий метод, що дозволяє на порядок підвищити точність апроксимації горизонтальної
координати. Виконано моделювання вимірювання частот бетатронних коливань.
144
PACS: 29.20.-c, 29.27.Fh, 02.30.Mw
Error
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REFERENCES
|