Application of permanent magnets for forming solenoidal fields
In the paper the possibility of forming a solenoidal magnetic field with the help of the permanent ring-shaped magnets is considered. The results of modeling a magnetic field for the magnets with the various inside diameter is shown. The possibility of the magnitude control of the magnetic field by...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2001 |
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| Формат: | Стаття |
| Мова: | Англійська |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Application of permanent magnets for forming solenoidal fields / А.М. Bovda, A.N. Dovbnya, A.O. Mytsykov, N.G. Reshetnyak, V.V. Zakutin // Вопросы атомной науки и техники. — 2001. — № 5. — С. 114-116. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860239532741361664 |
|---|---|
| author | Bovda, A.М. Dovbnya, A.N. Mytsykov, A.O. Reshetnyak, N.G. Zakutin, V.V. |
| author_facet | Bovda, A.М. Dovbnya, A.N. Mytsykov, A.O. Reshetnyak, N.G. Zakutin, V.V. |
| citation_txt | Application of permanent magnets for forming solenoidal fields / А.М. Bovda, A.N. Dovbnya, A.O. Mytsykov, N.G. Reshetnyak, V.V. Zakutin // Вопросы атомной науки и техники. — 2001. — № 5. — С. 114-116. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In the paper the possibility of forming a solenoidal magnetic field with the help of the permanent ring-shaped magnets is considered. The results of modeling a magnetic field for the magnets with the various inside diameter is shown. The possibility of the magnitude control of the magnetic field by the passive and active methods is investigated. In the work the estimation of the cost, mass and size of various magnets was done.
|
| first_indexed | 2025-12-07T18:28:28Z |
| format | Article |
| fulltext |
APPLICATION OF PERMANENT MAGNETS FOR
FORMING SOLENOIDAL FIELDS
А.М. Bovda, A.N. Dovbnya, A.O. Mytsykov, N.G. Reshetnyak, V.V. Zakutin
IHEPNP NSC KIPT, Kharkov
In the paper the possibility of forming a solenoidal magnetic field with the help of the permanent ring-shaped mag-
nets is considered. The results of modeling a magnetic field for the magnets with the various inside diameter is
shown. The possibility of the magnitude control of the magnetic field by the passive and active methods is investi-
gated. In the work the estimation of the cost, mass and size of various magnets was done.
PACS numbers: 02.30.Dk, 02.30.Em.
1 INTRODUCTION
For some problems, for example, beam shaping in
magnetron guns with secondary-emission cathodes [1,
2] it is necessary to have an enough homogeneous mag-
netic field of great magnitude. Now such fields form
with the help of solenoids, powered direct current. The
advent of new magnetic material enables to expand an
area of application of permanent magnets. One of such
possibilities is generation of the strong (~0.3-0.4T)
solenoidal fields for klystrons on the basis of magnetron
guns with secondary-emission cathodes and transporting
of a charged beams in various systems.
2 MATHEMATICAL MODEL
For description of a magnetic field B we shall use
the known relation [3]:
)rot(A=B , (1)
where A is the vector potential equal [3]:
∫
×=
V
dV
S 3
SMA , (2)
where S is the vector, directed from the point Pm, in the
neighbourhood of which is the volume dV, to the obser-
vation point P; M is the vector of magnetization of the
volume element dV.
The formula (2) is valid on a sufficient distance of
the point Pm from P.
For description of a field created by cylindrical mag-
netics we shall use a frame and labels shown in Fig. 1.
Fig. 1. Definition of a vector- potential (2).
Using the convention shown in Fig. 1 it is possible
to show, that a vector potential of an infinitely thin ring
with the radius Rm, each segment of which has only
longitudinal (Mz), and radial (Mr) components of mag-
netization, in a view point P(z, r) looks like:
( ) ( )( )
( )( )2222
3
3231 442
ZmzRmrr
rRmKrRmE
−+−
−+−−
=
ζ
ζζζζ
ϕA , (3)
where:
( )( )
( )( );)( 222
222
1
ZmzrRmZmzMr
ZmzrRmMzRm
−++−
+−+−=ζ
( )( )
( ) ( )( ) ( ) ( )( );)( 2222
2222
2
ZmzRmrZmzRmrZmzMr
ZmzrRmMzRm
−++−+−−
+−++=ζ
( ) ( ) 22
3 ZmzRmr −+−=ζ .
As the problem is axial, a potential has only the
ϕ-component and does not depend on an angle ϕ. It is
known [2], that in areas, where there are no sources
(namely such a field we consider) the axial-symmetric
field is completely determined by the value of the field
on the axis.
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) .
644
'''
2!!
1
;
16
'''
2
'
2!1!
1
4
4
1
22
2
2
1
31212
−+−=
−=
−+−=
−
−=
∑
∑
∞
=
∞
=
−−
rzBrzBzBr
k
zBBz
rzBrzBr
kk
zBBr
k
kkk
k
kkk
(4)
Therefore let us determine only the z-component of the
field on an axis. It essentially simplifies the expression:
( )1 2
0
rA
z Rm
rr r
ϕ π
∂
= = − ×
=∂
B
( )( ) ( )
( )( )
22
5/ 222
2 3Mz Rm z Zm MrRm z Zm
Rm z Zm
− − + −
×
+ −
(5)
In Fig. 2 the dependence of the magnitude Bz along
the axis z at different directions of "elementary" ring
magnetization is shown.
-4 -2 2 4
-1.5
-1
-0.5
0.5
1
Fig. 2. Field on the axis of the ring composed of the
magnet with a magnetization direction designated
by the corresponding arrows.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 114-116.
114
3 FIELD OF THE SYSTEM OF RINGS
Using above-mentioned expressions one can calcu-
late the system of rings, the field on an axis of which
has a certain preset value. Let us suppose that there is a
ring with the inner radius R1, and outer radius R2 and the
length L0. Make also a system from several rings packed
along the axis z. At the top of such a cylinder we lay a
similar system of rings with an inner radius R2 and out-
er radius R3 (see Fig. 3). In Fig. 3 the half of the cylin-
der composed from the separate homogeneous magne-
tized rings is shown. The second half is ambidextrous
concerning a plane 0, R.
2 4 6 8 10
4
6
8
10
12
L0
α 1 4
R,cm
R3
R2
R1
Z,cm
M21M22 M23 M24
M25
M15
M13M12
M11
Fig. 3. Half of cylinder composed from separate ho-
mogeneous magnetized rings.
Varying number of rings in a consist of the cylinder
and the directions of their magnetization at its given
magnitude, were selected such parameters, which al-
lowed to realized the preset field in the indicated area
with a pointed exactitude. One of variants, which allows
to make the field of 3кGs in area ±8cm, with the exacti-
tude 1% represented in the Fig. 3. The angles αij of a
magnetization of separate rings in this variant are:
.
2088.478962.26
4499.214057.36
61662.56347.1
282978.032708.5
81172.496745.1
,
−
−
−
−
=jiα
The geometrical parameters of a ring were obtained
analytically with usage of expression (4). The magnet
with the analytically obtained parameters by the pro-
gram PANDIRA (part of POISSON [5]) was calculated.
The outcomes of these evaluations are shown in a
Fig. 4. In both calculations was supposed, that the mate-
rial of a ring is characterized in following parameters
(see Fig. 5):
Br=1053Gs; Hc=-1053; the permeability in a perpendic-
ular direction to easy magnetization is 1.
Such performances are representative of rare-earth
materials (for example samarium-cobalt).
0 1 2 3 4 5 6 7 8
-3100
-3090
-3080
-3070
-3060
-3050
-3040
-3030
-3020
-3010
-3000
-2990
-2980
-2970
-2960
-2950
B
,G
s
z,cm
pandira
analytical
Fig. 4. Comparison of calculation results of the
magnetic field by analytical methods ((4) applica-
tion) and by numerical program PANDIRA.
B| |
Hc
Br
H| |
Fig. 5. The coercive force Hc (in Oersteds) and the re-
manent field Br (in Gauss) for fields parallel to the ax-
is.
4 CONTROL OF A FIELD
Let us consider influence of the presence of the ma-
terial with the penetrability different from 1 on the field
of inside and outside the cylinder.
In Fig. 6 the model of the magnetic cylinder with the
location of magnetic screens is shown. Radius of an ori-
fice is 4 cm, outside radius of the cylinder is 12 cm, bar-
rel length is 10 cm. This figure maps a dextral half-
plane of the magnetic cylinder, as it is symmetrically di-
chotomized by a vertical axis. In first case, the calcula-
tions were done for outside screens of 1 cm thickness,
one of which is parallel to the axis (Armco1), the sec-
ond screen is arranged perpendicularly to the axis (Arm-
co2). In the second case the calculations were done for
two interior screens (Armco 3) and (Armco 4) 0.5 cm
thick.
In Fig. 7 the dependence of the field for the magnet-
ic cylinder (Fig. 3) are shown at the presence of iron
outside of the cylinder (see Fig. 6). The curve 1 corre-
sponds to availability of two screens (Armco 1) and
(Armco 2), the curve 2 corresponds to availability of a
perpendicular axis of the screen (Armco 2), the curve 3
corresponds to availability of a parallel axis of the
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 115-116.
115
screen (Armco 1). In Fig. 8 the similar dependence for
presence of iron inside the cylinder (see Fig. 6) is
shown. The figures above are demonstrate that a field
inside the cylinder can be controlled by the presence of
iron. These are the bare bones of a passive method. In
application of permanent magnets for making magnetic
fields in magnetron guns it is very important, as the va-
riation of the value and longitudinal allocation of a mag-
netic field disable generation of a beam coupling [1].
There is one more apparent possibility to control a
field inside the magnetic cylinder i.e. current windings.
Their application is easily described in an analytical as-
pect as at absence of nonlinear devices a magnetic field
is equal to superpositions of fields of magnetic rings and
current.
2 4 6 8 10
4
6
8
10
12R,cm
αM11 M12 M13
M14 M15
M21 M22 M23 M24 M25
1cmArmco(1)
A
rm
co
( 2
)
Z,cm
Armco(1)
A
rm
co
( 2
)
1cm
Armco(3) Armco(4) 0.5cm
Fig. 6. The magnetic cylinder in environment
of iron.
0 10 20 30 40 50
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2
1
3
B
,G
s
z,cm
Fig. 7. The field distribution along the axis in the
presence of iron outside of cylinder. 1 - armco (1) +
armco (2); 2- armco (2); 3-armco (1).
0 5 10 15 20
-4000
-3000
-2000
-1000
0
1000
2000
3
2
1
B
,G
s
z,cm
Fig. 8. The field distribution along the axis in the
presence of iron inside of cylinder. 1 – armco(3)+
armko(4); 2–armco(3); 3-armco(4).
5 ECONOMICAL PARAMETERS OF MAG-
NETS
To estimate the economic efficiency of usage of per-
manent magnets for generation of solenoidal fields we
shall estimate material consumption by a current soleno-
id in this process and compare them with expenditures
on the permanent magnets. In Table 1 shown are the
mass, leading dimensions and electro-technical para-
meters of permanent magnets and current solenoids with
the help of which the field in the area ±8см of different
radius, with a heterogeneity ∆В/В~1 % is realized.
Table 1. Main specifications of magnets
Inner
radius
cm
Outer
radius,
cm
Маss,
кg
Dispersed
power of the
current
Pe
rm
an
en
t m
ag
ne
t
Solenoid
W
ith
c
oo
lin
g
W
ith
ou
t
co
ol
in
g Pe
rm
an
en
t m
ag
ne
t
Solenoid
solenoid,
kW.
W
ith
c
oo
lin
g
W
ith
ou
t
co
ol
in
g
W
ith
c
oo
lin
g
W
ith
ou
t
co
ol
in
g
0.5 4 5 18 8 14 125 2.2 0.9
1. 5 5.5 18 11 14 130 2.2 0.9
2. 8 6.5 20 31 19 145 2.8 1.
3. 10 7.5 20 50 22 153 3.4 1.
4. 12 8.5 21 79 27 161 4. 1.1
When evaluating the parameters of solenoids it was
supposed, that the current in the noncooled solenoid is
10 A and the run on a wire by cross-section is 7 mm2. In
the chilled solenoid the current 500 А flows past a bus
8.5×8.5∅4. In both cases the solenoids should be iron-
clad (penetrability ~1000, thickness 1 сm).
6 CONCLUSION
In each concrete case the application of permanent
magnets or solenoids is determined by service condi-
tions, infrastructure etc. At high diameters of an orifice
a weight and the cost of a magnetic material can exceed
a weight, cost of manufacture and operation of current
solenoids. The application of permanent magnets for
generation of solenoidal fields can be preferential when
it is necessary to create a long solenoidal field and rela-
tive small radius (1-2 cm).
REFERENCES
1. Yu.Ya.Volkolupov, A.N.Dovbnya, V.V.Zakutin et
al. // JТP. 2001, v. 71, is. 2, p. 98-104, (in Russian).
2. A.N.Dovbnya, V.V.Zakutin et al. // JТP. 2001,
v. 71, is. 3, p. 78-80, (in Russian).
3. I.Е.Tamm. Fundamentals of the theory of an elec-
tricity. Moscow: Nauka, 1976, (in Russian).
4. M.Szilgyi Electron and Ion Optic. Plenum Press
New York and London, Мoscow: Мir, 1990. 640 p.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5
Серия: Ядерно-физические исследования (39), с. 116-116.
116
(in Russian).
5. POISSON Group Programs: User's Guide / CERN.
1965. 450 p.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 117-116.
117
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| id | nasplib_isofts_kiev_ua-123456789-79015 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:28:28Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bovda, A.М. Dovbnya, A.N. Mytsykov, A.O. Reshetnyak, N.G. Zakutin, V.V. 2015-03-24T17:26:22Z 2015-03-24T17:26:22Z 2001 Application of permanent magnets for forming solenoidal fields / А.М. Bovda, A.N. Dovbnya, A.O. Mytsykov, N.G. Reshetnyak, V.V. Zakutin // Вопросы атомной науки и техники. — 2001. — № 5. — С. 114-116. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS numbers: 02.30.Dk, 02.30.Em. https://nasplib.isofts.kiev.ua/handle/123456789/79015 In the paper the possibility of forming a solenoidal magnetic field with the help of the permanent ring-shaped magnets is considered. The results of modeling a magnetic field for the magnets with the various inside diameter is shown. The possibility of the magnitude control of the magnetic field by the passive and active methods is investigated. In the work the estimation of the cost, mass and size of various magnets was done. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Application of permanent magnets for forming solenoidal fields Применение постоянных магнитов для генерации соленоидальных полей Article published earlier |
| spellingShingle | Application of permanent magnets for forming solenoidal fields Bovda, A.М. Dovbnya, A.N. Mytsykov, A.O. Reshetnyak, N.G. Zakutin, V.V. |
| title | Application of permanent magnets for forming solenoidal fields |
| title_alt | Применение постоянных магнитов для генерации соленоидальных полей |
| title_full | Application of permanent magnets for forming solenoidal fields |
| title_fullStr | Application of permanent magnets for forming solenoidal fields |
| title_full_unstemmed | Application of permanent magnets for forming solenoidal fields |
| title_short | Application of permanent magnets for forming solenoidal fields |
| title_sort | application of permanent magnets for forming solenoidal fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79015 |
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