CN1061486A - Can produce the saddle-type coil of uniform magnetic field - Google Patents
Can produce the saddle-type coil of uniform magnetic field Download PDFInfo
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- CN1061486A CN1061486A CN 90109340 CN90109340A CN1061486A CN 1061486 A CN1061486 A CN 1061486A CN 90109340 CN90109340 CN 90109340 CN 90109340 A CN90109340 A CN 90109340A CN 1061486 A CN1061486 A CN 1061486A
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Abstract
Can produce the saddle-type coil of uniform magnetic field, belong to the uniform magnetic field coil technology.It provides the magnetic field that the uniformity is very high, intensity is bigger, and the intensity Senior Three order of magnitude than existing shape of a saddle uniform magnetic field coil reaches 10
-1T.The power that compare the volume of its coil, used lead with helmholtz coil under same technical indicator, applies has significantly and descends.Its magnetic field intensity and the uniformity can be calculated by formula.
This coil satisfies magnetic two utmost point field character, is to be formed by stacking with the array radius identical or inequality and the saddle-type coil of length, and the straight line portion of coil will satisfy certain angular distribution.
It can be used in the physical apparatus, also can be used as the standard Magnetic Field metering.
Description
The invention belongs to the uniform magnetic field coil technology.
The design of magnetic field sources and manufacturing are directly connected to produces and science and technology development, it is except having certain magnetic field intensity, also should be in certain space by certain requirements distribution, as the uniformity in magnetic field, promptly at the intensity and the distribution basically identical of certain space internal magnetic field.All depositing the very high Standard Magnetic Field Source of the uniformity in the various countries Bureau of Standards, as the measurement standard of this country, this standard generally adopts making toroidal coil, as helmholtz coil.
CN 85 1 02592-7 patent documentations, a kind of saddle-type coil that can produce uniform magnetic field has been proposed, it is to place three groups of saddle-type coils at the same plane of symmetry, their radius and length are mutually the same, and make the central point of three groups of coils also identical, and length is 3.96 to 4.04 times of radius, and the two ends circular arc of saddle-type coil is respectively 167 ° to 168.5 ° to the subtended angle of the garden heart; 119 ° to 121 °; 71 ° to 72.5 °, the number of ampere turns between every group of coil is identical with the sense of current.If subtended angle is changed into 143.5 ° to 145 °; 119.5 ° to 121.5 °; 23.5 ° to 24.5 °, its uniformity is more lower slightly than first kind of coil, these two kinds of coils stacks are a kind of uniform magnetic field coil equally.If first kind of coil and second kind of coil number of ampere turns scale are decided to be 1: 0.3 to increase again to 0.4 its uniformity.
The design philosophy of documents is: " with document ' theory analysis and the calculating of magnetic deflection field field parameter ' (Ding Shouqian, Acta Physica Sinica 30,1981,459) is theoretical foundation, and this radius R of array, length L is identical, but the different coil stack of θ makes H
2(z) be zero, make H simultaneously again
4(z) be minimum.”
Magnetic deflection field field Parameter H
0(z), H
2(z), H
4(z) generally being used for analysis of magnetic two utmost point fields is the Distribution of Magnetic Field of the near axis area of magnetic deflection field, is not suitable for remote axis area, for example obviously finds out when x=0.5 and only considers H
4(z) limitation.Theoretical Calculation by two kinds of methods compares below:
xδB
yδH
y
0.1 -1.64E-7 -1.79E-7
0.2 -2.30E-6 -2.50E-6
0.3 -8.86E-6 -9.84E-6
0.4 -1.57E-5 -3.63E-6
0.5 0 2.28E-4
0.6 \ 1.96E-3
X=x/R in the table, x are the distance along the x axle, and R is the radius of saddle-type coil, δ B
ySelect from CN 85 1 02592-7 patent documentation tables 2, δ H
yThe uniformity when showing up the contribution of parameter high-order term for consideration, current ratio is 1: 3.
Our use parameter theory has been analyzed the uniformity of x=0.6 with interior saddle-type coil magnetic field, has considered H during calculating
0(z) to H
12(z) a parameter theory formula and H
14(z) to H
20(z) field parameter approximate expression.The expression formula of these high-order term field parameters does not find in all disclosed documents that so far these parameters are very useful to analyzing the saddle-type coil magnetic field properties.Coil of the present invention can be used as the standard Magnetic Field metering.
Only provide the coil of two groups of different angles distributions and the stack of these two groups of coils in the CN 85 1 02592-7 patent documentations, other angular distribution that satisfies uniform magnetic field does not propose.The invention solves the problem of this respect, and pointed out the principle that observe in the even place of this class, provided a series of physical dimension and the angular distribution that satisfies the saddle-type coil of uniform field, importantly this angular distribution can be continuous.
Winding wire described in the CN 85 1 02592-7 patent documentations takes up space very narrow and small, and the magnetic field intensity that is produced is a low-intensity magnetic field, be generally≤10
-4T(T is a tesla), this has just limited the range of application of this uniform magnetic field coil.Coil proposed by the invention not only has the feature of uniform field, and its field intensity can reach 10
-1The T magnitude is compared and has been improved three orders of magnitude with the contrast patent documentation, has enlarged usage range, thus can extensively use with the Contemporary Physics instrument in.
CN 85 1 02592-7 patent documentations once pointed out, it is higher one more than the order of magnitude than the uniformity of the helmholtz coil of same radius.The present invention has this characteristics equally, because coil angle of the present invention distributes can be continuous, so can obtain high-intensity uniform magnetic field, and the volume of comparing the weight of its used lead and coil under same technical indicator with helmholtz coil has significantly and reduces.Now be exemplified below (Theoretical Calculation):
Technical indicator: central magnetic field intensity is B
0=0.01T; The homogeneity range radius is 18mm; The uniformity is 5 * 10
-5
Helmholtz coil: external diameter 484mm, height 260mm, the shared spatial volume of coil is 4.78 * 10
7Mm
3, conductor length 14.7km(line footpath Φ 0.35), consumed power is 611W, data computing please refer to " generation in magnetic field " and opens precious even volume, China Machine Press in 1987, P100～101.
Coil of the present invention: l
0=180mm, R
0=90mm, △ l=14mm, △ R=10mm, θ
1Be 0 °～4 °, θ
2Be 24 °～28 °, θ
3Be 32 °～36 °, θ
4Be 60 °～64 °, external diameter is 200mm, highly is 388mm, and volume is 1.22 * 10
7Mm
3, conductor length is 6.3km(line footpath Φ 0.35), power is 263W.
Coil of the present invention is 0.43 with the ratio of the used conductor length of helmholtz coil, and the ratio of volume is 0.26, and the ratio of power is 0.43.
The electric current that coil of the present invention applied not only is applicable to direct current, but also applicable to the interchange of tens KHz.
The objective of the invention is: find out a series of structural condition and reasons that meet the saddle-type coil that can produce uniform magnetic field, and make the central magnetic field intensity of this class coil reach 10
-1The T magnitude, perhaps stronger, satisfy and produce and scientific research requirements, the power ratio helmholtz coil of the volume of this coil its coil under same technical indicator, used number of conductors and consumption all has reduction significantly simultaneously.
The present invention is the saddle-type coil that has proposed to produce uniform magnetic field according to following theory:
In rectangular coordinate system, saddle-type coil satisfies the requirement of two utmost point fields, and the principal direction of establishing magnetic field is the y direction, and then on the xz plane, three components in magnetic field are:
H
x（x，0，z）＝0 （1）
H
y（x，0，z）＝H
0（z）+∑H
2s（z）x
2s
+△H （2）
H
z（x，0，z）＝0 （3）
Wherein: H
0(z) and H
2s(z) be parameter, △ H is an error, x=x/R, R be the radius of saddle-type coil circular arc portion [1] this coil straight line portion [2] is from the distance of z axle in other words, ∑ is summation number, from s=1 to s=6.The schematic diagram of one group of saddle-type coil as shown in Figure 1, wherein l represents half of coil total length, R represents the radius of coil.Saddle-type coil is as shown in Figure 1 superposeed, and the field parameter theory formula of this single turn with a plurality of angular distribution or multiturn saddle-type coil is as follows:
H
0（z）＝A·C
1·B
01（4）
H
2（z）＝A（C
3·B
23+C
1·B
21） （5）
H
4（z）＝A（C
5·B
45+C
3·B
43+C
1·B
41） （6）
H
6（z）＝A（C
7·B
67+C
5·B
65+C
3·B
63+
C
1·B
61） （7）
H
8（z）＝A（C
9·B
89+C
7·B
87+C
5·B
85+
C
3·B
83+C
1·B
81） （8）
H
10（z）＝A（C
11·B
1011+C
9·B
109+C
7·B
107
+C
5·B
105+C
3·B
103
+C
1·B
101） （9）
H
12（z）＝A（C
13·B
1213+C
11·B
1211+C
9·B
1209
+C
7·B
1207+C
5·B
1205+C
3·B
1203
+C
1·B
1201） （10）
Wherein:
A＝（μ
0·I）/（π·R），μ
0＝4π×10
-7
B
01＝F
1+F
3
B
23＝B
01-（4F
3-3F
5-5F
7）/8
B
21＝3（-F
5+5F
7）/8
B
45＝B
23-（40F
7-35F
9-63F
11）/128
B
43＝105（-F
9+3F
11）/128
B
41＝5（4F
7-49F
9+63F
11）/64
B
67＝B
45-（252F
11-231F
13-429F
15）2
-10
B
65＝231（-5F
13+13F
15）2
-10
B
63＝63（24F
11-143F
13+143F
15）2
-10
B
61＝35（-8F
9+180F
11-561F
13+429F
15）2
-10
B
89＝B
67-143（48F
15-45F
17-85F
19）2
-15
B
87＝6435（-7F
17+17F
19）2
-15
B
85＝6435（4F
15-19F
17+17F
19）2
-13
B
83＝1155（-16F
13+156F
15-351F
17+221F
19）2
-13
B
81＝63（64F
11-2288F
13+12584F
15-22165F
17+
12155F
19）2
-14
B
1011＝B
89-221（220F
19-209F
21-399F
23）2
-18
B
109＝138567（-3F
21+7F
23）2
-18
B
107＝12155（112F
19-475F
21+399F
23）2
-18
B
105＝2145（-840F
17+6188F
19-11951F
21+
6783F
23）2
-18
B
103＝6435（64F
15-920F
17+3468F
19-4845F
21+
2261F
23）2
-17
B
101＝231（-128F
13+6656F
15-56160F
17+
167960F
19-205751F
21+88179F
23）2
-17
B
1213＝B
1011-2261（312F
23-299F
25-575F
27）2
-22
B
1211＝676039（-11F
25+25F
27）2
-22
B
1209＝88179（180F
23-713F
25+575F
27）2
-21
B
1207＝323323（-96F
21+612F
23-1081F
25+
575F
27）2
-21
B
1205＝7735（7040F
19-73568F
21+230736F
23-
283613F
25+120175F
27）2
-22
B
1203＝3003（-5760F
17+114240F
19-7752（82F
21-
189F
23）-22287（67F
25-25F
27））2
-22
B
1201＝429（512F
15-36480F
17+435200F
19-1938000F
21
+2261（1740F
23-1633F
25+575F
27））2
-20
C
n＝∑a
icos（nθ
i），n＝1，3，5，7，9，11，13…，
I is a current strength, unit be the ampere (A), ∑ be the summation number, from i=1 to M, M is the number of angle, a
iBe current coefficient, θ
iBe the orientation values on the xy plane, coil straight line portion [2] place, be generally the angle of radius vector and x axle in the first quartile.
F
nBe distribution function, be defined as:
F
n＝P/（1+P
2）
n/2+Q/（1+Q
2）
n/2
P＝l/R-z/R，Q＝l/R+z/R
In order to analyze the uniformity at x=0.6 place, calculate reasoning according to the rule of field parameter expression, work as l=2R, during z＜0.3R, a Parameter H
14(z)～H
20(z) approximate expression is:
H
14（z）＝2AC
15（11）
H
16（z）＝2AC
17（12）
H
18（z）＝2AC
19（13）
H
20（z）＝2AC
21（14）
Therefore △ H becomes in (2) formula
△H＝H
14（z）x
14+H
16（z）x
16+H
18（z）x
18
+H
20（z）x
20+△ （15）
In order to analyze the uniformity in magnetic field easily, the uniformity δ H in definition magnetic field is
δH＝｜1-H
y（x，0，z）/H
y（0，0，0）｜ （16）
Interior first of △ is H as can be known from (15) formula
22(z) x
22, H
22(z) contain C
23, can release, when | C
23|/C
1≤ 1 o'clock, the error of △ can be by x to the contribution of uniformity δ H
22Calculate, when x=0.6, error herein is 1.3 * 10
-5, that is to say, when utilizing (4)～(14) formula to calculate x=0.6 uniformity δ H on be limited to 10
-5Magnitude, in like manner during x=0.5 uniformity δ H on be limited to 10
-7Magnitude.
According to (2) formula and (4)～(15) formula, the uniformity of magnetic field δ H that make saddle-type coil then requires H for minimum
0(z) with the minimum that is changed to of z, because H
0(z) be the main component in magnetic field, H
0(z) change minimum with z, can make uniformity of magnetic field the best of z direction.According to the definition of uniformity δ H, require to remove in (2) formula H
0(z) other summation is minimum in addition.
In order to realize above-mentioned 2 requirements, designed coil should satisfy following principle:
1. because H
0(z) be proportional to (F
1+ F
3), distribution function F
nRelevant with the physical dimension of coil, irrelevant with the azimuthal distribution of lead, it is the function of z, this just needs to select best physical dimension l, R, and according to documents CN 85 1 02592-7, we get l=2R equally, show the H of this physical dimension structure by calculating
0(z) variation with z is minimum substantially, but also can prove, when l=2R, and F in (5) formula
nThe H when resultant effect of item makes z=0
2(0)=0, this is for realizing that uniform field is very useful.In the time of also can seeing l=2R by (1)～(14) formula, H
14(z)～H
20(z) very little with the variation of z, this uniformity of analyzing magnetic field in theory is very useful, the limiting value that provides uniformity of magnetic field that like this can be quantitative.Comprehensive above effect, the geometry l=2R of coil is an optimum size.
2. reach 10 for the magnetic field intensity that makes uniform field
-1The T magnitude, need coil that certain number of ampere turns is arranged, when electric current needs to increase the number of turn once timing, lead take up space will depart from the optimum geometry of coil, to reduce the uniformity to a certain extent like this, if make coil still have the character of uniform field, what scope is the limit that departs from? reference half length that we establish coil is l
0, reference radius is R
0, the scope that lead took up space is l
0± △ l, R
0± △ R, the combined influence that stacks up then has:
（l
0-△l）/R
0+（l
0+△l）/R
0＝2l
0/R
0（17a）
l
0/（R
0-△R）+l
0/（R
0+△R）
＝2l
0/R
0·1/（1-（△R/R
0）
2） （17b）
As (△ R/R)
2＜＜1 o'clock, the value of (17) formula all was approximately 4, so satisfy l substantially
0=2R
0
This shows:
I is with R
0For the reference position symmetry increases △ R length, if satisfy (△ R/R
0)
2＜＜1, then little to the influence of the uniformity of coil, so selection △ R on be limited to 0.3R
0, in addition, also can R according to Theoretical Calculation
0For the reference position asymmetricly increases △ R
1With △ R
2Length, but △ R
1+ △ R
2=2 △ R, △ R
2≤ △ R
1
II is with l
0Be that the reference position symmetry increases △ l length, consider that its uniformity influence to coil is little, but considers also to have above-mentioned similar influence from circular arc portion [3] from straight line portion [4], thus selection △ l on be limited to 0.3l
0But, also l in addition
0For the reference position asymmetricly increases △ l
1With △ l
2Length, but △ l
1+ △ l
2=2 △ l, △ l
1≤ △ l.
III has increased △ l, △ R, also needs to derive another essential condition that satisfies uniform field, and promptly the shared azimuth of lead should have continuous distribution, could increase number of ampere turns effectively.
3. after the physical dimension of coil is certain, its H
0(z)/H
0(0) normalized value does not change with angle, and H
2s(z)/H
0(0) size is relevant with angular distribution, finds out certain angular distribution and can make a Parameter H
2s(z) some C in
nItem is zero, then H
2s(z) value is just little, and this is that the design uniform field is desirable.Can find out by the trigonometric function rule:
Work as θ
i± θ
J=180m/n, m, n=1,3,5,7,9,
Cos(n θ then
i)+cos(n θ
J)=0, θ
i, θ
J＜270 °.
According to mentioned above principle, select θ
i, θ
JMake it to satisfy following formula:
cos（3θ
i）+cos（3θ
J）＝0， （18）
cos（5θ
i）+cos（5θ
J）＝0。（19）
Then also satisfy:
cos（9θ
i）+cos（9θ
J）＝0， （20）
cos（15θ
i）+cos（15θ
J）＝0， （21）
cos（21θ
i）+cos（21θ
J）＝0。（22）
If angular distribution satisfies above-mentioned condition, then H
2s(Z) some C in
nItem just has:
C
3＝∑cos（3θ
i）＝0，
C
5＝∑cos（5θ
i）＝0，
C
9＝∑cos（9θ
i）＝0，
C
15＝∑cos（15θ
i）＝0，
C
21＝∑cos（21θ
i）＝0。
By (4)～(10) formula as can be known, C
3, C
5Have very big weight in the parameter expression on the scene, it is whether this coil of decision is one of condition of uniform field.Therefore the requirement of (18)～(22) formula will be satisfied in the shared azimuth of arrangement of conductors of coil, the rule that the angular distribution of Here it is coil of the present invention is followed, and also available computers is directly calculated the requirement that angular distribution makes it to satisfy uniform field, for example,
θ
1＝11.64°，θ
2＝26.95°，θ
3＝56.05°
We have found out a series of saddle-type coils that can produce uniform magnetic field according to above-mentioned three principles, and are divided into two big classes with the size of field intensity.
(1) low-intensity magnetic field coil
This coil is formed by stacking by the saddle-type coil of array same radius and length, and its physical dimension should satisfy l=2R, and l is half length of coil, and R is the radius of coil, the azimuth angle theta of straight line portion [2]
iShould satisfy:
<1>θ
1＝11.64°，θ
2＝26.95°，θ
3＝56.05°
<2>0°≤θ
1≤36°，θ
2＝36°-θ
1，θ
3＝24°+θ
1，
θ
4＝60°+θ
1
<3>0°＜θ
1≤12°，θ
2＝36°+θ
1，θ
3＝24°-θ
1，
θ
4＝60°-θ
1
<4>0°＜θ
1＜42°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4＝96°+θ
1
<5>0°≤θ
1≤60°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4＝108°+θ
1
<6>0°＜θ
1≤24°，θ
2＝48°-θ
1，θ
3＝60°+θ
1，
θ
4＝108°-θ
1
<7>0°＜θ
1＜6°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4＝168°+θ
1
<8>12°＜θ
1≤40°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4＝168°+θ
1
＜9〉above-mentioned eight kinds of coils can superpose mutually, and the size of current that applies between them is different.
(2) high-intensity magnetic field coil
This coil is that the saddle-type coil with array different radii and length is formed by stacking, and its physical dimension should satisfy:
l
0＝2R
0
R
0-△R
1≤R≤R
0+△R
2（23）
△R
1≥△R
2，△R
1+△R
2＝2△R，△R＜0.3R
0
l
0-△l
1≤L≤l
0+△l
2（24）
△l
1≤△l
2，△l
1+△l
2＝2△l，△l＜0.3l
0
L wherein
0Be reference half length of coil, R
0Be the reference radius of coil, R is the scope that the lead of coil distributes in the radius vector direction, and L is the scope that the lead circular arc portion [3] of coil distributes in the z direction.△ R can be determined by following formula:
△R＝5.82×10
2·B
0/（w·J·C
＊） （25）
B wherein
0Be central magnetic field intensity, unit is the T of tesla, and w is the occupation efficiency of lead, and w＜1, and J is the current density in the lead, and unit is ampere/square millimeter (A/mm
2), the unit of △ R is a millimeter.
C
＊＝∫δ（θ）cos（θ）dθ，
When logical forward current, when δ (θ)=1, no lead, δ (θ)=0, δ (θ)=-1 when leading to reverse current, the range of integration of ∫ is respectively pi/2 and 0.△ l can be determined by following formula:
△l＝8.73×10
-3·k·R
0·∑Θ
i（26）
K is a correction factor in the formula, general 1≤k＜2, Θ
iBe θ
iPairing garden heart angle, summation ∑ are from 1 to M, and M is the group number of lead, R
0Unit be millimeter, the unit of △ l be millimeter.The azimuthal distribution θ of coil straight line portion [4]
iShould satisfy:
<1>0°≤θ
1≤6°，θ
2＝36°-θ
1，θ
3＝24°+θ
1，
θ
4＝60°+θ
1
<2>18°≤θ
1≤36°，θ
2＝36°-θ
1，θ
3＝24°+θ
1，
θ
4＝60°+θ
1
<3>0°≤θ
1≤12°，θ
2＝36°+θ
1，θ
3＝24°-θ
1，
θ
4＝60°-θ
1
<4>0°≤θ
1≤24°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4＝96°+θ
1
<5>24°≤θ
1≤36°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4＝96°+θ
1
<6>36°≤θ
1≤42°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4＝96°+θ
1
<7>0°≤θ
1≤6°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4＝108°+θ
1
<8>6°≤θ
1≤30°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4＝108°+θ
1
<9>30°≤θ
1≤60°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4＝108°+θ
1
<10>0°≤θ
1≤24°，θ
2＝48°-θ
1，θ
3＝60°+θ
1，
θ
4＝108°-θ
1
<11>0°≤θ
1≤6°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4＝168°+θ
1
<12>12°≤θ
1≤30°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4＝168°+θ
1
＜13〉above-mentioned 12 kinds of coils that angular distribution constituted can superpose between mutually, and the size of current that applies between them is different.In order to guarantee the uniformity preferably, do not allow to organize and organize overlapping between the angular distribution, but allow their part angular distribution overlapping, and the group on this angular distribution is identical with the size of current that applies of lead between the group and direction is opposite, at this moment being considered as does not have lead on this angular distribution.
The electric current that lead applies that different angles distribute in above-mentioned strong, the low-intensity magnetic field coil has following regulation:
0 °≤θ
1≤ 90 °, logical forward current, a
i＞0;
90 °＜θ
1≤ 180 °, Ψ
i=180 °-θ
1, logical reverse current, a
i＜0;
180 °＜θ
1≤ 270 °, Φ
i=θ
i-180 °, logical reverse current, a
i＜0,
Ψ wherein
iAnd Φ
iBe θ
iPairing angular distribution when being folded to first quartile, a
iBe current coefficient.
After the angular distribution of first quartile was known, according to the symmetry of two pole fields, the angle of other quadrants just can have been known.Therefore only provide the angular distribution of first quartile in this specification and claims.The arrangement of conductors of low-intensity magnetic field saddle-type coil is referring to Fig. 2, and the arrangement of conductors of high-intensity magnetic field saddle-type coil is referring to Fig. 3, and relevant parameter marks in the drawings.
The magnetic field intensity that the low-intensity magnetic field coil is produced is generally 10
-4The T magnitude is unless use the superconducting line coiling.General ERROR CONTROL is in l=(2 ± 0.03 when manufacturing and designing this class coil) R, (θ
i± 0.3) °, angle can be monodrome or continuous distribution, for example:
Monodrome: θ
1=12 °, θ
2=48 °
θ
1＝0.5°，θ
2＝35.5°，θ
3＝24.5°，θ
4＝60.5°
Continuously: θ
1=0 °～6 °, θ
2=24 °～36 °, θ
3=60 °～66 °
For the low-intensity magnetic field coil, we have provided the recurrence formula of eight groups of angular distribution, can obtain many angular distribution that can produce the saddle-type coil of uniform magnetic field thus, this designs this class coil for the technical staff is very useful, and they can design and manufacture the coil that different angles distribute according to different requirements.Below we when providing coil sections z=0 along the uniformity δ H(Theoretical Calculation of x axle):
x ① ② ③
0.1 9.54E-07 -1.79E-07 -5.96E-08
0.2 7.15E-07 -3.34E-06 5.72E-06
0.3 -3.90E-05 -1.62E-05 8.57E-05
0.4 -4.04E-04 5.58E-06 5.58E-04
0.5 -2.40E-03 6.34E-04 2.56E-03
0.6 -1.04E-02 5.36E-03 1.02E-02
x ④ ⑤ ⑥
0.1 -1.19E-07 -1.79E-07 -1.79E-07
0.2 4.77E-07 -2.03E-06 -2.21E-06
0.3 1.38E-05 -5.66E-06 -7.51E-06
0.4 -2.76E-05 -7.78E-07 -9.06E-06
0.5 -1.14E-03 -1.80E-06 5.56E-06
0.6 -9.17E-03 -4.08E-04 -5.33E-05
Above-mentioned pairing angular distribution is:
① 11.64°，26.95°，56.05°
② 1°，35°，25°，61°
③ 1°，37°，23°，59°
④ 15.95°，51.95°，75.95°，111.95°
⑤ Ⅰ∶1°，35°，25°，61°;
Ⅱ∶14.45°，45.55°，62.45°，122.45°
Current ratio is an I: II=1: 2.4
⑥Ⅰ：1.05°，34.95°，25.05°，61.05°;
Ⅱ：15.95°，51.95°，75.95°，111.95°;
Ⅲ：14.45°，45.55°，62.45°，122.45°
Current ratio is an I: II: III=0.64: 0.2: 1
By the data that provide above as can be seen uniformity δ H be limited to 10 at the following of x=0.4
-4Magnitude.The magnetic field intensity of low-intensity magnetic field hub of a spool is calculated formula:
B
0=8.59NIC
1/ R * 10
-4(T tesla) (27)
Wherein NI is number of ampere turns (ampere), and the unit of R is a millimeter, C
1Be defined as:
C
1＝∑a
icos（θ
i）
The design of high-intensity magnetic field coil at first will be determined the technical indicator of this coil: magnetic field intensity, the uniformity, homogeneous area.
At first we select θ
iAngular distribution because H
0(z) be the main component in magnetic field, so arrangement of conductors generally will be taken in 60 °.Obtain △ R by (25) formula, according to △ R＜0.3R
0Can make R
0, △ R/R
0＜＜1 tells us, R
0Some can select satisfied R for well according to technical indicator and coil cost greatly in selection
0Then according to l
0=2R
0Determine l
0And utilize (26) formula to determine △ l, at first make △ R
1=△ R
2=△ R, △ l
1=△ l
2=△ l, use parameter theory computing formula (2), (4)～(14) and (16) formula are calculated the uniformity and homogeneous area, see whether meet the demands, otherwise change △ R
1Or △ R
2, △ l
1Or △ l
2Recomputate, if △ is R
1≠ △ R
2, △ l
1≠ △ l
2The time, they should satisfy △ R
1＞△ R
2, △ R
1+ △ R
2=2 △ R, △ l
1＜△ l
2, △ l
1+ △ l
2The condition of=2 △ l.Angular distribution θ
iVery big to these three the index influences of magnetic field intensity, the uniformity and homogeneous area, secondly be △ R
1, △ R
2, △ l
1With △ l
2Therefore to select best angular distribution θ
1The invention provides 13 kinds of angular distribution, can superposition between them, the size of current that applies can be different.
Above-mentioned coil is not all considered to utilize magnetic screen, if be surrounded by uniform permeability magnetic material in the outside of coil, removing to increase magnetic field intensity, also can improve the uniformity in magnetic field.Calculate proof through theory, when the shielding cylinder hard-pressed bale of permeability magnetic material in the outside of coil, the magnetic field intensity at its center generally can be brought up to 1.8B
0If coil outer diameter is 0.7～0.8 o'clock with the ratio of the internal diameter of shielding cylinder, its central magnetic field intensity is about 1.4B
0, but that the latter improves the effect of the uniformity is more obvious than the former, so the ratio of the external diameter of coil and the internal diameter of shielding cylinder can be 0.7～1.
Make this class coil and all need the skeleton supporting lead, a kind of be with lead directly on skeleton with metallic channel, another kind of mode is with self-adhesion lead wire coiling and being shaped in the mould of coil winding machine, again around coil groups be contained on the skeleton.Skeleton is made with non-magnet material, as pottery, glass, plastics etc.
It should be noted that when coil applied bigger electric current, coil will generate heat, need cool off coil, air-cooled or apply cooling fluid.
After making, coil has certain error, can be placed on the outer wall of coil with permeability magnetic material (as silicon steel sheet), certainly also can be attached to inwall correction, because its magnetic conduction effect, can change the Distribution of Magnetic Field in the coil, therefore can paste while measuring, make the uniformity in magnetic field reach designed requirement.
In sum, the saddle-type coil that can produce uniform magnetic field proposed by the invention is to have drawn a series of related parameters that have that satisfy the uniform field coil under theory instructs, importantly the angular distribution of this coil is continuous, so can bring up to 10 to the central magnetic field intensity of this class coil
-1The T magnitude, in addition stronger, and like this, this coil can obtain to use more widely in production and scientific research, has overcome the technical deficiency in the CN 85 1 02592-7 patent documentations.Compare with helmholtz coil except that the uniformity than it high one more than the order of magnitude, all have significantly at the power of the volume of coil, used number of conductors and consumption and to reduce.
Fig. 1. one group of saddle-type coil schematic diagram.
Fig. 2. low-intensity magnetic field saddle-type coil schematic diagram.This figure is formed by stacking by four groups of saddle-type coils, and the azimuth of straight line portion is respectively θ
1, θ
2, θ
3And θ
4, the radius of circular arc portion is R, half length of coil is 2R.Xy coordinate diagram among the figure is the vertical view of this coil, and the xz coordinate diagram is the end view of this coil.[1] circular arc portion of expression low-intensity magnetic field saddle-type coil, the straight line portion of [2] expression low-intensity magnetic field saddle-type coil.
Fig. 3. high-intensity magnetic field saddle-type coil schematic diagram.This figure is formed by stacking by two groups of multiturn saddle-type coils, and the pairing central angle of the azimuthal distribution of straight line portion is respectively Θ
1And Θ
2, the radius distribution scope of circular arc portion is (R
0-△ R
1) to (R
0+ △ R
2), R here
0Be reference radius, coil half length is 2R
0+ △ l
2, circular arc portion is (2R in the distribution of z direction
0-△ l
1) to (2R
0+ △ l
2).Xy coordinate diagram among the figure is the vertical view of this coil; Another width of cloth is a cutaway view, and the xz coordinate diagram is the end view of this coil.[3] circular arc portion of expression high-intensity magnetic field saddle-type coil, the straight line portion of [4] expression high-intensity magnetic field saddle-type coil.
Above-mentioned figure all in the xyz coordinate system, among the figure → the expression sense of current.
The top saddle-type coil of narrating that can produce uniform magnetic field is divided into low-intensity magnetic field coil and high-intensity magnetic field coil, and given physical dimension, angular distribution and design formula all can be used as the foundation of enforcement.Below we still provide the structure embodiment (Theoretical Calculation) of three high-intensity magnetic field coils:
1. central magnetic field intensity is B
0=1 * 10
-2T, homogeneity range radius are 18mm, and the uniformity is 10
-5Magnitude, l
0=180mm, R
0=90mm, △ R=10mm, △ l=14mm, θ
1=0 °～4 °, θ
2=24 °～28 °, θ
3=32 °～36 °, θ
4=60 °～64 °.
2. central magnetic field intensity is B
0=3 * 10
-2T, homogeneity range radius are 15mm, and the uniformity is 10
-5Magnitude, l
0=150mm, R
0=75mm, △ R
1=20mm, △ R
2=10mm, △ l
1=25.9mm, △ l
2=36.9mm, θ
1=0 °～24 °, θ
2=36 °～60 °.
3. central magnetic field intensity is B
0=1 * 10
-1T, homogeneity range radius are 180mm, and the uniformity is 10
-5Magnitude, l
0=1800mm, R
0=900mm, △ R=100mm, △ l=140mm, θ
1=0 °～4 °, θ
2=24 °～28 °, θ
3=32 °～36 °, θ
4=60 °～64 °.
Above-mentioned three kinds of coils are as adding shroud sleeve, and central magnetic field intensity generally rises to B
01.4～1.8 times.Embodiment 3 is that the physical dimension of embodiment 1 is amplified, and magnetic field intensity if desired is bigger, can amplify the relevant physical dimension of coil in proportion.
Claims (7)
1, a kind of coil that can produce uniform magnetic field, it is formed by stacking by the saddle-type coil of array same radius and length, and physical dimension satisfies l=2R, it is characterized in that the azimuth angle theta of straight line portion [2]
1For:
(1) θ
1=11.64 °, θ
2=26.95 °, θ
3=56.05 °, or
(2)0°≤θ
1≤36°，θ
2=36°-θ
1，θ
3=24°+θ
1，
θ
4=60 °+θ
1, or
(3)0°＜θ
1≤12°，θ
2=36°+θ
1，θ
3=24°-θ
1，
θ
4=60 °-θ
1, or
(4)0°＜θ
1≤42°，θ
2=36°+θ
1，θ
3=60°+θ
1，
θ
4=96 °+θ
1, or
(5)0°≤θ
1≤60°，θ
2=60°-θ
1，θ
3=48°+θ
1，
θ
4=108 °+θ
1, or
(6)0°＜θ
1≤24°，θ
2=48°-θ
1，θ
3=60°+θ
1，
θ
4=108 °-θ
1, or
(7)0°＜θ
1＜6°，θ
2=60°+θ
1，θ
3+108°+θ
1，
θ
4=168 °+θ
1, or
(8)12°＜θ
1≤40°，θ
2=60°+θ
1，θ
3=108°+θ
1，
θ
4=168 °+θ
1, or
(9) above-mentioned eight kinds of coils that angular distribution constituted can superpose each other, apply the different sizes of electric current between them.
2, a kind of coil that can produce uniform magnetic field, it is formed by stacking by the saddle-type coil of array different radii and length, it is characterized in that:
The physical dimension of coil should satisfy:
l
0＝2R
0
R
0-△R
1≤R≤R
0+△R
2
△R
1≥△R
2，△R
1+△R
2＝2△R，△R＜0.3R
0
△R＝5.82×10
2·Bo/（w·J·C
＊）
l
0-△l
1≤L≤l
0+△l
2
△l
1≤△l
2，△l
1+△l
2＝2△l，△l＜0.3l
0
△l＝8.73×10
-3·k·R
O·∑Θ
1
The azimuthal distribution θ of coil straight line portion [4]
1Should satisfy:
（1）0°≤θ
1≤6°，θ
2＝36°-θ
1，θ
3＝24°+θ
1，
θ
4=60 °+θ
1, or
（2）18°≤θ
1≤36°，θ
2＝36°-θ
1，θ
3＝24°+θ
1，
θ
4=60 °+θ
1, or
（3）0°≤θ
1≤12°，θ
2＝36°+θ
1，θ
3＝24°-θ
1，
θ
4=60 °-θ
1, or
（4）0°≤θ
1≤24°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4=96 °+θ
1, or
（5）24°≤θ
1≤36°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4=96 °+θ
1, or
（6）36°≤θ
1≤42°，θ
2＝36°+θ
1，θ
3＝60°+θ
1，
θ
4=96 °+θ
1, or
（7）0°≤θ
1≤6°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4=108 °+θ
1, or
（8）6°≤θ
1≤30°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4=108 °+θ
1, or
（9）30°≤θ
1≤60°，θ
2＝60°-θ
1，θ
3＝48°+θ
1，
θ
4=108 °+θ
1, or
（10）0°≤θ
1≤24°，θ
2＝48°-θ
1，θ
3＝60°+θ
1，
θ
4=108 °-θ
1, or
（11）0°≤θ
1≤6°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4=168 °+θ
1, or
（12）12°≤θ
1≤30°，θ
2＝60°+θ
1，θ
3＝108°+θ
1，
θ
4=168 °+θ
1, or
(13) above-mentioned 12 kinds of coils that angular distribution constituted can superpose between mutually, and the size of current that applies between them is different, and do not allow overlappingly between the angular distribution, but the size of current that applies when allowing angular distribution overlapping is identical and direction is opposite.
3, coil according to claim 1 is characterized in that:
l
0＝（2±0.03）R
0
θ
1±0.3°
4, coil according to claim 2 is characterized in that:
l
0＝180mm，R
0＝90mm，△R＝10mm，△l＝14mm，
θ
1=O ° to 4 °, θ
2=24 ° to 28 °, θ
3=32 ° to 36 °,
θ
4=60 ° to 64 °.
5, coil according to claim 2 is characterized in that:
l
0＝150mm，R
0＝75mm，△R
1＝20mm，△R
2＝10mm，
△ l
1=25.9mm, △ l
2=36.9mm, θ
1=0 ° to 24 °,
θ
2=36 ° to 60 °.
6, coil according to claim 2 is characterized in that:
l
0＝1800mm，R
0＝900mm，△R＝100mm，△l＝140mm，
θ
1=0 ° to 4 °, θ
2=24 ° to 28 °, θ
3=32 ° to 36 °,
θ
4=60 ° to 64 °.
7, according to the described coil of claim 1～6, it is characterized in that being surrounded by the uniform dielectric permeability magnetic material in the outside of coil, the external diameter of its coil is 0.7～1 with the ratio of the internal diameter of shielding cylinder.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 90109340 CN1022873C (en) | 1990-11-16 | 1990-11-16 | Saddle-type coil capable of producing uniform magnetic field |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 90109340 CN1022873C (en) | 1990-11-16 | 1990-11-16 | Saddle-type coil capable of producing uniform magnetic field |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN1061486A true CN1061486A (en) | 1992-05-27 |
| CN1022873C CN1022873C (en) | 1993-11-24 |
Family
ID=4881383
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 90109340 Expired - Fee Related CN1022873C (en) | 1990-11-16 | 1990-11-16 | Saddle-type coil capable of producing uniform magnetic field |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN1022873C (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102290231A (en) * | 2011-05-10 | 2011-12-21 | 中国科学院近代物理研究所 | Winding device of saddle-shaped copper conductor coils |
| CN102759721A (en) * | 2012-07-17 | 2012-10-31 | 北京卫星环境工程研究所 | Non-plug-in type single-turn magnetizing and demagnetizing coil |
| CN105527594A (en) * | 2014-10-23 | 2016-04-27 | 北京自动化控制设备研究所 | 3D magnetic coil with large uniform region and manufacture method of 3D magnetic coil |
| CN108666069A (en) * | 2018-07-06 | 2018-10-16 | 北矿机电科技有限责任公司 | A kind of continuous magnetizer of permanent magnetic separator packaged type entirety magnetic pole and method |
| CN108761372A (en) * | 2018-08-09 | 2018-11-06 | 西红柿科技（武汉）有限公司 | A kind of magnetic leakage probe testboard |
| CN109243751A (en) * | 2018-10-31 | 2019-01-18 | 中国人民解放军国防科技大学 | Consider even magnetic field coil in universe of magnetic screen coupling |
| CN111060858A (en) * | 2018-10-17 | 2020-04-24 | 北京自动化控制设备研究所 | Method for generating high-uniformity magnetic field and gradient composite magnetic field in magnetic shielding barrel |
-
1990
- 1990-11-16 CN CN 90109340 patent/CN1022873C/en not_active Expired - Fee Related
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102290231A (en) * | 2011-05-10 | 2011-12-21 | 中国科学院近代物理研究所 | Winding device of saddle-shaped copper conductor coils |
| CN102759721A (en) * | 2012-07-17 | 2012-10-31 | 北京卫星环境工程研究所 | Non-plug-in type single-turn magnetizing and demagnetizing coil |
| CN105527594A (en) * | 2014-10-23 | 2016-04-27 | 北京自动化控制设备研究所 | 3D magnetic coil with large uniform region and manufacture method of 3D magnetic coil |
| CN105527594B (en) * | 2014-10-23 | 2018-08-28 | 北京自动化控制设备研究所 | A kind of big homogeneity range three-dimensional magnetic coil and its manufacturing method |
| CN108666069A (en) * | 2018-07-06 | 2018-10-16 | 北矿机电科技有限责任公司 | A kind of continuous magnetizer of permanent magnetic separator packaged type entirety magnetic pole and method |
| CN108666069B (en) * | 2018-07-06 | 2024-05-28 | 北矿机电科技有限责任公司 | Permanent magnet separator packaging type integral magnetic pole continuous magnetizing device and method |
| CN108761372A (en) * | 2018-08-09 | 2018-11-06 | 西红柿科技（武汉）有限公司 | A kind of magnetic leakage probe testboard |
| CN111060858A (en) * | 2018-10-17 | 2020-04-24 | 北京自动化控制设备研究所 | Method for generating high-uniformity magnetic field and gradient composite magnetic field in magnetic shielding barrel |
| CN111060858B (en) * | 2018-10-17 | 2021-12-10 | 北京自动化控制设备研究所 | Method for generating high-uniformity magnetic field and gradient composite magnetic field in magnetic shielding barrel |
| CN109243751A (en) * | 2018-10-31 | 2019-01-18 | 中国人民解放军国防科技大学 | Consider even magnetic field coil in universe of magnetic screen coupling |
Also Published As
| Publication number | Publication date |
|---|---|
| CN1022873C (en) | 1993-11-24 |
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International patent classification (main classification): H01F5/00 |