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ORN-P- of 88
DTE-Sopil
HIGH FIELD SUPERCONDUCTORS AND THE DEVELOPMENT
OF SUPERCONDUCTING MAGNETS*
MASTER
W. 7, Gauoter
Oak Ridge National Laboratory, Oak Ridge, Tennessee
I. Introduction
In this paper I will not try to describe bystematically whut 18
known at present about the physics of high field superconductors. I
will restrict myself to discussing the results of several rather
straightforward experiments and tests. This will lead to the concepts
of a few simple models which have proved to be very useful for descrit.
ing some important properties of high field superconductore. It 18 the
goal of the following two papers on experiments with and on the theory
of type II superconductors, respectively, to preoent an outline of the
present state of this field of physics, especially to discuss how much
can be explained by applying first principles.
On the other hand it would not be interesting and there would not
be time enough to go into many details of the technological development
of superconducting magnet coils. I would be satisfied 1 during this
lecture I could succeed in describing the most important phenonena, in
discussing a few userul models and 1 I could demonstrate that the .
engineering of superconducting coils 18 presently already above the
first stage of trial and error. Even within these limits it will be
unavoidable to give an incomplete and sometimes an over-simplified
picture.
II. Superconductors of Type I, II, and III
First let us consider three different types of superconductors.
Type I are the well-known soft superconductors like Hg, Sn, In, etc.
Their critical field strength 18 a few hundred gause, and they display
the Meisbr.er-Ochsenfeld effect. Figure 1, I, shows a typical (idealized)
magnetization curve of a sample (solid cylinder) with a very small
demagnetization factor. We assume that this sample has been cooled
dowa in zero field. The performance with increasing external field.
can be simply explained by assuming a specific resistance p = 0. With
decreasing field, p = 0 alone would lead to flux trapping (broken line);
*Research sponsored by the U.S. Atomic Energy Commission under contract
with the Union Carbide Corporationi
however, the Meissner-Ochsenfeld effect makes the magnetization curve
completely reversible. The performance expected from a banpie with
Os O but not displaying the Meissner Ochsenfeld effest 18 show by a
type I superconductor (SCI) in the shape of a hollow cylinder (F17. 1,
I, broken line).
A solid cylindrical sample of a type II superconductor (SCII) 18
characterized by the reversible magnetization curve, Fig. 2, II. No
flux penetrates for 0 38 382 H 18 called the lower critical field.
Between this field strength and the upper critical field 1.2 flux pene-
trates gradually; at Hc2 the flux penetration is complete. The SCII 18
said to be in the "wixed state" in the region I <I<Hc2. The
thermodynamic bulk critical field Has to determined by the area betweeu
the magnetization curve and the I-exie at the diagram, which lo absumed
to be equal to 8B9%8«. The performance of a SCII is determined by the
Ginsburg Landau Constant'. For a SCII the value of " lo large: than
; for a SCI, however, K .
• Finally, a type II superconductor (SCIII, Bee Fig. 1, III) dio-
plays a very different performance. The magnetization curve of a
sampie in the form of an "1081: itely long" solid cylinder 18 highly
irreversible (Fig. 1, III). There is again do flux penetration between
zero field and the lower critical field I.1. However, the magnetization
curves reach a maximum at a hicher field strength and decrease to zero
at the upper critical field oun sth 8.2: When reducing the external
field H to zero, an appreciable quantity of magnetic flux 18 trapped.
Figure 1 shows, la addition to the magnetization curves, dlegrams
which represent the average bulk flux density B as a function of the
external field H. In SCI and SCDI samples with zero demagnetization
factor, a constant buls flux density can be considered. In type III
superconductors, however, for I <3 <8c2, B changes inside the sample
· and the Bmcurve shown in Fig. 1 represents average values of B defined
by the equation
B. 1 + (4*) M;
(1)
M being the total magnetic moment divided by the sample volume. The : :
factor 48 holds when physical units are used. Often (especially for ::
measurements on SCIII), I 10 measured in kilo-oerated, B and X are
indicated in kilogmuss, and the factor de 10 anitted.
.
.
.
..
.
.
i
6
..
M
arriors .. ::
::.:..
...
IN
.
2
.
III. Wendelssohn'e Sponge Model
More than thirty ycars ago superconducting alloys were fisvesti-
Güted which yielded magnetization curves of very different shu;08, in
principle, however, similar to those shows in Fig. I, III. K. Mendele-
sohn. suggested his famous "Sponge Model": The structure of an alloy
should rc6cmble that of a spongc, whose me shes have a much higher criti.
cal field than that of the enclosed material (mat: 1x). An increasing
field starts to penetrate into the sample, but this procene 16 hampered
by the still superconducting me bhes. In spite of the high crinical
field of the meshes, they cannot prevent further flux penetration into
the specimen because the cross sections of these meshes (or fijaments)
are supposed to be small compared with the London penetration (iepth do
Finally the field penetration is almost complete., Due to the citiu
superconducting Pllaments, however, even at this state a small super-
current can flow through the sample. Mendelssohn'o aponge model applied,
of course, to various kinds of SCI since the concept of superconductors
type II was not developed at this time.
'This model has been used to explain the irregular performance of
superconducting lead. It can also be extended to the case of SCI moshes
in a non-superconducting matrix. Such experiments with "artificial
superconductors" were made by Bean et al. and Seraphim et al.
IV. Superconductors Type III
Recently, experiments showed that very pure Nb and various well. .
annealed alloys display properties very olmilar to those of .deal
type II superconductors. ' A nice example are the experiments by Heaton
and Rose-Innes with N-(45% at.)Ta (Fig. 2). The unannealed "original"
wires tested in longitudinal fields yielded highly irreversible magneti.
zation curves. Critical current experiments in transversal fields
showed a relativeiy.bigh current carrying capacity. After carefully
annealing in high vacuum the magnetization curve became almost reversi.
ble and of a shape typical for SCII. The current carrying capacity was
... reduced to extremely low values which is again in accordance with the
: performance of SCII.
These experiments are to be interpreted to indicate that physical
imperfections (which can be removed by care u. annealing) in a matrix
of a type II superconductor determine the properties of such alloya. .
Experiments by Maxwell and strongin gave evidence for a multiply .
connected network structure of the physical imperfections.
11
v.
11. london's and C. P. Beun'o Model of IFSC
.
ll. london and independently C. P, Dean suggested a simple model
for type III Quperconductors which is bused on the following assump-
tions: SCIII's can carry a limited macroscopic super-current density
J.(B), and any electromotive force will induce this full current density
to flow locally. The simplest case of Jc conetant, 1.e. independent of
B, lo conoidered. It mot be kept in mind, of course, that at in certain
field 1 mperconductivity breaks domi completely. In the following it
18 assumed that the external field I stays always below this l:.12it. As
an example F18: 3 shows - "infinitely long" nollow cylinder (unoile
radius a, outelde radius b, wall thickness a-b o w) made of SCIAI
materiul which is placed in a longitudinal external field H. his tube
18 cooled down in zero field; thereafter the extemal field 18 raised
to a value 87. A negative current density 16 induced in the aiter part
of the tube (a • * Srsa) which shields the inner part of the hollow
cylinder (B - 0 for o srsa •x). From Maxwell's Eq. follows for
(a - xz) <r <a
..k J...
......
(2)
(B in gaubi, xin cm, J. 10 amp/cm2).
After increasing the external fleid I to
the whole tube wall carries a current with the density Jc. A further .
increase of the external field to Hy will not change the current; now. .
ever, the field inside the tube will be raised from zero to Hj (F 18. 3a).
When the external field 18 decreased to Hz (Fig. 6b), the negative
current still flows in the luner part of the tube (0 <r <a - is)
whereas the outer tube wall (a - Xg <r <a) carries a positive current
JcFurther decrease of the external field 1 down to Hy does not change
the inner field Hy. For H - Az a positive current file the whole tube ...
wall and does not change when the external field is decreased to lower
values.
Figure 3c showe an 1-' diagram which is often called "Tube Magnet-
ization Diagram." For the considered case of an "infinitely long"
hollow cylinder, 1. 'London's and C. P. Bean'a model predicts a current
density distribution, diagram which depends for a given Je on the wall
thickness w (Eq. 3) cnly, independently of the radius a. Tee average
5
magnetic moment M per unit volume depends, however, on the radius a,
too. From the definition
hale
Zar(B-1) dr
1
ra² - 02) reb
(4)
S.
we obtain a simple expression for M which is graphically represented in
Fig. 4. Curves are shown for thin-walled and solid cylinders. i high-
Tv Irreversible performance 16 predictea; however, the typical sijape of
experimental magnetic moment curves of type III superconductors with a
maximum value Mmax decreasing to M = 0 for H - Hcz does not result.
Furthermore, for OCH <Hc, no perfect flux exclusion 18 predicted.
Nevertheless, for magnetization loops with external fields up to about
H6/2 experimental data agree well with the model 11 J. 18 chosen with
an appropriate value. For instance, C. P. Bean determines for a sample
of sintered VzGa a constant critical current density Jc - 6.6 x 105
amp/cm2.
One interesting case where this model has been successfully applied.
to an experiment with a type III superconductor in the following: A
sample of No35n was produced by hydrostatically pressing a mixture of
niobium and tin powder. After vacuum sintering for eight hours at
1200°c, the sample was ground in a cylindrical shape (0.48 cm dialdeter,
1.9 cm length with hemispherical ends (F18. 5). In the first experiment
the sample was cooled down in zero field, then the external field was
raised to 7.5 X oe and finally lowered to zero. The sample showed...
permanent diamagnetic properties characterized by B Hmax = 1.7 M 8 oe.
The second experiment was performed by cooling down the sample in an
external field of 7.5 X oe which was lowered to zero after the sample
had reached thermal equilibrium. Now B Hmax was over 15 times as large,
namely 26 Mgoe. These results can be predicted by applying Eq. (2)
to (4) when a critical current density J. - 1.2 x 105 amp/cm2 16 assumed.
VI. Magnetization of a SCIII Hollow Cylinder
The magnetization curve of a SCIII cylinder as ahown in Fig. 1, III,
gives some indication how 8. London's and C. P. Bean's model should be
modified to describe more realistically the stages of the magnetization :
of a type III superconductor. Figure 6 shows a cross section of the
wall of a bollow cylinder. The wall thickness w 18 assumed to be much
: smaller than the radius a., With this assumption the area determined by
.
.
.
. .
.
:


the outside field strength x and the internal local flux densit; B 18
proportional to the magnetic moment of the cylinder.
We consider the following cases represented in Fig. 6, each typical
for a certain value of the external field H.
0 <lli <Hai No flux penetration, B = 0
Ha <H2 <H: 'In the SCII matrix partial flux penetratior occurs
(sce the size-independent part due to flux penetration of the
magnetization curve indicated at the lower right side of Fig. 6),
Shielding supercurrents are induced in the outer part of the
cylinder which reduce B in the inner part of the cylinder wall to
zero. In the schematic presentation of Fig. 6 for this stage of
magnetization a diference between B and the external field Hz at
the outer cylinder surface of 3/4 Hcl 18 arbitrarily abounieid.
H = H: The field just penetrates to the inner cylinder surface.
H. <H <H.2: The difference between B and I at the outer cylinder
surface is still smaller. Compared with the stage H - Hg the
magnetization 18 noticeably reduced until for
H = Hc2 perfect flux penetration occurs, and therefore M becomes
8
zero.
It would be desirable to find a simple model of type III super-
conductors which describes correctly the stages of magnetization as
shown schematically in Fig. 6 and yields data in good quantitative
accordance with actual sample teste.
VII. Kim's et al. Model
Kim's et al. work, based on "Tube Magnetization Measurements,"
elucidated greatly the performance of type III superconductors. Such
superconductors with high upper critical field H.2 and with high current
carrying capacity (such as Nb2sn, No-Zr, etc.) are of great interest
for various technical applications, especially for the design of super-
conducting wagne ;8. For these superconductors the designations "High
Field and High Current Superconductors" or, more briefly, "High Field ....
Superconductors" are widely used. In the following we will employ the
abbreviation HFSC. Several authors prefer still the older expression
"Hard Superconductors" for both HFSC. and for SCIII in general.
Kim's et al. experiments were performed with tubes made of pressed
No powder, No-Zr and NbzSn, respectively. The field I' was measured
with a magnetic probe inside the tube (Fig. 7). Care was taken to
raise the external liel, slowly and steadily in order to avoid, 11
and from Fig. 6 follows that with lacreasing local values ar B the
slope and herewith J decreases. This muggests trying the power
series expansion
* -- ||-* 7.48%
vas
The oluplest assumption, of courae, 16
:
lu-BOTTIT
.
This relation can be used to find for
'=2(2) + [363]
(x' + 2)2 = (1 + B.)2 - 12.00 kv.
the relations
and
(H' + Bol2 + (1 - 2.2 - 2 (Qc * w+ 3.9). (9)
Eq. (8) holds for the branches 1 and 2, and 1 and 2', respectively, of
the tube magnetization curves shown in 718. 7.. Eq. (9) applies to the
branches 1" and 2"..
Eq. (8) can be written as
x' +1-720 kw
(20)
• 2 B
Therefcre, H' + H as a Unear function of can be represented
in & diagram by a straight line (with the slope 2:ac k w) which inter.
sects the ordinate axis at - 2 B.. In general, experimental data fit
well this prediction and therefore Eq. (6) can be considered at least
... as a good approximation. . .'
: These experiments showed. In a large range a Unear temperature
i
;
.
i dependence
.
..o - Ag - A T
.
.
.
:
(21)
Y. B. Kim's et al. model can be used to calculate magnetization curves
for hollow or solla "10finitely long". cylinders in Longdtudinal fields. :
&.
Figure 8 shows such curves which are normalized as follows:
(12)
(13)
v-2 ac tv
n-&; --
For these calculations the special value
bo - 0.7
'
(14)
was arbitrarily assumed.
Experiments with different samples of the same material yield
reproducible values for ac which vary, however, greatly from one speci-
men to another. The orders of magnitude are shown in Table I.
Table I
ac14.2°)(G amp/cm2)
Nb Powder Pressed: ~ 107
No-Zr
~ 107 to 109
Noz-Sn
~ 109 to 2010
The values of B. are of the order o? several hundred gause to a few
kilogau88.
Kim mentions that his model holds in general for flux densities
B up to about 15 B.. The calculated magnetization M does not go to
zero for H = H2 but reaches zero asymptotically for H +00. For low
external fields H no complete flux exclusion 18 predicted which would
determine a lower critical field Haq
From Eq. (12) Kim calculates for Nb.Sn with a = 8 x 209 G amg/cm2
and w = 0.5 cm a value of Hg = 10% gaurs. That means that such a hollow
cylinder with only 0.5 cm wall thickness and with any outside radius ..
should be good for trapping a magnetic field of 100 kg. We mentioned
previously that the current density J in a hollow cylinder which is in
the critical state assumes the highest value Je compatible with the
local B. This would be also the optimum current density distribution
for a wire wound magnet coil. Of course, allowance must be made for
the packing factor d, which is the ratio of the total conductor volume
1
??;

-9.
to the total vinding volume. Therefore, for an "infinitely long"
optimized solenoid
1.- V2KX Qw
-
-
(15)
The simplest way to wind a magnet coil 18, of course, to use wire
with one constant cross section, i.e. to produce a uniform current
density in the whole winding volume. Furthermore, the finite length
of the coil must be considered. A fair approximation 18 to omit the
factor k = 40/10. Thus a simple calculation yields
2. H-Vaan
(16)
A
:
..
.
88 an approximation for the field strength generated by a superconducta
ing magnet coil. Kim gives the following exampies: For Nb, Sn,
Q = 8 x 109 G amp/cm; 2 - 0.5; w = 2.5 cm; 1. - 100 kg. For Izr,
2. = 3 x 209 G amp/cm2; 1 * 0.5; w= 1.7 cm; 4. * 50 kg.
Unfortunately these values are of theoretical interest only. The
actual performance of superconducting hollow cylinders and, even to a
greater extent, that of superconducting magnets 18 very much influenced
by 'Flux Jumpe," 1.e. the magnetic breakdown under certain conditions.
This phenomenon is clos ely related with Flux
Flux Flow"
88 will be discussed in the following section.
VIIJ. Flux Creep and Flux Flow
Simultaneously with Kim's et al. basic paper on their model of
HFSC, P. W. Anderson published his theory of flux creep in hard super-
conductors. Whereas in an ideal SCII the Lorentz force J x B causée
lateral flux movement, in a HFSC flux 1s retained by the so-called
"Pinning Forces," These are caused by physical defects in this kind of
superconductors which are sometimes called "airty" type II super-
conductors. Physical defects are impurities (especially precipitations),
strains due to cold work, dislocations, etc.
The process of "Flux Pinning" can be explained by considering the
free energy distribution inside a HFSC. A "perfect hole" of unear.
dimension d (order of magnitude 10-5 to 10-6 cm) would produce a free
energy difference
(17)
where HB stands for the bulk critical field. Ya can assume that flux
bundies (with a volume of the order of magnitude a3) are formed. Actually
:
(FA - 83) 13.
03
........

-
---
---
-10-
the average free energy dưference will be appreciably smaller; this
shall be expressed by a factor p. Therefore the average energy barrier
experienced by the bundles is
.
B2
F. - po 23
(18)
A shielding or transport current density J wilch 18 perpradicular to B
will produce Lorentz forces JB on the flux bundles. This corresponde
to a reduction of the energy barrier dy ." (1t the units amp, cm,
and gauss are used). Therefore the resulting energy barrier 18
# B2
(19)
per a3 - 24 - Dorp a3 - Q = F, -
It has been assumed here that because of B >> B. this latter constant
can be neglected in Eq. (6). The introduction of the quantities F, and
a takes in account that the factors d3 und a" are only order of magni.
tude approximates for the quantities involved.
Thermal activation enables the flux bundles to "hop over" the
energy barriers and flux bundle movement in the direction of the Lorentz.
Porces will result. The "Flux Creep Velocity" can be represented by
.
.
- qa
1:02
KT
.
(20)
From similar equations P. W. Anderson derived expressions for ac and for
the temporal change as of the field inside a HFSC tube. In some wat
modified form they are:
:
...
.
V
.
...
.::.::
(21)
and
A'..49 .kI en t
A' + B. a
(22)
'Eq. (21) explaina Kim's et al. .experimental result expressed by Eq. (u).
Also Eq. (22) has been experimentally verified by the same research ...
team. Exact measurement showed that I' decays following a logarithmic".
law. Let us assume that a decrease of the 21eld' I' by 1% was observed
after 10 sec. Then a 2. decrease can be expected after 100 sec, 3% .
after 1000 sec, etc. The flux creep becomes soon extremely slow and
after a relatively short time the "ciltieal" state cannot be dist:lngulab.
ed from an equilibrium state. :
imi i
.:. ::..;" •:: 618.7
.
It is, however, possible to produce a continuous "Flux Flow" by :
Torcing a certain transport current density through a wire by means of
an external electromotive force. Under appropriate experimental condi-
tions the wire remains in the mixed state, i.e. completely superconduci.
ing, although a voltage drop along the wire can be measured. This
voltage drop V is not produced by ohmic resistance but by electromotive ...
forces due to a contimous movement of flux bundles. The dependence of
V on a = J(B + B) and the temperature T can be qualitatively understood ::.
by the existing theories. It als raised beyond a critical value ap,
the thermal conductivity becomes insufficient and a catastrophic transi.
tion of the wire into the normal state occurs.
Il we designed the last mentioned breakdown of Flux Flow under
special conditions, we can consider "Flux Creep" and "Flux Flow" as .. ::
"quasi static," i.e. as cases of "quasi equilibrium.". This is in
contrast to the already previously mentioned phenomenon of "Flux Jumps."
IX. Flux Jumps
Figure 7 representa a tube magnetization diagram obtained under
experimental conditions which avoided carefully disturbances by flux
Jumps. Without special precautions these flux jumps are almost una
avoidable. A somewhat over-simplied, schematic tube magaetization
diagram is showa in Fig. 9a. We distinguish total and partial flux
Jumps. Figure 90 represents the corresponding magnetization curve. A
total ilux jump at H = Hraises the value Ha of the internal field to
H = Hi, the full value of the external field.
The magnetic moment breaks down to zero. A slow increase of the
external field from Hy to Hy might result in moving back to a point Pa
of the undisturbed tube megnetization curve.
Figire 9c gives a qualitative picture of the flux density distri.
bution due to the shielding currents in the tube wall. After the total
flux Jump the shielding current has been dissipated and complete flux ....
penetration takes place (B = 1 = H). The slow raising of the external
field from H, to Hinduces supercurrents in the outer parts of the.. "
HFSC tube and flux penetrates gradually from outside to inside. At
H = liz the whole tube wall is just flux penetrated (B = B2). This 10,
however, the same state which had been achieved by raising A, to 82
without the occurrence of a flux rump and corresponde' to reaching the . . . .
wodisturbed
Leation curve la
-12-
Even under very carefully arranged experimental conditions, flux
jumps can hardly be entirely avoided. They might be not "dangerous,"
1.e. they might be restricted to local disturbances only. There is,
however, the possibility that & complete breakdowa takes place, ine.
that the specimen cannot recover to the critical state. Such "dangerous"
flux jumps can be observed at low fields and high current densities.
This seems to be plausible, since the energy dissipated in this case 18
large.
Experience shows also that HFSC's with high ac, especially at low
temperatures, are prone to dangerous flux jumps. Since these two
conditions correspond to a strong fixation of f.lux bundles, an explana-
tion seems to be difficult. It must be borne in mind, however, that
flux jumps do not result from uniform bulk properties. There might be
one "hot spot" from which a kind of avalanche pronegates. The energy
release connected with a total breakdown in the small volume around the
hot spot becomes larger with larger a, and lower temperature.
The following naive picture might be applied to this case: Suppose
a body can be moved on a surface 12. "sticking forces" are overcome.
With small sticking forces a smooth movement can be easily achieved.
If the sticking forces are high, the movement tends to become jerky.
The avalanche-like propagation of a disturbance starting from a
"hot spot" is principally due to electromagnetic disturbances and to
heat transfer. Electromagnetic forces and the enhancement of the ther-
mal activation off set the quasi equilibrium conditions in adjacent
volume elements. The propagation of the superconducting-normal state
boundary due to heat production and heat transfer, especially in soft
SC, has been carefully studied and seems to be fairly well understood.
For HFSC the much faster electromagnetic propagation mechanism seems
to be, however, even more important.
Experience showed that coating of HFSC with non-superconducting
dietals of high electric and thermal conductivity restricts appreciably
the occurrence of dangerous flux jumps. This is due to the shielding
of electromagnetic disturbances; to some extent the electric bridging
of the relatively high resistance of HFSC material in the normal state
by a well-conducting metal might be advantageous; finally, heat transfer
and heat capacity of the metal coating act against the propagation of
local disturbances.'

-13-
· X. HFSC Wires and Ribbons
Previously the influence of metal coating of UFSC on the occurrence
of flux jumps has been mentioned. These observations are closely related
to special designs of HFSC wires and ribbons which are widely used at
present. Nb(25 to 60 at.%)Zr wires with 5 to 20 mils (5/40 to 1/2 mm)
diameter are being manufactured with copper coatings of around one mil
radial thickness. The insulation is fused nylon or formvar. No-Zr :
ribbons are not often employed. Kunzler's et al. well-known wire
design consists of sintered NoSn in a Nb jacket. Various types of
No,Sr. conductors are manufactured by 'application of metallurgical
aiffusion processes. They comprise wires with single or multiple cores
and various shapes of ribbons. Another way of producing No Sn conduce
tors 18 a vapor deposit process on a stainless steel (Hastelloy) ribbon
as the mechanical carrier. In this case too, copper coating 18 employed.
In all the mentioned cases the details of the metallurgical treatment
(cold work, heat treatment, etc.) are of great influence.
A very important quality test of such superconducting wires and
ribbons is to measure the critical ("quenching") current as a function
of a transverse external field. These tests are performed with straight
pieces of a few centimeters length or with coils non-inductively wound:
with a conductor of about 3 m length. In both cases the test results
are about the same ("short sample tests"). It 18, however, of influence
whether first the field and then the current is raised, or whether this
sequence is reversed. The first method, which is most frequently ..
employed, yields in general higher quenching currents.
Typical short sample test results with a ribbon with vapor deposited :
No Sn are shown in Fig. 20a. Two different directions of the external
field (Hll I and HLI) are indicated in the figure. Test results with a
field perpendicular to the plane of the ribbon are not shown. The ILLI
quenching current characteristic follows approximately a relation
IH = constant
For Hll I the quenching current 18 roughly constant. For an external
field H which is parallel to the plane of the ribbon and which forms '.
..an angle 8 with the direction of I, Kim's formula for J.(Eg. 6) has
been generalized by G. D. Cody and G. W. Cullen to ,
:....... ac
(23) ...
.
-
..

.
•
-14
n maat...
ithin
e
med
...
wewewe---rammen
-
-
-
. In this special case Q. - 12.5 x 109 G amp/cms and B. - 2.4 kg.
Short sample quenching characteristics of a No-Zr wire are showa
in Fig. 10b. A 10-mil N0-33% Zr wire, without copper.coating, epoxy
potted, has been used. Here the high increase of the quenching current
for longitudinal fields up to about 35 kG 18 very remarkable. This
phenomenon 35 presently only partly understood.
XI. Degradation Effect of SC Magnet Coils
For calculating the field strength which can be produced with a
superconducting magnet coil, a simple formila was mentioned (Eq. 16) .
in Section VII. This and other similar formulae are based on the
following reasoning (Fig. 11a): In a magnet coil with uniform current
density J, the maximum field strength HM , H. occurs on the inner sur .
face of the cylindrical windings volume in the midplane of the coil.
- In this region the turns are exposed to the maximum field Hy which 18 . .
transverse to the wire elements, 1.e. these "critical" turns of the wind.
ing "see" the maximum field. A thorough analysis of the conditions 10 . "
a solenoid wound with soft superconductor wire shows that the field
distribution around the critical turns of such a coil is very different
from the homogeneous external field as applied in a short sample test.. ::.
For HFSC, however, especially at high fields, such an appreciable
difference in the shape of the surrounding field might not exist and a
simple graph (Fig. 110) should yield the quenching current of the
critical turns intersection of a straight line (which respresents the
number of gauss per ampere) with the short sample characteristic.
In fact, the very first HFSC magnet coils performed in accordance ;
with the mentioned straightforward consideration: Kunzler's et al.
Mo Re coil (which used "gold insulated" 0.07 w wire) and the solenoids
wound with "Bell Telephone Laboratory Wire" (6 mil diameter NoSn sinter
core in a relatively thick No Jacket). Later on, solenoids made of .
copper coated No-li wire (with low ac) and copper coated No-33% Zr witia
: only 5 mils diameter showed the same easily predictable performance.
This 18 in striking contrast to the experience with magnet coils
I wound with standard No-2x. wire. The expected coil quenching current .. :-
(Fig. 210) 18 much larger than actually observed. The magnitude of the '::'.
"degradation factor"
. .. ..... . (25)
act
13 in general from around 2 (for coils with small inside diameter
--
.
.
.
.
..
.
producios aigh aields) up to wuch higher values, say, 5. Vario:is
experiments indicated that tse transition from superconducting to
normal state of the wire elements did not occur in the critical wind. .
ing region of such coils. Sometimes the first transitions to the
normal state were observed rather randomly distributed inside the wind .
ing volume. Other experimenta indicated winding sections which were
exposed to relatively low fields as the starting points for going normal..
These experiences combined with other considerations point out the
great importance of flux Jumpe. The mentioned coils with degradation
factors of about one use well-shielded winding material, sometines with
low ac, which has uttle tendency toward "dangerous" flux Jumps.
Oscillographical observations of HFSC magnet coils with varying current
strength show clearly the reproducible occurrence of flux jumps of varyo
ing intensity and duration. It seems that coils with a degradation
factor of about one are operating under "Quasi Equilibrium Conditions,"
those with higher a degradation factor under my lux Jump Conditions."
This statement 18 backed by observations with magnet coils exposed
to additional external fields and HFSC solenoids operating at variable
temperatures.
Figure 12a represents the test results with coils wound with ribbon
with vapor deposited Nozsa. The carrier 1a Hastelloy ribbon, 2.2 mm
wide and 0.5 more thick. On both sides NozSa layers of 5 to 8 u thickness
are provided. The thickness of the copper coating 18 about the same.
The short sample quenching characteristics in a transverse external:
field is shown in the figure. A coil with 3.2 cm ID and 4.5 cm OD,..
5.1 cm long was tested in an external field. In Figi 12a the coil
quenching current has been plotted against the total field in the coil
center. A "degradated" coil current of 95 amp 18 almost constant up
to a total field of 33 KG which consists of 20 KG coil self-field and
13 KG background field, At 30 KG background field tilie coil quenching
current reaches 140 amp, corresponding to around 30 KG self-field
(60 KG total field). At this point the short sample characteristic 16 :
reached and D - 1 stays on up to the highest observed total field of ...
. 100 kg. These test results can be interpreted as follows: With a
total field up to 30 KG the coil quenches under "Flux Jump Condition"
with 4 29 > 2.5. After a transition zone from 30 to 60 20 total field
the coil reaches "Quasi Equilibrium Condition" with Dw I which persists
up to the highest observed total field.
-16-
.
Experiments by Meyerhofl and Heise showed the influence of the
temperature on the quenching currents of small HFSC magnet coils. On
a copper coil form 1460 turns of 10 mil No-65% Zr wire with fortivas
insulation (however, without copper coating) were wound. The coil
dimensions were ID - 0.25 inch, OD = 0.9 inch and b 0.6 inch. A
special test cell produced background temperatures from 4 to 11%,
kept constant with up to a + 0.1% toierance at each experiment. Wire si
with various metallurgical treatments has been used.
Results of these experiments are represented in Fig. 12b. Curve I :
shows a monotonic decrease of the critical current with increasinis
temperature. No flux jumps could be observed and the coil did not
show degradation or triming effects. The short sample quenching
currents of this sort of wire were low and special measurements (using
B. H. Heise's method) showed low pinning energies. We can assume that
the short sample and the coll performances are determined by quasi
equilibrium conditions.
Curves II, III, and IV indicate quite different performance. Up
to certain "Degradation temperatures,". Ta, the quenching currents are
almost Independent of the temperature. In order to make the diagrams
clearer no individual test points have been shown. However, the scatter .
ing 18 amazingly low (a few tenths of amperes). At Ta very short dis-
continuities could be observed and with increasing temperatures the
quenchi:ng currents decreased almost linearly.
The following conclusion of these experiments 18 suggested: HIFSC
wires with low quenching currents and low penning forces perform due to
quasi equilibrium conditions in the entire temperature range of 4.2°
to T. ~ 10%. Coils made of wires with higher quenching currents and
pinning forces show wlmost constant critical currents in certain tempera..
ture intervals 4.20% < T < Ta. These low, constant critical currents
are due to flux jump conditions. For Ta <T<T. the quasi equilibrium
conditions seem to prevail.
The author does not know results of similar tests made with copper ...
coated wires. Especially it very small wire cross sections (say, 5 mil
diameter) would be used, it should be expected that the transitions ...
become much smoother.
XII. The Present State of the Art on Mamit acturing Superconducting :
Magnets
. During the last year the first superconducting magnet colls for
fields of up to 100 200 were built (see the following table). ::. .: :


".
Table II. 200 Kilogauss Superconducting Coils
(3.). General Electric Research Lab., D. Iv. Martin et al. (Cryogenics, Sept. 1963).
(2) Westinghouse Research Lab., H. T. Coffey et al. (APS, April 1964).
:. (3) Radio Corporation of America Research Lab., Press Release May 21, 1964.
itesi

g
.
Feet'
Cond. L.
Inches
ID
Ampka
I. H.
Reference
t ing
Bore
OD
Coil L.
Conductor
.
19.30
0.25
1.78
600
1.8
265
101
.
2.19
.
Si. :
ntich
0.194
3.61
@
3.x 4250
7;10;16
0.125
4.0
100
3.73
7.36
2 x 42501"
@
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.
Wenn es troben A
3.55
1.25
3.5
2.8
4.3
5.6
5.44
(a)
3300
3600
7750
T.
95
4.2
205
.
4.3
73
(a) 27 mils tin clad Nb wire (Nb3Sn), ceramic ins., heat treatment 950°C after winding.
(0) · 20 mils No Ti; copper plated. (c) 10 mils Nbēr; copper plated.
. (a) 2 x 0.25 mils Nozsn deposited on 90 x 2 mils Hastelloy, 2 x 2.25 mils copper or silver.
::
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The inner part (made of No Ti wire) consists of three, the outside
part (made of Nb Zr wire) of two coils. If the innermost No Ti coil
(ID = 1/8 inch) 18 removed, the remaining parts of the solenoid produce
92 kg in a bore of 1 Inch ID. After removing all three inner parts
wound with NbTi wire the remaining NoZr solenoid produces 50 kg in a
bore of 3.7 inch ID. It 18 of interest that with the Westinghouse
solenoid the increase of field strength from 92 to 100 kG 18 "bought"
by a decrease of diameter from 1 to 1/8 inch.
Figure 13 showa a plot of field strength versus inside diameter of
superconducting coils built by June 1964. The largest diameter super-
conducting coils built up to now have been manufactured in the Lockheed
Research Laboratory and have the following data:
(a) Inside diameter: 2 ft; coil cross section: 3/4 x 3/4 inches.
2050 turns of 10 mil No-25% Zr wire, copper plated, wire length
about 13,000 ft. With 20.75 amp the field in the coil center
1s about 850 gau88, at the coll inside surface 8.5. kilogauus,
the quenching current is over 27 amperes.
(0) Inside diameter: 6 ft; coil cross section 1-1/4 x 1-1/4 inches.
About 6000 turns of No-Zr wire (see above); wire length about
113,000 ft. It is expected that a current of 21 amp will generate
fields of 850 gauge, and 14.5 kilogauss, respectively.
These large coils are supposed to produce only relatively weak
fields for shielding purposes.
Many technological problems are connected with the design of
superconducting magnet coils: For instance, reliable low-loss joints
between the copper and the HFSC current leads are needed; it must be
possible to dissipate the high energy stored in the magnetic field
without damaging the coil; it is desirable to divide the entire solenoid
into an appropriate number of coils each of not excessive wire length
in order to make coil repairs not too difficult and expensive, etc,
Many problems of this kind already have been solved successfully during
the short period since Kunzler's first publications on HFSC in the
spring of 1961. The future development of superconducting colls depends"
greatly on a better understanding of the very complicated and partly
still obscure physical phenomena. Of special importance is the progress
in the metallurgy of HFSC. For many applications superconducting mag-
nets are already widely employed because of their convenience in
operation, reliability, and economical advantages. It seems, however,

wantidratare
.
-19-
n g and
wetencias dari tanawinin maki
at this time impossible to predict the eventual Imits in the develop-
zent of superconductor magnet coils in respect of achievable field
strength and dimensions and concerning their applicability for special
purposes such as thermonuclear research, MDD power production and
active shielding 1o space flight. '
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LEGAL NOTICE

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