**CONTROL OF STATIC AND DYNAMIC FIELD-ERROR (AC LOSS)**

**IN COS-Θ DIPOLES**

**E.W. Collings and M.D. Sumption**

**Laboratory for Applied Superconductivity and Magnetism**

Department of Materials Science and Engineering

The Ohio State University

Columbus, OH 43210

U.S.A.

Supported

by

The U.S. Department of Energy

Division of High Energy Physics

*under contract number*

**DE-FG02-95ER 40900**

**CONTROL OF STATIC AND DYNAMIC**

**FIELD-ERROR (AC LOSS) IN COS-Θ DIPOLES**

**INTRODUCTION**

Copper-wound, DC-excited, cos-θ dipoles can, in principal, be designed
to deliver a very uniform transverse bore field (i.e. with small or
negligible harmonic or multipolar field distortion).

But if the Cu is replaced by (a) **superconducting strand** that is (b)
present in the form of **Rutherford cable** the extra magnetizations
present within the windings cause distortions of the otherwise uniform
bore field.

The magnetizations take two forms:

(a) static or persistent-current magnetization of the

> superconducting filaments.

\(b\) dynamic magnetizations due to dB/dt-generated coupling currents
between the strands of the cable, currents that also give rise to AC
loss.

We discuss these effects and go on to show how they can be compensated
and suppressed.

**THE STATIC MAGNETIZATION**

Referred to here is the intrinsic diamagnetism of the super-conductors
shielding critical state. The strand magnetization, M~str~, is
proportional to the filament\'s critical current density, J~c~, and
effective diameter, d~eff~. It is negligible at the magnet\'s maximum
operating field. But as the operating field decreases, M~str~ increases
and hence becomes disproportionately large at injection field.

Over the years M~sat~ has been minimized by reducing d~eff~. As for the
residue, several active and passive compensation schemes (involving the
ferromagnetic elements Fe or Ni) have been devised.

**DYNAMIC MAGNETIZATION**

During field ramping circulating B-dot-generating coupling currents are
another source of field error. As \"AC loss\" they contribute to the
system\'s cryogenic loading, and by augmenting the transport current
they reduce the stability of the magnet.

Both the \"normal interstrand coupling currents\" and
widely-circulating, long-time-constant \"Boundary Induced Coupling
Currents\" can be suppressed by increasing the interstrand contact
resistance, an upper limit to which is imposed by stability
(current-sharing) constraints.

The desired interstrand contact resistance is achieved by applying
strand coatings or the introduction of an \"insulating\" core.

**STATIC MAGNETIZATION**

The half-height of the filament magnetization loop, or the magnetization
in the shielding critical state, say, is

With the SSC strand it was found that with decreasing d, M~str~
minimized at a d = 6 μm. Proximity effect coupling then took over to
produce d~eff~s \> 6 μm until the introduction of the dilute **Cu**-Mn
matrix.

As an interesting aside, the Mn idea would not have surfaced had the
filaments not been clad in a protective barrier film of Nb. Niobium
helps to launch NbTi\'s superelectrons into the surrounding Cu matrix.

As a second interesting aside, the apparent PE-suppressing action of Si
additions to the Cu matrix is probably due to the absence of the Nb
barrier in the NbTi/Cu-Si test strands.

The fine-filament NbTi/Cu strands still needed to be magnetically
compensated, for which purpose various schemes have been suggested
including:

\(i\) The placing of small pieces of ferromagnetic material within the
bore of the magnet or in one of the coil wedges.

\(ii\) The inclusion of ferromagnetic material, in particular Ni, within
the strand itself.

**MAGNETIC COMPENSATION**

The goal off magnetic compensation is to cancel out the shielding (i.e.
field-increasing) magnetic moment resident in the superconducting
windings. On a per-unit-length basis this is achieved by setting:

where σ~s~ is the saturation magnetization of the ferromagnetic element
and M~SC~ is the magnetization of the SC. The As represent cross
sectional areas.

Taking for pure Ni a σ~s~ of 507-521 emu/cm^3^ we found that SSC-type
NbTi/Cu strand could be compensated at fields of 0.5-0.7 T by:

\(1\) applying an electroplated Ni coating of thickness 2.4-1.9 μm, or

\(2\) replacing some of the NbTi filaments with Ni ones, NbTi/Ni ratios
47/1-57/1.

Calculations of sextupole ratio at R = 1 cm by M. Green predicted
substantial reductions in both cases.

**MAGNETIZATIONS OF NbTi AND Nb~3~Sn**

For NbTi we might expect a J~c~ of about 8,500 A/mm^2^ at 0.5 T,
yielding for d = 6 μm a J~c~d product of 5.10 in the units
\"A/mm^2^cm\".

For a Nb~3~Sn strand we find a non-Cu J~c~ by taking some recently
published J~c~(B) data, scaling it to 2200 A/mm^2^ at 12 T and using a
Kramer plot to extrapolate to 0.5 T. The result was 46,300 A/mm^2^.
Taking a d~eff~ of 20 μm we obtain a J~c~d~eff~ product in the above
units of 93.

Based on a J~c~d~eff~ 18X larger than that of NbTi, the magnetization of
Nb~3~Sn, and its effect on injection field quality, becomes a serious
problem. Even so, ferromagnetic compensation of the Rutherford cable
through the insertion of a Ni ribbon may be worth serious consideration.
For compensation we require

where

A~Ni~ is the c/s area of the Ni ribbon

f~c~ is the packing factor of the standard cable

w and t are the width and thickness of the original cable

λ is the nonCu/(Cu+nonCu) ratio for the strand

**STRIP THICKNESS**

Picture a cable of dimensions 1.5 cm x 0.2 cm wound with the above
Nb~3~Sn strand; assume nonCu/(Cu+nonCu) = 0.5, and a packing factor of
90%. Then the thickness, t~Ni~ cm, of a 1.3-cm wide strip of Ni (assume
σ~s~ = 510 emu/cm^3^) that would provide magnetic compensation at 0.5 T
is given by

which yields a t~Ni~ of 0.400 mm (i.e. \"**15.7 mils**\").

**DEPLOYMENT AND PROPERTIES**

**OF THE STRIP**

At half the thickness of a typical strand, the strip is fairly thick. It
may be preferable to employ three strips each of thickness **5** mils.,
sandwiching the cable between two of them and employing the other as a
core.

Stabrite cables with stainless steel cores of thicknesses **0.5**,
**1**, and **2** mils have already been successfully produced.

Such cores increase the effective interstrand contact resistance and by
so doing suppress dynamic field error.

**USE OF IRON INSTEAD OF NICKEL**

With an M~s~ of 1745 emu/cm^3^ compared to Ni\'s 510 emu/cm^3^ the core
thickness could be reduced by a factor 0.29 down to a value of 0.117 mm
or 5 mils.

Such a core would not be unreasonable from the standpoints of
fabrication and space utilization.

However, demagnetization considerations would require the field to be
directed **parallel** to the surface of the cable rather than normal to
it.

**SUPPRESSION OF DYNAMIC MAGNETIZATION**

**\-- CORE-TYPE CABLES**

During excitation of the magnet the induced interstrand coupling
currents (ICRs) cause both energy losses and distortions of the field at
the beam line. They are moderated by the magnitude of the interstrand
contact resistance (ICR). There are both \"normal\" ICRs that can be
envisioned as looping around a half pitch of the cable, and
\"supercurrents\" (Schmidt) otherwise known as Boundary Induced Coupling
Currents (BICCs, Verweij) that can flow over a whole cable length and
induce field errors that vary with the period of the twist pitch. The
latter are caused by a dB/dt or an ICR that varies sharply with distance
along the cable (hence the term \"boundary\").

Coupling currents are suppressed by increasing the crossover and
side-by-side ICRs \-- R~c~ and R~a~, respectively. For a standard
uncored LHC-type cable, it is generally agreed that R~c~ should be not
less than 15±5 μΩ and R~a~ not less than 0.2 μΩ.

In the case of a cored cable, we have replaced R~c~ by a numerically
equivalent R~eff~.

R~c~ (or R~eff~) is upper limited by a need to preserve interstrand
current sharing and hence cable stability.

**CHANGING THE ICR**

Over the years various groups have modified ICR by:

\(1\) applying metallic or insulating coatings to the individual strands
of the cable.

\(2\) inserting a metallic or insulating ribbon between the two layers
of the cable

We ourselves have applied almost a dozen coatings and have measured AC
loss in cables with cores of titanium, kapton, stainless steel, and
nichrome-80. The latter was used as a core for HTSC-2212/Ag cables, and
we have settled on AISI 316 stainless steel ribbon as a core for cables
wound with:

bare NbTi/Cu

stabrite-coated NbTi/Cu

Cu-stabilized Nb~3~Al

Nb~3~Sn.

The core can increase R~c~ by two orders of magnitude.

For Nb~3~Sn cables the effect of a core on AC loss is illustrated by the
following pair of curves:

![](media/image1.png){width="5.729166666666667in"
height="5.545833333333333in"}

AC loss in uncored and cored Rutherford cables

wound with Nb~3~Sn strand and heat treated under

uniaxial compactions of 5, 10, and 20 MPa

**CONTROL OF ICR AND STABILITY**

The ICR of a fully cored cable will vary with processing conditions \--
heat treatment temperature and level of uniaxial pressure and its
application cycle. For example:

Cable Type HT Temp, R~eff,LHC~,

deg.C μΩ

\(1\) stabrite NbTi 170 75

\(2\) Nb~3~Sn 660 36

\(3\) Nb~3~Al 750 5

With cables (1) and (2) the R~eff~s were too high to ensure stability;
however we have shown that they can easily be reduced (fine-tuned, in
fact) by reducing the width of the core.

![](media/image2.png){width="4.428472222222222in"
height="4.155555555555556in"}

**CONCLUDING DISCUSSION**

**I MAGNETIZATION**

High-J~c~ Nb~3~Sn strands will have correspondingly higher J~c~s at
injection field. Assuming a J~c,4K,12T~ of 2200 A/mm^2^ and a Kim
J~c~(B) model, the J~c~ at 0.5 T is expected to be a factor of 22
higher, or 48.4 kA/mm^2^

Associated with this is critical-state magnetization proportional to
J~c~ x d~eff~. This magnetization has two consequences that have to be
borne in mind during the development of strands with higher and higher
J~c~.

**(1) Field Error**

There is the magnetization itself which contributes multipolar field
distortion of the dipole magnet. Already at 2200 A/mm^2^ (12 T) and
d~eff~ = 20 μm the calculated magnetization, viz. ∆M = 3.93 x 10^2^
emu/cm^3^, is equivalent to that contributed by 346 mT/s-generated
coupling currents.

The question of compensation becomes very important. For passive
ferromagnetic compensation the volume of added Ni would need to be 20%
of the strand volume.

Line of equal dynamic and static 0.5 tesla magnetizations, the latter
calculated on the basis of a 12 tesla J~c~ of 2200 A/mm^2^

![](media/image3.png){width="5.8381944444444445in"
height="5.379861111111111in"}

Influence of effective filament diameter on a Sytnikov-calculated
LHC-type cable equivalent ramp rate

**(2) Flux-Jump Instability**

The strand tends to become adiabatically flux-jump unstable. It has been
shown, in terms of the full hysteresis-loop height, ∆M, that the
flux-jump threshold for adiabatic flux-jump instability can be expressed
in the form

where t = T/T~c~ and the heat capacity of the SC is represented by
β~c~T^3^.

At ∆M = 2.67 x 10^2^ emu/cm^3^ this is already smaller than the
above-mentioned loop height of 3.93 x 10^2^ emu/cm^3^.

Clearly some extra dynamic or cryostabilization is playing a role,
nevertheless the strand must be approaching its flux-jump stability
limit.

**The Significance of d~eff~**

As indicated above, the controlling low-field parameter is the
**MAGNETIZATION.**

d~eff~ is just a secondary parameter associated with magnetization;
furthermore it cannot be derived at low fields where J~c~ is
immeasurably large in most laboratories.

Nevertheless its high-field-measured value is still a useful number from
a processing standpoint, since it indicates very clearly the extent to
which interfilament bridging has taken place.

**II COUPLING CURRENTS IN CABLES**

To suppress coupling in Nb~3~Sn Rutherford cable a core is needed.

In case the full width core produces too much R~eff~ a fine tuning can
be achieved by varying the width of the core. This has already been
demonstrated with stabrite cables.

By selecting Ni for the core partial magnetic compensation can be
achieved.

**BIBLIOGRAPHY**

**ENHANCEMENT AND CONTROL OF PROXIMITY EFFECT COUPLING BETWEEN FILAMENTS
IN A NbTi MULTIFILAMENTARY COMPOSITE**

**PROXIMITY EFFECT SUPPRESSION**

**BY MEANS OF A Cu-Mn ALLOY MATRIX**

100\. **STABILIZER DESIGN CONSIDERATIONS IN FINE FILAMENT Cu/NbTi
COMPOSITES,**

E. W. COLLINGS, Adv. Cryo. Eng. (Materials) [34,]{.underline} 867
(1988).

111\. **A CONDUCTOR WITH UNCOUPLED 2.5 μm DIAMETER FILAMENTS DESIGNED
FOR THE OUTER CABLE** **OF SSC DIPOLE MAGNETS,**

E. GREGORY, T. S. KREILICK, J. WONG, E. W. COLLINGS, K. R. MARKEN, Jr.,
R. M. SCANLAN, AND C. E. TAYLOR, IEEE Trans. Magn. [25]{.underline},
1926-1929 (1989).

**PROXIMITY EFFECT ENHANCEMENT**

**FOLLOWING THE NIOBIUM COATING OF THE FILAMENTS**

182\. **ENHANCED PROXIMITY EFFECT COUPLING DUE TO THE PRESENCE OF A Nb
BARRIER IN FINE NbTi MULTIFILAMENTARY COMPOSITES**

M. D. SUMPTION, H. LIU, E. GREGORY, AND E. W. COLLINGS, Adv. Cryo. Eng.
(Materials) **42**, 1175-1182 (1997).

198\. **PROXIMITY EFFECT CURRENT STRENGTHS IN NbTi MULTIFILAMENTARY
SAMPLES WITH AND WITHOUT Nb BARRIERS AND PROCESSED UNDER VARIOUS
CONDITIONS**

M. D. SUMPTION AND E. W. COLLINGS, IEEE Trans. Appl. Supercond. **7**,
1117-1121 (1997).

209\. **CRITICAL CURRENTS AND SUPERCONDUCTING BOUNDARY EFFECTS IN S-N-S
MULTIFILAMENTARY COMPOSITES**

M.D. SUMPTION, S. TAKÁCS, AND E.W. COLLINGS, Adv. Cryo. Eng. (Materials)
**44,** 843-850 (1998).

**COMPENSATION OF \"PERSISTENT-CURRENT\"**

**(STRAND) MAGNETIZATION**

117\. **DESIGN OF COUPLED OR UNCOUPLED MULTIFILAMENTARY SSC-TYPE STRANDS
WITH ALMOST ZERO RETAINED MAGNETIZATION AT FIELDS NEAR 0.3 T**,

E. W. COLLINGS, K. R. MARKEN, Jr., AND M. D. SUMPTION, Adv. Cryo. Eng.
(Materials) [36]{.underline}, 247-254 (1990).

123\. **INTERFILAMENT AND INTRAFILAMENT MAGNETIZATIONS IN FINE-FILAMENT
COMPOSITE STRANDS FOR PRECISION-DIPOLE MAGNET APPLICATIONS**

E. W. COLLINGS, K. R. MARKEN, Jr., AND M. D. SUMPTION, Cryogenics
[30]{.underline}, 48-55, (1990).

124\. **DESIGN, FABRICATION, AND PROPERTIES OF MAGNETICALLY COMPENSATED
SSC STRANDS**

E. W. COLLINGS, K. R. MARKEN, Jr., M. D. SUMPTION, G. IWAKI, AND S.
SAKAI, IEEE Trans. Magn. [27]{.underline}, 1787-1790 (1991).

128\. **FERROMAGNETIC MATERIAL IN THE SUPERCONDUCTOR AND ITS EFFECT ON
THE MAGNETIZATION SEXTUPOLE AND DECAPOLE IN THE SSC DIPOLES AT
INJECTION**

M. A. GREEN, E. W. COLLINGS, K. R. MARKEN, M. D. SUMPTION, in
[Supercollider 3]{.underline}, Plenum Press, 1991, pp. 365-373.

172\. **MATERIALS SELECTION FOR FERROMAGNETIC COMPENSATION IN
ACCELERATOR MAGNETS**

E. W. COLLINGS AND M. D. SUMPTION, IEEE Trans. Appl. Supercond. **5**,
408-411 (1995).

**FLUX-JUMP STABILITY**

218\. **LOW FIELD FLUX JUMPING IN HIGH PERFORMANCE MULTIFILAMENTARY
Nb~3~Al AND Nb~3~Sn COMPOSITE STRANDS**

M.D. SUMPTION AND E.W. COLLINGS, IEEE Trans. Appl. Supercond. **9**,
1455-1458 (1999).

# CONTACT RESISTANCE AND AC LOSS

175\. **CONTACT RESISTANCE AND CABLE LOSS MEASUREMENT OF COATED STRANDS
AND CABLES WOUND FROM THEM**

M. D. SUMPTION, H. H. J. TEN KATE, R. M. SCANLAN, AND E. W. COLLINGS,
IEEE Trans. Appl. Supercond. **5**, 692-696 (1995).

216\. **INFLUENCE OF STRAND SURFACE CONDITION ON INTERSTRAND CONTACT
RESISTANCE AND COUPLING LOSS IN NbTi-WOUND RUTHERFORD CABLES**

M.D. SUMPTION, E.W. COLLINGS, R.M. SCANLAN, A. NIJHUIS, H.H.J. ten KATE,
S.W. KIM, M. WAKE, AND T. SHINTOMI, Cryogenics **39,** 197-208 (1999).

**AC LOSS IN NbTi CABLES**

183\. **MAGNETIC STUDIES OF AC LOSS IN PRESSURIZED RUTHERFORD CABLES
WITH COATED STRANDS AND RESISTIVE CORES**

E. W. COLLINGS, M. D. SUMPTION, R. M. SCANLAN, S. W. KIM, M. WAKE, AND
T. SHINTOMI, Adv. Cryo. Eng. (Materials) **42**, 1225-1232 (1997).

184\. **CALORIMETRIC MEASUREMENTS OF THE EFFECT OF NICKEL AND STABRITE
COATINGS AND RESISTIVE CORES ON AC LOSS IN ACCELERATOR CABLES UNDER
FIXED PRESSURE**

M. D. SUMPTION, R. M. SCANLAN, A. NIJHUIS, H. H. J. ten KATE AND E. W.
COLLINGS, Adv. Cryo. Eng. (Materials) **42**, 1303-1311 (1997).

193\. **SUPPRESSION OF EDDY CURRENT LOSS IN BARE-COPPER RUTHERFORD
CABLES USING STAINLESS STEEL CORES OF VARIOUS THICKNESSES**

E.W. COLLINGS, M. D. SUMPTION, S. W. KIM, M. WAKE, AND T. SHINTOMI,
Proc. 16^th^ICEC/ICMC Conference, ed. by T. Haruyama, T. Mitsui, and K.
Yamafuji, (Elsevier Science Japan, 1997) pp. 1767-1770.

200\. **SUPPRESSION AND CONTROL OF COUPLING CURRENTS IN STABRITE-COATED
RUTHERFORD CABLE WITH CORES OF VARIOUS MATERIALS AND THICKNESSES**

E. W. COLLINGS, M. D. SUMPTION, S. W. KIM, M. WAKE, T. SHINTOMI, A.
NIJHUIS, H. H. J. ten KATE, AND R. M. SCANLAN, IEEE Trans. Appl.
Supercond. **7**, 962-966 (1997)

226\. **COUPLING CRRENT CONTROL IN STABRITE-COATED NbTi RUTHERFORD CABLE
BY VARYING THE WIDTH OF A STAINLESS STEEL CORE**

M.D. SUMPTION, E.W. COLLINGS, A. NIJHUIS, AND R.M. SCANLAN, Adv. Cryo.
Eng. (Materials) **46** \-- to be published

**AC LOSS IN Nb~3~Sn AND Nb~3~Al CABLES**

207\. **AC LOSS AND CONTACT RESISTANCE IN Nb~3~Sn RUTHERFORD CABLES WITH
AND WITHOUT A STAINLESS STEEL CORE**

M.D. SUMPTION, E.W. COLLINGS, R.M. SCANLAN, A. NIJHUIS, AND H.H.J. ten
KATE, Adv. Cryo. Eng. (Materials) **44**, 1077-1084 (1998).

217\. **CORE-SUPPRESSED AC LOSS AND STRAND-MODERATED CONTACT RESISTANCE
IN A Nb~3~Sn RUTHERFORD CABLE**

M.D. SUMPTION, E.W. COLLINGS, R.M. SCANLAN, A. NIJHUIS, AND H.H.J. ten
Kate, Cryogenics **39**, 1-12 (1999).

221\. **AC LOSSES IN Nb~3~Sn RUTHERFORD CABLES WITH A STAINLESS STEEL
CORE**

F. SUMIYOSHI, S. KAWABATA, T. GOHDA, A. KAWAGOE, T. SHINTOMI, E.W.
COLLINGS, M.D. SUMPTION AND R.M. SCANLAN, IEEE Trans. Appl. Supercond.
**9,** 731-734 (1999).

227\. **AC LOSS AND CONTACT RESISTANCE IN COPPER-STABILIZED Nb~3~Al
RUTHERFORD CABLES WITH AND WITHOUT A STAINLESS STEEL CORE**

M.D. SUMPTION, R.M. SCANLAN, A. NIJHUIS, AND E.W. COLLINGS, EUCAS-99,
Inst. of Physics, Ser. \-- to be published

**AC LOSS IN Bi:2212/Ag CABLES**

212\. **COUPLING CURRENT CONTROL IN RUTHERFORD CABLES WOUND WITH NbTi,
Nb~3~Sn, AND Bi:2212/Ag**

M.D. SUMPTION, R.M. SCANLAN, AND E.W COLLINGS, Proc. ICMC\'98, Topical
Conference on AC Loss and Stability of Low and High-T~c~
Superconductors, Physica C **310**, 291-295 (1998).

213\. **AC LOSS PROPERTIES OF SOME Bi:2212/Ag RUTHERFORD CABLES AND A
COMPARISON WITH THOSE OF CABLES WOUND WITH NbTi AND Nb~3~Sn**

M.D. SUMPTION, R.M. SCANLAN, AND E.W. COLLINGS, Cryogenics **38**,
1225-1232 (1998).

214\. **LOW COUPLING LOSS CORE-STRENGTHENED Bi:2212/Ag RUTHERFORD
CABLES**

E..W. COLLINGS, M.D. SUMPTION, R.M. SCANLAN, L.R. MOTOWIDLO, IEEE Trans.
Appl. Supercond. **9**, 758-761 (1999)

215\. **Bi:2212/Ag-BASED RUTHERFORD CABLES: PRODUCTION, PROCESSING, AND
PROPERTIES**

R.M. SCANLAN, D.R. DIETERICH, E.W. COLLINGS, M.D. SUMPTION, L.R.
MOTOWIDLO, Y. AOKI, AND T. HASEGAWA, Supercond. Sci. and Tech. **12**,
87-96 (1999).

223\. **DESIGN, PROCESSING, AND PROPERTIES OF Bi:2212/Ag RUTHERFORD
CABLES**

E.W. COLLINGS, M.D. SUMPTION, R.M. SCANLAN, D.R. DIETDERICH, L.R.
MOTOWIDLO, R.S. SOKOLOWSKI, Y. AOKI, AND T. HASEGAWA, Advances in
Superconductivity-XI, N. Koshizuka and S. Tajima, eds. (Springer-Verlag
Tokyo 1999) pp. 1369-1372.