A Superconducting transformer system for high current cable testing Page: 3 of 10
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The relations that describe the system are (1) and:
Up + Mps dt
IpRp + Lp f.
Mps = RIs + (Ls + Lsa) t. (3)
Usec J Ui dt =A2 fUr dt (4)
1000 Lsa = 1 pH
Lsa = 2 pH
10 15 20
Up A1 (Uset Usec) . (5)
The amplification factor of the transformer can be
found by integrating (3) which gives a current amplifi-
-s - p (6)
Ip Ls + Lsa'
when ignoring the (small) resistance in the secondary and
alternating current (AC) losses, and when Is is assumed
to be initially zero when Ip = 0 at the beginning of the
It is evident from (6) that, though in principle a single
turn secondary is sufficient, it is important to use mul-
tiple turns to enhance the amplitude of the mutual and
secondary inductances, thereby reducing the sensitivity
of the amplification factor on the load inductance.
To illustrate the role of load inductance and secondary
turn number, consider the cross-section of the secondary
being composed of n2 turns. Equation (6) then takes the
Is. _ n2ps .(7)
Ip nzLs + Lsa (
The resulting amplification as a function of secondary
turn number is shown in Figure 2, for various load in-
ductance values. Note that the measured amplification
factor is a sensitive diagnostic of small load inductance.
The current specification of the primary power sup-
ply follows directly from (6) and the desired headroom
to compensate for the AC and resistive losses in the sec-
ondary. The voltage requirement for the primary power
supply follows from (2), and is therefore determined by
the desired ramprate for the secondary current combined
with the resistive voltages in the primary current leads.
A NbTi cable for the secondary was custom made from
wire that was developed for the U.S. Superconducting
Supercollider Program (SSC), and insulated with S-glass
braided sleeve. A Formvar insulated NbTi wire from ex-
isting inventory was selected for the primary windings.
The secondary cable and primary wire specifications are
summarized in Table I.
The primary coil is solenoidal wound on a 80 mm di-
ameter, 150 mm high stainless steel holder and the sec-
ondary coil is wound on top of the primary, with a 2 mm
FIG. 2. Amplification factor Is/Ip as a function of secondary
turns (n) for load inductances from 0 to 10 pH, based on the
geometry used in the transformer described here. The actual
turn number chosen is ~ 6.5, yielding reasonable performance
for both low-inductance short samples and higher-inductance
TABLE I. Secondary cable
and primary wire specifications
Cable Cable Ic Number Wire Wire Ic
dimensions at 5 T of strands diameter at 5 T
mm x mm [kA] [mm] [A]
1.626 x 21.267 31.26 51 0.386 110
insulating spacer in between the primary and secondary
turns, and insulated on the outside with S-glass sheet.
The primary and secondary windings are optimized for
the mutual inductance between the turns. The coil set
is clamped inside an Al-alloy support structure and vac-
uum impregnated with CTD101 epoxy. Table II provides
an overview of the calculated transformer specifications.
The design of the transformer is shown in Figure 3,
including the Rogowski coils for the current measurement
that are described in more detail in section II C. The
secondary leads leave the transformer at the top and are
folded down and brought together on the side the the
transformer to limit the required height of the system.
The outer dimensions of the entire transformer, excluding
the splices to the sample, are 190 x 180 x 220 mm3.
The inductances and mutual inductances of the trans-
former are calculated from the primary and secondary
coil dimensions. The primary resistance Rp is estimated
from the voltage drop that is commonly observed in cop-
per welding cable current leads. The secondary resistance
Rs is a worst case estimate that is based on past expe-
rience that good solder joints between Rutherford cables
commonly exhibit resistances of 0.5 nQ or lower.
The inductance of a bifilar set of Rutherford cables
per unit length is approximately L po d/w. Here,
d 2 mm is the cable center separation and w 20 mm
is the cable width, leading to Lsa 1.5 x 10-7 H for
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Godeke, A.; Dietderich, D. R.; Joseph, J. M.; Lizarazo, J.; Prestemon, S. O.; Miller, G. et al. A Superconducting transformer system for high current cable testing, article, February 15, 2010; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1012815/m1/3/: accessed February 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.