Magnetization Process of DT Conductor
Magnetization process of DT conductor is a
little bit more complicated than that of usual Nb3Sn conductors. Since it has
Nb barrier that partially becomes Nb3sn, filaments are shielded in the initial
stage. A finite element analysis to see the magnetization process of DT
conductor presents a good idea of the magnetization process. Here, the number
of filament in the conductor is reduced to 7 for the simplicity. Although the fluxes
fully penetrate into the filament at high field, the magnetization coming from
the barrier still has a large contribution.
step0: fully shielded
by the barrier

step1: partial penetration
in the barrier

step2: full penetration
through the barrier

step3: start penetration
into the filament

step4: most of the
filaments penetrated

step5: full penetration
in to filaments


The above simulation is still imperfect. For example, the penetration of
magnetic flux has to be zero in total; persistent current should be internal.
Improvement in this simulation is the forcing of symmetric
penetration. It looks like almost prefect in the flux distribution.
Now the calculation of the magnetization should be possible.


Let me start with a slab model. It is easier to compare with the
analytical model. The magnetization behavior of the model turned out to be close to the theoretical model. Still there are some glitches at the turning points of the field. This is due to the blanked field sensitivity introduced
to model the system in the finite element method. There could be some more improvement.


These two curves are the magnetization of DT conductor with and without barrier magnetization based on the test geometry of 7strand. The field dependence of Jc is not included yet. The twostep magnetization coming from the barrier effect is clearly seen in the curve and the increase of loss due to the barrier is evident.


A simple
field dependence of jc=jc0*4/(2+B) was introduced in this simulation for a 7filament conductor with and without barrier. The model is getting close to the reality. The magnetization shape and the difference between Ta barrier and Nb barrier are evident. By the use
of real geometry, it should be possible to evaluate the loss of the real DT conductor. It will just take more CPU time.


The flux behavior is best visualized by a motion picture. Click the
left icon to see the lux movie. The penetration of the flux into the virgin state and the redistribution of the shielding current for the decrease of the field is in the show.


Although magnetization curve would not be much affected, the symmmetric penetration is a little too much restriction for the flux. the symmmety axis has to be at least tilted at near the barrir. Improvement in this picture is the introduction of asymmmetric penetration. Now the persistent current is zero in total in each filament and yet the penetration into the filament is not forced to be symmmetric. It looks like more natural.

Magnetization at saturation
The magnetization of N filament with radius
a can be calculated as the sum of current moment:
(1)
, where jc is the current density in the filament. The magnetization is measured
par volume base. The volume of the conductor is:
(2)
, where eta is the nonsuperconductor to superconductor ratio. Then the measured
magnetization, using Jc(over all current density including copper stabilizer)
is:
(3)
Effective diameter of the conductor is often evaluated using this equation.
(4)
We have used this equation in our publication. However, if the measurement
system is calibrated against a niobium cylinder, we should have used
.(5)
If the calibration was made using Nb wire of the same size, eq.(4) is correct.
The magnetization of the barrier with outer radius R and inner radius r is:
(6)
If we measure the conductor with no filament,
(7)
is the volume and
(8)
would give the measured magnetization par volume. This expression should be
effective for tube method conductor or PIT conductor.
Since N=126
R=350u a=25u r=354(effective with reduced jc) in our case,
Mb and M becomes about the same. Since the filament magnetization is reduced by
the shielding effect of the barrier, total magnetization would be a little less
than the sum of the filament and the barrier magnetization. This agrees with
our measurement assuming that most of the discrepancy between geometrical size
of the filament bundle and the effective diameter comes from the barrier
magnetization.
If the diameter of the strand is reduced to 0.7mm the barrier magnetization
will be greatly reduced. At diameter 1mm, the use of tantalum barrier is a good
way of reducing magnetization.