f Fermilab Fermi National Accelerator Laboratory

P.O. Box 500 Batavia, Illinois 60510

TD-01-058

July 10, 2001

## Effect of BEND Parameters-Shift and Blunt

## On the Design of Superconducting Magnet End Parts

S. Yadav

# *Fermi National Accelerator Laboratory*

# *MS 316, PO Box 500*, *Batavia, IL, USA*

1.  **Introduction**

Program BEND \[[^1]\] is used at Fermilab for the design of cosine-theta
type superconducting magnet end parts. Although this program is very
powerful, there is no user documentation for this program. In this note,
we show graphically the effect of two of the BEND parameters-Shift and
Blunt on the shape of the end parts. We illustrate this for the inside
and outside bounding surfaces of the different conductor groups from the
first high-field dipole model, HFDA01 cross-section \[[^2], [^3]\].

2.  **Parameter Shift**

Parameter Shift is used to change the distribution of twist along the
guiding strip \[[^4]\]. Positive values of shift cause more of the twist
to be distributed early in the strip, while negative values distribute
more twist late in the strip. The recommended values for this parameter
are between -2 to 2. We show graphically the effect of this parameter in
Figures 1 to 7.

Figures 1 and 2 show the top view of the inside and outside surfaces of
the outer layer, return end conductor group 3 (OR3) for an A-length of
110 mm and an inclination angle of 40.17° (as suggested by program
BEND). It is observed that increasing the value of shift from -2 to 2
has the same effect as pulling the free edge out as indicated by the
arrow in the figure. However, this effect is observed to reverse in
direction and decrease in magnitude if a smaller inclination angle of
25° is used, as seen in Figures 3 and 4.

![](media/image1.wmf){width="6.104330708661418in" height="3.85in"}Figure
1: Inside surface of outer layer-return end conductor group 3, A length
= 110 mm, Inclination Angle=40.17.

![](media/image2.wmf){width="6.104330708661418in" height="3.85in"}Figure
2: Outside surface of outer layer-return end conductor group 3, A length
= 110 mm, Inclination Angle=40.17.

![](media/image3.wmf){width="6.145669291338582in"
height="3.87992125984252in"}**Figure 3: Inside surface of outer
layer-return end conductor group 3, A length = 110 mm, Inclination
Angle=25.**

Figure 4: Outside surface of outer layer-return end conductor group 3, A
length = 110 mm, Inclination Angle=25.

Figure 5: Outside surface of outer layer-return end conductor group 1, A
length = 40 mm, Inclination Angle=28.9.

Figure 5 shows the top view of the outside surface of the outer layer,
return end conductor group 1 (OR1) for an A-length of 110 mm and an
inclination angle of 28.9° (as suggested by program BEND). It is
observed once again that increasing shift from -2 to 2 has the same
effect as pulling the free edge outwards as indicated by the arrow.
However, for this conductor group the magnitude of this effect is
observed to be much smaller than that for the previous conductor group,
OR3. Once again, this effect is observed to reverse in direction on
using a smaller inclination angle, as shown in Figures 6 and 7 that use
an inclination angle of 20° instead of 28.9°. However, in contrast to
the previous case, the magnitude of this effect is observed to increase
on using a smaller inclination angle.

![](media/image5.wmf){width="6.145669291338582in"
height="4.083464566929134in"}

Figure 6: Inside surface of outer layer return-end conductor group 1, A
length = 40 mm, Inclination Angle=20.

![](media/image6.wmf){width="6.145669291338582in"
height="3.690157480314961in"}

Figure 7: Outside surface of outer layer-return end conductor group 1, A
length = 40 mm, Inclination Angle=20.

![](media/image7.wmf){width="5.77007874015748in"
height="3.6401574803149606in"}

3.  **Parameter Blunt**

Parameter Blunt is used to change the radius of curvature of the free
edge \[Error: Reference source not found\]. A blunt of zero is the
default value and has no effect on the strip. Positive values of blunt
pull the free edge of the strip out near its termination and are used to
relieve sharp radii at the nose of the group. Negative values pull the
free edge out near its middle and are used to improve areas between
groups that may be too thin to support part manufacturing integrity. The
recommended values for this parameter are between 0 to 0.5.

Figures 8 and 9 show the top view of the inside and outside surfaces of
the outer layer, return end conductor group 3 (OR3) for an A-length of
110 mm and an inclination angle of 40.17° (as suggested by program BEND)
for different values of blunt. It is observed that as expected the
effect of increasing the blunt value is to pull the free edge outward as
shown in these figures. Similar effect is observed, for example, for the
inside surface of the outer layer, lead end conductor group 3 (OLL3), as
shown in Figure 10.

![](media/image8.wmf){width="6.1in" height="4.0472222222222225in"}

Figure 8: Outer layer-return end conductor group 3, A length = 110 mm,
Inclination Angle=40.17.

![](media/image9.wmf){width="6.090277777777778in"
height="4.0472222222222225in"}

Figure 9: Outer layer-return end conductor group 3, A length = 110 mm,
Inclination Angle=40.17.

![](media/image10.wmf){width="5.995138888888889in"
height="4.0993055555555555in"}

Figure 10: Outer layer-lead end conductor group 3 (oll3), A length = 50
mm, Inclination Angle=22.0.

**References**

[^1]: \[?\] J.M. Cook, "Strain energy minimization in SSC magnet
    winding," IEEE Transaction on Magnetics, Vol. 27, pp. 1976-1980,
    (1991).

[^2]: \[?\] V. Kashikhin, "First high field magnet cross-section
    design," Fermilab Technical Note TD-99-027, (1999).

[^3]: \[?\] S. Yadav, "Design Parameters for the Coil Ends for the First
    High Field Dipole Model-HFDA01," Fermilab Technical Note TD-01-056,
    (2001).

[^4]: \[?\] J.S. Brandt, et al., "Coil end design for the SSC collider
    dipole magnet," Fermilab-TM-1735, Fermi National Accelerator
    Laboratory, Batavia, IL, July (1991).