1. Discussion of modification to DID field for detectors with TPC
B. Parker, A. Seryi
September 27, 2005

2. Motivation Effect of DID fields were discussed at Snowmass intensively
At the last day of Snowmass and after that, in discussion of Witold Kozanecki and Dan Peterson, the following suggestion was given:
Dan Peterson clarified that “a uniform magnetic field is required at small z for the purpose of performing a track-based calibration the magnetic field. The region of uniform field would allow us to isolate the effects of the field distortions on track trajectories from the effects of field distortions on the drift path. I believe that uniformity is less important at larger z; the current DID design field of 0.08T at |z|= 2.2m would be acceptable.”
According to Dan, “the uniformity requirement is dB/B < 4 10^-4 for |z| < 50 cm. This is about a factor of 10 less than the current DID design at |z|=50cm. “

3. Standard DID
DID field
Standard DID consist of two halves, powered asymmetrically
Let’s try to combine two DID coils, wound on the same radius R, but shifted longitudinally, and adjust current to reduce the field in the center.

4. Two models Very simplified Matlab model of straight conductors
slides 5-7
just proof of principle, can skip and go to:
Realistic DID design and field calculation
slides 8-17

5. Approximate model of single DID
Single DID. Current Ic1=1.68 units
Model each half of DID as straight current. Ignore connecting currents. Integrate the field in Matlab.
This is very crude model. But it gives reasonable field shape.

6. Combined DID
Double DID. Currents: Ic1=4.98 units ; Ic2=-2.46 units
Shorten the first DID and add one more closer to center Adjust currents to minimize the field in |z| < 0.25R
Increase currents (~3 times) to have the same max field

7. Compare single and combined DID
With combined DID, the field within z=|0.25R| reduced 30 times
If R=2m, then within |z|<0.5m the DID field reduced more than what Dan suggested
Given the fact that smaller crossing angle is now considered (~14mrad), the margin is even bigger

8. Realistic design of DID and its field calculation
Brett earlier designed DID coil for LDC detector ( “long”, July 13)
it has radius R=3.5m and 3.8m long
yesterday designed shortened DID coil (“short”, Sep 26)
same radius R=3.5m and length of winding 1.5m
and today designed another long coil (“long” Sep 27)
same R=3.5m and winding length 3m
In field calculation the effect of detector iron is neglected (we checked earlier that this is reasonable approximation, see Appendix)
Will combine “short” DID with either of “long” and adjust currents to flatten the field in the center

9. Short DID (Sep 26)

10. Long DID (Sep 27)

11. Field due to half of DID
To obtain the full field of DID, effect of one half need to be added with effect of another half, taken with negative z and different sign

12. DID field for long (Jul 13) and short coils
Let’s now adjust currents of these two DID to flatten the field in the central region

13. Combined DID (Long Jul 13 + short)
To flatten the field, current of the short DID should be * current of the long DID
For the combined DID to have the same max field, both currents increased 1.8 times

14. Field in the center (Long Jul 13 + short)
Reduction of the field in central region (|z| < 0.5m) is about 65 times with respect to the long DID

15. DID field for long (Sep 27) and short coils
Let’s again adjust currents of these two DID to flatten the field in the central region

16. Combined DID (Long Sep 27 + short)
To flatten the field, current of the short DID should be * current of the long DID
For the combined DID to have the same max field, both currents increased 2.5 times

17. Field in the center (Long Sep 27 + short)
Reduction of the field in central region (|z| < 0.5m) is about 65 times with respect to the long DID (same as in previous case)

18. Conclusion
One can modify DID to flatten the field in the central area to ease TPC calibration
Field in |z|<0.5m can be reduced about 65 times with respect to earlier DID design

19. Appendix: effect of detector iron
Full 3d simulations of DID for SiD case have shown that air model of DID give realistic field shape
The DID field integral is actually ~20% higher with iron and solenoid ON (iron saturation is important)
When solenoid is off, there is ~20% decrease of DID strength, since some flux is sucked into the iron

20. Appendix: Effect of iron

21. Appendix: Effect of iron