sPHENIX discussion of the superconducting solenoid

["Makdisi, Yousef I" <makdisi AT bnl.gov>]

To all,

      Wuzheng's calculations of the forces at 1000 amps. 

Yousef

From: <Meng>, Wuzheng Meng <meng AT bnl.gov>
Date: Friday, November 7, 2014 12:17 PM
To: Yousef Makdisi <makdisi AT bnl.gov>
Cc: Wuzheng Meng <meng AT bnl.gov>
Subject: Forces on the Babar air coils at 1000 A

Yousef, 

At 1000 A operation without the return yoke, the center field of solenoids will be 0.27 Tesla.

I calculated forces from a 2d cylindric symmetry model. The vertical force is essentially zero. The radial summary of force at 1000 Ampere is 1191486.9 Newton (over 360 degree surface area).

The mean radius of 6 coils is Ro = 1.53 m.

The length of the solenoid is 3.51 m. 

These gives the area = 33.74 m**2 = 52297 inch**2.

The force per unit area is then 35323.1 Newton per meter-square. 

1 Newton = 0.2248 lb force.

So that the force per unit area is  5.12 PSI (pound per square inch) at 1000 A, without return yoke.

You may verify this result by using analytical rough estimate method suggested by Martin Wilson "Superconducting Magnets" page 41 --- 

The magnetic force (in 2d), so called "pressure", can be estimated by using the central field Bo ---

Bo**2/(2*mu), where mu is permeability = 4*pi*E-7, which gives (0.27)**2/(2*4*pi*E-7) = 29006 Newton per meter-square. This agree with my result 35323.1 Newton/m**2 to the order of magnitude. 

Force always goes with current**2, in case if you want other current settings.

Please comment.

Wuzheng