Shielding the cryostat: 2D analysis

1. Shielding the cryostat: 2D analysis 12 March 2013 Kiril Marinov

2. Preliminary analysis A ferromagnetic cylinder in an external homogeneous field B0=0.1T Flux through the side of the cylinder Binmax<<<B0 ferromagnetic

3. Preliminary analysis II A ferromagnetic cylinder in an external homogeneous field B0=0.1T Seems crude, but not so bad as a zeroth-order approximation Let’s now assume that A 1cm thick can is useless  Since Bs=2.2T we need Law of the can? Cans of smaller radii need to be thinner to achieve the same shielding effect! Since

4. Preliminary analysis III The “one big can” approach requires the thickest can. The “many small cans” approach would permit a thinner and lighter solution. The value obtained numerically is 1.4T. The equation is, therefore, useful for estimations obtained numerically Continuous across the interface Cans of smaller radii are more efficient: they need to be thinner to achieve the same (or similar) shielding effect.

5. Numerical results

6. Summary The can will have to be at least 7 cm in order to reach Bmin~5 mT somewhere inside the can. Field inside the can is inhomogeneous. Most sensitive components in lower field strength areas? Maximum thickness is only needed where Bw is strong. Can use this to lower the weight by adding steel where it is needed only. Needs further investigation An approximate scaling “law” has been established: cans of smaller radii need to be thinner in order to achieve the same shielding effect. In this aspect using many small cans instead of one big can will allow thinner walls. Maximum thickness is only needed where Bw is strong. Can use this to lower the weight. I will further investigate the effect of gaps and how to minimize it. Gaps should be placed in regions of small field?