Improving a magnetic shield: what works and what does not 26 March 2013 Kiril Marinov 1

Cylindrical shell in an external homogeneous field A ferromagnetic cylinder in an external homogeneous field B 0 =0.1T B in max <<<B 0 Is there anything else other than using a thicker shielding box?

Suggested ideas Adding a second layer of mu-metal besides the steel? Adding steel only where the flux density is higher? Using co-axial cylinders with gaps (zero gauss chambers)? Keep size within reason.

Mu-metal Two BH curves obtained from different sources, similar but not identical. Data has been read from the plot and then smoothed to produce the red curve in the LHS plot.

Mu-metal vs. 1010: permeability

7 cm steel and 1.8 cm mu-metal vs 7 cm of steel 7 cm steel and 1.8 cm of mu-metal 7 cm steel only Improvement is visible but is the mu-metal layer really working?

7 cm steel and 1.8 cm mu-metal vs 8.8 cm of steel 7 cm steel and 1.8 cm of mu-metal 8.8 cm steel All-steel, 8.8 cm-thick shield preforms better

Permeability distribution 7 cm steel and 1.8 cm of mu-metal The mu-metal layer is fully saturated. Bringing mu-metal in contact with or close to strongly magnetized steel results in mu-metal saturation. The permeability of the mu-metal layer is lower than that of the steel layer. This results is poor shielding Introducing gaps between the two materials does not eliminate the problem.

Boundary conditions If μ 2 /μ 1 >100 and B 1 ~1.5T is B 2 >150T? An interface between two magnetic materials: H || must be continuous across the interface The mu-metal has to saturate. This results in μ 2 <μ 1 and the boundary conditions can now be satisfied. μ 1, B 1|| μ 2, B 2|| Note, that the steel can be far from saturation. Mu-metal and steel should only be combined with care. 0.7T mumeta l steel Shielding factor is low

Adding steel where the flux density is higher 5 cm-thick can and a second, 5cm layer, 1cm away, covering half of the surface area of the can. Mirror symmetry w.r.t. both X and Y axes, 5 cm-thick can acting alone 9-fold reduction of B max ; 25% lighter than a 10 cm can. If we get the shield thickness wrong we can still fix this by adding steel at the appropriate places. No need for a good contact between the two layers.

Adding steel where the flux density is higher 5 cm-thick can and a second, 5cm layer, 1cm away, covering half of the surface area of the can. Mirror symmetry w.r.t. both X and Y axes, 10 cm-thick can acting alone If we get the shield thickness wrong we can still fix this by adding steel at the appropriate place(s). No need to worry about good contact.

Co-axial cylinders with air gaps 5 cm-thick can, 1 cm air gap, 4cm steel Solid 9 cm-thick can acting alone The 1 cm gap results in lowering the field in the shielded region (by 13%) without increasing the weight of the shield.

Co-axial cylinders with air gaps 5 cm-thick can, 2 cm air gap, 4cm steel Solid 9 cm-thick can acting alone The 2 cm gap results in lowering the field in the shielded region (by 26 %) without increasing the weight. The gap results in the outer layer carrying higher flux density thus allowing higher permeability and lower flux density in the inner layer.

Summary Three different strategies for improving shield performance have been considered: Adding a second layer of mu-metal to the steel? Adding steel only where the flux density is higher? Using co-axial cylinders with gaps (quasi-zero-gauss chambers)? Does not work at flux density levels typical for the MICE shielding problem. Works. Allows corrections to be made at a later stage Works. Could be implemented, if needed. If you can recommend a good Physics article on zero-gauss chambers please, me. Thanks.