Analytical modeling, computational modeling and testing of a square Helmholtz coil setup to determine how sensitive SuperCDMS SQUID arrays are to ambient magnetic fields

This project was used for my undergraduate thesis at the University of Colorado Denver

Summary

The effective area of a SQUID is the ratio of the magnetic field to the magnetic flux coupling into the SQUID loop in an area in and around the SQUID loop. The effective area project attempts to examine the couplings created by ambient magnetic field at all of the axes around the SQUID, the field perpendicular to the sensing area and both axes parallel to the sensing area. Our research goal is to determine how sensitive SuperCDMS SQUID arrays are to ambient magnetic fields, to obtain enough information to influence the design of future SQUIDs and to characterize SQUIDs in response to external magnetic fields.

Square Helmholtz Coil

We will be using a Helmholtz coil to generate a region of uniform magnetic field. We will place a SQUID chip in this uniform region to examine the effective area of the SQUID. In order to accomplish this result we have made many models in COMSOL to evaluate these coils. In COMSOL you can set the current direction of the coils and create a magnetic field. This experiment will use square versions of a Helmholtz coil instead of circular coils. The purpose of a square coil, as opposed to a more traditional circular coil, will be to easily fit the coil inside the circular probe. The square geometry will be imperative when designing the coils so that they can attach to one another in a multi-axes arrangement. Another motivator of using a square coil is that the geometry of the SQUID array is also square and so the uniform area will match the geometry of the SQUID array.

COMSOL model of a square Helmholtz coil showing current direction.

COMSOL model of the magnetic field of a square Helmholtz coil inside a mu-metal shield.

Magnetic Field Produced by Coil

This figure shows the magnetic field produced by the square Helmholtz coils inside a mu metal shield. The mu metal shield has a very high magnetic permeability and eliminates almost all ambient magnetic fields from outside the can. This has the consequence that any fields produced inside the can will remain inside the can. These ambient magnetic fields then have the potential of coupling to the SQUID which is placed inside the coils. These specific SQUIDs are manufactured to have a gradiometric design to reduce the couplings perpendicular to the SQUID sensing area but some preliminary results in our lab demonstrate couplings coming from both axes parallel to the sensing area.

Coil Placed in Earth's Field

The mu-metal shield is also placed in the Earth’s magnetic field. This figure shows how these field lines are eliminated from entering the inside of the shield due to the high magnetic permeability of the mu-metal shield. This figure also shows the magnetic field lines created from the coil itself where the magnetic field lines produced by the coil loop back around on the shield and go through the center of the coils to create the uniform region in the center of the square Helmholtz coil.

COMSOL model of Helmholtz coil setup with shield in the Earth’s magnetic field.

Magnetic Field Interaction with Shield

This contour plot shows the interaction of the shield with the magnetic field strength produced by the square Helmholtz coil. As shown the field is concentrated at the center of the coils and decays very quickly near the outside edge of the coils. When analyzing the field outside the coils the field approaches 0. This is an important examination because we now know that the magnetic field lines will not have as much effect on the shield as we preliminarily assumed they would. Because the field lines do not loop back around to affect the uniformity produced by the square Helmholtz coils we can make the coils much larger and push their physical boundaries to the edge of the shield. This gives us more area to work with inside the probe when we build the real size setup.

COMSOL model of square Helmholtz coil interactions with shield.

Large Scale Prototype

A large scale prototype of the square Helmholtz coil was developed as a way to compare the data we receive from our COMSOL model. There is no analytical model that includes the interaction of the shield with a square helmholtz coil so we need to rely on the comparison of these two models. This large scale prototype is a four times scaled up version so that we could accurately probe the coil. If the coil were the real size then the magnetometer could only make a few measurements in the uniform region. This is obviously not enough points for us to analyze so we made the coil bigger to take hundreds of measurements. As it turned out the models compare very well to each other and are only off by a 3% scale factor.

Translation Stage. Large scale prototype with shield.

Translation Stage. Large scale prototype without shield (for better view of square coil).

Real Size Setup

Once both models were analyzed and compared to each other we began to design the real size setup. The real size setup is incredibly small to fit inside our probe, which will be placed in liquid helium. These probes need to fit all of the wires to the SQUID and coils along with their connections. We determined that a third set of coils would not fit inside the largest set of coils. The figure above is of two coils that will surround the SQUID chip. We decided to design a rotation mechanism so that when we are done examining two axes, we can take the probe out, quickly rotate the SQUID chip and cool back down to analyze the third axis. These parts are currently in their technical and preliminary design phase.

Fusion 360 model of both square Helmholtz coils showing how the smaller one will be inserted into the larger one.

Current conceptual model of probe in Fusion 360

If you would like to dive deeper into this project please look at my thesis and defense in the top navigation bar in my website. If you would like any further information or would like to talk about the project in general please feel free to reach out.

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