mfs

mfs is a library for calculating and visualising magnetic fields for neutral atom trapping. (C) Simon Ball 2018-2020

Originally written to assist in designing the Ytterbium quantum optics experiment at the University of Southern Denmark (SDU) in 2018. Cleaned up and published in 2020 for use by a project at the Norwegian University of Science and Technology (NTNU)

Install directly from github with pip:

pip install git+https://github.com/simon-ball/nqo-mfs

Usage

Sources

mfs implements four types of magnetic field source:

• mfs.sources.PermanentMagnet : A cuboid permanent magnet.

• mfs.sources.CircularCoil : A single circular loop of wire carrying a current

• mfs.sources.RectangularCoil : A single rectangualr loop of wire carrying a current

• mfs.sources.CoilPair : A pair of coils, each containing 1 or more individual coils, either rectangular or circular

Geometry

Each magnetic field source is generated in their own frame of reference (referred to by dashes throughout), controlled by two angles, theta and phi. All angles are handled in degrees.

• theta : azimuthal angle If phi is 0°, then theta corresponds to a rotation of the X'-Y' plane around the Z = Z' axis

• phi : polar angle If theta is 0°, then phi corresponds to a rotation of the Y'-Z' plane around the X = X' axis

Rectangular magnet field sources are always square to the X'-Y'-Z' axes

Rotation calculations can be adjusted to cope with a rotation around the Y = Y' axis if needed, but are not currently implemented

Rotations are implemented around the (0,0,0) origin. Rotations around arbitrary origins are not currently supported.

Magnetic axis

mfs uses the convention that the magnetisation points along the +ve Y' axis:

• permanent magnets have their magnetisation pointing along the Y' axis

• Circular and rectangular magnets are in the X'-Z' plane, wrapped around the Y' axis

• A negative value for strength reverses the direction

Units

SI units are used throught - distances are in metres, current is in Teslas, current in Amps, and magnetisation in Tesla/metres

Angles are always in degrees.

Initalising magnets

Each geometry specific magnet class is based on a generic template:

magnet = mfs.sources.MagnetClass(strength, rDash, dimsDash, theta, phi)

where:

• strength : float Magnetisation or current
• rDash Origin (centre) of the magnet in the frame of the magnet, i.e. rotated by theta and phi with respect to the laboratory frame
• dimsDash Dictionary of magnet specific parameters
• theta, phi : float
  Angle of the magnet frame of reference with respect to the laboratory frame of reference

PermanentMagnet

• strength is given in Tesla/metre

• dimsDash requires the following keywords:

  • "axDash" : float Full length of the magnet in metres in the X' direction
  • "ayDash" : float Full length of the magnet in metres in the Y' direction
  • "azDash" : float Full length of the magnet in metres in the Z' direction

CircularCoil

• strength is given in Amps.

• dimsDash requires the following keywords:

  • radius : float Radius of the coil, from origin to centre of conductor

RectangularCoil

• strength is given in Amps.

• dimsDash requires the following keywords:

  • "axDash" : float Full length of the coil in metres in the X' direction, from conductor-centre to conductor-centre
  • "azDash" : float Full length of the coil in metres in the z' direction, from conductor-centre to conductor-centre

CoilPair

• strength is given in Amps. Positive current implies current flowing such that the magnetisation is in the +ve Y' direction, away from the origin. Provide a negative current to reverse the direction

• dimsDash requires the following keywords in addition to the geometry specific keywords given above:

  • "shape" : str All coils are circular or rectangular. Accepted values are circ, rect and some variations Relevant circular or rectangular parameters given above are required in addition to keywords below
  • "configuration" : strength Helmholtz or anti-Helmholtz. Accepted values are hh, ahh, and some variations. Assuming the ahh and that strength is positive, then the magnetisation will flow out from the coil origin along the Y' axis, and return in the X'-Z' plane.
  • "full spacing" : float Distance in metres along the Y' axis between the origins of the top and bottom coils. If spatially distributed is True, then this is the closest distance from conductor-centre to conductor-centre.
  • "axial layers" : int Number of layers of windings along the axial direction, in each coil
  • "radial layers" : int Number of layers of windings along the radial direction, in each coil
  • "spatially distributed" : bool Flag to set the detail of the simulation. If True, then each coil of wire is simulated independently, based on the specified axial spacing and radial spacing. In this case, the additional axial layers exist further away from the origin of the CoilPair. Can result in dramatically slower calculations. NB: coils are modelled as independent rings, each carrying the same current, not as a spiral. If False, then the coil is modelled as a single loop of wire with strength increased by a factor of axial_layers * radial_layers. Significantly quicker to calculate, but less accurate.
  • "axial spacing" : float if spatially distributed is true, use this value of offset each additional coil in the axial direction
  • "radial spacing" : float if spatially distributed is true, use this value of offset each additional coil in the radial direction

References

Permanent magnets

https://link.springer.com/content/pdf/10.1007%2FBF01573988.pdf This function implements the approach taken by Metzger in Archiv fur Elektrotechnik 59 (1977) 229-242.

Circular coils

https://doi.org/10.1103/PhysRevA.35.1535 Bergeman, Magnetostatic trapping fields for neutral atoms, 1987, PRA 35 1535

Rectangular coils

https://dx.doi.org/10.6028%2Fjres.105.045 Misiaken, Equations for the Magnetic Field produced by One or More Rectangualr Loops of Wire in the Same Plane J Res Natl Inst Stand Technol. 2000 Jul-Aug; 105(4): 557–564