Magnetic Force Theory
The Magnetic Force feature adds a magnetic force Fm to the total force on the particles,
where B (SI unit: T) is the magnetic flux density. When the magnetic flux density is computed in the frequency domain it is complex-valued. The field must be cast into a real value which depends on the angular frequency and the simulation time:
where is the complex-valued electric field, ω is the angular frequency, φ0 is the initial phase angle, and t is time.
Computing Earth’s Magnetic Field
The Magnetic Force includes a model of Earth’s magnetic field. The data used is the International Geomagnetic Reference Field (IGRF; Ref. 2) and is based on the Geomag 7.0 software. The IGRF data consists of sets of Gauss coefficients that define a spherical harmonic expansion for the magnetic scalar potential:
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 r (SI unit: m) is the radial distance from Earth’s center,
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 L (dimensionless) is the maximum degree of the expansion,
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 Φ (SI unit: rad) is the East longitude,
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 Θ (SI unit: rad) is the co-latitude (polar angle),
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 Re = 6371.2 km is Earth’s radius,
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and (SI unit: T) are Gauss coefficients, and
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are the Schmidt normalized associated Legendre functions of degree l and order m.