The compressed geomagnetic field as a function of dipole tilt

The currents on the precisely calculated magnetosphere surface previously reported have been integrated with the same accuracy as used in the surface calculation to give the magnetic field at 688 points within the magnetosphere for each of eight surfaces for the tilt of the Earth's dipole in steps of 5° between 0° and 35°. The magnetic fields have then been used to fit the coefficients of a 35 term spherical harmonic expansion of the scalar magnetic potential representing the field by the method of least squares fit. The coefficients for each of the eight surfaces were then represented as a power series in dipole tilt angle, λ so that the complete field can be given very conveniently for any λ. For λ = 0, the first two coefficients g₁₀ and g₂₁ are the dominant terms and the azimuthally dependent term g₂₁ is 30 per cent less than that calculated by Mead and Midgley from older less accurate surface and field calculations.