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Tamao 1986
Tamao, T. (1986). Direct contribution of oblique field-aligned currents to ground magnetic. Journal of Geophysical Research 91: doi: 10.1029/JA091iA01p00183. issn: 0148-0227.

An attempt has been made to evaluate the direct contribution of the horizontal component of oblique field-aligned currents (FAC's) to the surface magnetic field variations in the auroral region associated with a localized electric potential distribution on the horizontal plane, in comparisn with that of the ionospheric eddy current. A relative importance of this direct contribution of oblique FAC's to that from the ionospheric eddy current is proportional to a product of two ratios, the Pedersen to Hall conductivities and the horizontal to vertical components of the local dipole magnetic field intensity. In addition, the shorter the horizontal scale length in the east-west direction compared with an isotropic horizontal structure at 60¿ geomagnetic latitude the direct effect of oblique FAC's to the ground magnetic field attains about 80% of the magnetic contribution of the associated ionospheric Hall current at the earth's surface. It is also shown that only the vertical component of the oblique FAC's connects with the irrotational part of ionospheric currents and that the effective conductance in the magnetosphere for three-dimensional current systems is reduced to a smaller value than that for the case of vertical field lines.

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Journal of Geophysical Research
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