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By conserving momentum during the mixing of fast solar wind flow and slow\udplanetary ion flow in an inelastic way, mass loading converts kinetic energy\udto other forms – e.g. first to electrical energy through charge separation and\udthen to thermal energy (randomness) through gyromotion of the newly born cold\udions for the comet and Mars cases. Here, we consider the Earth's exterior\udcusp and plasma mantle, where the ionospheric origin escaping ions with\udfinite temperatures are loaded into the decelerated solar wind flow. Due to\uddirect connectivity to the ionosphere through the geomagnetic field, a large\udpart of this electrical energy is consumed to maintain field-aligned currents\ud(FACs) toward the ionosphere, in a similar manner as the solar wind-driven\udionospheric convection in the open geomagnetic field region. We show that the\udenergy extraction rate by the mass loading of escaping ions (ΔK) is\udsufficient to explain the cusp FACs, and that ΔK depends only on the\udsolar wind velocity accessing the mass-loading region (usw) and the\udtotal mass flux of the escaping ions into this region (mloadFload),\udas ΔK ∼ −mloadFloadu2sw∕4. The expected distribution\udof the separated charges by this process also predicts the observed flowing\uddirections of the cusp FACs for different interplanetary magnetic field (IMF)\udorientations if we include the deflection of the solar wind flow directions\udin the exterior cusp. Using empirical relations of u0 ∝ Kp + 1.2 and Fload ∝ exp(0.45Kp) for\udKp = 1–7, where u0 is the solar wind velocity upstream of the bow\udshock, ΔK becomes a simple function of Kp as\udlog10(ΔK) = 0.2 ⋅ Kp + 2 ⋅ log10(Kp + 1.2) + constant. The major contribution of\udthis nearly linear increase is the Fload term, i.e. positive feedback\udbetween the increase of ion escaping rate Fload through the increased\udenergy consumption in the ionosphere for high Kp, and subsequent\udextraction of more kinetic energy ΔK from the solar wind to the\udcurrent system by the increased Fload. Since Fload significantly\udincreases for increased flux of extreme ultraviolet (EUV) radiation, high EUV\udflux may significantly enhance this positive feedback. Therefore, the ion\udescape rate and the energy extraction by mass loading during ancient Earth,\udwhen the Sun is believed to have emitted much higher EUV flux than at\udpresent, could have been even higher than the currently available highest\udvalues based on Kp = 9. This raises a possibility that the ion escape has\udsubstantially contributed to the evolution of the Earth's atmosphere

Energy conversion through mass loading of escaping ionospheric ions for different Kp values