The small electric field in the solar wind must be retained if the physics is to be consistent with the relativity principle. The special theory of relativity shows the charge density responsible for this electric field is due to Lorentz contraction of the current source in the moving planet as seen in the solar wind frame. The small electric field in the plasma which is neglected in ideal MHD is necessary for the generation of the boundary current. Ideal MHD fluids do not have this capability since the total magnetic flux is conserved, dϕ /dt = 0 and ε ℳ ℱ is not generated. Chapman and Ferraro (1931) showed that a boundary current will be formed as the solar wind interacting with the planetary magnetic field induces an electromotive force ( ε ℳ ℱ). Consider a solar wind that is approaching a magnetized planet. We demonstrate from observing how a solar or stellar wind interacts with electromagnetic fields of magnetized objects, like planets, that the ideal MHD equation E + V×B = 0 is not adequate to describe the dynamics of space plasmas. Parks, in Multiscale Coupling of Sun-Earth Processes, 2005 Abstract (2015), showing that the nonthermal losses of the planet are insignificant during the planet’s lifetime. (2013), considering negligible magnetic moments, or for a nonmagnetized Venus-like planet in Cohen et al. This result is reproduced as well for the Super-Earths of the Kepler-11 planetary system ( Kislyakova et al., 2014b), where nonthermal losses constitute a few percentages of the thermal losses predicted by Lammer et al. (2013) studied the contribution of nonthermal processes to the total escape of H-rich, no-hydrostatic atmospheres in Earth-like and super-Earth-like planets under high levels of XUV radiation, concluding that nonthermal losses constitutes only a small fraction of the total planetary escape. In the latter scenario, Kislyakova et al. These nonthermal losses may become important in weakly magnetized planetary environments, where the stellar wind penetrates deeper in the planetary atmosphere ( Cohen et al., 2015), or by contrast, in highly irradiated atmospheres, expanded well-beyond the planet’s magnetospheric protection. The magnetic field embedded in the stellar wind plasma may pick-up the resulting ions, consequently resulting in particle losses. Photoionization by incident EUV and Lyα photons, along with collisions with stellar wind electrons and charge-exchange reactions driven by fast stellar wind protons, ionize the neutral particles present at the upper atmosphere of a planet. The well-studied case of Proxima b showed enhanced levels of mass loss, showing a wind 40–80 times larger than seen at the present Earth ( Ribas et al., 2016). (2011) derived the wind properties of V374Peg, a very active M star, showing that its wind produces a ram pressure (Pram = rho∗v∗v) five orders of magnitude higher than the Sun at 1 AU.
Winds of M dwarf stars are difficult to measure. However, this relation is not valid for the most active stars of the sample, including the young (500 Myr) solar-like star π Uma ( Wood et al., 2014) and the 2 M stars of the sample, Proxima Cen, and EV Lac.
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