The stated conversion gives Θc≃0.10 eV. Hence the ideal longitudinal bath temperature isThis estimate equates the cooled proton thermal-energy scale with the effective electron bath scale, not the two particles' random speeds. The proton root-mean-square speed for a one-component convention mpσv2=kBT would be about 2.2ms−1.
Θ∥≃4(5.0×104eV)(0.10eV)2=5.0×10−8eV,Tp,eq∼5.8×10−4K.
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