Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
Critical ionization velocity produced which when it had expanded so that it was hit by the solar wind gave rise to superthermal electrons." In the laboratory, critical ionization velocity has been recognised for some time, and is seen in the penumbra produced by a dense plasma focus device (or plasma gun). Its existence in cosmic plasmas has not been confirmed. In 1986, Gerhard Haerendel, suggested that critical velocity ionization may stabilize the plasma flow in a cometary coma. In 1992, E. Golbraikh and M. Filippov argued that critical ionization velocity could play a role in coronal mass ejections and solar flares, and in