Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
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