A Division of union carbide, L-Tec patented the plasma process in 1957 or so, L-Tec later became Linde Corp and then Esab in the 1980's. Thermal Dynamics corp came along in around 1960 with some slightly different technology (dual flow) and then Hypertherm in 1968 with water injection technology. Today, Hypertherm is the biggest producer of plasma cutting equipment, and holds over 100 patents on the process.
That's the condensed version of the history of plasma cutting....there are many more details including patent infringement suits, buildings where all the records were stored that mysteriously burned and records were destroyed, etc. It would probably make a good book for technical geeks!
Jim Colt