A simple theoretical model describing physics of the plasma torch plume is developed in connection with its applications to the arc-plasma waste-treatment system. The theoretical analysis is carried out by making use of Bernoulli's pressure-balance equation, which provides a stable equilibrium solution of the gas density in the plume ejected from the torch into a high-pressure reactor chamber with 4ε < 1. The pressure depression parameter ε is proportional to the gas temperature and inversely proportional to the square of the chamber pressure. In a low-pressure chamber, characterized by 4ε >1, there is no stable equilibrium solution satisfying Bernoulli's equation. Therefore, it is expected that the observable plasma data may change abruptly as the chamber pressure crosses the borderline defined by 4ε = 1. Indeed, most of the plasma data measured in an experiment change abruptly at the pressure borderline of 4ε = 1. The oxygen torch plume is theoretically analyzed for the arc-plasma waste-treatment system. Due to a very high arc-plasma temperature inside the torch, most of the oxygen molecules are atomized when they exit the torch and enter the reactor chamber. The oxidation process of materials by oxygen atoms can be easily achieved at a reaction rate of a million limes faster than that by oxygen molecules. It is therefore essential to evaluate the oxygen atom concentration in the oxygen plume propagating through the waste-treatment system. A numerical example indicates that a high concentration of oxygen atoms exists even at a considerable distance (i.e., 40 cm) from the torch exit in typical torch operation conditions.