NOVELTY - The reactor (410) comprises a first reaction chamber, a second reaction chamber in communication with the first reaction chamber through a discharge channel (405), a third reaction chamber, a processing unit, a separator for separating the nanoparticles with the carbon nanotubes from gaseous hydrocarbons, a unit for supplying additional gaseous hydrocarbons into the second and third reaction chambers, and a unit for supplying gaseous hydrocarbons, catalyst nanoparticles and carbon nanotubes from the one reaction chamber into a next reaction chamber.    USE - The reactor is useful for producing carbon nanotubes such as single-walled carbon nanotubes and multi-walled carbon nanotubes, which are useful in the field of electronics, optics and material science and in construction methods.    ADVANTAGE - The reactor is capable of efficiently and economically producing the carbon nanotubes with excellent strength, unique electrical properties, high efficiency and quality, uniform dimensionality, and good mechanical flexibility.    DETAILED DESCRIPTION - The reactor (410) comprises a first reaction chamber, a second reaction chamber in communication with the first reaction chamber through a discharge channel (405), a third reaction chamber, a processing unit, a separator for separating the nanoparticles with the carbon nanotubes from gaseous hydrocarbons, a unit for supplying additional gaseous hydrocarbons into the second and third reaction chambers, and a unit for supplying gaseous hydrocarbons, catalyst nanoparticles and carbon nanotubes from the one reaction chamber into a next reaction chamber. The reaction chambers include electrodes. One of the electrodes is partially melted so as to form a reservoir of liquid phase catalyst material. A solid portion of the electrodes serves as a boundary of the reservoir. The reservoir is evaporated by an electrical arc discharge between the two electrodes such that catalyst vapors generated from the melted electrode condense to form catalyst nanoparticles. The reaction chamber forms carbon nanotubes on surfaces of the catalyst nanoparticles. The reaction chamber comprises: an inlet port (418) for admitting gaseous hydrocarbons to the reaction chamber, where the hydrocarbons are decomposed and interact with the catalyst nanoparticles to form the carbon nanotubes; and an outlet port for outputting the catalyst nanoparticles. The processing unit comprises a processing input port for accepting the catalyst nanoparticles. The electrodes are formed of a catalyst material. The electrode in the first reaction chamber is maintained partly in a solid phase and partly in a liquid phase. The discharge channel maintains an electric discharge arc between the first and second chambers. The catalyst nanoparticles, the gaseous hydrocarbons and products of gaseous hydrocarbon breakdown are supplied from the first reaction chamber into the second reaction chamber and from the second reaction chamber into the third reaction chamber. The third reaction chamber is maintained a temperature of 500-1200 degrees C. The partially melted electrode comprises metal. The solid electrode comprises graphite, a refractory metal or a refractory metal alloy. The material of the electrodes consists of a Group 8 transition metal, a Group 6B transition metal, a Group 5B transition metal, and a mixture of two, three or four transition metal elements. The electrical arc discharge is formed using plasma arc torch, and passes through the discharge channel. A plasma-forming gas is injected into the discharge channel in a form of a vortex stream.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a system for carbon nanotube synthesis.    Discharge channel (405)    Reactor (410)    Reaction chambers (412, 414)    Inlet port (418)    Vortex chamber. (419)