Apparatus for plasma synthesis of carbon nanotubes, the apparatus comprising: a plasma nozzle coupled to a reaction tube or chamber; means for supplying a process gas comprising a carbon-containing species to the plasma nozzle; means for supplying radio frequency radiation to the process gas within the plasma nozzle in use, so as to sustain a plasma within the plasma nozzle in use, and thereby cause cracking of the carbon-containing species; and means for providing a catalyst; wherein the plasma nozzle is arranged such that, in use, an afterglow of the plasma extends into the reaction tube/chamber, the cracked carbon-containing species also passes into the reaction tube/chamber, and the cracked carbon-containing species recombines within the afterglow, so as to form carbon nanotubes in the presence of the catalyst; and wherein the reaction tube/chamber incorporates means for cooling the afterglow on exiting the plasma nozzle; characterised in that the plasma nozzle is shaped and configured so as to cause, in use, three concentric vortices to be formed in the process gas within the plasma nozzle, said three concentric vortices being subjected to said radio frequency radiation; wherein the plasma nozzle comprises: one or more inlets for receiving a stream of the process gas, that forms a first vortex in use; an open end in communication with the reaction tube/chamber; and a vortex-reflecting end opposite the open end; wherein the plasma nozzle is internally tapered towards the open end; such that, in use, a second vortex is created by the vortex-reflecting end, and a third vortex is produced by reflection of the second vortex from the vortex-reflecting end, and such that, in use, the carbon-containing species is cracked in the plasma nozzle. a plasma nozzle coupled to a reaction tube or chamber; means for supplying a process gas comprising a carbon-containing species to the plasma nozzle; means for supplying radio frequency radiation to the process gas within the plasma nozzle in use, so as to sustain a plasma within the plasma nozzle in use, and thereby cause cracking of the carbon-containing species; and means for providing a catalyst; wherein the plasma nozzle is arranged such that, in use, an afterglow of the plasma extends into the reaction tube/chamber, the cracked carbon-containing species also passes into the reaction tube/chamber, and the cracked carbon-containing species recombines within the afterglow, so as to form carbon nanotubes in the presence of the catalyst; and wherein the reaction tube/chamber incorporates means for cooling the afterglow on exiting the plasma nozzle; characterised in that the plasma nozzle is shaped and configured so as to cause, in use, three concentric vortices to be formed in the process gas within the plasma nozzle, said three concentric vortices being subjected to said radio frequency radiation; wherein the plasma nozzle comprises: one or more inlets for receiving a stream of the process gas, that forms a first vortex in use; an open end in communication with the reaction tube/chamber; and a vortex-reflecting end opposite the open end; wherein the plasma nozzle is internally tapered towards the open end; such that, in use, a second vortex is created by the vortex-reflecting end, and a third vortex is produced by reflection of the second vortex from the vortex-reflecting end, and such that, in use, the carbon-containing species is cracked in the plasma nozzle. one or more inlets for receiving a stream of the process gas, that forms a first vortex in use; an open end in communication with the reaction tube/chamber; and a vortex-reflecting end opposite the open end; wherein the plasma nozzle is internally tapered towards the open end; such that, in use, a second vortex is created by the vortex-reflecting end, and a third vortex is produced by reflection of the second vortex from the vortex-reflecting end, and such that, in use, the carbon-containing species is cracked in the plasma nozzle.