We propose and investigate a new method for the synthesis of carbon nanostructures by electric arc discharge, which consists of a sharp cathode and a rotating anode specially designed to create a discontinuous and periodic discharge over block-shaped compacted powders of catalytic mixture. With this design it is possible to control the pulse time width and frequency of discharge by variation of the size of the catalytic blocks and of the anode angular speed. This arrangement imposes important changes to conventional growth conditions of carbon nanostructures which are of central relevance in nucleation and growth models, such as the stability of the plasma jet plume, and gradients in temperature and in carbon concentration, among others. To illustrate the type of structures that can be obtained with this method we present some results under the following conditions: catalytic mixture of C (graphite), Ni, Co, Fe and S powders in 95/0.5/2.8/1.4/0.3 % molar fraction concentrations, respectively, 200 torr hydrogen atmosphere, 360 rpm anode angular velocity, 13.8 ms discharge pulse time width and 24 Hz pulse repetition rate. Under these conditions we are able to synthesize double wall carbon nanotubes. Other carbon nanostructures obtained under diverse preparation conditions are described. The synthesized structures are analyzed with scanning electron microscopy, transmission electron microscopy as well as with Raman spectroscopy.