A model of a slotted waveguide antenna for microwave plasma enhanced chemical vapor deposition (MPECVD) of carbon nanostructures at low pressure is developed. The performance of two slot applicator for the production of dense plasma in the working gas (argon) at a frequency of 2.45 GHz is investigated by EM field simulator. Results show that dimensions of the symmetrical slots (length l ≤ λg/2, width of d = 6-10 mm) and optimized angle (φ=32° with respect to the waveguide central line) have a strong influence on the impedance matching of the waveguide to the dielectric window and plasma column (1.5 < SWR < 2.5), and on the radiation efficiency. The dielectric plate and plasma column density were taken into account in the model in the optimisation of the dimensions of the slots. The mode structure of standing surface waves in the plasma column is investigated at three values of plasma density and results for the radial (n=1) and azimuthal wave numbers (m=3, 4, 5) are in agreement with experimental results.