Mathematical methods for studying the kinetics of formation of carbon clusters in plasma

The paper considers the methods of modeling movement and interaction of charged particles in multicomponent plasma on the basis of the Boltzmann–Maxwell system of equations by the example of electric arc synthesis of carbon nanostructures (CNS). The paper presents the derivation of the final equations for the collision integrals in the proposed model. The authors suggest the algorithm and technology of numerical solution of the model with the use of the technology of parallelization of computations using nVidia CUDA (Compute Unified Device Architecture). The comparative analysis confirming the adequacy of the model to the physical process was performed. The authors investigated the conditions and regions satisfying the spatial and energy terms of probabilistic formation of linear cluster groups C=C–C (C$_3$) that form the basis of CNS. The authors obtained quantitative characteristics of binary collisions of carbon ions in plasma with formation of clusters C$_3$ for different parameters of synthesis. The authors investigated the influence of voltage and current density on the number of interactions and clusters C$_3$ in plasma of the interelectrode space.