Formation of an inverted sheath in a one-dimensional bounded plasma system studied by particle-in-cell simulation

Abstract

Formation of an “inverted sheath” is studied by particle-in-cell (PIC) simulation using the code XPDP1 [Verboncoeur et al., J. Comp. Phys. 104, 321–328 (1993)]. Examples of current carrying and floating sheaths are presented. It is shown that the results of the PIC simulation are in excellent agreement with the model developed recently [Gyergyek et al., Phys Plasmas 27, 023520 (2020)]. In this work, it is shown how to normalize the results from the simulations, which are given in SI units, to the dimensionless variables of the model. The procedure can also be reversed. From a given solution of the model, the input parameters of the simulation can be determined. Excellent matching between the results of the model and of the simulations is obtained in both cases. The length of the system is an eigenvalue of the model, while for the simulations, it has to be selected in advance and it is fixed. The appropriate selection of the length of the system is briefly discussed, and so it is the role of the external circuit in the XPDP1 code. Injection of particles into the system is such that monotonically decreasing potential profiles are enforced. A monotonic space charge density profile with surplus of negative charge at the left (collector) electrode and surplus of positive charge at the right (source) electrode must be created. As a consequence, a neutrality point must exist somewhere between the electrodes. The “inverted sheath” is the region between the neutrality point and the collector. By appropriate injection of the particles, the location of the neutrality point can be enforced to any position between the electrodes including the electrodes themselves.