Multiple steady-state solutions existing in the theory of dc glow discharges are computed for the first time. The simulations are performed in 2D in the framework of the simplest self-consistent model, which accounts for a single ion species and employs the drift-diffusion approximation. Solutions describing up to nine different modes were found in the case where losses of the ions and the electrons due to diffusion to the wall were neglected. One mode is 1D, exists at all values of the discharge current, and represents in essence the well-known solution of von Engel and Steenbeck. The other eight modes are axially symmetric, exist in limited ranges of the discharge current, and are associated with different patterns of current spots on the cathode. The mode with a spot at the centre of the cathode exhibits a well pronounced effect of normal current density. Account of diffusion losses affects the solutions dramatically: the number of solutions is reduced, a mode appears that exists at all discharge currents and comprises the Townsend, subnormal, normal and abnormal discharges. The solutions that exist in limited current ranges describe patterns, and these patterns seem to represent axially symmetric analogues of the 3D patterns observed in dc glow microdischarges in xenon.

Spectra of perturbations of steady-state current transfer to cathodes of high-pressure argon arcs are computed in the framework of the model of nonlinear surface heating. The following pattern of stability has been established for a current-controlled arc on a cylindrical cathode on the basis of the numerical results and trends derived previously by means of an approximate analytical treatment: the diffuse mode is stable beyond the first bifurcation point and unstable at lower currents; steady-state modes with more than one spot are unstable; the axially symmetric mode with a spot at the centre of the front surface of the cathode is unstable; the 3D steady-state mode with a spot at the edge is unstable between the bifurcation point and the turning point and stable beyond the turning point; the transition between the latter mode and the diffuse mode is non-stationary and accompanied by hysteresis. Theoretical results are in agreement with trends observed in the experiment.

Bifurcations and/or their consequences are frequently encountered in numerical modelling of current transfer to cathodes of gas discharges, also in apparently simple situations, and a failure to recognize and properly analyse a bifurcation may create difficulties in the modelling and hinder the understanding of numerical results and the underlying physics. This work is concerned with analysis of bifurcations that have been encountered in the modelling of steady-state current transfer to cathodes of glow and arc discharges. All basic types of steady-state bifurcations (fold, transcritical, pitchfork) have been identified and analysed. The analysis provides explanations to many results obtained in numerical modelling. In particular, it is shown that dramatic changes in patterns of current transfer to cathodes of both glow and arc discharges, described by numerical modelling, occur through perturbed transcritical bifurcations of first-and second-order contact. The analysis elucidates the reason why the mode of glow discharge associated with the falling section of the current-voltage characteristic in the solution of von Engel and Steenbeck seems not to appear in 2D numerical modelling and the subnormal and normal modes appear instead. A similar effect has been identified in numerical modelling of arc cathodes and explained.

Abstract-Three-dimensional simulations of self-organization in dc glow microdischarges are reported. The results describe a mode with a normal spot and modes with patterns of multiple spots, qualitatively similar to those observed in experiments with microdischarges in xenon.Index Terms-Glow discharge, self-organization, normal discharge. IMPORTANT advances have been achieved in selfconsistent modeling of self-organization in gas discharges, such as patterns in DBDs and the normal current density effect in dc glow discharges (e.g., [1] and [2], respectively). The initial steps toward a self-consistent modeling of self-organization in dc glow discharges have been taken in [3] and [4]. It was shown that the simplest self-consistent model of glow discharges admits multiple solutions which exist at the same value of the discharge current. Those of the solutions that are 2-D (axially symmetric) were calculated and found to describe either the normal mode or patterns which appear to be 2-D analogs of patterns observed in microdischarges in Xe [5].In this paper, simulations of 3-D patterns in dc glow microdischarges are reported for the first time. The model is the same as in [4]; it accounts for only one ion species (molecular ions) and makes use of the local approximation for electron kinetics and transport. Note that results [6] indicate that an account of detailed plasma chemistry and the nonlocality of electron energy does not alter results qualitatively. A steady-state solver of Comsol Multiphysics was employed. (The use of a nonstationary solver would not allow finding and understanding the whole pattern of existing steady-state solutions since such solvers do not compute sections of solutions which are unstable with the power supply circuit being considered.) Information on where to look for multiple solutions and what they are like was obtained by means of bifurcation analysis, similarly to how it was done in [4].The results reported in this paper refer to a cylindrical discharge vessel with parallel electrodes and a reflecting lateral wall. The pattern of multiple solutions for such vessel is the

The Mediterranean fruit fly (medfly), Ceratitis capitata (Wied.), like many other polyphagous tephritids (Diptera: Tephritidae), preforms a lek as mating system. The sterile insect technique (SIT) requires released males to survive in the field, and to compete with wild males in attracting, courting and mating with wild females. The effects of the juvenile hormone analogue, methoprene, and the incorporation of hydrolyzed yeast protein into the adult diet, on survival, sexual maturation and sexual performance of male C. capitata were evaluated for the four possible combinations of methoprene‐treated or untreated, and protein‐fed or deprived flies. The incorporation of protein had a positive impact on laboratory survival and accelerates the sexual maturation of mass‐reared males. In addition, in the laboratory, male sexual performance was significantly higher in treatments with methoprene. However, field cage tests with mature and protein‐fed wild males and females failed to show any effects of either factor on male sexual performance. The increased survival and the earlier sexual maturation of sterile males due to the addition of protein to the adult diet can positively influence the efficacy of SIT application against C. capitata.