## 1 Introduction  
Thin films of aluminum oxide Al\({}_{2}\)O\({}_{3}\) are an excellent choice when one needs to secure surface hardness and enhance surface protection coupled with good optical transparency. They are widely used in demanding applications [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] in optics, sensors, and spectroscopy. They serve as diffusion-barrier coatings and protective layers in metal-cutting tools and insulating layers in microelectronics. One of the most popular methods for obtaining metal oxide coatings is reactive magnetron sputtering. The process is known to be accompanied by nonlinear hysteresis effects when the content of the reaction gas in the mixture changes [11; 12; 13; 14]. Hysteresisbehavior affects the discharge parameters and properties of the resulting coatings. The most critical influence of this phenomenon is the complication of fixing the working point of the reactive sputtering process in the desirable region (having a decent deposition rate together with good stoichiometry of the growing compound layer), or even the simple inability to do so [15; 16; 17; 18; 19; 20]. The magnitude and impact of this effect vary significantly depending on the power supply mode used and are most severe in direct current (DC) magnetron sputtering (DCMS). In the pulsed power modes, such as high-current impulse magnetron sputtering (HiPIMS), modulated pulsed power magnetron sputtering (MPPMS), and deep oscillation magnetron sputtering (DOMS), these effects might be either mitigated or properly controlled for, improving the deposition rates [21; 22; 23; 24; 25; 26; 27; 28; 29]. The position of the working point and the corresponding properties of aluminum oxide coatings obtained by the reactive magnetron sputtering process are influenced by various parameters such as the cathode voltage, condition of the target surface, constituent ion fluxes, discharge current density, proportion of flow rates of reactive and working gases, power rating, and type of power supply used. The abrupt changes in discharge voltage, current, and deposition rate give a clear indication of the occurrence of target poisoning, i.e., covering it with a compound layer [30; 31; 32; 33; 34]. Target poisoning is determined by the reactive oxygen gas flow rate and its partial pressure. This phenomenon occurs at a specified region of inflation or transition of the parameters such as partial pressure of the reactive gases which is governed by the gettering of the gas by the sputtering system. One of the most popular methods for investigating and controlling the discharge in the reactive mode is optical emission spectroscopy (OES) [18; 35; 36; 37]. The available instruments of deposition process control and fixation of the working point are largely based on the optical measurements. While being a solid proven method for process stabilization, the interpretation of OES results regarding the properties of growing film might be a complicated task. The coating composition and properties are governed by the fluxes of particles incident at the substrate, which can hardly be directly reconstructed from the OES data, especially when chemically active species are present in plasma [38]. For the analysis of the sputtering processes, the particle diagnostics (ion energy and mass spectrometry) are perfectly suitable, which enable measurement of constituent plasma ion fluxes in the magnetron discharge [35; 37; 39; 40; 41; 42; 43; 44; 45; 46]. For oxygen-based reactive processes, the role of negative ions in the overall particle ensemble should also be taken into account and can be thoroughly analyzed by ion mass spectrometry [40; 41; 47; 48; 49; 50]. These ions can impinge the substrate with greater kinetic energies and thereafter can cause damage to the deposited layer. Despite the large number of studies concerning the hysteresis processes in reactive magnetron sputtering, few of them explicitly demonstrate the dependence of particle fluxes of different kinds on the reactive gas flow rate in the metallic-to-compound mode transition.