A Monte Carlo technique has been used to simulate ionization in a magnetron-like model. Spatial distribution of ionization as well as electron loss under non-uniform magnetic fields of various strengths has been investigated. It is found that ionization increases with the magnetic field over a wide range ( approximately 0.15 T), but due to electron loss via cathode absorption it decreases at strong fields. With increasing field strength, ionization is found close to the cathode, concentrated at the place where the magnetic field is parallel to the cathode surface, and dominant at the E*B drift direction. It is also found that electron loss is decreased by the confinement given by the non-uniform magnetic field component parallel to the electric field, while, increased by the E*B drift in the model and increased by the cathode absorption when the magnetic field is made stronger. Analyses of the results are given; the results can be applied to magnetron discharges.

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Monte Carlo simulations have been used to study the influence of the magnetic field on ion impact at the cathode surface of a sputtering magnetron discharge. The ion parameters (energy, incident angle at the cathode and transit time) have been investigated under four magnetic field strengths and two pressures (1 and 10 Pa). It has been confirmed that the magnetic field has little influence on ion motion. Also, it was found that the magnetic field's influences on ion parameters are given through its influence on electron motion, namely on the ionization site, which is most important in determining the ion energy and transit time. It is proposed that, taking into consideration both the ion energy and the transit time, the appropriate ionization site is the edge of the cathode fall region.

The photon-number distribution of lasers generated via pump-noise suppression is derived in the photon-number representation. The derivation shows that the negative probability emerging in the calculation of the photon-number distribution in the photon-number representation is not caused by the representation itself but by the truncation of the master equation. Here without truncating the master equation we derive the characteristic function and the distribution function of the photon-number distribution of the laser system with regular pump and with spontaneous atomic decays being eliminated. It is convenient to use the characteristic function to calculate any order of the moment of the photon-number distribution. Such a method can be used to some more general cases, in which the laser system has imperfectly regular pump and the spontaneous atomic decays are also considered.