Using the hydrodynamic model and considering a planar geometry, the modified Bohm’s sheath criterion is investigated in a magnetized, collisional plasma consisting of electron and positive ions with finite temperature. It is assumed that the singly charged positive ions enter into the sheath region obliquely, i.e., their velocity at the sheath edge is not normal to the wall, and the electron densities obey Boltzmann relations. It is shown that there are both upper and lower limit for the Bohm entrance velocity of ions in this case and both of these limits depend on the magnitude and direction of the applied magnetic field. To determine the accuracy of our derived generalized Bohm’s criterion, it reduced to some familiar physical condition. Also, using this generalized Bohm’s criterion, the behavior of the electron and positive ion density distributions are studied in the sheath region.

Taking into account the effect of collisions and positive ion temperatures, the sheath formation criterion is investigated in a weakly magnetized electronegative plasma consisting of electrons, negative and positive ions by using the hydrodynamics equations. It is assumed that the electron and negative ion density distributions are the Boltzmann distribution with two different temperatures. Also, it is assumed that the velocity of positive ions at the sheath edge is not normal to the wall (oblique entrance). Our results show that a sheath region will be formed when the initial velocity of positive ions or the ion Mach number M lies in a specific interval with particular upper and lower limits. Also, it is shown that the presence of the magnetic field affects both of these limits. Moreover, as an practical application, the density distribution of charged particles in the sheath region is studied for an allowable value of M, and it is seen that monotonically reduction of the positive ion density distribution leading to the sheath formation occurs only when M lies between two above mentioned limits.

The effects of ion–neutral collision on the characteristics of a magnetized plasma sheath which consists of two species of positive ions are investigated. It is assumed that the ions have different masses. In contrast to our previous work, the effects of ion–neutral collision frequency are added to the magnetized plasma sheath. Using a three-fluid hydrodynamic model and some dimensionless variables, the dimensionless equations are obtained and solved numerically. By taking into account the ion–neutral collision effects on a magnetized three-component plasma sheath, it is shown that apart from the presence of the second ion species, by increasing the collision frequency of two ions with neutrals, the amplitude of fluctuations of ion species density distributions increases and the position of these fluctuations is shifted towards the plasma sheath edge. Also, by increasing the ion–neutral collision frequency these fluctuations turn off faster than those in a collisionless case. It is shown that in the collisional magnetized plasma sheath, the effects of the presence of the heavier ion species on the lighter ion density turn off much faster in comparison with what happens in a collisionless magnetized plasma sheath. Furthermore, it is found that in a collisionless plasma sheath by increasing the density of the heavier ion species, the normalized electrostatic potential decreases while in a collisional plasma sheath the presence of the heavier ion species does not have any considerable effect on the normalized electrostatic potential. In addition, it is shown that when the distance of each ion species from the plasma sheath boundary becomes larger than five times the electron Debye length (x > 5λDe) the fluctuations of the ion species velocities disappear by increasing the ion–neutral collision frequency. Also, it is found that the electron density distribution decreases by increasing the ion–neutral collision frequency.

The effects of the magnitude and direction of an oblique magnetic field and the effect of the ion densities ratio on a plasma sheath of electrons and two species of positive ions are investigated by using a three-fluid hydrodynamics model. These ions have different masses but the same ionization ratio (Z=1). It is shown that the density distribution and velocity of the lighter and heavier ion species begin to fluctuate under the action of the electrostatic and Lorentz forces when the ratio of electron Debye length to lighter ion species Larmor radius becomes greater than 1 and 3, respectively. Also, it is found that the velocity fluctuations of the lighter ion species are much higher than those of the heavier ion species. Furthermore, the obtained results due to the presence of the second ion (the heavier ion) are compared to the reported results of the magnetized plasma sheath including single positive ion species. In the presence of the second ion, it is shown that the velocity and density distribution of the lighter ion species in the magnetized plasma sheath decreases and increases, respectively.

The Bohm criterion in an electropositive plasma containing nonextensively distributed electrons and warm ions is investigated by using a steady state two-fluid model. Taking into account the ion-neutral collisions and finite temperature of ions, a modified Bohm criterion is derived which limits both maximum and minimum allowable velocity of ions at the sheath edge (u0i). It is found that the degree of nonextensivity of electrons (q) and temperature of positive ions (Ti) affect only the lower limit of the entrance velocity of ions into the sheath while the degree of ion collisionality (α) influences both lower and upper limits of the ion velocities at the sheath edge. In addition, depending on the value of q, it is shown that the minimum velocity of positive ions at the sheath edge can be greater or smaller than its Maxwellian counterpart. Moreover, it is shown that, depending on the values of α and Ti, the positive ions with subsonic velocity may enter the sheath for either q > 1 or −1 < q < 1. Finally, as a practical application, the density distribution of charged particles in the sheath region is studied for different values of u0i, and it is shown that monotonical reduction of the positive ion density distribution occurs only when the velocity of positive ions at the sheath edge lies between two above mentioned limits.