Critical flow of high-speed ions in a high-current vacuum-arc discharge

A theoretical study of the impact of magnetic field of Hall current on the parameters of a high-current vacuum-arc discharge

“…Within the 1.5D model, it is much simpler to take into account the electron heat conductivity and the work of thermal force. This model enables one to find the j r ( z ), T e ( z ), and v z ( z ) distributions and find the parameters of VAD for which the crisis of flow occurs [2]. Therefore, in case the magnetic field of Hall current makes no significant impact on the parameters of VAD, it is more convenient to use the 1.5D model.…”

“…The radial potential drop due to the force j z B θ depends on the discharge current I 0 . The voltage drop between the center of discharge and the external boundary of plasma at j z = const satisfies the ratio ϕ ( R 0 )/ I 0 ≈ 17 V/kA [2]. For example, at I 0 = 50 kA, ϕ ( R 0 ) = 850 V. This value is two orders of magnitude higher than the discharge voltage defined by the force g rad z p e and by the axial component of Ampere force ( F A ) z .…”

“…If one ignores the effect of magnetic field of Hall current, the mathematical model of VAD is significantly simplified. In this case, a flow of relatively simple type is realized in the external axial magnetic field [2], where the lines of current are inclined to the axis at a very small angle δ ( r ) . In so doing, the 2D model may be replaced by a simpler 1.5D model [2], in which the longitudinal motion of ions is one-dimensional, and the non-one-dimensionality effect is associated with the presence of Ampere force j r B θ .…”

“…In these models, the effect of magnetic field of Hall current is ignored. In the models of [2,7], the magnetic field of Hall current is included; however, no systematic studies were made heretofore of the impact made by this field on the modes of current flow and on the parameters of VAD. This aspect is of significant importance.…”

“…Such models have been developed [2][3][4][5][6][7][8] and are used for the calculations of various modes of VAD. These models are based on different mathematical approaches and are characterized by different ways of taking into account the impact made by the intrinsic magnetic field of discharge current.…”