Influence of aspect ratio, plasma viscosity, and radial position of the resonant surfaces on the plasmoid formation in the low resistivity plasma in Tokamak

In the present paper, we systematically investigate the nonlinear evolution of the resistive kink mode in the low resistivity plasma in Tokamak geometry. We find that the aspect ratio of the initial equilibrium can significantly influence the critical resistivity for plasmoid formation. With the aspect ratio of 3/1, the critical resistivity can be one magnitude larger than that in cylindrical geometry due to the strong mode-mode coupling. We also find that the critical resistivity for plasmoid formation decreases with increasing plasma viscosity in the moderately low resistivity regime. Due to the geometry of Tokamaks, the critical resistivity for plasmoid formation increases with the increasing radial location of the resonant surface.

Analytical Solution of a Non-isothermal Flow in Cylindrical Geometry

This study proposes analytical solution to the problem of transport in a Newtonian fluid within a cylindrical domain. The flow is assumed to be dominated along the channel axis, and is taken to be axi-symmetric. No-slip boundary condition is considered for velocity while the temperature and concentration have Dirichlet boundary values. The resulting problem is transformed into a set of non-trivial variable coefficient differential equations in a cylindrical geometry. By adopting the series solution method of Frobenius, the closed-form analytical solutions are derived for the flow variables. We conduct an analysis of the derived model, and showed that, indeed, the flow variables are axi-symmetric. We also state and prove another theorem to show that the derived concentration model is positivity preserving – meaning that it yields positive concentration - provided the boundary value is non-negative. Finally, we present graphical results for the flow variables and discuss the effect of the relevant flow parameters. The results showed that (i) an increase in the cooling parameter, reduces the fluid velocity, (ii) the temperature decreases as the cooling parameter increases and (iii) an increase in the injection parameter, leads to increase in the concentration.

Microwave hologram reconstruction for cylindrical geometry

Microwave imaging is a technique for evaluation of hidden or embedded objects in an optically opaque structure (or media) using electromagnetic waves in microwave regime. The result of the study is a microwave image of the internal structure of the investigated object, which is built by reconstructing the electromagnetic field scattered by the object (microwave hologram), recorded using some radar system at some aperture. Along with the widespread flat aperture, a cylindrical aperture is often used in personnel screening systems, microwave system for automated body measurement for apparel fitting, and medical tomographic scanners. Cylindrical geometry requires special holograms reconstruction methods. The work is dedicated to comparison of three hologram reconstruction methods: №1 – back projection, №2 – back propagation and №3 – Gauss–Newton, and identifying the advantages and disadvantages of each method. All methods were adopted to cylindrical geometry, software implemented using Python programming language and compared. Comparison was performed by reconstruction of microwave holograms of the same objects. Microwave holograms for comparison were calculated in accordance with the principles of physical optics for point scatterers and using the computational electromagnetics software product FEKO for solid objects. Comparison criteria were: speed of calculations, quality of obtained microwave images, required random access memory (RAM) of the computer. Based on the results of numerical experiments, the following conclusions can be made. For both point and solid objects, all methods have showed a similar quality of the obtained microwave images, the difference turned out to be minimal both in visual and numerical estimation. The advantage of method №1 is the simplicity of its software implementation. In addition, using the first method, you can easily do reconstruction for any area (line, surface, volume), the position of which can be arbitrary in relation to the positions of the samples of the radar signal. Method №2 is the fastest method. With the parameters considered in the article, it is two orders of magnitude faster than method №1, and its performance can be easily increased by parallelizing calculations for different radii. Among the shortcomings, one can note the complexity of its software implementation and the dependence of the position and size of the reconstructed area on the location and number of samples of the radar signal. A significant drawback of method №3 is its high requirements to the RAM of the computer, as well as low speed of calculations. When processing microwave holograms with a large number of samples, calculations may require more memory than is installed in the computer, and the calculation time will increase many times due to the continuous exchange of data with the hard disk, or it will be impossible to do the calculations at all.