Quasi-static modes of oscillation of a cold toroidal plasma

1975 ◽  
Vol 14 (1) ◽  
pp. 25-37 ◽  
Author(s):  
John D. Love
Keyword(s):  
Dispersion Relation ◽  
Cross Section ◽  
Normal Modes ◽  
Toroidal Plasma ◽  
Cylindrical Plasma ◽  
Aspect Ratios ◽  
Plasma Ring ◽  
Toroidal Geometry

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.

Effect of Geometry on Droplet Generation in a Microfluidic T-Junction

2013 ◽  
Author(s):  
Katerina Loizou ◽  
Wim Thielemans ◽  
Buddhika N. Hewakandamby
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Main Channel ◽  
Superficial Velocity ◽  
Droplet Generation ◽  
Dispersed Phase ◽  
Aspect Ratios ◽  
The Cross

The main aim of this study is to examine how the droplet formation in microfluidic T-junctions is influenced by the cross-section and aspect ratio of the microchannels. Several studies focusing on droplet formation in microfluidic devices have investigated the effect of geometry on droplet generation in terms of the ratio between the width of the main channel and the width of the side arm of the T-junction. However, the contribution of the aspect ratio and thus that of the cross-section on the mechanism of break up has not been examined thoroughly with most of the existing work performed in the squeezing regime. Two different microchannel geometries of varying aspect ratios are employed in an attempt to quantify the effect of the ratio between the width of the main channel and the height of the channel on droplet formation. As both height and width of microchannels affect the area on which shear stress acts deforming the dispersed phase fluid thread up to the limit of detaching a droplet, it is postulated that geometry and specifically cross-section of the main channel contribute on the droplet break-up mechanisms and should not be neglected. The above hypothesis is examined in detail, comparing the volume of generated microdroplets at constant flowrate ratios and superficial velocities of continuous phase in two microchannel systems of two different aspect ratios operating at dripping regime. High-speed imaging has been utilised to visualise and measure droplets formed at different flowrates corresponding to constant superficial velocities. Comparing volumes of generated droplets in the two geometries of area ratio near 1.5, a significant increase in volume is reported for the larger aspect ratio utilised, at all superficial velocities tested. As both superficial velocity of continuous phase and flowrate ratio are fixed, superficial velocity of dispersed phase varies. However this variation is not considered to be large enough to justify the significant increase in the droplet volume. Therefore it can be concluded that droplet generation is influenced by the aspect ratio and thus the cross-section of the main channel and its effect should not be depreciated. The paper will present supporting evidence in detail and a comparison of the findings with the existing theories which are mainly focused on the squeezing regime.

Helicon waves in a cylindrical plasma

1999 ◽  
Vol 77 (5) ◽  
pp. 385-391
Author(s):  
M Shoucri
Keyword(s):  
Dispersion Relation ◽  
Coupling Mechanism ◽  
Electron Mass ◽  
Cylindrical Plasma ◽  
Bounded Plasma ◽  
Helicon Waves

The dispersion relation for helicon waves in a uniform bounded plasma is derived by including the finite electron mass. The eigenmodes are identified and the coupling mechanism between the Ez and Bz modes is discussed. This is important since an essential part of the physics associated with the application of helicon waves for the generation and heating of plasmas consists in coupling the whistler branch with the Ez mode, which can interact directly with the electrons.PACS No.: 52.35-g

scholarly journals Computing Effective Hamiltonians of Coupled Electromagnetic Systems

2021 ◽  
Author(s):  
Shaolin Liao ◽  
Lu Ou
Keyword(s):  
Boundary Condition ◽  
Dispersion Relation ◽  
Normal Modes ◽  
Computational Procedure ◽  
Hamiltonian Matrix ◽  
Effective Hamiltonian ◽  
Electromagnetic System ◽  
Wave Dynamics ◽  
Potential Applications ◽  
Free Port

In this paper, we present an efficient procedure to compute the effective Hamiltonian matrix of a coupled electromagnetic system consisting of subsystems that are coupled to a discrete number of channels through couplers. Each subsystem is described by its own effective non-Hermitian Hamiltonian and the corresponding Quasi-normal Modes (QNMs), while the coupler connecting the subsystems and the channels is described by the scattering matrix, which is equivalent to the transfer matrix, in terms of port vectors defined for the coupler. Due to the constraints imposed by the QNMs of the subsystems and the wave dynamics of the channels, as well as boundary condition constraints, constraint-free port vectors need to be chosen efficiently and they follow two rules: 1) port vectors forming loops with couplers; 2) port vectors of couplers with most constraints or with less freedom. With the constraint-free port vectors chosen, the effective Hamiltonian matrix of the coupled electromagnetic system can be obtained by imposing the boundary condition constraints. After the effective Hamiltonian is obtained, the eigenvalues, eigenvectors and dispersion relation of the coupled electromagnetic system, as well as other quantities such as the reflection and transmission, can be calculated. A 2D interstitial square coupled MRRs array is used as an example to demonstrate the computational procedure. The computation of the effective Hamiltonian matrix of a coupled electromagnetic system has many potential applications such as MRRs array, coupled Parity-Time Non-Hermitian electromagnetic system, as well as the dispersion relation of finite and infinite arrays.

Accuracy of Cotton-Mouton polarimetry in sheared toroidal plasma of circular cross-section

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Yury Kravtsov ◽  
Janusz Chrzanowski
Keyword(s):  
Simple Model ◽  
Phase Shift ◽  
Perturbation Method ◽  
Cross Section ◽  
Amplitude Ratio ◽  
Circular Cross Section ◽  
Shear Angle ◽  
Tokamak Plasma ◽  
Toroidal Plasma ◽  
Small Shear

AbstractThe Cotton-Mouton effect in sheared plasma with helical magnetic lines is studied on the basis of the equation for complex amplitude ratio (CAR). A simple model for helical magnetic lines in sheared plasma of toroidal configuration is suggested. The equation for CAR in the sheared plasma is solved by perturbation method, using the small shear angle deviations as is characteristic for tokamak plasma. It is shown that the inaccuracy in polarization measurements caused by deviations of the sheared angle amounts to some percentage of the shearless Cotton-Mouton phase shift. One suggested method is to subtract the “sheared” term, which may improve the accuracy of the Cotton-Mouton measurements in the sheared plasma.

Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

scholarly journals Influence of an MgTiTaON Inserted Layer on Magnetic Properties and Microstructure of FePtAgC Films

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 238 ◽  
Author(s):  
Jai-Lin Tsai ◽  
Cheng Dai ◽  
Jyun-you Chen ◽  
Ting-Wei Hsu ◽  
Shi-Min Weng ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Cross Section ◽  
Lattice Relaxation ◽  
Fept Film ◽  
Perpendicular Magnetization ◽  
Aspect Ratios ◽  
Out Of Plane ◽  
Temperature Deposition ◽  
Critical Lattice ◽  
C 30

The FePt film above 10 nm critical lattice relaxation thickness was prepared and the ultrathin MgTiTaON layer was interleaved in between FePt film and the multilayer stack is FePt(6 nm)/[MgTiTaON(1 nm)/FePt(4 nm)]2. Next, the FePt films were co-sputtered with (Ag, C) segregants during deposition and the layer stacks is FePt(6 nm)(Ag, C)(x vol %)/[MgTiTaON (1 nm)/FePt(4 nm)(Ag, C) (x vol %)]2 (x = 0, 10, 20, 30, 40). After high temperature deposition at 470 °C, the granular FePt(Ag, C, MgTiTaON) film illustrated perpendicular magnetization and the out-of-plane coercivity (Hc) was increased with (Ag, C) segregants and the highest Hc is 18.3 kOe when x = 40. From cross-section images, the FePt layer are more continuous with 0 and 10 vol% (Ag, C) segregants and changed to an island structure when the (Ag, C) segregants increase to 20–40 vol %. The FePt grains were grown in separated islands in 20, 30 vol % (Ag, C) and changed to dense columnar-like morphology in 40 vol%. The second nucleated grains which contribute the in-plane magnetization are found in FePt (Ag, C) (40 vol %) film. The FePt islands are reached by inserting the ultrathin MgTiTaON layer and the island heights of FePt(Ag, C) (30, 40 vol %) are around 31–38 nm and the aspect ratios are 0.6–0.8.

Topology of vortex breakdown in closed polygonal containers

2017 ◽  
Vol 820 ◽  
pp. 263-283 ◽  
Author(s):  
Igor V. Naumov ◽  
Irina Yu. Podolskaya
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Vortex Breakdown ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Cylindrical Container ◽  
Stagnation Points ◽  
Aspect Ratios ◽  
Particle Visualization ◽  
Cross Section Geometry

The topology of vortex breakdown in the confined flow generated by a rotating lid in a closed container with a polygonal cross-section geometry has been analysed experimentally and numerically for different height/radius aspect ratios $h$ from 0.5 to 3.0. The locations of stagnation points of the breakdown bubble emergence and corresponding Reynolds numbers were determined experimentally and numerically by STAR-CCM+ computational fluid dynamics software for square, pentagonal, hexagonal and octagonal cross-section configurations. The flow pattern and velocity were observed and measured by combining seeding particle visualization and laser Doppler anemometry. The vortex breakdown size and position on the container axis were identified for Reynolds numbers ranging from 500 to 2800 in steady flow conditions. The obtained results were compared with the flow structure in the closed cylindrical container. The results allowed revealing regularities of formation of the vortex breakdown bubble depending on $Re$ and $h$ and the cross-section geometry of the confined container. It was found in a diagram of $Re$ versus $h$ that reducing the number of cross-section angles from eight to four shifts the breakdown bubble location to higher Reynolds numbers and a smaller aspect ratio. The vortex breakdown bubble area for octagonal cross-section was detected to correspond to the one for the cylindrical container but these areas for square and cylindrical containers do not overlap in the entire range of aspect ratio.

Toroidal plasma configuration with non-planar magnetic axis

1984 ◽  
Vol 32 (2) ◽  
pp. 179-196
Author(s):  
Hussain M. Rizk
Keyword(s):  
Cross Section ◽  
Ohmic Heating ◽  
Circular Cross Section ◽  
Magnetic Axis ◽  
Toroidal Plasma ◽  
Mhd Equilibrium ◽  
Special Cases ◽  
Magnetic Surfaces ◽  
Plasma Configuration ◽  
The Ideal

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

scholarly journals Slender body theory for particles with non-circular cross-sections with application to particle dynamics in shear flows

2019 ◽  
Vol 877 ◽  
pp. 1098-1133 ◽  
Author(s):  
Neeraj S. Borker ◽  
Donald L. Koch
Keyword(s):  
Cross Section ◽  
Relative Motion ◽  
Cross Sections ◽  
Stokes Flow ◽  
Unit Length ◽  
Fluid Velocity ◽  
Simple Shear Flow ◽  
Slender Body Theory ◽  
Aspect Ratios ◽  
Cross Sectional Dimension

This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ($A=l/a_{0}$) is defined as the ratio of the particle size ($l$) to the cross-sectional dimension ($a_{0}$) and $\unicode[STIX]{x1D6FC}$ is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e. $\unicode[STIX]{x1D6FC}\sim O(1)$). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section, and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios (${\sim}10$) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers.

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