scholarly journals Decayless Kink Oscillations Excited by Random Driving: Motion in Transitional Layer

Solar Physics ◽  
2021 ◽  
Vol 296 (8) ◽  
Author(s):  
M. S. Ruderman ◽  
N. S. Petrukhin ◽  
E. Pelinovsky
Keyword(s):  
Coronal Loop ◽  
Radial Displacement ◽  
Oscillation Amplitude ◽  
Radial Distance ◽  
Magnetic Pressure ◽  
Pressure Perturbation ◽  
Transitional Layer ◽  
Thin Boundary Layer ◽  
Plasma Displacement ◽  
Thin Tube

AbstractIn this article we study the plasma motion in the transitional layer of a coronal loop randomly driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This average can be considered as the square of the oscillation amplitude of this quantity. Then we calculate the oscillation amplitudes of the radial and azimuthal plasma displacement as well as the perturbation of the magnetic pressure. We find that the amplitudes of the plasma radial displacement and the magnetic-pressure perturbation do not change across the transitional layer. The amplitude of the plasma radial displacement is of the same order as the driver amplitude. The amplitude of the magnetic-pressure perturbation is of the order of the driver amplitude times the ratio of the loop radius to the loop length squared. The amplitude of the plasma azimuthal displacement is of the order of the driver amplitude times $\text{Re}^{1/6}$ Re 1 / 6 , where Re is the Reynolds number. It has a peak at the position in the transitional layer where the local Alfvén frequency coincides with the fundamental frequency of the loop kink oscillation. The ratio of the amplitude near this position and far from it is of the order of $\ell$ ℓ , where $\ell$ ℓ is the ratio of thickness of the transitional layer to the loop radius. We calculate the dependence of the plasma azimuthal displacement on the radial distance in the transitional layer in a particular case where the density profile in this layer is linear.

scholarly journals Resonant damping of kink oscillations of thin expanding magnetic tubes

2018 ◽  
Vol 615 ◽  
pp. A156 ◽  
Author(s):  
A. A. Shukhobodskiy ◽  
M. S. Ruderman
Keyword(s):  
Magnetic Flux ◽  
Oscillation Frequency ◽  
Density Variation ◽  
Magnetic Pressure ◽  
Transitional Region ◽  
Transitional Layer ◽  
Flux Tubes ◽  
Flux Function ◽  
Plasma Displacement ◽  
Magnetic Flux Tubes

We study the resonant damping of kink oscillations of thin expanding magnetic flux tubes. The tube consists of a core region and a thin transitional region at the tube boundary. The resonance occurs in this transitional layer where the oscillation frequency coincides with the local Alfvén frequency. Our investigation is based on the system of equations that we previously derived. This system is not closed because it contains the jumps of the magnetic pressure perturbation and plasma displacement across the transitional layer. We calculate these jumps and thus close the system. We then use it to determine the decrements of oscillation eigenmodes. We introduce the notion of homogeneous stratification. In accordance with this condition the ratio of densities in the tube core and outside the tube does not vary along the tube, while the density in the transitional layer can be factorised and written as a product of two function, one depending on the variable along the tube and the other on the magnetic flux function. Our main result is that, under the condition of homogeneous stratification, the ratio of the decrement to the oscillation frequency is independent of a particular form of the density variation along the tube. This ratio is also the same for all oscillation eigenmodes.

The Effect of Stepped Field Shaper on Magnetic Pressure and Radial Displacement in Electromagnetic Inside Bead Forming: Experimental and Simulation Analyses Using maxwell and abaqus Software

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Rasoul Chaharmiri ◽  
Alireza Fallahi Arezoodar
Keyword(s):  
Radial Displacement ◽  
Experimental Tests ◽  
Magnetic Pressure ◽  
Geometric Parameters ◽  
Electrically Conductive ◽  
Mechanical Parts ◽  
Forming Technology ◽  
Pressure Concentration ◽  
High Strain Rate Forming ◽  
Abaqus Software

Electromagnetic forming (EMF) is a high strain rate forming technology which can effectively deform and shape high electrically conductive materials at room temperature. A field shaper is frequently used for concentrating the magnetic pressure in the desired forming area. The geometric parameters of a field shaper, as an intermediate device, affect the magnetic pressure and radial displacement in electromagnetic inside bead forming. EMF consists of electromagnetic and mechanical parts simulated using maxwell and abaqus software, respectively. The effects of geometric parameters of the stepped field shaper on magnetic pressure and radial displacement were investigated, and the best parameters were determined. Experimental tests were performed at various discharge voltages and the results were compared with simulation. The results indicated that using the stepped field shaper, the magnetic pressure concentration ratio increased from about 23–85% in comparison with using a direct coil. The maximum magnetic pressure increased by approximately 21% due to the effective concentration of magnetic pressure. Consequently, regardless of the electromagnetic energy losses because of using a field shaper, the radial displacement increased by 8% in simulation and 6% in experiment. The result of this study would be also helpful in designing field shapers in similar applications which is highly crucial and strongly recommended.

scholarly journals Structure of a Sequence of Two Zone Polytropic Stellar Models with Indices 0 and 1

1983 ◽  
Vol 36 (3) ◽  
pp. 453 ◽  
Author(s):  
JO Murphy
Keyword(s):  
Radial Displacement ◽  
Radial Distance ◽  
Density Variation ◽  
Uniform Density ◽  
Constant Density ◽  
Surface Phenomena ◽  
Composite Function ◽  
Emden Equation ◽  
Stellar Models ◽  
Type Composite

The structure and physical properties of a sequence of two zone polytropic stellar models, based on E-type composite analytical solutions of the Lane-Emden equation for indices n = 0 and 1, have been determined. The resulting models are characterized by an inner zone of constant density, corresponding to the n = 0 component, and a relatively small envelope with a steep polytropic density gradient and index n = 1. At the surface of these near uniform density composite configurations the physically significant condition p = 0 is always satisfied, a condition which is not fulfilled by the complete poly trope of index n = O. In each model the surface corresponds to the first zero of the associated composite function, which in turn is given by one of the higher order zeros of the E solution of the Lane-Emden equation for n = 1. The radial pulsational properties of these low central condensation type models have also been investigated with the relative amplitudes of radial displacement and density variation given as a function of radial distance for the first six modes of some selected models. Overall, these results establish that the radial displacement amplitudes are only significant in the n = 1 outer layer and accordingly the pulsations can be classified as essentially surface phenomena

Magnetohydrodynamic standing oscillations in a spherical dipole field

1986 ◽  
Vol 36 (2) ◽  
pp. 243-250 ◽  
Author(s):  
H. Murata
Keyword(s):  
Differential Equation ◽  
Pressure Effect ◽  
Fluid Pressure ◽  
String Model ◽  
Magnetic Pressure ◽  
Pressure Perturbation ◽  
Pressure Term ◽  
Dipole Magnetic Field ◽  
Infinite Conductivity ◽  
Coupled Equation

The coupled toroidal and poloidal modes forming a standing oscillation along the line of force and propagating azimuthally in a spherical dipole magnetic field are investigated under the magnetohydrodynamic (MHD) approximation with infinite conductivity, including the pressure effect but neglecting compressibility. We obtain a linearized coupled differential equation. When the azimuthal wavenumber becomes zero in the coupled equation, the axisymmetric toroidal wave equation is obtained with no pressure effect. For a large azimuthal wavenumber, on the other hand, a differential equation of the poloidal wave associated with a compressional magnetic component, which is different from the equation hitherto obtained under the zero pressure term, is derived from the coupled equation. It is found that the fluid pressure perturbation acts on the poloidal wave like the spring for the stretched string model and then contributes to the enhancement of the eigenvalues of the standing oscillations, especially for the first few. In this case, the magnetic pressure perturbation is in antiphase to that of the fluid pressure.

Transient Stresses and Displacement Around a Wellbore Due to Fluid Flow in Transversely Isotropic, Porous Media: II. Finite Reservoirs

1968 ◽  
Vol 8 (01) ◽  
pp. 79-86 ◽  
Author(s):  
M.S. Seth ◽  
K.E. Gray
Keyword(s):  
Porous Media ◽  
Radial Displacement ◽  
Outer Boundary ◽  
Stress Gradient ◽  
Fluid Pressure ◽  
Radial Distance ◽  
Transversely Isotropic ◽  
Vertical Stress ◽  
State Flow ◽  
Constant Rate

Abstract In Part 1 of this work,1 equations of elasticity were formulated for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure. Equations of elasticity and the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant rate of pressure or a constant rate of flow is maintained at the wellbore. In this paper, the approach presented earlier is extended to finite reservoirs for the cases ofsteady-state flow,constant pressures at the well bore and outer boundary andconstant pressure at the wellbore and no flow at the outer boundary. Results of this work show that radial and tangential stress gradients are high near the wellbore but diminish rapidly away from the well; the vertical stress gradient behaves in the same way but is less severe. Radial stresses are compressive or neutral, whereas tangential and vertical stresses may be tensile, neutral or compressive, depending upon the boundary conditions, the physical properties of the system and the radial distance involved (vertical stresses are always compressive in an unbounded system1). For constant boundary pressures, both radial and tangential stresses increase with time whereas they both decrease for a closed outer boundary and constant pressure at the wellbore. The vertical stress decreases with time for both systems. For steady-state systems, radial displacement may be positive or negative, depending upon the dimensions of the system, the pressure differential and the porosity. Radial displacement may be positive or negative for a closed outer boundary but is positive for constant pressures at both boundaries. INTRODUCTION The importance, utility and complexity of a realistic appraisal of the stress state at and local to a wellbore were indicated in Part 1. In this paper the analytical approach presented earlier is extended to finite, cylindrical reservoir geometry for the cases ofsteady-state flow,constant pressures at wellbore and outer boundary andconstant pressure at the wellbore and no flow at the outer boundary. Other than the outer boundary of the reservoir being finite, the physical system and assumptions pertinent thereto are the same as before. The reader may wish to review the mathematical development through Eq. 49 of Part 1 before proceeding here.

Unusual extension–torsion–inflation couplings in pressurized thin circular tubes with helical anisotropy

2018 ◽  
Vol 24 (9) ◽  
pp. 2694-2712 ◽  
Author(s):  
Raushan Singh ◽  
Pranjal Singh ◽  
Ajeet Kumar
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Radial Displacement ◽  
Applied Pressure ◽  
Nonlinear Ordinary Differential Equation ◽  
Algebraic Equations ◽  
Circular Tubes ◽  
Thin Tube ◽  
Analytical Expressions ◽  
Helical Anisotropy

We present a thin tube formulation for coupled extension–torsion–inflation deformation in helically reinforced pressurized circular tubes. Both compressible and incompressible tubes are considered. On applying the thin tube limit, the nonlinear ordinary differential equation to obtain the in-plane radial displacement is converted into a set of two simple algebraic equations for the compressible case and one equation for the incompressible case. This allows us to obtain analytical expressions, in terms of the tube’s intrinsic twist, material constants, and the applied pressure, which can predict whether such tubes would overwind/unwind on being infinitesimally stretched or exhibit positive/negative Poisson’s effect. We further show numerically that such tubes can be tuned to generate initial overwinding followed by rapid unwinding as observed during finite stretching of a torsionally relaxed DNA. Finally, we demonstrate that such tubes can also exhibit usual deflation initially followed by unusual inflation as the tube is finitely stretched.

The Plastic Buckling of Thin-Walled Tubes Subject to Magnetomotive Forces

1974 ◽  
Vol 16 (2) ◽  
pp. 59-70 ◽  
Author(s):  
S. T. S. Al-Hassani
Keyword(s):  
Aluminium Alloy ◽  
Radial Displacement ◽  
Capacitor Bank ◽  
Magnetic Pressure ◽  
Experimental Results ◽  
Tube Length ◽  
Current Waveform ◽  
Hoop Strain ◽  
Plastic Buckling ◽  
Thin Walled

Aluminium alloy tubes and rings can be reduced in diameter by means of external coils through which a large capacitor bank is discharged, due to the high radial transient magnetic pressure. Both the radial and perturbed motions are investigated theoretically and experimentally. Predictions of the current waveform, radial displacement and the number of wrinkles on the tube agree well with the experimental results. The number of wrinkles increases with tube length and diameter. However, geometrically similar tubes, when reduced to the same final hoop strain, have similar buckled shapes with the same number of wrinkles.

scholarly journals Second-order perturbations in Alfvén waves in cold plasma approximatio

2019 ◽  
Vol 5 (2) ◽  
pp. 81-87
Author(s):  
Ирина Дмитриенко ◽  
Irina Dmitrienko
Keyword(s):  
Cold Plasma ◽  
Alfven Waves ◽  
Magnetic Pressure ◽  
Second Order ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Plasma Flows ◽  
Plasma Displacement ◽  
Environment Model ◽  
The Waves

The second-order amplitude perturbations driven by Alfvén waves are studied. Equations for such second-order perturbations are derived and their solutions are found. The second-order perturbations are shown to be generated by the magnetic pressure of the waves. They represent plasma flows and magnetic field perturbations in a plane perpendicular to the direction of the field perturbation and plasma displacement in the Alfvén wave. In connection with the interpretation of fast plasma flows observed in the magnetotail, of particular interest is the description of second-order flows, which relates their properties to properties of Alfvén waves and the disturbance that generates them. The results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves. The environment model and cold plasma approximation in use are quite applicable for the plasma sheet boundary layers, where an essential part of the fast plasma flows occurs.

scholarly journals Significance of Cooling Effect on Comprehension of Kink Oscillations of Coronal Loops

2021 ◽  
Vol 7 ◽  
Author(s):  
Daria Shukhobodskaia ◽  
Alexander A. Shukhobodskiy ◽  
Chris J. Nelson ◽  
Michael S. Ruderman ◽  
Robert Erdélyi
Keyword(s):  
Coronal Loop ◽  
Thermal Evolution ◽  
Oscillation Amplitude ◽  
Density Ratio ◽  
Resonant Absorption ◽  
Coronal Loops ◽  
The Past ◽  
Kink Mode ◽  
Mode Oscillation ◽  
Complex Damping

Kink oscillations of coronal loops have been widely studied, both observationally and theoretically, over the past few decades. It has been shown that the majority of observed driven coronal loop oscillations appear to damp with either exponential or Gaussian profiles and a range of mechanisms have been proposed to account for this. However, some driven oscillations seem to evolve in manners which cannot be modeled with purely Gaussian or exponential profiles, with amplification of oscillations even being observed on occasions. Recent research has shown that incorporating the combined effects of coronal loop expansion, resonant absorption, and cooling can cause significant deviations from Gaussian and exponential profiles in damping profiles, potentially explaining increases in oscillation amplitude through time in some cases. In this article, we analyze 10 driven kink oscillations in coronal loops to further investigate the ability of expansion and cooling to explain complex damping profiles. Our results do not rely on fitting a periodicity to the oscillations meaning complexities in both temporal (period changes) and spatial (amplitude changes) can be accounted for in an elegant and simple way. Furthermore, this approach could also allow us to infer some important diagnostic information (such as, for example, the density ratio at the loop foot-points) from the oscillation profile alone, without detailed measurements of the loop and without complex numerical methods. Our results imply the existence of correlations between the density ratio at the loop foot-points and the amplitudes and periods of the oscillations. Finally, we compare our results to previous models, namely purely Gaussian and purely exponential damping profiles, through the calculation of χ2 values, finding the inclusion of cooling can produce better fits in some cases. The current study indicates that thermal evolution should be included in kink-mode oscillation models in the future to help us to better understand oscillations that are not purely Gaussian or exponential.

scholarly journals Second-order perturbations in Alfvén waves in cold plasma approximatio

2019 ◽  
Vol 5 (2) ◽  
pp. 89-96
Author(s):  
Ирина Дмитриенко ◽  
Irina Dmitrienko
Keyword(s):  
Cold Plasma ◽  
Alfven Waves ◽  
Magnetic Pressure ◽  
Second Order ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Plasma Flows ◽  
Plasma Displacement ◽  
Environment Model ◽  
The Waves

The second-order amplitude perturbations driven by Alfvén waves are studied. Equations for such second-order perturbations are derived and their solutions are found. The second-order perturbations are shown to be generated by the magnetic pressure of the waves. They represent plasma flows and magnetic field perturbations in a plane perpendicular to the direction of the field perturbation and plasma displacement in the Alfvén wave. In connection with the interpretation of fast plasma flows observed in the magnetotail, of particular interest is the description of second-order flows, which relates their properties to properties of Alfvén waves and the disturbance that generates them. The results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves. The environment model and cold plasma approximation in use are quite applicable for the plasma sheet boundary layers, where an essential part of the fast plasma flows occurs.

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