Instability and transition of a vertical ascension or fall of a free sphere affected by a vertical magnetic field

2018 ◽  
Vol 859 ◽  
pp. 33-48 ◽  
Author(s):  
Jun-Hua Pan ◽  
Nian-Mei Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Interaction Parameter ◽  
Scaling Law ◽  
Density Ratio ◽  
Vertical Magnetic Field ◽  
Streamwise Vorticity ◽  
Close Relationship ◽  
Wake Patterns ◽  
The Magnetic Field ◽  
Solid System

When the Galileo number is below the first bifurcation, the instability and transition of a vertical ascension or the fall of a free sphere affected by a vertical magnetic field are investigated numerically. A compact model is used to explain that the magnetic field can destabilize the fluid–solid system. When the interaction parameter exceeds a critical value, the sphere trajectory is transitioned from a steady vertical trajectory to a steady oblique one. Furthermore, the trajectory will remain vertical at a sufficiently large magnetic field because of a double effect of the magnetic field on the fluid–solid system. Under the influence of an external vertical magnetic field, four wake patterns at the rear of the sphere are found and the physical behaviour of the free sphere is independent of the density ratio. The wake or trajectory of the free sphere is only determined by the Galileo number $G$ and the interaction parameter $N$. A close relationship between the streamwise vorticity and the sphere motion is found. An interesting ‘agglomeration phenomenon’ is also found, which shows that the vertical velocities are agglomerated into a point for a certain magnetic field regardless of the Galileo number and satisfy a scaling law $V_{z}\sim N^{-1/4}$, when $N>1$. The principal results of the present work are summarized in a map of regimes in the $\{G,N\}$ plane.

Effect of magnetic field on parametrically driven surface waves

2006 ◽  
Vol 463 (2079) ◽  
pp. 711-722 ◽  
Author(s):  
Supriyo Paul ◽  
Krishna Kumar
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Liquid Metals ◽  
Tricritical Point ◽  
Thin Layers ◽  
Vertical Magnetic Field ◽  
Harmonic Solution ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

scholarly journals Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

2018 ◽  
Vol 620 ◽  
pp. A191 ◽  
Author(s):  
M. Benko ◽  
S. J. González Manrique ◽  
H. Balthasar ◽  
P. Gömöry ◽  
C. Kuckein ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Temporal Evolution ◽  
Vertical Component ◽  
Field Vector ◽  
Linear Increase ◽  
Vertical Magnetic Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field ◽  
Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

Coupling of Buoyant Convections in Boron Oxide and a Molten Semiconductor in a Vertical Magnetic Field

2002 ◽  
Vol 124 (4) ◽  
pp. 643-649 ◽  
Author(s):  
Martin V. Farrell ◽  
Nancy Ma
Keyword(s):  
Magnetic Field ◽  
Boron Oxide ◽  
Maximum Velocity ◽  
Horizontal Velocity ◽  
Vertical Magnetic Field ◽  
Electrical Conductor ◽  
Interfacial Velocity ◽  
Rectangular Container ◽  
Vertical Walls ◽  
The Magnetic Field

This paper treats the buoyant convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady vertical magnetic field B. The magnetic field provides an electromagnetic (EM) damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The temperature gradient drives counter clockwise circulations in both the melt and encapsulant. These circulations alone would lead to positive and negative values of the horizontal velocity in the encapsulant and melt, respectively, near the interface. The competition between the two buoyant convections determines the direction of the horizontal velocity of the interface. For B=5 T, there is significant EM damping of the melt motion and the encapsulant drives a positive interfacial velocity and a small clockwise circulation in the melt. For a much weaker field B=0.1 T, the maximum velocity in the melt is hundreds of times larger than that of the encapsulant, thus causing nearly all the encapsulant to circulate in the clockwise direction.

Self-magnetic insulation in plasma opening switches

2020 ◽  
Vol 86 (6) ◽  
Author(s):  
Sergey V. Loginov
Keyword(s):  
Magnetic Field ◽  
Electric Fields ◽  
Drift Velocity ◽  
Electron Flow ◽  
Density Ratio ◽  
Conduction Time ◽  
Current Channel ◽  
Field Velocity ◽  
Current Cutoff ◽  
The Magnetic Field

The paper analyses the penetration of a magnetic field into the plasma bridge of nanosecond and microsecond opening switches. For switches with a conduction time of ~100 ns, simple formulae are derived to estimate the magnetic field velocity in collisionless and collisional plasmas. It is shown that in both cases this velocity is determined by the magnetic field rise rate to plasma density ratio raised to the power of 1/2. As the conduction time is increased to ~1 ${\rm \mu}$ s, the field velocity starts to depend on the plasma aggregation by a magnetic piston. At the same time, irrespective of the conduction time, the electron flow velocity is limited by the radial drift velocity in crossed magnetic and polarization electric fields. Such a limitation suppresses the current channel conductivity with respect to the Spitzer value by a factor equal to the electron magnetization parameter raised to one or another power. On completion of the conduction phase, the rate of rise of the switch resistance is proportional to the electron drift velocity. The peak switch voltage obtained in calculations is compared with its values recorded in experiments on mega-ampere current switching. A procedure is also presented for calculating the switch parameters to obtain the maximum possible voltage in the phase of current cutoff.

Magnetoresistance investigation in the mixed state of a high temperature superconductor

2020 ◽  
Author(s):  
Mustapha Bghour ◽  
A. Labrag ◽  
H. El hamidi ◽  
A. Abou El hassan ◽  
A. Taoufik
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Mixed State ◽  
High Temperature Superconductor ◽  
Scaling Law ◽  
Good Alternative ◽  
Magnetic Field Direction ◽  
Flux Flow ◽  
The Magnetic Field ◽  
Good Agreement

In this work we analyze the behavior of magnetoresistance R(H,T) of a high temperature superconductor YBa2Cu3O7-delta thin film optimally doped. Measurements of magnetoresistance were carried out in the mixed state for a magnetic field up to 14T applied in the c-axis then parallel to ab-plane with a DC transport current of 100 and 500nA, 0.1 and 0.3mA perpendicular to the magnetic field direction in both cases. The obtained results show that the magnetoresistance is in a good agreement with the thermally assisted flux creep. However, the magnetoresistance in the flux flow regime cannot be described by the Barden-Stephen model which conjecture another origin of these results. In this sense, the quantum fluctuations of the order be parameter is a good alternative to understanding the shape of the magnetoresistance. The comparison of the magnetoresistance of the two directions shows that Rc(H,T) is larger than Rab(H,T) with anisot-ropy factor gamma=Rc/Rab depending on temperature and magnetic field. The irreversibility line Hirr(T) as well as Hc2(T) are determined and the first one is adjusted with the phenomenological model Hirr(T)=Hirr(0)(1-T/T0)^alpha where Hirr(0), T0 and alpha are parameters obtained from the fit. The investigation of the scaling law allows us to prove that a crossover from 3D to 2D behavior is a feature of our sample which justifies the existence of the decoherence effect.

Thermal Instability in Rivlin-Ericksen Elastico-Viscous Fluids in Hydromagnetics

1997 ◽  
Vol 52 (4) ◽  
pp. 369-371 ◽  
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Newtonian Fluid ◽  
Thermal Instability ◽  
Viscous Fluids ◽  
Sufficient Condition ◽  
Vertical Magnetic Field ◽  
Stationary Convection ◽  
Stabilizing Effect ◽  
The Magnetic Field

Abstract The thermal instability of a layer of Rivlin-Ericksen elastico-viscous fluid acted on by a uniform vertical magnetic field is considered. For stationary convection, a Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian fluid. The magnetic field has a stabilizing effect. It is found that the presence of a magnetic field introduces oscillatory modes which were non-existent in its absence. The sufficient condition for the non-existence of overstability is also obtained.

Three-dimensional MHD flows in rectangular ducts with internal obstacles

2000 ◽  
Vol 418 ◽  
pp. 265-295 ◽  
Author(s):  
B. MÜCK ◽  
C. GÜNTHER ◽  
U. MÜLLER ◽  
L. BÜHLER
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Magnetic Fields ◽  
Interaction Parameter ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Side Length ◽  
Two Dimensional ◽  
The Magnetic Field

This paper presents a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Kármán vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0 [les ] M [les ] 85 and the interaction parameter N in the range 0 [les ] N [les ] 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed. The spanwise wavelength of the rib vortices was found to be about 2–3 cylinder side lengths in the near wake. At Re = 250 the flow appears more organized showing a regular B mode pattern and a spanwise wavelength of about 1 cylinder side length. With an applied magnetic field a quasi-two-dimensional flow can be obtained at low N ≈ 1 due to the strong non-isotropic character of the electromagnetic forces. The remaining vortices have their axes aligned with the magnetic field. With increasing magnetic fields these vortices are further damped due to Hartmann braking. The result that the ‘quasi-two-dimensional’ vortices have a curvature in the direction of the magnetic field can be explained by means of an asymptotic analysis of the governing equations. With very high magnetic fields the time-dependent vortex shedding can be almost completely suppressed. By three-dimensional visualization it was possible to show characteristic paths of the electric current for this kind of flow, explaining the action of the Lorentz forces.

scholarly journals The magnetic nature of umbra–penumbra boundary in sunspots

2018 ◽  
Vol 611 ◽  
pp. L4 ◽  
Author(s):  
J. Jurčák ◽  
R. Rezaei ◽  
N. Bello González ◽  
R. Schlichenmaier ◽  
J. Vomlel
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Field Component ◽  
Vertical Component ◽  
Vertical Magnetic Field ◽  
Intensity Threshold ◽  
The Magnetic Field ◽  
Magnetic Nature

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aim. Here, we aim at studying the magnetic nature of umbra–penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Methods. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra–penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. Results. We statistically prove that the umbra–penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849–1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. Conclusions. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra–penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.

scholarly journals Turbulent amplification of interstellar magnetic fields

1991 ◽  
Vol 147 ◽  
pp. 519-522
Author(s):  
Anthony Whitworth
Keyword(s):  
Magnetic Field ◽  
Scaling Law ◽  
Hii Regions ◽  
Turbulent Energy ◽  
Radiative Cooling ◽  
Stellar Winds ◽  
Interstellar Gas ◽  
Stellar Jets ◽  
Supernova Explosions ◽  
The Magnetic Field

We show that the radiative cooling properties of the interstellar gas lead naturally to a scaling law for the magnetic field of the form B ∝ n1/2, if the magnetic field is amplified by a vigorous injection of turbulent energy due to expanding HII regions, stellar winds, supernova explosions, stellar jets, etc.

scholarly journals Magnetic properties of a long-lived sunspot

2018 ◽  
Vol 620 ◽  
pp. A104 ◽  
Author(s):  
M. Schmassmann ◽  
R. Schlichenmaier ◽  
N. Bello González
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Field Component ◽  
Active Regions ◽  
Magnetic Field Component ◽  
Stable Phase ◽  
Vertical Magnetic Field ◽  
Continuum Intensity ◽  
The Magnetic Field

Context. In a recent statistical study of sunspots in 79 active regions, the vertical magnetic field component Bver averaged along the umbral boundary is found to be independent of sunspot size. The authors of that study conclude that the absolute value of Bver at the umbral boundary is the same for all spots. Aims. We investigate the temporal evolution of Bver averaged along the umbral boundary of one long-lived sunspot during its stable phase. Methods. We analysed data from the HMI instrument on-board SDO. Contours of continuum intensity at Ic = 0.5Iqs, whereby Iqs refers to the average over the quiet sun areas, are used to extract the magnetic field along the umbral boundary. Projection effects due to different formation heights of the Fe I 617.3 nm line and continuum are taken into account. To avoid limb artefacts, the spot is only analysed for heliocentric angles smaller than 60°. Results. During the first disc passage, NOAA AR 11591, Bver remains constant at 1693 G with a root-mean-square deviation of 15 G, whereas the magnetic field strength varies substantially (mean 2171 G, rms of 48 G) and shows a long term variation. Compensating for formation height has little influence on the mean value along each contour, but reduces the variations along the contour when away from disc centre, yielding a better match between the contours of Bver = 1693 G and Ic = 0.5Iqs. Conclusions. During the disc passage of a stable sunspot, its umbral boundary can equivalently be defined by using the continuum intensity Ic or the vertical magnetic field component Bver. Contours of fixed magnetic field strength fail to outline the umbral boundary.

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