Alfven Velocity Research Articles

Effects of Modified Ohm's and Fourier’s Laws on Electromagnetic Micropolar Fluid Subjected to Ramp-Type Heating

Effects of modified Ohm's and Fourier's laws on two-dimensional electromagnetic (EM) flow of an incom- pressible micropolar fluid over a moving plate are studied. Ohm's law is modified by the inclusion of two terms, one for the temperature gradient and the other for the cross product of the velocity with the initial magnetic field. Fourier's law of heat conduction is modified to include the relaxation time. The effects of the modified Ohm's law (ko parameter) and Alfven velocity parameter α in two cases the first for strong concentration (n=0) and the other for weak concentration (n=1/2) have discussed. The purpose of the latter term is to produce finite speed of heat conduction. Laplace and exponential Fourier transform techniques are used to obtain the solution by a direct approach. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The distributions of the velocity components, the temperature, and the induced magnetic and electric fields are obtained. The numerical values of these functions are represented graphically.

Break up of returning plasma after the 7 June 2011 filament eruption by Rayleigh-Taylor instabilities

A prominence eruption on 7 June 2011 produced spectacular curtains of plasma falling through the lower corona. At the solar surface they created an incredible display of extreme ultraviolet brightenings. The aim is to identify and analyze some of the local instabilities which produce structure in the falling plasma. The structures were investigated using SDO/AIA 171A and 193A images in which the falling plasma appeared dark against the bright coronal emission. Several instances of the Rayleigh-Taylor instability were investigated. In two cases the Alfven velocity associated with the dense plasma could be estimated from the separation of the Rayleigh-Taylor fingers. A second type of feature, which has the appearance of self-similar branching horns, is also discussed.

Magnetogravitational Vortex-Sheet Instability of Two Superposed Conducting Fluids in Porous Medium Under Strong Magnetic Field

The instability of two superposed homogeneous streaming ‡uids is discussed under gravitational force and uniform magnetic eld in porous medium. The two streams are moving in opposite directions with equal velocities parallel to the horizontal plane. The solution has been obtained through the normal mode technique, and the most gen- eral dispersion relation has been obtained as 20th-order equation for the growth rate with quite complicated coe¢ cients. Solving numeri- caly the dispersion relation for appropriate boundary conditions with high Alfven and sound velocities, it is found that ‡uid velocities and porosity of porous medium have stabilizing e¤ects, and Alfven and sound velocities have destabilizing e¤ects, while medium permeabil- ity has a slightly stabilizing e¤ect, and the dynamic viscosities have slightly destabilizing e¤ect. The limiting cases of non-porous medium have also been studied for both streaming and stationary ‡uids. Key words : Hydrodynamic stability; Conducting ‡uids; Flows through porous media; Gravitational force; Magnetohydrodynamics

THE TRANSPORT OF LOW-FREQUENCY TURBULENCE IN ASTROPHYSICAL FLOWS. I. GOVERNING EQUATIONS

Numerous problems in space physics and astrophysics require a detailed understanding of the transport and dissipation of low-frequency turbulence in an expanding magnetized flow. We employ a scale-separated decomposition of the incompressible MHD equations (based on an Elssasser description) and develop a moment hierarchy to describe the transport of the total energy density in fluctuations, the cross-helicity, the energy difference, and correlation lengths corresponding to forward- and backward-propagating modes and to the energy difference. The dissipation terms for the various transport equations are derived. One-point closure schemes are utilized. The technical elements of this work that distinguish it from previous studies are (1) the inclusion of the large-scale background inhomogeneous Alfvenic velocity V A at a level of detail greater than before, (2) the introduction of a tractable slow timescale closure to eliminate high-frequency interference terms that is likely to prove a useful approximation for practical problems related to the transport of turbulence in an inhomogeneous flow such as the solar wind or solar corona, and finally, (3) we develop a simplified phenomenology for the energy difference or equivalently residual energy that may be useful for practical applications. This yields a coupled system of six equations that describes the transport of turbulence in inhomogeneous sub-Alfvenic and super-Alfvenic flows. The turbulence transport equations are quasi-linear in their spatial evolution operators and nonlinear in the dissipation terms, making the model equations relatively tractable to analysis.

Tether radiation in Juno-type and circular-equatorial Jovian orbits

[1] Wave radiation by a conductor carrying a steady current in both a polar, highly eccentric, low perijove orbit, as in NASA's planned Juno mission, and an equatorial low Jovian orbit (LJO) mission below the intense radiation belts, is considered. Both missions will need electric power generation for scientific instruments and communication systems. Tethers generate power more efficiently than solar panels or radioisotope power systems (RPS). The radiation impedance is required to determine the current in the overall tether circuit. In a cold plasma model, radiation occurs mainly in the Alfven and fast magnetosonic modes, exhibiting a large refraction index. The radiation impedance of insulated tethers is determined for both modes and either mission. Unlike the Earth ionospheric case, the low-density, highly magnetized Jovian plasma makes the electron gyrofrequency much larger than the plasma frequency; this substantially modifies the power spectrum for either mode by increasing the Alfven velocity. Finally, an estimation of the radiation impedance of bare tethers is considered. In LJO, a spacecraft orbiting in a slow downward spiral under the radiation belts would allow determining magnetic field structure and atmospheric composition for understanding the formation, evolution, and structure of Jupiter. Additionally, if the cathodic contactor is switched off, a tether floats electrically, allowing e-beam emission that generate auroras. On/off switching produces bias/current pulses and signal emission, which might be used for Jovian plasma diagnostics.

Some properties of the development of the perturbed zone and shock preceding a coronal mass ejection

SOHO/LASCO C2 and C3 data have been used to carry out a detailed study of the perturbed zone and shock that form as a coronal mass ejection (CME) moves away from the Sun, as a result of its interaction with the ambient solar wind. The event of January 4, 2002 is used as an example. The perturbed zone is most extensive along the direction of propagation of the CME, decreases away from this direction, and reaches its minimum values perpendicular to this direction. The mass of the perturbed zone is ≥0.1 of the total mass of the CME. The condition for the formation of a shock preceding the CME (in the direction of propagation of the CME) is V − V SW > V A , where V, V SW , and V A are the CME, solar wind, and Alfven velocities, respectively. Perpendicular to the CME axis, at distances of ≈4–6R ⊙ fromthe center of the Sun, the condition for the formation of shock is V/2 > V A .

Feedback instability analysis for dipole configuration with ionospheric and magnetospheric cavities

[1] Linear eigenmodes of ionospheric feedback instability in the dipole magnetic field geometry are investigated by considering the ionospheric and magnetospheric resonant cavities with inhomogeneous Alfven velocity profiles. The two-field reduced magnetohydrodynamic model is used to describe shear Alfven wave dynamics, associated with auroral arcs, in a strongly nonuniform magnetic flux tube. Linear properties of ionospheric cavity modes (eigenfrequency and eigenfunctions) are examined for a wider parameter range than the previous works. It is found that several harmonics, denoted by the mode numbers of n = 3, 6–7, 10–11, …, are trapped in the cavity region, and their magnetic fluctuations have a large amplitude at the ionosphere, leading to a high growth rate. By steepening a gradient of the Alfven velocity on the magnetospheric side, the properties of ionospheric cavity modes are fully dismissed from these low n harmonics, although their growth rates remain small positive values. On the other hand, the fundamental field line resonant mode (n = 0) has a high growth rate with a large amplitude of magnetic fluctuations at the ionosphere owing to the magnetospheric cavity. Possible spatial and temporal scales of auroral arcs and ULF wave resonances in a realistic situation are discussed.

Ejection of cool plasma into the hot corona

We investigate the processes that lead to the formation, ejection and fall of a confined plasma ejection that was observed in a numerical experiment of the solar corona. By quantifying physical parameters such as mass, velocity, and orientation of the plasma ejection relative to the magnetic field, we provide a description of the nature of this particular phenomenon. The time-dependent three-dimensional magnetohydrodynamic (3D MHD) equations are solved in a box extending from the chromosphere to the lower corona. The plasma is heated by currents that are induced through field line braiding as a consequence of photospheric motions. Spectra of optically thin emission lines in the extreme ultraviolet range are synthesized, and magnetic field lines are traced over time. Following strong heating just above the chromosphere, the pressure rapidly increases, leading to a hydrodynamic explosion above the upper chromosphere in the low transition region. The explosion drives the plasma, which needs to follow the magnetic field lines. The ejection is then moving more or less ballistically along the loop-like field lines and eventually drops down onto the surface of the Sun. The speed of the ejection is in the range of the sound speed, well below the Alfven velocity. The plasma ejection is basically a hydrodynamic phenomenon, whereas the rise of the heating rate is of magnetic nature. The granular motions in the photosphere lead (by chance) to a strong braiding of the magnetic field lines at the location of the explosion that in turn is causing strong currents which are dissipated. Future studies need to determine if this process is a ubiquitous phenomenon on the Sun on small scales. Data from the Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO) might provide the relevant information.

Evolution of symmetric reconnection layer in the presence of parallel shear flow

The development of the structure of symmetric reconnection layer in the presence of a shear flow parallel to the antiparallel magnetic field component is studied by using a set of one-dimensional (1D) magnetohydrodynamic (MHD) equations. The Riemann problem is simulated through a second-order conservative TVD (total variation diminishing) scheme, in conjunction with Roe’s averages for the Riemann problem. The simulation results indicate that besides the MHD shocks and expansion waves, there exist some new small-scale structures in the reconnection layer. For the case of zero initial guide magnetic field (i.e., By0 = 0), a pair of intermediate shock and slow shock (SS) is formed in the presence of the parallel shear flow. The critical velocity of initial shear flow Vzc is just the Alfven velocity in the inflow region. As Vz∞ increases to the value larger than Vzc, a new slow expansion wave appears in the position of SS in the case Vz∞ < Vzc, and one of the current densities drops to zero. As plasma β increases, the out-flow region is widened. For By0 ≠ 0, a pair of SSs and an additional pair of time-dependent intermediate shocks (TDISs) are found to be present. Similar to the case of By0 = 0, there exists a critical velocity of initial shear flow Vzc. The value of Vzc is, however, smaller than the Alfven velocity of the inflow region. As plasma β increases, the velocities of SS and TDIS increase, and the out-flow region is widened. However, the velocity of downstream SS increases even faster, making the distance between SS and TDIS smaller. Consequently, the interaction between SS and TDIS in the case of high plasma β influences the property of direction rotation of magnetic field across TDIS. Thereby, a wedge in the hodogram of tangential magnetic field comes into being. When β → ∞, TDISs disappear and the guide magnetic field becomes constant.

Excitation of magnetosonic waves in the terrestrial magnetosphere: Particle-in-cell simulations

[1] Two-dimensional electromagnetic particle-in-cell simulations are performed to study the temporal development of an ion Bernstein instability driven by a proton velocity distribution with positive slope in the perpendicular velocity distribution fp(v⊥), where ⊥ denotes directions perpendicular to the background magnetic field B0. A subtracted Maxwellian distribution is first used to construct the positive slope in fp(v⊥), and linear kinetic dispersion analysis is performed. The results of a simulation using such an initial proton distribution agree well with the linear kinetic analysis. The simulation results demonstrate that the ion Bernstein instability grows at propagation angles nearly perpendicular to B0 and at frequencies close to the harmonics of the proton cyclotron frequency. The distribution in the simulation is further generalized to contain a proton shell with a finite thermal spread and a relatively cold ion background. The simulation results show that the presence of the cold background protons and the increase of the shell velocity shift the excited waves close to the cold plasma dispersion relation for magnetosonic waves, i.e., ωr = kvA, where ωr is the wave frequency, k is the wave number, and vA is the Alfven velocity. The general features of the simulated field fluctuations resemble observations of fast magnetosonic waves near the geomagnetic equator in the terrestrial magnetosphere. A test particle computation of energetic electrons interacting with the simulated electromagnetic fluctuations suggests that this growing mode may play an important role in the acceleration of radiation belt relativistic electrons.

Cluster observations of multiple dipolarization fronts

We present Cluster observations of a series of dipolarization fronts (DF 1 to 6) at the central current sheet in Earth's magnetotail. The velocities of fast earthward flow following behind each DF 1.3 are comparable to the Alfven velocity, indicating that the flow bursts might have been generated by bursty reconnection that occurred tailward of the spacecraft. Based on multispacecraft timing analysis, DF normals are found to propagate mainly earthward at 160.335 km/s with a thickness of 900-1500 km, which corresponds to the ion inertial length or gyroradius scale. Each DF is followed by significant fluctuations in the x and y components of the magnetic field whose peaks are found 1.2 min after the DF passage. These (B(sub x), B(sub y)) fluctuations propagate dawnward (mainly) and earthward. Strongly enhanced field-aligned beams are observed coincidently with (B(sub x), B(sub y)) fluctuations, while an enhancement of cross-tail currents is associated with the DFs. From the observed pressure imbalance and flux tube entropy changes between the two regions separated by the DF, we speculate that interchange instability destabilizes the DFs and causes the deformation of the midtail magnetic topology. This process generates significant field-aligned currents and might power the auroral brightening in the ionosphere. However, this event is associated with neither the main substorm auroral breakup nor the poleward expansion, which might indicate that the observed multiple DFs have been dissipated before they reach the inner plasma sheet boundary.

Multipoint Spectroscopy Measurement of Spherical Tokamak Heating by Magnetic Reconnection in UTST

The temporal evolution of ion temperature and flow was observed to investigate the heating effect of plasma merging in the UTST device by using a multipoint Doppler spectroscopy measurement system. The bulk plasma ion temperature measured by a carbon impurity line was about 15-20 eV after plasma merging. In addition, anomalous broadening of the carbon line width was observed only in the early phase of plasma merging. Since carbon impurity emission comes mainly from the X-point and the vicinity of the center stack, the broad spectrum is considered to consist of a radially bi-directional outflow component from the X-point and a stationary component near the center stack. The outflow velocity estimated from the spectroscopy was about 24 km/s, which agreed well with both an Alfven velocity of 22 km/s and a velocity of the reconnected field line motion of 35 km/s.

Alfvén Waves: Coherent Phenomena in Coronal Loops and Open-Field Regions

We analyze two situations where coherent properties of Alfvenic perturbations influence the behaviour of a turbulent system. The first case is a coronal loop where large scales are dominated by coherent fluctuations (eigenmodes) excited by resonance with motions at the loop bases. The input energy flux is mainly determined by the zero-frequency eigenmode which is independent of the background Alfven velocity profile; the resulting scaling law gives values compatible with the flux necessary to sustain the active-region corona. Nonlinear interactions are also influenced by coherence effects. From the resulting nonlinear flux a scaling law for the velocity perturbation is derived, which is compatible with measures of nonthermal velocities in corona. In second case we studied how monochromatic Alfven waves, propagating upward from the coronal base in a coronal hole region, develop small scales in form of a power-law spectrum when they go across a thin 3D inhomogeneous layer (∼104 km thick) located at the base of the corona. Though the obtained spectrum is steeper than what would be obtained by means of nonlinear interactions, it could influence the subsequent nonlinear dynamics of the system by reducing the time of heat deposition, with consequences on the acceleration of the solar wind.

Effect of Hall current on the Jeans instability of magnetized viscous quantum plasma

The effect of Hall current on the Jeans instability of an infinitely conducting, homogeneous, viscous quantum plasma is investigated. The basic equations of the problem are constructed and linearized by using the quantum magnetohydrodynamic model. The contributions of Hall current and viscosity of the medium are incorporated into the present analysis because of their astrophysical importance. The general dispersion relation is obtained using the normal mode analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Hall current, while the transverse mode is unaffected by the presence of the Hall parameter. The Jeans criterion of instability is obtained, which is modified by Alfven velocity and quantum corrections but is unaffected by the presence of the Hall parameter and viscosity. The longitudinal mode is found to be modified by Alfven speed and the Hall parameter and is independent of quantum corrections. Viscosity, magnetic field and quantum corrections all have a stabilizing influence on the growth rate of the Jeans instability.

Obliquely propagating solitary kinetic Alfven wave in a collisional dusty plasma

An obliquely propagating solitary kinetic Alfven wave in a low beta dusty plasma (β⪡me/mi) is studied by considering the ion motion along the magnetic field and the collisional effect of electrons. The existence condition for a solitary wave for a collisionless dusty plasma is re-examined. It is found that there is an upper limit of the possible Alfvenic Mach velocity, imposed by dust particles. The Mach number lies between lz and lz/Nd, where lz is the directional cosine and Nd is the dust particle charge density. In the collisional case, the same upper limit of the Mach velocity is found, and the solitary wave turns into an oscillating double layer. The damping scale and the size of the oscillation structure increase with increasing dust particle charge density. The damping scale and the size of the oscillation structure are estimated by using the virial theorem.

Three-dimensional evolution of the fast reconnection mechanism in a sheared current sheet

Extending the previous simulation model with the plane symmetry boundaries, the present paper studies the three-dimensional (3D) fast reconnection evolution in the presence of an initial sheared field by employing the axis symmetry boundary conditions. The fast reconnection evolution for the open system, where the reconnection outflow is open to free space, is not significantly influenced by the sheared field, although for the larger magnitude of the sheared field its onset time is more delayed and the fast reconnection process tends to proceed more steadily. In any case, the diffusion region remains to be localized around the X neutral line, and the fast reconnection outflow jet is accelerated to the Alfven velocity by standing slow shocks. The initial sheared field lines are swept away by the reconnection jet, and attached to the jet, a large-scale plasmoid is formed and propagates outward. In the plasmoid, the reconnected sheared field lines are accumulated near the interface between the reconnection jet and the plasmoid, and the sheared field is piled up in the form of a core. The 3D plasmoid propagation is considerably distorted in the direction of the sheared magnetic field since the plasma tends to be accelerated along the sheared field lines.

Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium

The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed.

TOWARD A MAGNETOHYDRODYNAMIC THEORY OF THE STATIONARY ACCRETION SHOCK INSTABILITY: TOY MODEL OF THE ADVECTIVE-ACOUSTIC CYCLE IN A MAGNETIZED FLOW

The effect of a magnetic field on the linear phase of the advective-acoustic instability is investigated, as a first step toward a magnetohydrodynamic (MHD) theory of the stationary accretion shock instability taking place during stellar core collapse. We study a toy model where the flow behind a planar stationary accretion shock is adiabatically decelerated by an external potential. Two magnetic field geometries are considered: parallel or perpendicular to the shock. The entropy-vorticity wave, which is simply advected in the unmagnetized limit, separates into five different waves: the entropy perturbations are advected, while the vorticity can propagate along the field lines through two Alfven waves and two slow magnetosonic waves. The two cycles existing in the unmagnetized limit, advective-acoustic and purely acoustic, are replaced by up to six distinct MHD cycles. The phase differences among the cycles play an important role in determining the total cycle efficiency and hence the growth rate. Oscillations in the growth rate as a function of the magnetic field strength are due to this varying phase shift. A vertical magnetic field hardly affects the cycle efficiency in the regime of super-Alfvenic accretion that is considered. In contrast, we find that a horizontal magnetic field strongly increases the efficiencies of the vorticity cycles that bend the field lines, resulting in a significant increase of the growth rate if the different cycles are in phase. These magnetic effects are significant for large-scale modes if the Alfven velocity is a sizable fraction of the flow velocity.

Tayler instability of toroidal magnetic fields in MHD Taylor‐Couette flows

AbstractThe nonaxisymmetric Tayler instability (TI) of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two infinitely long corotating cylinders. For given Reynolds number of rotation the magnetic Prandtl number Pm of the liquid conductor and the ratio of the cylinder's rotation rates are the free parameters. It is shown that for resting cylinders the critical Hartmann number for instability does not depend on Pm hence the TI also exists in the limit Pm → 0. By rigid rotation the instability is suppressed where for Pm = 1 the rotational quenching takes its maximum. Rotation laws with negative shear (i.e. dΩ /dR < 0) strongly destabilize the toroidal field if the rotation is not too fast. In galaxies with their quadrupolar magnetic field geometry this effect could have drastic implications. For sufficiently high Reynolds numbers of rotation, however, the TI completely disappears. For the considered magnetic constellation the superrotation laws support the rotational stabilization. The angular momentum transport of the instability is anticorrelated with the shear so that an eddy viscosity can be defined which proves to be positive.We have also shown the possibility of laboratory TI experiments with a wide‐gap container filled with fluid metals like sodium or gallium. Even the effect of the rotational stabilization can be reproduced in the laboratory with electric currents of only a few kA (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The radiation impedance of electrodynamic tethers in a polar Jovian orbit

Juno, the second mission in the NASA New Frontiers Program, will both be a polar Jovian orbiter, and use solar arrays for power, moving away from previous use of radioisotope power systems (RPSs) in spite of the weak solar light reaching Jupiter. The power generation at Jupiter is critical, and a conductive tether could be an alternative source of power. A current-carrying tether orbiting in a magnetized ionosphere/plasmasphere will radiate waves. A magnitude of interest for both power generation and signal emission is the wave impedance. Jupiter has the strongest magnetic field in the Solar Planetary System and its plasma density is low everywhere. This leads to an electron plasma frequency smaller than the electron cyclotron frequency, and a high Alfven velocity. Unlike the low Earth orbit (LEO) case, the electron skin depth and the characteristic size of plasma contactors affect the Alfven impedance.