Stability analysis of the polytropic solar wind

2014 ◽  
Vol 92 (11) ◽  
pp. 1419-1424 ◽  
Author(s):  
P.K. Karmakar ◽  
M. Gohain ◽  
U. Deka
Keyword(s):  
Growth Rate ◽  
Solar Wind ◽  
Stability Analysis ◽  
Dispersion Relation ◽  
Dynamic Equilibrium ◽  
Nonlinear Function ◽  
Linear Growth Rate ◽  
Polytropic Index ◽  
Solar Plasma ◽  
Polytropic Model

A linear stability analysis of a simple polytropic model for the solar wind dynamics within the framework of a magnetohydrodynamic equilibrium configuration is theoretically proposed. The simplistic analysis is based on the model developed based on the data available from the Advanced Composition Explorer (ACE) spacecraft mission. A unique form of dispersion relation is derived by coupling the adiabatic and polytropic processes in the limit of ideal gas approximation for the solar wind gas in accordance with the standard Fourier technique. Applying usual variable-separation methodology on the dispersion relation, we obtain the linear growth rate of the fluctuations. It is seen that the growth rate is an explicitly nonlinear function of the variable polytropic index (α) and radial position (r) with respect to the considered center of the Sun. Numerical analyses are carried out to understand the physical insight of the growth profiles of the fluctuations. It is shown that the growth is maximized near the solar corona, where α ∼ 1, relative to that observed elsewhere in the entire solar plasma system. The source for this growth may be attributed to the free flow of energy coming from the dynamic equilibrium of the solar plasma itself. As compared with existing model predictions, our results are qualitatively capable of reproducing the average behavior of the solar wind fluctuation and stability behaviors on the astrophysical scales of space and time.

scholarly journals Are Numerical Simulations Reliable? Proposed Improvements and Tests

1987 ◽  
Vol 117 ◽  
pp. 279-279
Author(s):  
F. R. Bouchet
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Numerical Experiments ◽  
Linear Growth ◽  
Numerical Dispersion ◽  
Linear Growth Rate ◽  
Linear Regime ◽  
Grid Spacing ◽  
Gravitational Clustering ◽  
Theoretical Predictions

When one builds a code to simulate numerically a process, the first concern is the range of validity of the results. This can be accessed empirically, though the results can be misleading if the tests are too naive. For particle-mesh codes simulating the gravitational clustering, an analytical theory has been proposed in Bouchet et al. 1985. It yields the numerical dispersion relation of the system in the linear regime, and thus describes how the linear growth rate is affected by the discretisation. The theoretical predictions are in agreement with the results of actual numerical experiments: both show that the results of standart particle-mesh codes should not be trusted at distances smaller than 6 to 8 grid-spacing Δx (depending on the detail of the algorithm).

scholarly journals Velocity Shear Instabilities in the Anisotropic Solar Wind

1985 ◽  
Vol 107 ◽  
pp. 371-374
Author(s):  
Stefano Migliuolo
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solar Wind ◽  
Magnetic Energy ◽  
Equilibrium Temperature ◽  
Acoustic Mode ◽  
Plasma Pressure ◽  
Velocity Shear ◽  
Linear Growth Rate ◽  
Quasilinear Theory

The linear and quasilinear theory of perturbations in finite-β (β is the ratio of plasma pressure to magnetic energy density), collisionless plasmas, that have sheared (velocity) flows, is developed. A simple, one-dimensional magnetic field geometry is assumed to adequately represent solar wind conditions near the sun (i.e., at R ≃ 0.3 AU). Two modes are examined in detail: an ion-acoustic mode (finite-β stabilized) and a compressional Alfven mode (finite-β threshold, high-β stabilization). The role played by equilibrium temperature anisotropies, in the linear stability of these modes, is also presented. From the quasilinear theory, two results are obtained. First, the feedback of these waves on the state of the wind is such as to heat (cool) the ions in the direction perpendicular (parallel) to the equilibrium magnetic field. The opposite effect is found for the electrons. This is in qualitative agreement with the observed anisotropies of ions and electrons, in fast solar wind streams. Second, these quasilinear temperature changes are shown to result in a quasilinear growth rate that is lower than the linear growth rate, suggesting saturation of these instabilities.

scholarly journals Weibel instability in a plasma with nonzero external magnetic field

2012 ◽  
Vol 30 (7) ◽  
pp. 1051-1054 ◽  
Author(s):  
O. A. Pokhotelov ◽  
M. A. Balikhin
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
External Magnetic Field ◽  
Linear Growth ◽  
Cyclotron Frequency ◽  
Linear Growth Rate ◽  
Temperature Anisotropy ◽  
Formal Similarity ◽  
Weibel Instability

Abstract. The theory of the Weibel instability is generalized for the case of a plasma immersed in a nonzero external magnetic field. It is shown that the presence of this external field modifies the dispersion relation for this mode which now possesses a nonzero frequency. The explicit expression for the real and imaginary parts of the frequency is then calculated. It turns out that the linear growth rate remains unchanged, whereas the frequency becomes nonzero due to the finite value of the electron cyclotron frequency. The frequency of the Weibel mode is found to be proportional to the electron temperature anisotropy. The formal similarity of the Weibel and drift-mirror instabilities is outlined.

scholarly journals Nonlinear saturation of the Weibel instability in a dense Fermi plasma

2009 ◽  
Vol 75 (2) ◽  
pp. 251-258 ◽  
Author(s):  
F. HAAS ◽  
P. K. SHUKLA ◽  
B. ELIASSON
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Magnetic Fields ◽  
Intense Laser ◽  
Linear Growth Rate ◽  
Quantum Plasma ◽  
Temperature Anisotropy ◽  
Nonlinear Saturation ◽  
Linear Dispersion ◽  
Transverse Waves

AbstractWe present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi–Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner–Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields are proportional to the linear growth rate of the instability. The present results are important for understanding the origin of intense magnetic fields in dense Fermionic plasmas, such as those in the next-generation intense laser–solid density plasma experiments.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

Microborings and growth in Late Ordovician halysitids and other corals

1993 ◽  
Vol 67 (6) ◽  
pp. 922-934 ◽  
Author(s):  
Robert J. Elias ◽  
Dong-Jin Lee
Keyword(s):  
Growth Rate ◽  
Linear Growth ◽  
Inverse Correlation ◽  
Weight Percent ◽  
Late Ordovician ◽  
Coral Growth ◽  
Linear Growth Rate ◽  
Skeletal Density ◽  
Rugose Coral ◽  
Endolithic Algae

Microborings in the Late Ordovician tabulate corals Catenipora rubra (a halysitid) and Manipora amicarum (a cateniform nonhalysitid) and in an epizoic solitary rugose coral differ from nearly all of those previously reported in Paleozoic corals. These microborings were formed within the coralla by endolithic algae and fungi located beneath living polyps. Comparable structures in the Late Ordovician tabulate Quepora ?agglomeratiformis (a halysitid) represent algal microborings, not spicules, and halysitids are corals, not sponges as suggested by Kaźmierczak (1989).Endolithic algae in cateniform tabulates relied primarily on light entering through the outer walls of the ranks rather than through the polyps; lacunae within coralla permitted appropriate levels of light to reach many corallites. The direction of boring was determined by corallum microstructure and possibly also by the distribution of organic matter within the skeleton. There is an apparent inverse correlation between boring activity and coral growth rate.The location and relative abundance of pyritized microborings within calcareous coralla can be established quantitatively and objectively from electron microprobe determinations of weight percent sulfur along appropriate traverses of the coral skeleton. The distribution of such microborings in Catenipora rubra and Manipora amicarum is comparable to algal banding in modern corals; this is the first report of such banding in the interiors of Paleozoic corals. Change in the intensity of boring within each corallum was evidently a response to variation in the linear growth rate of the coral, or to fluctuation in an environmental factor (perhaps light intensity) that could control both algal activity and growth rate in these corals. Change in the algal boring intensity and linear growth rate of the coral was generally but not always seasonal and usually but not invariably associated with change in the density of coral skeletal deposition.Cyclic bands of boring abundance maxima within fossil colonial corals provide a measure of annual linear growth comparable to the widely accepted method based on skeletal density bands. Algal bands are more sporadically developed than density bands within and among coralla, thus increasing the difficulty of interpretation. Fluctuations in the abundance of algal microborings apparently provide a detailed record of changes in the linear growth rate of colonies and of individuals within colonies. Combined analyses of microboring abundance and skeletal density will contribute significantly to our understanding of the biological and environmental factors involved in endolithic activity and coral growth.

scholarly journals TRACKING DOWN LOCALIZED MODES IN PT-SYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY

2014 ◽  
Vol 54 (2) ◽  
pp. 79-84 ◽  
Author(s):  
Bijan Bagchi ◽  
Subhrajit Modak ◽  
Prasanta K. Panigrahi
Keyword(s):  
Growth Rate ◽  
Refractive Index ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Time Reversal ◽  
Time Parameter ◽  
Optical Systems ◽  
Localized Modes ◽  
Symmetric Structures ◽  
Schrödinger System

The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

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