Linearized theory of inhomogeneous multiple ‘water-bag’ plasmas

The problem of the stability of inhomogeneous, electrostatic, multiple water-bag plasmas is considered. Equations are derived for general stationary water-bag equilibria, as well as for the corresponding perturbations. Particular attention is directed to systems with trapped particles in periodic equilibria, and special boundary conditions for the perturbation equations at the trapped-particle turning points are introduced. A normal-mode analysis is carried out for a configuration involving trapped particles occupying a finite region in the vicinity of the trough of an equilibrium wave (BGK mode). The results confirm the validity of the bunched-beam approximation.

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Stability of isothermal magnetohydrodynamic shock waves

Journal of Plasma Physics ◽

10.1017/s0022377800007868 ◽

1973 ◽

Vol 10 (2) ◽

pp. 301-316 ◽

Cited By ~ 2

Author(s):

Nicole Bel ◽

Colette Laury-Micoulaut

Keyword(s):

Shock Waves ◽

Normal Mode ◽

Normal Mode Analysis ◽

Mode Analysis ◽

Magnetohydrodynamic Shock ◽

The Stability

The stability of normal isothermal magnetohydrodynamic shock waves is studied with respect to isothermal as well as adiabatic perturbations. The problem is solved by the normal-mode analysis. The isothermal normal MHD shock appears to be stable.

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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2020052 ◽

2020 ◽

Author(s):

Christophe Besse ◽

Jean-Francois Coulombel ◽

Pascal Noble

Keyword(s):

Boundary Conditions ◽

Normal Mode Analysis ◽

Mode Analysis ◽

General Strategy ◽

Computational Domain ◽

Two Dimensional ◽

Transparent Boundary Conditions ◽

Finite Difference Approximations ◽

Four Corners ◽

The Stability

We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with a Cartesian grid. For the two-dimensional leap-frog scheme, we explain why our strategy provides with explicit numerical boundary conditions on the four sides of the rectangle and why it does not require prescribing any condition at the four corners of the computational domain. The stability of the numerical boundary condition on each side of the rectangle is analyzed by means of the so-called normal mode analysis. Numerical investigations for the full problem on the rectangle show that strong instabilities may occur when coupling stable strategies on each side of the rectangle. Other coupling strategies yield promising results.

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RAMAN SPECTRA OF TITANIUM DI-, TRI-, AND TETRA-CHLORIDES

International Journal of Modern Physics B ◽

10.1142/s021797920100886x ◽

2001 ◽

Vol 15 (28n30) ◽

pp. 3865-3868 ◽

Cited By ~ 2

Author(s):

H. MIYAOKA ◽

T. KUZE ◽

H. SANO ◽

H. MORI ◽

G. MIZUTANI ◽

...

Keyword(s):

Force Constant ◽

Raman Spectra ◽

Normal Mode ◽

Raman Band ◽

Normal Mode Analysis ◽

Force Constants ◽

Mode Analysis ◽

Oxidation Number

We have obtained the Raman spectra of TiCl n (n= 2, 3, and 4). Assignments of the observed Raman bands were made by a normal mode analysis. The force constants were determined from the observed Raman band frequencies. We have found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases.

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