Normal modes and dispersion relations in a beaded string: An experiment for an undergraduate laboratory

We show what corrections have to be made to the equations of ideal magneto-hydrodynamics when there is fast-time-scale turbulence present in a magnetized plasma. We show how the dispersion relations for the ideal Alfvén and magnetoacoustic MHD normal modes are modified when such turbulence is present. Finally, we discuss the relation of our work to that of other authors.

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Dispersion relation analysis of turbulent magnetic field fluctuations in fast solar wind

Annales Geophysicae ◽

10.5194/angeo-31-1949-2013 ◽

2013 ◽

Vol 31 (11) ◽

pp. 1949-1955 ◽

Cited By ~ 21

Author(s):

C. Perschke ◽

Y. Narita ◽

S. P. Gary ◽

U. Motschmann ◽

K.-H. Glassmeier

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

High Speed ◽

Energy Transport ◽

Normal Modes ◽

Frequency Dispersion ◽

Dispersion Relations ◽

Wave Number ◽

Magnetic Fluctuations ◽

Speed Solar Wind

Abstract. Physical processes of the energy transport in solar wind turbulence are a subject of intense studies, and different ideas exist to explain them. This manuscript describes the investigation of dispersion properties in short-wavelength magnetic turbulence during a rare high-speed solar wind event with a flow velocity of about 700 km s−1 using magnetic field and ion data from the Cluster spacecraft. Using the multi-point resonator technique, the dispersion relations (i.e., frequency versus wave-number values in the solar wind frame) of turbulent magnetic fluctuations with wave numbers near the inverse ion inertial length are determined. Three major results are shown: (1) the wave vectors are uniformly quasi-perpendicular to the mean magnetic field; (2) the fluctuations show a broad range of frequencies at wavelengths around the ion inertial length; and (3) the direction of propagation at the observed wavelengths is predominantly in the sunward direction. These results suggest the existence of high-frequency dispersion relations partly associated with normal modes on small scales. Therefore nonlinear energy cascade processes seem to be acting that are not described by wave–wave interactions.

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II. A program for computing normal modes of molecules, crystal phonon dispersion relations and structure factors for neutron inelastic scattering

Computer Physics Communications ◽

10.1016/0010-4655(78)90016-4 ◽

1978 ◽

Vol 14 (3-4) ◽

pp. 219-243 ◽

Cited By ~ 3

Author(s):

Flemming Yssing Hansen

Keyword(s):

Inelastic Scattering ◽

Phonon Dispersion ◽

Normal Modes ◽

Dispersion Relations ◽

Neutron Inelastic Scattering ◽

Crystal Phonon ◽

Structure Factors ◽

Phonon Dispersion Relations

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Dispersion relations and normal modes for magnetoelastic waves in ferromagnetic insulators

IEEE Transactions on Magnetics ◽

10.1109/tmag.1977.1059515 ◽

1977 ◽

Vol 13 (4) ◽

pp. 1075-1077

Author(s):

L. Goncalves ◽

N. Zagury

Keyword(s):

Normal Modes ◽

Dispersion Relations ◽

Magnetoelastic Waves

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Wave propagation in pulsar magnetospheres - Dispersion relations and normal modes of plasmas in superstrong magnetic fields

The Astrophysical Journal ◽

10.1086/163978 ◽

1986 ◽

Vol 302 ◽

pp. 120 ◽

Cited By ~ 131

Author(s):

J. Arons ◽

J. J. Barnard

Keyword(s):

Wave Propagation ◽

Magnetic Fields ◽

Normal Modes ◽

Dispersion Relations

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II. A program for computing normal modes of molecules, crystal phonon dispersion relations and structure factors for neutron inelastic scattering

Computer Physics Communications ◽

10.1016/s0010-4655(84)82663-6 ◽

1984 ◽

Vol 35 ◽

pp. C-462-C-463

Author(s):

Flemming Yssing Hansen

Keyword(s):

Inelastic Scattering ◽

Phonon Dispersion ◽

Normal Modes ◽

Dispersion Relations ◽

Neutron Inelastic Scattering ◽

Crystal Phonon ◽

Structure Factors ◽

Phonon Dispersion Relations

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DISPERSION RELATIONS FOR PHONONS IN MAGNESIUM FLUORIDE

Canadian Journal of Physics ◽

10.1139/p67-254 ◽

1967 ◽

Vol 45 (9) ◽

pp. 3079-3090 ◽

Cited By ~ 19

Author(s):

R. S. Katiyar ◽

R. S. Krishnan

Keyword(s):

Secular Equation ◽

Normal Modes ◽

Theoretical Method ◽

Dispersion Relations ◽

Magnesium Fluoride ◽

Ionic Character ◽

Axially Symmetric ◽

Longitudinal Modes ◽

Modes Of Vibration ◽

Crystallographic Axes

The lattice dynamics of magnesium fluoride have been investigated theoretically. The group theoretical method is used to decompose the dynamical secular equation at the center of the Brillouin zone. In order to get the expressions for all the infrared-active transverse and longitudinal modes, it is necessary to decompose the secular equation for the wave vector approaching zero along the two nonequivalent crystallographic axes, say y and z, of the crystal. Analysis of the results shows that a rigid ion model of the crystal with axially symmetric forces can provide qualitative agreement with the observed frequencies appearing in Raman and infrared absorption. The ions in the crystal are found to retain 70% of their charges, showing thereby the ionic character of the crystal. The dispersion relations for normal modes of vibration propagating along the (0 0 qz) and (0 qy 0) directions have been evaluated.

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