Real Hamilton equations of geometric optics for media with moderate absorption

Suchy, K.

doi:10.1029/rs016i006p01179

Cited by 46 publications

(34 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A corresponding set of ordinary differential equations describing the evolution of whistler wave-vector, frequency and propagation trajectory can be found elsewhere (Suchy, 1981). This approach is valid when the characteristic scale of the medium property (density, temperature, distribution function, etc.)…”

Section: Ray Tracing Of Whistler Wave Packetsmentioning

confidence: 99%

Observations and modeling of forward and reflected chorus waves captured by THEMIS

et al. 2011

View full text Add to dashboard Cite

Abstract. Discrete ELF/VLF chorus emissions are the most intense electromagnetic plasma waves observed in the radiation belts of the Earth's magnetosphere. Chorus emissions, whistler-mode wave packets propagating roughly along magnetic field lines from a well-localized source in the vicinity of the magnetic equator to polar regions, can be reflected at low altitudes. After reflection, wave packets can return to the equatorial plane region. Understanding of whistler wave propagation and reflection is critical to a correct description of wave-particle interaction in the radiation belts. We focus on properties of reflected chorus emissions observed by the THEMIS (Time History of Events and Macroscale Interactions During Substorms) spacecraft Search Coil Magnetometer (SCM) and Electric Field Instrument (EFI) at ELF/VLF frequencies up to 4 kHz at L ≥ 8. We determine the direction of the Poynting flux and wave vector distribution for forward and reflected chorus waves. Although both types of chorus waves were detected near the magnetic equator and have similar, discrete structure and rising tones, reflected waves are attenuated by a factor of 10-30 and have 10% higher frequency than concurrently-observed forward waves. Modeling of wave propagation and reflection using geometrical optics ray-tracing allowed us to determine the chorus source region location and explain observed propagation characteristics. We find that reflected wave attenuation at a certain spatial region is caused by divergence of the ray paths of these non-ducted emissions, and that the frequency shift is caused by generation of the reflected waves at lower L-shells where the local equatorial gyrofrequency is larger.

show abstract

Section: Ray Tracing Of Whistler Wave Packetsmentioning

confidence: 99%

Observations and modeling of forward and reflected chorus waves captured by THEMIS

et al. 2011

View full text Add to dashboard Cite

show abstract

“…This can be achieved making use of real Hamiltonian equations in a medium with moderate absorption (Suchy, 1981), in other words, by using eikonal equations which allow one to express the Maxwell equations for electromagnetic waves in terms of geometrical rays. This approximation is called the WKB or geometrical optics approximation and usually leads to the system of ordinary differential equations (ODEs) that can be then integrated numerically (e.g.…”

Section: Appendix a Ray Tracing Technique And Numerical Code Descriptionmentioning

confidence: 99%

“…Then, a solution of this equation by the method of characteristics (Suchy, 1981), assuming moderate absorption, leads to the following ODE system (real Hamilton equations for complex space-time coefficients):…”

Section: Appendix a Ray Tracing Technique And Numerical Code Descriptionmentioning

confidence: 99%

Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

et al. 2012

View full text Add to dashboard Cite

Abstract. Discrete ELF/VLF (Extremely Low Frequency/Very Low Frequency) chorus emissions are one of the most intense electromagnetic plasma waves observed in radiation belts and in the outer terrestrial magnetosphere. These waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. The objective of our study is to reconstruct the realistic distribution of chorus wave-normals in radiation belts for all magnetic latitudes. To achieve this aim, the data from the electric and magnetic field measurements onboard Cluster satellite are used to determine the wave-vector distribution of the chorus signal around the equator region. Then the propagation of such a wave packet is modeled using three-dimensional ray tracing technique, which employs K. Rönnmark's WHAMP to solve hot plasma dispersion relation along the wave packet trajectory. The observed chorus wave distributions close to waves source are first fitted to form the initial conditions which then propagate numerically through the inner magnetosphere in the frame of the WKB approximation. Ray tracing technique allows one to reconstruct wave packet properties (electric and magnetic fields, width of the wave packet in k-space, etc.) along the propagation path. The calculations show the spatial spreading of the signal energy due to propagation in the inhomogeneous and anisotropic magnetized plasma.Comparison of wave-normal distribution obtained from ray tracing technique with Cluster observations up to 40 • latitude demonstrates the reliability of our approach and applied numerical schemes.

show abstract

“…For ray tracing, if v g is complex, dx /dt=Re(vg/vg)is assumed, where t = x° is the time. See Suchy (1981) and references therein for further details.…”

Section: Generalization Of Hayes' Argumentmentioning

confidence: 99%

A General Relationship between Group Velocity and Fluxes Quadratic in Wave Amplitude

Noda¹

1986

Journal of the Meteorological Society of Japan

View full text Add to dashboard Cite

As an extension of M. Hayes' argument (Hayes, 1977), a general relationship is derived between group velocity and fluxes quadratic in wave amplitude for single, weakly-modulated small amplitude plane waves propagating in an inhomogeneous, non-conservative, dispersive system. If a quadratic (4-) flux constructed from wave quantities with a common single harmonic phase is inserted into its linear governing equation, the resultant equation consists of a wave part with a hi-harmonic phase and a mean part, but both parts must vanish separately to satisfy the equation. The amplitude of the former gives the dispersion relation, H(k*)=0; this in turn gives the complex (4-)group velocity vector *g=*H/ * by varying the complex (4-)wavenumber vector k*(*=0, 1, 2 and 3). On the other hand, the latter gives a governing equation for the mean of the quadratic flux, and also gives, by taking the same variation, another mean quadratic flux. The latter flux is proportional to the group velocity *g. The general relationship is illustrated by application to Rossby wave motions. The group velocity and energy flux relation obtained by Longuet-Higgins (1964) is rederived as a special case.

show abstract

Real Hamilton equations of geometric optics for media with moderate absorption

Cited by 46 publications

References 8 publications

Observations and modeling of forward and reflected chorus waves captured by THEMIS

Observations and modeling of forward and reflected chorus waves captured by THEMIS

Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

A General Relationship between Group Velocity and Fluxes Quadratic in Wave Amplitude

Contact Info

Product

Resources

About