Theory of Quasi-Electrostatic Waves in a Magnetoplasma Applied to Antenna Measurements on Board Rockets and Satellites Evgenii A. Shirokov Institute of.

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Presentation transcript:

Theory of Quasi-Electrostatic Waves in a Magnetoplasma Applied to Antenna Measurements on Board Rockets and Satellites Evgenii A. Shirokov Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

Outline Introduction Excitation of quasi-electrostatic waves Propagation of quasi-electrostatic waves Reception of quasi-electrostatic waves Conclusion

LH < 0 < ce /2 < pe Whistler-Mode Waves kz LH < 0 < ce /2 < pe Electromagnetic waves Quasi-electrostatic waves (k >>2π/λem) (k) = 0 = const Resonance cone k┴

Quasi-Static Approximation k >> 2π/λem

– a resonance cone in r-space Green’s Function – a resonance cone in r-space

Excitation of Quasi-Electrostatic Waves Integral equation: 2a 2L << λem 2L given potential on the antenna surface S unknown surface charge density S Solution methods: 1. Analytical (only for simple geometry) 2. Numerical (the method of moments)

Real part Imaginary part

Propagation of Quasi-Electrostatic Waves unknown potential given charge distribution on the antenna Solution method: Fourier transform Key features of the radiation field: it is localized on the resonance cone; it is subject to a nondispersive pulse spreading and a significant group delay. t t t

OEDIPUS-C Experiment (1995)

Received Signals at 100 kHz noise level noise level initial pulse duration T = 0.3 ms

Effective Length of a Receiving Antenna γ Er exp(–it) lgeom E exp(–it) Reradiated (scattered) wave Incident wave U = Eleff cos γ lgeom ≠ leff due to reradiation

Calculation of the Antenna Response Reciprocity theorem: Charge fluctuation in a plasma Antenna trial charge 0exp(–it)  exp(–it)  exp(–it) 0exp(–it) Incident field Trial field

Resonance direction for the group velocity Source Model τ Spacecraft with receiving antennas H0 Resonance direction for the group velocity ξ Fictitious source of chorus emissions

Model of the Incident Wave Field and Its Source

Main Parameters of the Model The source length ltr kobsltrcos θres = 2√2 Distance τ0 from the source to the spacecraft along the resonance cone

Resulting Expression for the Effective Length Thin Straight Dipole Piecewise constant charge distribution Two Small Spheres Approximation with 2 point charges

Poynting Vector THEMIS C 28.08.2007 15:51:46.3 UT THEMIS A

Wave Normal Angle THEMIS C 28.08.2007 15:51:46.3 UT THEMIS A

Estimate of kobs kz θobs θres kobs k┴

THEMIS C A Date 28.08.2007 26.11.2008 UT (h:min:s) 15:51:48 03:18:23 λm (deg.) 15 L 5.4 5.0 ω0 (s-1) 9 425 15 708 ωce (s-1) 47 005 38 020 ωpe (s-1) 160 346 130 062 θres (deg.) 78.0 64.7 θobs (deg.) 75.0 58.0 leff/lrec 2.7, 2.7, and 0.4 13, 12, and 0.8

Conclusion The theory of quasi-electrostatic waves in a magnetoplasma covers all aspects of antenna measurements in the near-Earth plasma (excitation, propagation, and reception). This theory has been used to analyze the results of some antenna measurements on board rockets and satellites in the near-Earth plasma.