1. 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

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

3. 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┴

4. Quasi-Static Approximation
k >> 2π/λem

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

6. 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)

7. Real part
Imaginary part

8. 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

9. OEDIPUS-C Experiment (1995)

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

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

12. 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

13. 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

14. Model of the Incident Wave Field and Its Source

15. 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

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

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

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

19. Estimate of kobs kz
θobs
θres
kobs k┴

20. THEMIS C A
Date
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)
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

21. 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.