1. Dipole Antennas Driven at High Voltages in the Plasmasphere
Linhai Qiu
Mentor: Timothy Bell
Advisor: Umran Inan December 12, 2010

2. Outline Introduction Nonlinear Sheath Impedance
Number Densities of Electrons and Ions
Antenna Tuning
The Effects of Ion-to-electron Mass Ratio
Summary

3. Introduction
The plasma sheath characteristics have significant influence on the input impedance of antennas driven by high-voltages in magnetized plasmas.
Study the near-field properties of antennas driven by voltages from 86 V to 5000 V with AIP code developed by Timothy Chevalier.
Extracting accurate models of sheath capacitance and conductance from numerical results and developing the method of tuning high-voltage antennas in the plasmasphere.

4. Outline Introduction Nonlinear Sheath Impedance
Number Densities of Electrons and Ions
Antenna Tuning
The Effects of Ion-to-electron Mass Ratio
Summary

5. Simulation
Code: Fully parallel 3-D nonlinear multi-moment hydrodynamic code developed by Timothy Chevalier
Simulation object: Determine near field of antennas in the magnetosphere for various driving voltages.
To provide an example, consider the antenna located at L = 3 where the electron density is 1×10−9 m−3, the magnetic field is 1.165×10−6 T, the plasma temperature is 2000 K. The length of one antenna branch is 9 m, the gap between the two antenna elements is 2 m, the diameter of the antenna is 10 cm, and the frequency is 25 kHz.

6. Voltage at 103 V drive voltage
The voltage variation shown on the left is the voltage of one antenna element, defined to be the voltage with respect to the distant neutral plasma.
Maximum positive voltage: 10 V
Maximum negative voltage: -100 V

7. Conductive Current (103 V)
The currents shown on the left are the currents formed by the particles from the plasmas hitting on one antenna element.
Peak-to-peak magnitude: ~ 2 mA
Electron current has larger peak magnitude, but shorter duration
Proton current has smaller peak magnitude, but longer duration

8. Displacement Current (103 V)
The displacement currents shown on the left is defined as the derivative of the charge of one antenna element with respect to time.
Peak-to-peak magnitude: ~ 3 mA
Nonlinear and NOT sinusoidal
Conductive current is non-negligible compared to displacement current

9. Voltage at 1035 V drive voltage
Maximum positive voltage: 100 V
Maximum negative voltage: -950 V
It appears that there may be a small long-term variation of the average voltage. The cause of such variation is still under investigation.

10. Conductive Current (1035 V)
Peak-to-peak magnitude: ~ 10 mA
Peak-to-peak magnitude 5 times as large as that of 103 V
Indicating the sheath conductance decreases as the voltage increases

11. Displacement Current (1035 V)
Peak-to-peak magnitude: ~ 22.5 mA
Peak-to-peak magnitude 7.5 times as large as that of 103 V
Sheath capacitance decreases slower than sheath conductance as the voltage increases

12. Sheath Capacitance (86V)
The analytical model: Mlodnosky and Garriott (1963)
Analytical model assumes protons are stationary
Analytical model gives sheath capacitance as coaxial cylindrical capacitance

13. Sheath Capacitance (1035 V)
The splitting occurs at low voltage magnitude

14. Sheath Conductance (86V)
The analytical model: derived based on the theory of metallic structures in gaseous discharges formulated by Mott-Smith and Langmuir [1926]

15. Sheath Conductance (1035 V)
The splitting occurs at low voltage magnitude
The figures contain the data points of 8 RF cycles
Inertia is the primary cause of splitting

16. Outline Introduction Nonlinear Sheath Impedance
Number Densities of Electrons and Ions
Antenna Tuning
The Effects of Ion-to-electron Mass Ratio
Summary

17. Evolution of Proton Number Density
1 and 4 correspond to negative voltages
2 and 3 correspond to positive voltages
Antenna position: 30 m
Antenna orientation: perpendicular to the magnetic field, vertical in the figure

18. Number Density of Particles30 40 50 20 10
Position / m
Density / m-3 2 4 8 6
×109
Antenna position: 30 m
Antenna orientation: vertical

19. Large Depletion Region
Sheath region
Distinguish depletion region from the sheath region
The depletion region outside sheath region is almost neutral
The shape of the depletion region is found to be roughly spherical by examining several slice planes

20. Outline Introduction Nonlinear Sheath Impedance
Number Densities of Electrons and Ions
Antenna Tuning
The Effects of Ion-to-electron Mass Ratio
Summary

21. Circuit model Need accurate models of sheath capacitance
and sheath conductance

22. Extract New Models Sheath capacitance
Add correction factors to the parameters of the original model
Minimizing least square errors numerically

23. Extract New Models Sheath Conductance
Splitting is not reflected in the new models
Large errors at low voltages will not greatly influence the overall performance

24. Comparison at 103 V After reaching the quasi-steady state,
Errors of peak-to-peak magnitude of the conductive currents: ~ 12 %
Errors of peak-to-peak magnitude of the displacement currents: ~ 12 %

25. Comparison at 1035 V
Errors are large in the transient response, but after reaching quasi-steady state,
Errors of peak-to-peak magnitude of the conductive currents: ~ 6 %
Errors of peak-to-peak magnitude of the displacement currents: ~ 1 %
The errors become smaller when the drive voltage is larger.

26. Tuning the Antenna
The left plot shows how the peak-to-peak charge magnitude on the antenna element changes with the value of tuning inductance L
Drive Voltage: 1500 V
Optimum inductance: H
Maximum Charge: 680 nC

27. One Possible Tuning Scheme
Step 1: Calculate the real power and apparent power from the measured time domain v (t) and i (t)
Step 2: Calculate the reactive power Q from the apparent power S and the real power P according to the relation on the left.
Step 3: Estimate the change of tuning inductance needed to cancel the reactive power, so as to minimize the angle φ.
Step 4: Do tuning iteratively.

28. Mathematical Experiments
One example
Drive voltage: 1500 V
Optimum inductance: 0.66 H
Maximum charge: 0.68µC
Tuning process:
We will work with Ivan Galkin from UML to optimize the tuning scheme.
0H → H → H
0.19µC → µC → 0.65µC
43 mA → 107 mA → 113 mA

29. Outline Introduction Nonlinear Sheath Impedance
Number Densities of Electrons and Ions
Antenna Tuning
The Effects of Ion-to-electron Mass Ratio
Summary

30. Effects of Ion-electron Mass Ratio
Tim Chevalier used 200 as the proton-electron mass ratio to reduce the computation time.
The real mass ratio of proton to electron is 1835.
It can be predicted that both the proton and electron currents will decrease if using the mass ratio of 1835

31. Effects of Ion-electron Mass Ratio
Mass ratio mainly influences the conductive currents
The sheath capacitance and conductance model extracted at 86 V with 200 mass ratio correctly predicts the results at 1035 V with 1835 mass ratio

32. Summary
The efforts of modeling antenna-plasma coupling is extended to higher voltages that were not investigated before, from 86 V to 5000 V. The maximum voltage investigated by Timothy Chevalier was 86 V, due to the limited computer resources.
The terminal voltages, currents and input impedance of a dipole antenna in the plasmasphere are investigated from 86 V to 5000 V drive voltages with AIP code.
The particle number densities show a large quasi-neutral depletion regions surrounding the antenna elements
Models of conductance and capacitance of the sheath are extracted from the numerical results.
Tuning problems are investigated and an iterative tuning method is proposed and tested.

33. Thank you!