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Dipole Antennas Driven at High Voltages in the Plasmasphere

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Dipole Antennas Driven at High Voltages in the Plasmasphere

Linhai Qiu

Mentor: Timothy Bell

Advisor: Umran InanDecember 12, 2010

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

- 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.

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

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.

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

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

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

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.

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

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

- The analytical model: Mlodnoskyand Garriott(1963)
- Analytical model assumes protons are stationary
- Analytical model gives sheath capacitance as coaxial cylindrical capacitance

- The splitting occurs at low voltage magnitude

- The analytical model: derived based on the theory of metallic structures in gaseous discharges formulated by Mott-Smith and Langmuir [1926]

- The splitting occurs at low voltage magnitude
- The figures contain the data points of 8 RF cycles
- Inertia is the primary cause of splitting

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

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

Number Density of Particles

×109

8

Density / m-3

6

4

2

- Antenna position: 30 m
- Antenna orientation: vertical

0

40

50

10

20

30

Position / m

Large Depletion Region

Sheath region

Depletion 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

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

Need accurate models of sheath capacitance

and sheath conductance

- Sheath capacitance

- Add correction factors to the parameters of the original model
- Minimizing least square errors numerically

- Sheath Conductance

- Splitting is not reflected in the new models
- Large errors at low voltages will not greatly influence the overall performance

- 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 %

- 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.

- 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: 0.66 H
- Maximum Charge: 680 nC

- 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.

- 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 → 0.52 H → 0.71 H

0.19µC → 0.60µC → 0.65µC

43 mA → 107 mA → 113 mA

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

- 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

- 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

- 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.

Thank you!