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Dipole Antennas Driven at High Voltages in the Plasmasphere. Linhai Qiu Mentor: Timothy Bell Advisor: Umran Inan December 12, 2010. Outline. Introduction Nonlinear Sheath Impedance Number Densities of Electrons and Ions Antenna Tuning The Effects of Ion-to-electron Mass Ratio Summary.

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Dipole antennas driven at high voltages in the plasmasphere

Dipole Antennas Driven at High Voltages in the Plasmasphere

Linhai Qiu

Mentor: Timothy Bell

Advisor: Umran InanDecember 12, 2010


Outline
Outline

  • Introduction

  • Nonlinear Sheath Impedance

  • Number Densities of Electrons and Ions

  • Antenna Tuning

  • The Effects of Ion-to-electron Mass Ratio

  • Summary


Introduction
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.


Outline1
Outline

  • 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


Sheath capacitance 86v
Sheath Capacitance (86V)

  • The analytical model: Mlodnoskyand Garriott(1963)

  • Analytical model assumes protons are stationary

  • Analytical model gives sheath capacitance as coaxial cylindrical capacitance


Sheath capacitance 1035 v
Sheath Capacitance (1035 V)

  • The splitting occurs at low voltage magnitude


Sheath conductance 86v
Sheath Conductance (86V)

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


Sheath conductance 1035 v
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


Outline2
Outline

  • 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


Outline3
Outline

  • Introduction

  • Nonlinear Sheath Impedance

  • Number Densities of Electrons and Ions

  • Antenna Tuning

  • The Effects of Ion-to-electron Mass Ratio

  • Summary


Circuit model
Circuit model

Need accurate models of sheath capacitance

and sheath conductance


Extract new models
Extract New Models

  • Sheath capacitance

  • Add correction factors to the parameters of the original model

  • Minimizing least square errors numerically


Extract new models1
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


Comparison at 103 v
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 %


Comparison at 1035 v
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.


Tuning the antenna
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: 0.66 H

  • Maximum Charge: 680 nC


One possible tuning scheme
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.


Mathematical experiments
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 → 0.52 H → 0.71 H

0.19µC → 0.60µC → 0.65µC

43 mA → 107 mA → 113 mA


Outline4
Outline

  • Introduction

  • Nonlinear Sheath Impedance

  • Number Densities of Electrons and Ions

  • Antenna Tuning

  • The Effects of Ion-to-electron Mass Ratio

  • Summary


Effects of ion electron mass ratio
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


Effects of ion electron mass ratio1
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


Summary
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.



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