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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. - PowerPoint PPT Presentation
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Dipole Antennas Driven at High Voltages in the Plasmasphere
Linhai QiuMentor: Timothy BellAdvisor: Umran Inan
December 12, 2010
2
Outline
1. Introduction
2. Nonlinear Sheath Impedance
3. Number Densities of Electrons and Ions
4. Antenna Tuning
5. The Effects of Ion-to-electron Mass Ratio
6. 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
1. Introduction
2. Nonlinear Sheath Impedance
3. Number Densities of Electrons and Ions
4. Antenna Tuning
5. The Effects of Ion-to-electron Mass Ratio
6. 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.
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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
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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
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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
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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.
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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
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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)
The analytical model: Mlodnosky and Garriott (1963) Analytical model assumes protons are stationary Analytical model gives sheath capacitance as coaxial cylindrical capacitance
Sheath Capacitance (1035 V)
The splitting occurs at low voltage magnitude
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)
The splitting occurs at low voltage magnitude The figures contain the data points of 8 RF cycles Inertia is the primary cause of splitting
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Outline
1. Introduction
2. Nonlinear Sheath Impedance
3. Number Densities of Electrons and Ions
4. Antenna Tuning
5. The Effects of Ion-to-electron Mass Ratio
6. Summary
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Evolution of Proton Number Density
Antenna position: 30 mAntenna orientation: perpendicular to the magnetic field, vertical in the figure
1 and 4 correspond to negative voltages
2 and 3 correspond to positive voltages
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30 40 502010 Position / m
Den
sity
/ m
-3
2
4
8
6
×109
0
Number Density of Particles
Antenna position: 30 m Antenna orientation: vertical
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0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
10x 10
9
Position / m
dens
ity
Electron
Proton
Large 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
Depletion region
Sheath region
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Outline
1. Introduction
2. Nonlinear Sheath Impedance
3. Number Densities of Electrons and Ions
4. Antenna Tuning
5. The Effects of Ion-to-electron Mass Ratio
6. Summary
Circuit model
Need accurate models of sheath capacitanceand sheath conductance
Extract New Models
Sheath capacitance
Add correction factors to the parameters of the original model Minimizing least square errors numerically
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
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
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
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
( ) ( )
( ) ( )
Treal
apparent
v t i t dt
P PT
P S RMS v t RMS i t
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
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 H0.19µC → 0.60µC → 0.65µC 43 mA → 107 mA → 113 mA
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Outline
1. Introduction
2. Nonlinear Sheath Impedance
3. Number Densities of Electrons and Ions
4. Antenna Tuning
5. The Effects of Ion-to-electron Mass Ratio
6. Summary
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 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
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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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Thank you!