Transcript Document

Dipole Antennas Driven at High
Voltages in the Plasmasphere
Linhai Qiu
Mentor: Timothy Bell
Advisor: Umran Inan
December 12, 2010
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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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.
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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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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 nonnegligible 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
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Sheath Capacitance (86V)
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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
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
 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
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Number Density of Particles
Density / m-3
×109
8
6
4
2
0
10
20
30
40
50
Position / m
 Antenna position: 30 m
 Antenna orientation: vertical
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Large Depletion Region
9
10
x 10
Electron
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Proton
8
7
density
6
5
Sheath region
4
3
Depletion region
2
1
0
0
10
20
30
Position / m
40
50
60
 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
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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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Circuit model
Need accurate models of sheath capacitance
and 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
 Step 1: Calculate the real power and
apparent power from the measured
time domain v (t) and i (t)
Preal  P 
Papparent
 v(t )i(t )dt
T 
T
 S  RMS  v(t )  RMS 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:
0H → 0.52 H → 0.71 H
0.19µC → 0.60µC → 0.65µC
43 mA → 107 mA → 113 mA
 We will work with Ivan Galkin from UML to optimize
the tuning scheme.
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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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
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!
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