Experimental And Theoretical Investigation On Plasma Antennas
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Experimental and Theoretical Investigation on Plasma Antennas E. Vecchioni1, G. Cerri2, P. Russo3, V. Mariani Primiani4 1
Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona – Italy, [email protected] 2
[email protected], [email protected], [email protected]
Abstract Plasma antenna represents a completely new technology that used plasma elements instead of metal ones. This paper presents some of the experimental and theoretical results achieved in the plasma antenna research developed in our laboratories, in particular we developed a self-consistent model able to describe the ionization of a plasma due to the propagation of an electromagnetic wave. A preliminary comparison between numerical and experimental results concerning the plasma conductivity is reported.
1. Introduction A plasma antenna is constructed from insulating tubes filled with low pressure gas; the gas inside the tube can be ionized applying bursts of power, so that plasma can be rapidly generated and destroyed; it is well known that a surface wave propagating along the tube length can create and sustain a plasma column [1]. The plasma element can be used instead of metal wires or surfaces as a conducting medium for the radiated signal. Two different signals are needed in such antennas: the “pump or excitation signal”, which supply to the tube the power needed to ionize the gas, and the “radiated signal”, which support information to be transmitted. The main peculiarities related to this antenna follows from the possibility of changing the electric parameters of plasma. When the pump signal is switched off, the gas inside is not ionized and the tube is simply a dielectric with a very small radar cross section. On the contrary, when the pump signal is applied, the gas is ionized and the tube behaves like a metallic antenna. Because of this characteristic, plasma antenna was firstly studied for military applications; however, it can be also used in many civil applications to realize smart antennas, circular scan arrays, reconfigurable antennas, time and space selective shielding, frequency selective shielding [2]. The state of art concerning plasma antennas is still very poor and most of the papers available deal with experimental approaches [2,3]. From a theoretical point of view, plasma physics is a very rigorous and well known science, but the theory of plasma antennas is not completely characterized: the lack of a self-consistent model able to describe their behavior and useful to understand the complex phenomena involved prevent their optimized design. In this work we present some experimental and theoretical results. The experimental investigation regards: (i) the determination of plasma antenna efficiency, (ii) plasma antenna conductivity, (iii) different systems for the application of the pump signal. From a theoretical point of view, a numerical model has been developing. As plasma is generated and sustained by an electromagnetic wave, the interaction mechanism between plasma and an electromagnetic field is fundamental to characterize the antenna.
2. Experimental Investigation A commercially available tube designed for lightning purpose has been used to create plasma column; the tube has been inserted in a metallic box placed under a ground plane and fed by a single electrode (fig.1): the intense field between a copper ring placed around the tube and the ground plane provide the pump signal that propagates along the columns creating and sustaining the plasma. A second copper ring can be placed near the first one to apply the signal to be radiated. Thus, two different networks are needed: the excitation network and the signal one. The set-up used [4] allows to determine the efficiency of the antenna with respect to the radiated field as a function of the pump power delivered to the plasma column. The signal radiated when a copper tube replaces the plasma element was used as a reference for the efficiency calculation. The results obtained show that with the maximum power available the performance degradation of the plasma antenna with respect to the copper one is only 2.5 dB;
moreover, the efficiency plot exhibits a saturation corresponding to the maximum ionization of plasma.
Ground plane 0,7 cm
Excitation
3 cm 3 cm
Signal
3 cm
Figure 1: Excitation box geometry. Antenna efficiency depends on plasma conductivity; this key parameter can be evaluated as a function of the pump signal and distance from the excitation point: in fact the field rapidly decreases because of the wave attenuation along the longitudinal direction, thus also the conductivity varies; this profile allows to determine the effective length of the column. Using a reflectometric technique and a numerical tool (CST Microwave Studio [5]), the conductivity values were retrieved (fig. 2). These results are reported from [4] because they are used for a comparison with the numerical ones as shown in section 3.
σ [ S /m ]
100 90
15 W
80
14 W
70
13 W
60
12 W
50
10 W
40
8W
30 20 10 0 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
z [cm ]
Figure 2: Conductivity of the plasma tube vs the axis coordinate, recovered from the reflection measurements
3. Theoretical Investigation The propagation of an electromagnetic wave inside a plasma can be characterized solving a non-linear system of equations represented by the Maxwell curl equations and the Boltzmann equation (1).
∂F e ∂F + v ⋅ ∇ r F + (E + µ v × H ) ⋅ ∇ v F = ∂t m ∂t coll
(1)
The Boltzmann equation describes the evolution in time, space and velocity of the electron distribution function F(r, v, t ) (EDF): this is the main plasma statistical quantity, which univocally define plasma state and evolution, so that if it known, all the macroscopic parameters involved such electron density or conductivity can be determined [6]. The Boltzmann equations is an integro-differential equation in a six dimensional velocity-position space: at the moment, it is not possible to derive an exact solution for the equation in this space, but applying a very well known approximation, it is possible to expand the EDF in spherical harmonics retaining only the first two terms, the so called isotropic F0 (v ) and anisotropic F1 (v ) ones: F(v ) = F0 (v ) +
v ⋅ F1 (v ) v
(2)
The Boltzmann equation can be rewritten for them separately, simply substituting equation (2) into equation (1) and applying some analytical manipulations. To describe the ionization of a weakly ionized plasma due to the propagation of an electromagnetic field, also the continuity equation (3) has been introduced in the model. This equation describes the evolution in time and space of the electron density n:
∂n = −∇r ⋅ (nu ) + (< υi > −α ⋅ n )n ∂t
(3)
where u is the electron drift velocity and it can be directly related to the isotropic term of EDF as
∫
∞
4π 1 v 3 F1dv . The ionization rate < υi > is the frequency of production of new electrons due to the 3 n 0 ionization collisions between fast electrons and neutral particles and also this quantity can be determined from the EDF. Finally, the recombination coefficient α is the frequency of recombination between electrons and positive ions; in a microwave discharge it is assumed to be 10−12 m −3s −1 . The current distribution that flows inside the plasma is related to the EDF through the electron drift velocity according to J = −e ⋅n ⋅u . u=
In this preliminary investigation, the case study consists of a plane wave impinging on an air-plasma interface so that the problem is 1-D: the simple geometry chosen allows to check the accuracy and the self-consistency of the model, anyway it is shown that it is possible to achieve very interesting results also in this case. The Maxwell Boltzmann system has been solved using an FDTD approach: as in the classic Yee algorithm, the electromagnetic field, the EDF and the electron density are calculated in a staggered spatial grid and in an iterative way, but the EDF has to be calculated also in a velocity grid. With some simple assumptions it is possible to derive an analytical solution that compared with the numerical one validated our model [7]; afterwards a complete model has been developed and all the theoretical aspects has been introduced in the model. The argon plasma region is initially characterized by the typical parameters of a microwave discharge: electron density n= 1013 m −3 , neutral density N= 10 22 m −3 , temperature T=1eV, while the incident electromagnetic field has an input power density P=1200Wm-2 and a frequency f=2.45GHz. The FDTD approach can be used for the solution of the entire Maxwell-Boltzmann system, providing the evolution of the EDF terms (fig. 3), the electron density, the plasma conductivity and permittivity, the electromagnetic quantities (field, current); these quantities characterize the plasma state evolution during the propagation of the electromagnetic wave. Moreover the model allows a parametric investigation of the problem as a function of input power density and frequency (fig. 4), gas pressure and composition (fig. 5). 5
12
v^2 f0 ( t = t* ) ] -22
-8
]
v^2 f0 ( t = 0s )
f1x [ 10
2
v f0 [ 10
8
4
3 0 -3 -5
0 0
1
6
2
0.0
3
0.5
v [ 10 m / s ]
1.0
1.5
2.0
z[m]
Figure 3: Isotropic term of EDF vs velocity at t=0s and t=80µs for an argon plasma and anisotropic term along zaxis at a generic time step for an argon plasma 10
6
9
3
-3
m ]
4
8
16
5
7
n [ 10
n [ 10
16
m
-3
]
7
2
6
1
5
0
n 40 0.5
0
2
4
f [ GHz ]
6
8
0.8
1.2 3
1.5
1.8
-2
PI [ 10 Wm ]
Figure 4: Electron density vs frequency and input power density for an argon plasma
10
n ( ARGON )
6
n [ 10
16
m
-3
]
n ( NEON ) 8
4 2 0 0.0
0.5
1.0
1.5
2.0
z[m]
Figure 5: Electron density along z-axis for a neon and an argon plasma A qualitative comparison between experimental and numerical results is reported in Figure 6: it shows the conductivity decay along the propagation direction of the electromagnetic wave. Quantities have been normalized as they refer to completely different geometries; nevertheless it is a very significant result because it shows how the coupling mechanism between field and plasma during the wave propagation is well characterized by the model. 1
experimental
| σ | / | σ | max
0.8
numerical
0.6 0.4 0.2 0 0
0.2
0.4
0.6
z / zmax
0.8
1
Figure 6: Normalized conductivity along z-axis (experimental vs numerical)
4. Conclusion Preliminary experimental and theoretical investigations of plasma antennas have been conducted: the experimentally activity highlighted how the main physical properties of a plasma antenna are strongly affected from the variation of the input parameters involved. A numerical 1-D model was developed to conduct a parametric investigation of the interaction between electromagnetic field and plasma. It has been shown that the model is valid, reliable and helpful for understanding the complex phenomena concerning plasma antenna physics. Future work will concern the implementation of a more realistic cylindrical geometry.
5. References 1. A. W. Trivelpiece, R. W. Gould, “Space charge waves in cylindrical plasma column,” Journ. Applied Physics, vol.30, November 1959, pp. 1784-1793. 2. A. D. Cheetham, A. P. Whichello, J. P. Rayner, “Physical Characteristics of Plasma Antennas,” IEEE Trans. On Plasma Science, February 2004, vol.32, pp. 269-281 3. I. Alexeff, T. Anderson, S. Prameswaran, E.P. Pradeep, J. Hulloli, P. Hulloli, “Experimental and theoretical results with plasma antennas”, IEEE Trans. On Plasma Science, April 2006,.vol.33, pp. 166-171 4. G. Cerri, R. De Leo,V. Mariani Primiani, P. Russo, “Measurement of the properties of a plasma column used as a radiated element”, in course of publication on IEEE Trans. on IMT 5. Microwave Studio, CST-Computer Simulation Technology, Bad Nuheimer Str. 19, 64289 Darmstadt, Germany. 6. A. P. Žilinskij, I. E. Sacharov, V. E. Golant. Fundamentals Plasma Physics , MIR, Moscow, 1983 7. G. Cerri, V. Mariani Primiani, P. Russo, E. Vecchioni, “FDTD approach for the characterization of electromagnetic wave propagation in plasma for application to plasma antennas” EuCAP 2007 proceedings, 11-16 November 2007,Edinburgh, (Scotland)
Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona – Italy, [email protected] 2
[email protected], [email protected], [email protected]
Abstract Plasma antenna represents a completely new technology that used plasma elements instead of metal ones. This paper presents some of the experimental and theoretical results achieved in the plasma antenna research developed in our laboratories, in particular we developed a self-consistent model able to describe the ionization of a plasma due to the propagation of an electromagnetic wave. A preliminary comparison between numerical and experimental results concerning the plasma conductivity is reported.
1. Introduction A plasma antenna is constructed from insulating tubes filled with low pressure gas; the gas inside the tube can be ionized applying bursts of power, so that plasma can be rapidly generated and destroyed; it is well known that a surface wave propagating along the tube length can create and sustain a plasma column [1]. The plasma element can be used instead of metal wires or surfaces as a conducting medium for the radiated signal. Two different signals are needed in such antennas: the “pump or excitation signal”, which supply to the tube the power needed to ionize the gas, and the “radiated signal”, which support information to be transmitted. The main peculiarities related to this antenna follows from the possibility of changing the electric parameters of plasma. When the pump signal is switched off, the gas inside is not ionized and the tube is simply a dielectric with a very small radar cross section. On the contrary, when the pump signal is applied, the gas is ionized and the tube behaves like a metallic antenna. Because of this characteristic, plasma antenna was firstly studied for military applications; however, it can be also used in many civil applications to realize smart antennas, circular scan arrays, reconfigurable antennas, time and space selective shielding, frequency selective shielding [2]. The state of art concerning plasma antennas is still very poor and most of the papers available deal with experimental approaches [2,3]. From a theoretical point of view, plasma physics is a very rigorous and well known science, but the theory of plasma antennas is not completely characterized: the lack of a self-consistent model able to describe their behavior and useful to understand the complex phenomena involved prevent their optimized design. In this work we present some experimental and theoretical results. The experimental investigation regards: (i) the determination of plasma antenna efficiency, (ii) plasma antenna conductivity, (iii) different systems for the application of the pump signal. From a theoretical point of view, a numerical model has been developing. As plasma is generated and sustained by an electromagnetic wave, the interaction mechanism between plasma and an electromagnetic field is fundamental to characterize the antenna.
2. Experimental Investigation A commercially available tube designed for lightning purpose has been used to create plasma column; the tube has been inserted in a metallic box placed under a ground plane and fed by a single electrode (fig.1): the intense field between a copper ring placed around the tube and the ground plane provide the pump signal that propagates along the columns creating and sustaining the plasma. A second copper ring can be placed near the first one to apply the signal to be radiated. Thus, two different networks are needed: the excitation network and the signal one. The set-up used [4] allows to determine the efficiency of the antenna with respect to the radiated field as a function of the pump power delivered to the plasma column. The signal radiated when a copper tube replaces the plasma element was used as a reference for the efficiency calculation. The results obtained show that with the maximum power available the performance degradation of the plasma antenna with respect to the copper one is only 2.5 dB;
moreover, the efficiency plot exhibits a saturation corresponding to the maximum ionization of plasma.
Ground plane 0,7 cm
Excitation
3 cm 3 cm
Signal
3 cm
Figure 1: Excitation box geometry. Antenna efficiency depends on plasma conductivity; this key parameter can be evaluated as a function of the pump signal and distance from the excitation point: in fact the field rapidly decreases because of the wave attenuation along the longitudinal direction, thus also the conductivity varies; this profile allows to determine the effective length of the column. Using a reflectometric technique and a numerical tool (CST Microwave Studio [5]), the conductivity values were retrieved (fig. 2). These results are reported from [4] because they are used for a comparison with the numerical ones as shown in section 3.
σ [ S /m ]
100 90
15 W
80
14 W
70
13 W
60
12 W
50
10 W
40
8W
30 20 10 0 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
z [cm ]
Figure 2: Conductivity of the plasma tube vs the axis coordinate, recovered from the reflection measurements
3. Theoretical Investigation The propagation of an electromagnetic wave inside a plasma can be characterized solving a non-linear system of equations represented by the Maxwell curl equations and the Boltzmann equation (1).
∂F e ∂F + v ⋅ ∇ r F + (E + µ v × H ) ⋅ ∇ v F = ∂t m ∂t coll
(1)
The Boltzmann equation describes the evolution in time, space and velocity of the electron distribution function F(r, v, t ) (EDF): this is the main plasma statistical quantity, which univocally define plasma state and evolution, so that if it known, all the macroscopic parameters involved such electron density or conductivity can be determined [6]. The Boltzmann equations is an integro-differential equation in a six dimensional velocity-position space: at the moment, it is not possible to derive an exact solution for the equation in this space, but applying a very well known approximation, it is possible to expand the EDF in spherical harmonics retaining only the first two terms, the so called isotropic F0 (v ) and anisotropic F1 (v ) ones: F(v ) = F0 (v ) +
v ⋅ F1 (v ) v
(2)
The Boltzmann equation can be rewritten for them separately, simply substituting equation (2) into equation (1) and applying some analytical manipulations. To describe the ionization of a weakly ionized plasma due to the propagation of an electromagnetic field, also the continuity equation (3) has been introduced in the model. This equation describes the evolution in time and space of the electron density n:
∂n = −∇r ⋅ (nu ) + (< υi > −α ⋅ n )n ∂t
(3)
where u is the electron drift velocity and it can be directly related to the isotropic term of EDF as
∫
∞
4π 1 v 3 F1dv . The ionization rate < υi > is the frequency of production of new electrons due to the 3 n 0 ionization collisions between fast electrons and neutral particles and also this quantity can be determined from the EDF. Finally, the recombination coefficient α is the frequency of recombination between electrons and positive ions; in a microwave discharge it is assumed to be 10−12 m −3s −1 . The current distribution that flows inside the plasma is related to the EDF through the electron drift velocity according to J = −e ⋅n ⋅u . u=
In this preliminary investigation, the case study consists of a plane wave impinging on an air-plasma interface so that the problem is 1-D: the simple geometry chosen allows to check the accuracy and the self-consistency of the model, anyway it is shown that it is possible to achieve very interesting results also in this case. The Maxwell Boltzmann system has been solved using an FDTD approach: as in the classic Yee algorithm, the electromagnetic field, the EDF and the electron density are calculated in a staggered spatial grid and in an iterative way, but the EDF has to be calculated also in a velocity grid. With some simple assumptions it is possible to derive an analytical solution that compared with the numerical one validated our model [7]; afterwards a complete model has been developed and all the theoretical aspects has been introduced in the model. The argon plasma region is initially characterized by the typical parameters of a microwave discharge: electron density n= 1013 m −3 , neutral density N= 10 22 m −3 , temperature T=1eV, while the incident electromagnetic field has an input power density P=1200Wm-2 and a frequency f=2.45GHz. The FDTD approach can be used for the solution of the entire Maxwell-Boltzmann system, providing the evolution of the EDF terms (fig. 3), the electron density, the plasma conductivity and permittivity, the electromagnetic quantities (field, current); these quantities characterize the plasma state evolution during the propagation of the electromagnetic wave. Moreover the model allows a parametric investigation of the problem as a function of input power density and frequency (fig. 4), gas pressure and composition (fig. 5). 5
12
v^2 f0 ( t = t* ) ] -22
-8
]
v^2 f0 ( t = 0s )
f1x [ 10
2
v f0 [ 10
8
4
3 0 -3 -5
0 0
1
6
2
0.0
3
0.5
v [ 10 m / s ]
1.0
1.5
2.0
z[m]
Figure 3: Isotropic term of EDF vs velocity at t=0s and t=80µs for an argon plasma and anisotropic term along zaxis at a generic time step for an argon plasma 10
6
9
3
-3
m ]
4
8
16
5
7
n [ 10
n [ 10
16
m
-3
]
7
2
6
1
5
0
n 40 0.5
0
2
4
f [ GHz ]
6
8
0.8
1.2 3
1.5
1.8
-2
PI [ 10 Wm ]
Figure 4: Electron density vs frequency and input power density for an argon plasma
10
n ( ARGON )
6
n [ 10
16
m
-3
]
n ( NEON ) 8
4 2 0 0.0
0.5
1.0
1.5
2.0
z[m]
Figure 5: Electron density along z-axis for a neon and an argon plasma A qualitative comparison between experimental and numerical results is reported in Figure 6: it shows the conductivity decay along the propagation direction of the electromagnetic wave. Quantities have been normalized as they refer to completely different geometries; nevertheless it is a very significant result because it shows how the coupling mechanism between field and plasma during the wave propagation is well characterized by the model. 1
experimental
| σ | / | σ | max
0.8
numerical
0.6 0.4 0.2 0 0
0.2
0.4
0.6
z / zmax
0.8
1
Figure 6: Normalized conductivity along z-axis (experimental vs numerical)
4. Conclusion Preliminary experimental and theoretical investigations of plasma antennas have been conducted: the experimentally activity highlighted how the main physical properties of a plasma antenna are strongly affected from the variation of the input parameters involved. A numerical 1-D model was developed to conduct a parametric investigation of the interaction between electromagnetic field and plasma. It has been shown that the model is valid, reliable and helpful for understanding the complex phenomena concerning plasma antenna physics. Future work will concern the implementation of a more realistic cylindrical geometry.
5. References 1. A. W. Trivelpiece, R. W. Gould, “Space charge waves in cylindrical plasma column,” Journ. Applied Physics, vol.30, November 1959, pp. 1784-1793. 2. A. D. Cheetham, A. P. Whichello, J. P. Rayner, “Physical Characteristics of Plasma Antennas,” IEEE Trans. On Plasma Science, February 2004, vol.32, pp. 269-281 3. I. Alexeff, T. Anderson, S. Prameswaran, E.P. Pradeep, J. Hulloli, P. Hulloli, “Experimental and theoretical results with plasma antennas”, IEEE Trans. On Plasma Science, April 2006,.vol.33, pp. 166-171 4. G. Cerri, R. De Leo,V. Mariani Primiani, P. Russo, “Measurement of the properties of a plasma column used as a radiated element”, in course of publication on IEEE Trans. on IMT 5. Microwave Studio, CST-Computer Simulation Technology, Bad Nuheimer Str. 19, 64289 Darmstadt, Germany. 6. A. P. Žilinskij, I. E. Sacharov, V. E. Golant. Fundamentals Plasma Physics , MIR, Moscow, 1983 7. G. Cerri, V. Mariani Primiani, P. Russo, E. Vecchioni, “FDTD approach for the characterization of electromagnetic wave propagation in plasma for application to plasma antennas” EuCAP 2007 proceedings, 11-16 November 2007,Edinburgh, (Scotland)
