Electromagnetic Waves Part 14 pdf

The method has been used by the authors to determine the connection between surface structure of a fabric being a substrate and dielectric properties of obtained composite fabric –carbon

titanium (Ti), and of composites with the outer layer formed by a titanium monoxide (TiO) For composites with outer titanium layer (Ti and 3TiO samples) in the measuring frequency range, we observe very little differences in frequency spectrums of measured parameters and in the Cole-Cole diagrams independently from a number of layers Ti-TiO

In the diagram form of the imaginary component of the complex capacitance as a function of frequency, we do not observe a relaxation pick At the same time, the diagram form of this characteristic suggests the presence of a relaxation pick at frequencies higher than the measuring range Quite a different situation for composites with the outer layer formed by a titanium monoxide (1TiO and 2TiO samples) appears In this case we can observe the strong dependence of dielectric composite properties upon a number of formed Ti-TiO layers Frequency diagram forms of the imaginary component of the complex capacitance shows, in the examined measuring frequency range, the presence of a relaxation pick and a possibility

of a presence of the second relaxation phenomenon at higher frequencies The value and frequency of a relaxation pick presence are strictly depended on a number of Ti-TiO layers forming a composite Increasing a number of layers results in reducing of a relaxation pick value and in displacement in the lower frequencies direction It is confirmed by Cole-Cole diagrams of the complex capacitance, in which there is a clear presence of a displacement of the semicircle centre to the right for 1TiO sample

The capability of composite materials to shield electromagnetic fields is coherently associated with their dielectric properties in a wide frequency band The method of impedance spectroscopy allows one to connect the measured frequency characteristics with the physical structure of tested material and the alternations in the structure

The method has been used by the authors to determine the connection between surface structure of a fabric being a substrate and dielectric properties of obtained composite fabric –carbon (Jaroszewski et al., 2010) and to evaluate the correlation between dielectric response

of the system and surface resistance of the carbon layer (Pospieszna et al., 2010, Pospieszna

& Jaroszewski, 2010) The possibilities to design desired electric properties of composite materials are also used to improve the shielding properties of the materials Thus, the connection of the impedance spectroscopy method with those properties

6 Summary

It should be noted that the performed studies and collected experience in the field of modern technologies of shielding have already solved a lot of actual problems but there is still a challenge for further work to improve the efficiency of shielding and to develop new designs of electromagnetic shields They can also be used in the shielding of power engineering systems, where a compatibility with environment in a wide sense of this meaning is the main problem (i.e not only in the aspect of emission and electromagnetic disturbances) In the light of the latest experiences it seems that the future in the area of EM field shielding is connected with the application of modern technologies to fabricate thin-film composite coatings, including nano-composites The materials are capable to fulfil all conditions of effective shielding from EM fields and to eliminate all undesired occurrences associated with operation of the shielded systems The results of our investigations, presented above, point out the possibility of industrial fabrication of the composite shielding materials with the coefficient of shielding efficiency exceeding 50 dB Good mechanical properties and high resistance to environmental effects are additional advantages of such materials

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Reduction of Reflection from Conducting Surfaces using Plasma Shielding

Çiğdem Seçkin Gürel and Emrah Öncü

1Department of Electrical and Electronics Engineering, Hacettepe University,

2Communication Systems Group, TUBITAK Space Technologies Research Institute,

Turkey

1 Introduction

Plasma mediums have taken considerable interest in recent studies due to their tunable characteristics offering some advantages in radio communications, radio astronomy and military stealth applications Special plasma mediums have been used as electromagnetic wave reflectors, absorbers and scatterers Reflection, absorbtion and transmission of electromagnetic waves by a magnetized nonuniform plasma slab are analysed by different authors using different methods in literature It is known that plasma parameters such as length, collision frequency and electron density distribution function considerably affect plasma response Among those, especially the electron density distribution considerably affects the frequency selectivity of the plasma (Gurel & Oncu, 2009a, 2009b, 2009c) Conducting plane covered with plasma layer has been considered and analysed in literature for some specific density distribution functions such as exponential and hyperbolic distributions (Shi et al., 2001; Su et al., 2003 J Zhang & Z Liu, 2007) The effects of external magnetic field applied in different directions to the plasma are also important and considered in those studies

In order to analyze the characteristics of electromagnetic wave propagation in plasma, many theoretical methods have been developed Gregoire et al have used W.K.B approximate method to analyze the electromagnetic wave propagation in unmagnetized plasmas (Gregoire et al., 1992) and Cao et al used the same method to find out the absorbtion characteristics of conductive targets coated with plasma (Cao et al., 2002) Hu et al analyzed reflection, absorbtion, and transmission characteristics from nonuniform magnetized plasma slab by using scattering matrix method (SMM) (Hu et al., 1999) Zhang et al and Yang et al used the recursion formula for generalized reflection coefficient to find out electromagnetic wave reflection characteristics from nonuniform plasma (Yang et al., 2001; J Zhang & Z Liu, 2007) Liu et al used the finite difference time domain method (FDTD) to analyze the electromagnetic reflection by conductive plane covered with magnetized inhomogeneous plasma (Liu et al., 2002)

The aim of this study is to determine the effect of plasma covering on the reflection characteristics of conducting plane as the function of special electron density distributions and plasma parameters Plasma covered conducting plane is taken to model general stealth application and normally incident electromagnetic wave propagation through the

plasma medium is assumed Special distribution functions are chosen as linearly varying

electron density distribution having positive or negative slopes and purely sinusoidal

distribution which have shown to provide wideband frequency selectivity characteristics

in plasma shielding applications in recent studies (Gurel & Oncu, 2009a, 2009b, 2009c) It

is shown that linearly varying profile with positive and negative slopes can provide

adjustable reflection or absorbtion performances in different frequency bands due to

proper selection of operational parameters Sinusoidally-varying electron distribution

with adjustable phase shift is also important to provide tunable plasma response The

positions of maximums and minimums of the electron number density along the slab can

be changed by adjusting the phase of the sinusoid as well as the other plasma parameters

Thus plasma layer can be tuned to behave as a good reflector or as a good absorber In

this study, plasma is taken as cold, weakly ionized, steady state, collisional, nonuniform

while background magnetic field is assumed to be uniform and parallel to the magnetized

slab

2 Physical model and basic theory

There are several theoretical methods as mentioned in the previous section for the analysis

of electromagnetic wave propagation through the plasma which will be summarized in this

part

2.1 Generalized reflection coefficient formula

Firstly two successive subslabs of plasma layer are considered as shown in Fig 1

Fig 1 Two successive plasma subslabs

The incident and reflected field equations for the m th subslab can be written as

where E is the incident field and i E is the reflected field Then, incident and reflected field r

equations for the (m+1)th subslab can be similarly given as

m+1

m

z

where m and m1 are the intrinsic impedances of m th and m 1th subslabs

respectively The intrinsic impedance for the mth subslab is

m

r m

where d m1 is the thickness of the m 1th subslab

By using the following equalities,

m C

n i i

where n is the last boundary of the plasma slab which is located before conductive target

When we continue to write the field equations iteratively until m=0 which means the

boundary between free space and the first subslab of plasma, we have

00

n m m

r i

where  n is the reflection coefficient of the conductive target In order to calculate the

total reflection coefficient, the matrix M is needed to be computed

2.2 Wentzel-Kramers-Brillouin (WKB) approximate method

It is known that WKB method is used for finding the approximate solutions to linear partial

differential equations that have spatially varying coefficients This mathematical

approximate method can be used to solve the wave equation that defines the

electromagnetic wave propagation in a dielectric plasma medium

Let us write the wave equation as

2 2

exp

z Z

dk dz

The pyhsical meaning of (37) is that the wavenumber of the propagating electromagnetic

wave changes very little over a distance of one wavelength

It is assumed that the electromagnetic wave enters the plasma at z z 0and reflects back at

z r

where P is the normalized total reflected power r

2.3 Finite-difference time-domain analysis

Finite-difference time-domain analysis have been extensively used in literature to solve the

electromagnetic wave propagation in various media (Hunsberger et al., 1992; Young, 1994,

1996; Cummer, 1997; Lee et al., 2000; M Liu et al., 2007) When the electromagnetic wave

propagates in a thin plasma layer, the W.K.B method may not accurately investigate the

wave propagation (X.W Hu, 2004; S Zhang et al., 2006) The reason is the plasma thickness

is near or less than the wavelength of the plasma exceeds the wavelength of the incident

wave, the variation of the wave vector with distance cannot be considered as weak (M Liu

et al., 2007)

In the analysis electric field is considered in the x direction and propagation vector is in z

direction and the electromagnetic wave enters normally into the plasma layer

Lorentz equation (electron momentum equation) and the Maxwell’s equations can be

 is the magnetic permeability of free space, J is the current density, n e is the denstiy of

electron, m eand veare the mass and velocity vector of the electron, respectively and clis

collision frequency Then FDTD algorithm of equations (39), (40), (41) and (42) can be

written as (Chen et al., 1999; Jiang et al., 2006; Kousaka & Ono, 2002; M.H Liu et al., 2006)

where z  is the spatial discretization and t is the time step By using equations (43) to

(46), the electromagnetic wave propagation in a plasma slab can be simulated in time

domain (M Liu et al., 2007)

2.4 Scattering matrix method (SMM) analysis

This analytical technique is the manipulation of the 2x2 matrix approach which was

presented by Kong (Kong, 1986) SMM analysis gives the partial reflection and transmission

coefficients in the subslabs This makes it easy to analyze the partial absorbed power in each

subslab of the plasma (Hu et al., 1999)

Let us write the incident and reflected fields as follows

k is the z component of the free space wave number and A is the reflection

coefficient for the first subslab

The total electric field in incidence region is

where B m and C m are the unknown coefficients

After the last subslab there is only transmitted wave that travels in free space The electric

field for this region is

where D is the unknown coefficient After writing the total electric fields in each subslab,

boundary conditions can be applied

For the first boundary

1 1

S C

1 1

Lastly, for the last boundary

n p n

B

V D C

where S represents the first column vector and 1 S represents the last column vector of 2

the global scattering matrix Then equation (58) can be written (Hu et al., 1999) as

By using equation (60), A and D coefficients can be computed The coefficient A represents

total reflection coefficient and the coefficient B represents total transmission coefficient

Absorbed power values for each subslab and the total absorbed power inside the plasma

can be obtained by the help of equations (52), (54) and (56)

2.5 Formulation of reflection from plasma covered conducting plane

In this chapter another method is presented to analyze the characteristics of electromagnetic

wave propagation in a plasma slab This method is simple, accurate and provides less

computational time as compared to other methods mentioned in previous sections

Normally incident electromagnetic wave propagation through a plasma slab is assumed as

shown in Fig 2 In the analysis, inhomogenous plasma is divided into sufficiently thin,

adjacent subslabs, in each of which plasma parameters are constant Then starting with

Maxwell’s equations, reflected, absorbed and transmitted power expressions are derived

Here, plasma layer is taken as cold, weakly ionized, steady state and collisional Background

magnetic field is assumed to be uniform and parallel to the magnetized slab

For a magnetized and source free plasma medium, plasma permittivity is in tensor form

This tensor form permittivity can be approximated by a scaler permittivity Let us give the

details of this approximation

The equation of motion for an electron of mass m is

2

cl

mw r mv jwr eE ejwr B

where w is the angular frequency, r is the distance vector, clis the collison frequency and

B is the magnetic field vector

Fig 2 Electromagnetic wave propagation through a plasma (with subslabs) covered





 (64)

Z w

a

P

1 2 3 M

In equation (69), l x, l and y l z are the direction cosines of Y We can take the polarization

matrix by using equation (67)

where Y is the longitudinal component and l Y is the transverse component of Y t  In the

direction of the electromagnetic wave we have,

The solution of the equation (80) is given by

v j