NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Research Information Center

Gaithersburg, MD 20898

iW 1 1 United States Department of Commerce

I \JOI National Institute of Standards and Technology

NISTIR 3954

NEAR-FIELD AND FAR-FIELD

EXCITATION OF A LONG CONDUCTOR

IN A LOSSY MEDIUM

David A. Hill

NISTIR 3954

NEAR-FIELD AND FAR-FIELD

EXCITATION OF A LONG CONDUCTOR

IN A LOSSY MEDIUM

David A. Hill

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

September 1 990

Sponsored by

U.S. Army Belvoir RD&E Center

Fort Belvoir, Virginia 22060-5606

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director

NEAR- FIELD AND FAR- FIELD EXCITATION

OF A LONG CONDUCTOR IN A LOSSY MEDIUM

David A. Hill

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

Excitation of currents on an infinitely long conductor is

analyzed for horizontal electric dipole or line sources and for

a plane -wave, far -field source. Any of these sources can excite

strong currents which produce strong scattered fields for

detection. Numerical results for these sources indicate that

long conductors produce a strong anomaly over a broad frequency

range. The conductor can be either insulated or bare to model

ungrounded or grounded conductors.

Key words: axial current; axial impedance; electric dipole;

electric field; grounded conductor; insulated conductor; line

source; magnetic field; plane wave.

1 . INTRODUCTION

The excitation of currents on long, underground conductors is important

in many applications. Power lines and rails in tunnels can enhance

transmission for mine communication [1]. Cables or pipes can influence

electromagnetic probing of the earth [2].

In this report, we examine the feasibility of electromagnetic detection

of long conductors in tunnels. This approach differs from the usual tunnel

detection techniques that attempt to detect an air- filled cavity using VHF

frequencies and vertical electric field polarization [3,4]. For strong

excitation of currents on long, horizontal conductors, we consider the use

of lower frequencies and horizontal polarization [5].

Our model consists of an infinitely long conductor that can be bare or

insulated in a homogeneous, lossy earth. In section 2, we consider nearfield excitation with a horizontal electric dipole source; the analysis

parallels an earlier study of vertical magnetic dipole excitation [6]. The

extension to near- field excitation with an electric line source of finite

length is covered in section 3. In section 4, we consider far-field

1
excitation with a plane -wave source. In all cases, we assume that the

conductor is at a sufficient depth that we do not need to consider air- earth

interface effects [7-9], and we neglect the effect of the air-earth

interface on the excitation fields. The model is idealized, but it allows

us to consider most of the relevant features of the practical problem.

2. HORIZONTAL ELECTRIC DIPOLE EXCITATION

2.1 Formulation

The geometry is shown in figure 1. An infinitely long conductor of

outer radius b is centered on the z-axis. A short horizontal (z-directed)

electric dipole of current moment IL is located at (x^, y^, z^) . The earth

has permittivity e, conductivity o, and magnetic permeability /i.

The formulation for the fields of the dipole source and the infinitely

long conductor closely follows [6]

.

The fields due to the electric dipole

in the absence of the conductor can be derived from an electric Hertz vector

with only a z component 11^. For exp(jwt) time dependence, is

z z

z IL

4n(o + ju>e)

where

r/ s 2 , .2 ,

. 2 . 1/2

r

d

= [(x-x

d

) + (y-yd

) + (z-z d

) ]

and

k = w[/i(e - ja/o) ] 1//2

.

( 1 )

The electric and magnetic fields, E and H , due to the dipole are

E

d

- (W + k

2

)(e n

d

) z z and ( 2 )

2
H

d = (a + ja>e) Vx(e IId

) ,

where e is a unit vector in the z direction,

z

The current on the infinitely long conductor is determined by applying

an axial impedance condition in the transform domain. The transform of the

A current 1(A) is given by equation (A4) in [6]:

1(A)

where

IL

K0^Vp

d0^ ^ Azd

2 tt D(A)

6

v = ( A‘

- k

2

) 1/2

dO

2.1/2

+ yj

(3)

D( A) = K

Q

(vb) +

27r(g 4- jc^e)

2

v

VA) -

A is a spatial transform variable, and is the zero-order modified Bessel

function of the second kind [10]. The square root is taken so that the real

part of v is positive. Z

g

(A) is t^ie axi al impedance (series impedance per

unit length) of the conductor.

A useful model for a buried insulated conductor is shown in figure 2.

It consists of a metal center conductor of radius a surrounded by an

insulating region of outer radius b. The metal has conductivity and

magnetic permeability and the insulation has permittivity and free

space permeability . The axial impedance of this model is [8,11]

u

2

i

Z (A) = Z + —

Zn(b/a),

s m 2 ttjw6 . ' ’

where

(4)

3
zm

(j^/*mmAO

2?ra

1/2

I

Q

( j k

m

a) W>’

“<'Vi)

1/2 jkm (i^po) mm

1/2

and and are modified Bessel functions of the first kind [10]. If we

set b =» a, then Z (A) = Z . and we have a grounded conductor (such as a

s m

rail in a tunnel). If we set equal to the free-space permittivity

then we can model a conductor (such as a power line) suspended in an airfilled tunnel at a distance b - a from the tunnel wall.

2 . 2 Conductor Current

The current I(z) on the conductor is given as an inverse transform [6]

I(z) - J 1(A) e' jAzdA, (5)

— 00

A A where 1(A) is the transform current given in (3). 1(A) has branch points at

A - ± k and poles at A = ± A , where A is determined by

p p

D(A ) - 0.

P

( 6 )

The numerical solution of (6) is discussed in [6].

Ip(z) to the integral in (5) is

The pole contribution

I

P

(z) - jIL [ V^dO

D' (A)

)"]

Z ~ Z a\

I (7)

where D' (A) m

d \

4
The pole contribution in (7) is called the transmission line current or

quasi-TEM current. It exists only for b > a. The integral for the total conductor current I(z) in (5) is most easily

evaluated by fast Fourier transform (FFT) , and this method automatically

yields an array of z values. Numerical results for the magnitude of I(z)

are shown in figure 3 for the following parameters: IL = 1 A*m, = 15 m,

7

y, = 50 m, z, = 0, f = 20 kHz, o - 5.7 X 10 S/m, p — p. - , a - 0.5 cm, d d m mu

-3 €.=£_, £ / 6

10 , and a = 5 x 10 S/m. The currents are even in z. The

currents on the insulated conductor (b > a) have a slow z decay because of

the dominance of the transmission line current as given by (7). These

currents actually differ very little from I^(z) as given by (7). The

current on the bare (grounded) conductor has a higher peak value, but has

rapid exp(-jk|z|) decay corresponding to plane wave attenuation in the

earth.

2 . 3 Magnetic Field

In this section, we consider the primary magnetic field due to the

dipole and the secondary magnetic field due to the conductor. The ycomponent of the magnetic field is of most interest because we anticipate

reception with a vertical magnetic dipole in a vertical borehole.

The primary y- component of the magnetic field due to the electric

dipole source is obtained by substituting (1) into (2)

-(a + jw€) ( 8 )

jkr

IL , x x

d, ... ^1. e

4* ( r

> <J k +

r > r d d d

In general both the jk and the 1/r^ terms in (8) must be retained,

5
The secondary y-component due to the conductor is [6]

CO H

y “ l7p -T I(A) vK

l

(vp) e -jAz

(9)

where

/ 2 2 . 1/2

P = (x + y )

and 1(A) is given by (3). In general we choose to evaluate the integral in

C

(9) by FFT. However, the pole contribution H (z) for the case of the

insulated conductor is given by [6]

xvK (vp)

H° (z) = [-^ ] yp 2tt p A-A

I p(z >> P

( 10 )

where I^(z) I s given by (7).

In figure 4 we show the primary and secondary magnetic field strengths

observed at x = 15 m and y = 0 for the same parameters as used in figure 3.

The magnetic field due to an insulated conductor decays slowly in z because

it is dominated by the pole contribution given by (10). For large z, the

secondary magnetic field is larger than the primary field, and the insulated

conductor should be detectable. The secondary field for a grounded

conductor has a more rapid decay, but it still exceeds the primary field for

large z. These results are qualitatively the same as those for a magnetic

dipole source in [6]

.

In figure 5 we show the magnetic field results for three values of x,

and these results are relevant to reception at different horizontal

separations (ranges) . The insulation radius b is 1 cm, and the other

parameters are the same as in figures 3 and 4. Even though the magnetic

fields decrease for increasing x, the secondary field exceeds the primary

field for large values of z. In figure 6 we show the magnetic field results for different

frequencies from 4 kHz to 500 kHz for x = 15 m. The other parameters are

6
the same as those in figure 5. In all cases the secondary magnetic field

exceeds the primary field for large z. The largest secondary magnetic field

is obtained for a frequency of 20 kHz. These results apply to infinitely

long conductors; for conductors of finite length [12] the optimum frequency

could be higher.

2.4 Electric Field

The infinitely long conductor also produces a strong secondary electric

field which could be received with a horizontal electric dipole. We

consider the z -component of the primary and secondary electric fields

because this is the strongest component.

The primary z -component of the electric field due to the electric

z dipole source is obtained by substituting (1) into (2)

xr d fS— A i2v n

d

E

z - < 2

+ k > n

z

a z

-jkr

IL e

4?rr^(a + jo>e)

2 {kZ

[l

(z - 2

d>

] +

ik

r 3(z - z d

> r

d‘ r

2

1 3 ( z_zh)

U + \l—r r d d

- I])

In general all terms in (8) must be retained,

(ID

The secondary z- component E

c

z due to the conductor is [ 6 ]

-1

2tt(<7 + jwe) J I(A)v^K

Q

(vp)

-00 e -jAz

dA, ( 12 )

7
A where 1(A) is given by (3)

.

In general we choose to evaluate the integral

C

in (12) by FFT. However, the pole contribution E (z) for the case of the

2 13 insulated conductor is given by

E

; (z)

zp

[

-v K

0

(v/>)

2 n(a + jwe) ] ,

, I (A),

A”A

p

P

(13)

where I (z) is given by (7).

In figure 7 we show the primary and secondary electric field strengths

for the same parameters as used in figure 4. The electric field due to an

insulated conductor decays slowly in z because it is dominated by the pole

contribution given by (13). For large z, the secondary electric field is

larger than the primary field, and the insulated conductor should be

detectable. The secondary field for a grounded conductor has a higher peak,

but has a more rapid decay. These results are qualitively the same as those

for the magnetic field in figure 4.

In figure 8 we show electric field results for the same parameters as

used in figure 5, and the various values of x are relevant to reception at

different horizontal ranges. The electric fields decrease for increasing x,

but the secondary field exceeds the primary field for large values of z. These results are qualitively the same as those for the magnetic field in

figure 5.

In figure 9 we show the electric field results for different

frequencies for the same parameters as those in figure 6. In all cases the

secondary field exceeds the primary field for large z. The largest

secondary field is obtained for a frequency of 100 kHz.

3. LINE SOURCE EXCITATION

In this section we consider the case where the source is a horizontal

line current of finite length. This extension is of practical importance

because a long insulated wire grounded at both ends is a commonly used

8
antenna for producing a horizontally polarized electric field [5]. The

antenna could be located either at the earth surface [13] or underground

[14]. Since we neglect the air-earth interface in this analysis, the line

current is located in a homogeneous medium.

3 . 1 Formulation

The geometry shown in figure 10 is the same as that in figure 1 except

that the dipole source is replaced by a horizontal (z- directed) electric

current line source. The line source of length L is centered at

(x,, y,, z,) and carries a constant current I.

d d d

The z -component of the electric Hertz vector can be obtained by

integrating the short dipole result in (1) over the length of the line

source

Z

d

+

2

- jkr

d

n

Z 47T ( —

t

f

s—;— dz '

a + jwc) J r'

L d

Z d2

where

r

d

[(x-xd

) + (y-yd

) + (z-z') ] ,x2,l/2

(14)

The primary fields of the line source are obtained by substituting (14) into

( 2 ).

To determine the current induced on the infinitely long conductor, we

follow the method in [6]

The exponential in (14) can be written in

integral form [15]

,

and in (14) becomes

z

Z

d

+

2 «

2

1

f S K (vp ) e

-J A(z ' z,) dA dz'

,

(15)

47r (a + jwe) L -«

z d"2

where

9
P d - [(x-xd

)

/ + (y-yd

) 2

] 1/2

.

If we reverse the order of integration in (15), the z' integration can be

performed to yield

z IL2

4tt (a + jcoe)

COf K

0 (vpd

) -00

sin( AL/2) 'J A ( z ' z d

) (AL/2)

S dA. (16)

When L approaches zero in (16), the factor sin( AL/2)/(AL/2) approaches one,

and (16) reduces to the result for a short dipole.

3.2 Conductor Current

The transform of the conductor current is the same as given by (3) for

the short dipole source except that a factor sin( AL/2)/( AL/2) is introduced

to account for the length of the line source:

XL

K0^vp

d0^ sin( AL/2) ^ Azd

2 tt D(A) (AL/2) (16)

The current I(z) on the conductor is obtained by substituting (16) into the

inverse transform in (5)

.

For insulated conductors (b > a) , the current is approximately equal to

the pole contribution. Beyond the ends of the line source (|z - z^ | > L/2)

,

the pole contribution I (z) to the current is

I

P

(z) - jIL [ K

0

(v^

) d0 ) D'(A)

sin(AL/2) . (AL/2) J A=A

p

l z z d

i (17)

For convenience in studying the effect of source length L on the

conductor current, we define the following ratio R(L)

:

10
R(L) (18) ^(z)

1 m

where I

p

(z) i s given by (17). For the frequencies of interest here

(< 500 kHz) , R(L) is approximately given by

R(L)

sin(A L/2)

L E—

(A

p

L/2) (19)

where A

p

is determined from the mode equation (6) and L is given in m.

Numerical results for the magnitude of R are shown in figure 11 for

frequencies of 20 and 100 kHz and b = 1 cm. The remaining conductor and

earth parameters are the same as in figure 3. For small L, |R| is

proportional to L as is the induced current for a dipole source in (7)

For

larger L, phase cancellation begins to occur, and a maximum in |R| occurs

near L ^ 7r/Re(A

p

), where Re indicates the real part. From figure 11, the

first maximum in |R| occurs at L ~ 450 m for a frequency of 100 kHz. If L

is made too long, the assumption of constant source current is no longer

valid.

4. PLANE WAVE EXCITATION

When the source is located a great distance, the incident field can be

considered to be a plane wave. For example, a distant VLF station at a

frequency of 17.4 kHz has been found to be a useful source [5]. Since we

are considering low frequencies, the refractive index of the earth is large,

and the incident field is refracted normal to the earth surface. Thus the

incident field propagates vertically downward in the negative y direction as

shown in figure 12. The infinitely long conductor is the same as shown in

figures 1 and 2.

Of the two possible electric field polarizations of the electric field

(x and z) , only z polarization induces axial currents in the long z- directed

11
conductor

.

So we assume that the incident electric field has only a zcomponent

i

E given by

Z

z

( 20 )

where k is given by (1) . The incident magnetic field has only an xcomponent given by

H

0

e

jfcy

( 21 )

where = E^/ty and the intrinsic impedance rj — [/i/(e - j cx/c*>) ] 1/2

4.1 Conductor Current

For uniform field excitation, the conductor current I is a constant

independent of z. To determine I, we apply the axial impedance condition

that was used in [6] for the special case of a uniform field (A = 0):

( 22 )

Z

g Q

is obtained by setting A = 0 in Z

g

in (4)

:

Z

s0 " Zm

+ — te(b/a) (23)

The z- component of the electric field due to the conductor is

;C = - j

<*>/*!

J z E

~ - vjkp) (24)

12
If we substitute (23) and (24) into (22) and set /x - nQ

, we obtain the

following for I

zs0

+ U"V2 * )K

o

( j kb)

‘ (25)

A numerical evaluation of (25) indicated that the current I is

independent of the outer radius b of the insulation. The reason for this is

that for small |kb| the modified Bessel function can be approximated by [10]

K

Q (jkb) ~ - in(jkb). (26)

If we substitute (26) into (25) and perform some algebra, we obtain

I

(

j

coa* 0

/2tt) in(jka) ' (27)

This result is very different from the case of dipole excitation where the

insulation plays an important role in supporting a transmission line mode.

For uniform field excitation, the transmission line mode is not excited.

Numerical results for the magnitude of the current as a function of

frequency are shown in figure 13. The results depend on the metal radius a,

but not on the insulation radius b. The constitutive parameters of the

metal and the earth are the same as in the previous figures. The current

increases as the frequency is decreased, but the low-frequency limit of I is

a constant. This constant is obtained by letting u> approach zero in Z :

Z

m o) = 0 = l/(7ra a ) . ' m

(28)

This is the expected dc limit. If we substitute (28) into (27), we obtain

the dc limit of I:

13
I „ (29) n = E

n (na o )

.

u> = U U m

4.2 Electric and Magnetic Fields

The electric field due to the conductor current is given by (24) . From

c c Maxwell's curl equation, the x and y components, and H , of the magnetic

field due to the conductor current are

and

jw/i dy

-ikly

2?r p

K

x (jkp)

jco/i 3x

iklx

2np K^jkp).

(30)

Q The vertical component is of most practical interest because it is most

easily received in a vertical borehole and because it is orthogonal to the

incident magnetic field.

In figure 14 we show numerical results for the magnitude of the

vertical magnetic field as a function of height y for a number of

frequencies. The horizontal distance x is 15 m, and the conductor radius a

is 0.5 cm. The other parameters are the same as in figure 13. The field

peaks at y = 0 and is even in y. The largest response is at the lowest

frequency, 4 kHz, because the induced current is largest at the lowest

frequency. Under ideal circumstances, the conductor should be detectable

Q from the maximum in |H 1 because the incident field has no vertical

y

component. However, irregularities in the earth and in the earth surface

will generally cause some conversion from horizontal to vertical magnetic

field [16]

.

In figure 15 we show numerical results for the magnitude of the

vertical magnetic field for various horizontal distances x at a frequency of

20 kHz. The remaining parameters are the same as in figure 14. For larger

14
offsets of 50 and 100 m, the field strengths are lower and the peak at y

= 0

is not very sharp. So detection and location would be difficult.

c

In figure 16 we show numerical results for |E | as a function of y for

z various frequencies. The parameters are the same as those in figure 14.

Since the polarization is the same as the incident field and is only on the

order of 10% of the incident field, the secondary electric field is probably

not very useful for detection.

5. CONCLUSIONS

The results presented here indicate that a horizontal electric dipole

can excite significant axial currents on long horizontal conductors. These

currents produce secondary magnetic and electric fields that are smaller

than the primary fields near the source, but are larger than the primary

fields at large axial distances. An insulated conductor can support a

transmission line current that has slow decay in the axial direction . A

grounded conductor has a larger current excited near the source, but that

current decays more rapidly in the axial direction. In either case, the

secondary fields are large enough that detection of long conductors appears

promising. The same conclusions hold for an electric line source grounded

at the ends, and the effect of the length of the line source is discussed in

section 3. All of the above conclusions are qualitively the same as those

for a magnetic dipole source [6]. Numerical results have been presented for

frequencies from 4 kHz to 500 kHz, and the entire frequency range appears to

be useful.

If a controlled source is not available, then distant far- field

sources, such as VLF radio stations or atmospheric noise, can also be used.

Such sources will excite long conductors if the polarization of the electric

field is aligned along the conductor, but will not excite a transmission

line current. The secondary vertical magnetic field is the most useful

field component to use in detection because the incident magnetic field in

the earth should be horizontally polarized.

15
A number of extensions to this work would be useful. The presence of

the air- earth interface [9] could be included, and this would be useful in

providing a more precise evaluation of excitation by a line source at the

earth surface [13]. Multiple conductors or conductors of finite length

could be studied, and finite length conductors [12] have been shown to have

a significantly different frequency dependence because of resonance effects.

Also, earth layering or inhomogeneities could be studied to obtain an

estimate of the competing geologic noise [16-19]. This effect could be

particularly important in the case of a distant far- field source where

polarization is used to discriminate against the incident field.

6 . ACKNOWLEDGMENTS

This research was supported by the U.S. Army Belvoir RD&E Center. I

would like to thank Roy Greenfield and Larry Stolarczyk for helpful

discussions

.

7 . REFERENCES

[1] Wait, J.R.; Hill, D.A. Radio frequency transmission via a trolley wire

in a tunnel with rail return. IEEE Trans. Antennas Propagat., AP-25:

248-253; 1977.

[2] Wait, J.R.; Umashankar, K.R. Analysis of the earth resistivity

response of buried cables. Pure and Appl. Geophys . , 117: 711-742;

1978.

[3] Lytle, R.J.; Laine, E.F.; Lager, D.L.

;

Davis, D.T. Cross-borehole

electromagnetic probing to locate high-contrast anomalies. Geophys.,

44: 1667-1676; 1979.

[4] Olhoeft, G.R. Interpretation of hole-to-hole radar measurements.

Third Technical Symposium on Tunnel Detection. Golden, CO: January 12-

15, 1988.

[5] Bollen, R.L. Tunnel Detection by Low-Frequency Magnetic-Field

Emissions and the Controlled Source Audio Magneto Telluric Techniques.

SRI International: January 1989.

16
[6] Hill, D.A. Magnetic dipole excitation of a long conductor in a lossy

medium. IEEE Trans. Geosci. Rem. Sens., GE-26: 720-725; 1988.

[7] Wait, J.R. Electromagnetic wave propagation along a buried insulated

wire. Can. J. Phys . , 50: 2402-2409; 1972.

[8] Wait, J.R. Excitation of currents on a buried insulated cable. J.

Appl . Phys., 49: 876-880; 1978.

[9] Tsubota, K. ; Wait, J.R. The frequency and the time-domain responses of

a buried axial conductor. Geophys . , 45: 941-951; 1980.

[10] Abramowitz , M. ; Stegun, I. A. Handbook of Mathematical Functions.

Washington: National Bureau of Standards; 1964.

[11] Hill, D.A.; Wait, J.R. Coupling between a dipole antenna and an

infinite cable over an ideal ground plane. Radio Sci., 12: 231-238;

1977. .

[12] Hill, D.A. Magnetic dipole excitation of an insulated conductor of

finite length. IEEE Trans. Geosci. Rem. Sens., GE-28: 289-294; 1990.

[13] Hill, D.A. ; Wait, J.R. Subsurface electromagnetic fields of a grounded

cable of finite length. Can. J. Phys., 51: 1534-1540; 1973.

[14] Hill, D.A. Electromagnetic surface fields of an inclined buried cable

of finite length. J. Appl. Phys., 44: 5275-5279; 1973.

[15] Wait, J.R. Electromagnetic Waves in Stratified Media. New York:

Pergamon; 1970.

[16] Hill, D.A.; Wait, J.R. Theoretical noise and propagation models for

through- the -earth communication. National Telecommunications and

Information Administration; May 1982.

[17] Eaton, P.A.; Hohmann, G.W. An evaluation of electromagnetic methods in

the presence of geologic noise. Geophys., 52: 1106-1126; 1987.

[18] Greenfield, R. Borehole radar clutter. National Radio Science

Meeting: Boulder, CO; January 4-6, 1989.

[19] Hill, D.A. Clutter models for subsurface electromagnetic applications.

Nat. Inst. Stand. Tech. (U.S.) NISTIR 89-3909; 1989.

17
Figure 1

y

Geometry for a horizontal electric dipole source and an

infinitely long conductor.

18
Figure 2. Geometry for an insulated conductor.

19
Figure 3 . Current induced on a conductor by a horizontal electric dipole

source

.

20
Figure 4.

• Q Q Primary |H^| and secondary |H | magnetic field strength for

different values of insulation radius b.

21
Magnetic

Field

Strength

(/i

A/m)

j=\ s' x = 15 m | —50 m

: \

X i i i i i i i

X

V-IOOm b = 1 cm

nn^TTi]"

/

y

/

x = 15 m

\

E \ 50 m

E Vv

F \ \\

100 m

i i i

l \ 1L—1 i J—_J

0 100 200 300 400 500

Z(m)

Figure 5

.

- Q C Primary |H j and secondary |H j magnetic field strength for

y y

different values of horizontal separation x.

22
Magnetic

Field

Strength

(/M/m)

20

Figure 6. Primary |H^| and secondary |H^| magnetic field strength for

different frequencies.

23
Electric

Field

Strength

(/j

V/

m)

200

Ez

c

l,b = 0.5cm

\

\

\

\

\

\

i =

\ b = 1 cm

10

him

\ \

\ \

\ \ b = 10cm

—

\

\

' \ \ b = 1 m

— \ \

L i

1 l\ 1 M 1 1 i J 0 100 200 300 400 500

z (m)

Figure 7. Primary j j and secondary j j electric field strength for

different values of insulation radius b.

24
200

o'

’( 4—

o

0)

LU

100

>

3

O)

c0

-t—

cn

32

0

10 K \\ t \ \ - \

\

0.

0.05

\

: \

, \

\\

\\

x = 15 m

50 m —100 m

\\

X. \

v

x \

\\ \

\\V~

\\\"

wY

\ \

\ w

\ \

\

\ \

a_a.

LAJl

x = 15 m

50 m

100 m

o 100 200 300 400 500

z(m)

j c

Figure 8. Primary |E | and secondary |E | electric field strength for

z’ ' z different values of horizontal separation x.

25
Electric

Field

Strength

(/iV/m)

200

Figure 9

.

CL C Primary | E | and secondary | E | z z different frequencies.

electric field strength for

26
y

Figure 10. Geometry for a horizontal line source and an infinitely long

conductor

27
1400

Figure 11. Magnitude of R versus line source length L.

28
y

Figure 12. Geometry for a plane wave incident on an infinitely long

conductor

29
Ill

(A)

Figure 13. Magnitude of the current induced on an infinitely long conductor

for plane wave incidence. = 1 V/m.

30
HyVH

Figure 14. Magnetic field strength for scattering by an infinitely long conductor for plane wave incidence.

31
Hy

C

/H

figure 15. Magnetic field scattered at different horizontal distances x for

plane wave incidence.

32
Figure 16. Electric field strength for scattering by an infinitely long

conductor for plane wave incidence.

33

u.S. GOVERNMENT PRINTING OFFICE: 1990 - 573-5*1/45020
L-114A U.S. DEPARTMENT OF COMMERCE

-90) NATIONAL SNSTSTUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NISTIR 3954

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBLICATION DATE

September 1990

TITLE AND SUBTITLE

Near-Field and Far-Field Excitation of a Long Conductor in a Lossy Medium

AUTHOR(S)

David A. Hill

PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BOULDER, COLORADO 80303-3328

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

U.S. Army Belvoir RD&E Center

Fort Belvoir, Virginia 22060-5606

J. SUPPLEMENTARY NOTES ______________ — _____ — ________

. .

'

. . ........ • j

1. ABSTRACT (A 280-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

Excitation of currents on an infinitely long conductor is analyzed for

horizontal electric dipole or line sources and for a plane-wave, farfield source. Any of these sources can excite strong currents which

produce strong scattered fields for detection. Numerical results for

these sources indicate that long conductors produce a strong anomaly

over a broad frequency range. The conductor can be either insulated

or bare to model ungrounded or grounded conductors.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

axial current; axial impedance; electric dipole; electric field; grounded conductor;

insulated conductor; line source; magnetic field, plane wave.

13. AVAILABILITY 14. NUMBER OF PRINTED PAGES

X UNLIMITED

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS). 40

ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 28402.

15. PmCE

; X ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22181.

1 ELECTRONIC FORM