Four Models used for 

Numerical Simulation of a 

Borehole Radar Antenna 

By Karl J. Ellefsen and David L. Wright 

This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey editorial 

standards or with the North American Stratigraphic Code. 

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement 

by the U.S. Government. 

Open-File Report 2003-03-155 

U.S. Department of the Interior 

U.S. Geological Survey 
ABSTRACT 

In this report are four different models that represent an antenna used by personnel at the 

U.S. Geological Survey for crosswell investigations. The four models vary in complexity 

and concomitantly the accuracy with which they represent the actual antenna. These 

models are used in numerical simulations of the antenna to determine how it radiates 

radar waves. 

2
INTRODUCTION 

The transmitting antenna used at the U.S. Geological Survey was represented by four 

different models that were used in numerical simulations to calculate its radiation pattern. 

The complexity of the models and concomitantly the accuracy with which they represent 

the transmitting antenna varied. 

These four models will be useful in future investigations, and so detailed descriptions of 

the models are in this report. Because the descriptions are straightforward, only a few 

remarks are necessary: 

• The four models are labeled MODEL 1, MODEL 2, MODEL 3, and MODEL 4. 

The complexity of the models increases with model number. In other words, 

model 1 is the least complex, and model 4 is the most complex. 

• Each model is described in a separate section of the report. 

• The parts in the models are labeled with numbers. The same numbers are used for 

the same (or nearly the same) part in different models, to make their comparison 

somewhat easy. For example, the fiberglass cover in all models is labeled “3.” 

Because of this method of numbering, the numbering for the parts in models 1, 2, 

and 3 is not consecutive. For example, model 1 has parts labeled “1” and “3,” but 

not “2.” 

• The dimensions of the models are specified in the circular cylindrical coordinate 

system, and its origin is at the center of the driving point. The models have 

cylindrical symmetry, and so locations within the model are completely specified 

with just the radial and the axial distances (ρ and z, respectively). All dimensions 

use five digits to the right of the decimal place (for example, 0.00520). 

• The electromagnetic properties are specified using three significant digits. 

• In all four models, the space occupied by the coaxial cable (regions 27, 28, and 

29) overlaps the space occupied by the driving point and the cylindrical 

conductors (region 10). While this appears to be an error, it is not. One finite 

difference grid is used for the coaxial cable, and another, larger grid is used for 

the rest of the antenna. The two grids are joined at the driving point. 

3
--- 

MODEL 1 

Figure 1. Model 1. Both diagrams are to scale and may be compared to the diagrams in 

Figures 2, 3, and 4. Each region of the model is referenced by a number. The 

electromagnetic properties and the dimensions of each region are listed in Tables 1 

through 4. 

Table 1. Regions of model 1, except for the coaxial cable (Figure 1). Type “s” refers to a 

region with standard or typical electromagnetic properties. Type “pc” refers to a region 

that is a perfect conductor. For such a region, both the relative dielectric permittivity and 

the relative magnetic permeability have no significance; consequently, the associated 

table entries are leaders (---). The dimensions of the regions are listed in Table 2. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

1 Formation s 0.00 5.80 1.00 

3 Fiberglass cover of the sonde s 0.00 4.70 1.00 

6 Air near the driving point s 0.00 1.00 1.00 

7 Plastic cover of the driving point s 0.00 3.70 1.00 

10 Driving point and the cylindrical conductors pc ∞ ---

4
--- 

--- 

Table 2. Dimensions of regions 1, 3, 6, 7, and 10 in model 1 (Figure 1). Each region has a 

different shape, and so the number of coordinates needed to describe that shape generally 

varies. 

Region 1 Region 3 Region 6 Region 7 Region 10 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 -30.00000 0.00000 -0.48490 0.00200 -0.00510 0.03810 0.08100 0.00000 -0.47980 

0.00000 -0.48490 0.00000 -0.47980 0.00570 -0.00510 0.00570 0.00510 0.03810 -0.47980 

0.04320 -0.48490 0.03810 -0.47980 0.00570 0.00510 0.00570 -0.00510 0.03810 -0.08100 

0.04320 0.48490 0.03810 0.47980 0.00200 0.00510 0.03810 -0.08100 0.00570 -0.00510 

0.00000 0.48490 0.00000 0.47980 0.00200 -0.00510 

0.00000 30.00000 0.00000 0.48490 0.00200 0.00510 

30.00000 30.00000 0.04320 0.48490 0.00570 0.00510 

30.00000 -30.00000 0.04320 -0.48490 0.03810 0.08100 

0.03810 0.47980 

0.00000 0.47980 

Table 3. Coaxial cable used in model 1 (Figure 1). Type “s” refers to a region with 

standard or typical electromagnetic properties. Type “pc” refers to a region that is a 

perfect conductor. For such a region, both the relative dielectric permittivity and the 

relative magnetic permeability have no significance; consequently, the associated table 

entries are leaders (---). The dimensions are listed in Table 4. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

27 Inner Conductor pc ∞ ---

28 Dielectric Sheath s 0.00 1.30 1.00 

29 Outer Conductor pc ∞ ---

Table 4. Dimensions of the coaxial cable used for model 1 (Figure 1). 

Region 27 Region 28 Region 29 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 -0.02910 0.00200 -0.02910 0.00520 -0.02910 

0.00000 -0.00510 0.00200 -0.00510 0.00520 -0.00510 

0.00200 -0.00510 0.00520 -0.00510 0.00550 -0.00510 

0.00200 -0.02910 0.00520 -0.02910 0.00550 -0.02910 

5
--- 

MODEL 2 

Figure 2. Model 2. Both diagrams are to scale and may be compared to the diagrams in 

Figures 1, 3, and 4. Each region of the model is referenced by a number. The 

electromagnetic properties and the dimensions of each region are listed in Tables 5 

through 9. 

Table 5. Regions of model 2, except for the coaxial cable (Figure 2). Type “s” refers to a 

region with standard or typical electromagnetic properties. Type “pc” refers to a region 

that is a perfect conductor. For such a region, both the relative dielectric permittivity and 

the relative magnetic permeability have no significance; consequently, the associated 

table entries are leaders (---). The dimensions of the regions are listed in Tables 6 and 7. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

1 Formation s 0.00 5.80 1.00 

2 Water in borehole s 0.00 81.00 1.00 

3 Fiberglass cover of the sonde s 0.00 4.70 1.00 

6 Air near the driving point s 0.00 1.00 1.00 

7 Plastic cover of the driving point s 0.00 3.70 1.00 

10 Driving point and the cylindrical conductors pc ∞ ---

6
--- 

--- 

Table 6. Dimensions of regions 1, 2, 3, 6, and 7 in model 2 (Figure 2). Each region has a 

different shape, and so the number of coordinates needed to describe that shape generally 

varies. 

Region 1 Region 2 Region 3 Region 6 Region 7 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.07500 -30.00000 0.07500 -30.00000 0.00000 -0.48490 0.00200 -0.00510 0.03810 0.08100 

0.07500 30.00000 0.07500 30.00000 0.00000 -0.47980 0.00570 -0.00510 0.00570 0.00510 

30.00000 30.00000 0.00000 30.00000 0.03810 -0.47980 0.00570 0.00510 0.00570 -0.00510 

30.00000 -30.00000 0.00000 0.48490 0.03810 0.47980 0.00200 0.00510 0.03810 -0.08100 

0.04320 0.48490 0.00000 0.47980 

0.04320 -0.48490 0.00000 0.48490 

0.00000 -0.48490 0.04320 0.48490 

0.00000 -30.00000 0.04320 -0.48490 

Table 7. Dimensions of region 10 in model 2 (Figure 2). 

Region 10 

ρ (m) z (m) 

0.00000 -0.47980 

0.03810 -0.47980 

0.03810 -0.08100 

0.00570 -0.00510 

0.00200 -0.00510 

0.00200 0.00510 

0.00570 0.00510 

0.03810 0.08100 

0.03810 0.47980 

0.00000 0.47980 

Table 8. Coaxial cable used in model 2 (Figure 2). Type “s” refers to a region with 

standard or typical electromagnetic properties. Type “pc” refers to a region that is a 

perfect conductor. For such a region, both the relative dielectric permittivity and the 

relative magnetic permeability have no significance; consequently, the associated table 

entries are leaders (---). The dimensions are listed in Table 9. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

27 Inner Conductor pc ∞ ---

28 Dielectric Sheath s 0.00 1.30 1.00 

29 Outer Conductor pc ∞ ---

Table 9. Dimensions of the coaxial cable used for model 2 (Figure 2). 

Region 27 Region 28 Region 29 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 -0.02910 0.00200 -0.02910 0.00520 -0.02910 

0.00000 -0.00510 0.00200 -0.00510 0.00520 -0.00510 

0.00200 -0.00510 0.00520 -0.00510 0.00550 -0.00510 

0.00200 -0.02910 0.00520 -0.02910 0.00550 -0.02910 

7
MODEL 3 

Figure 3. Model 3. Both diagrams are to scale and may be compared to the diagrams in 

Figures 1, 2, and 4. Each region of the model is referenced by a number. The 

electromagnetic properties and the dimensions of each region are listed in Tables 10 

through 16. 

8
--- 

Table 10. Regions of model 3, except for the coaxial cable (Figure 3). Type “s” refers to a 

region with standard or typical electromagnetic properties. Type “pc” refers to a region 

that is a perfect conductor. For such a region, both the relative dielectric permittivity and 

the relative magnetic permeability have no significance; consequently, the associated 

table entries are leaders (---). Type “cs” refers to a conductive sheet that is used to 

simulate the resistive loading on the antenna. The dimensions of the regions are listed in 

Tables 11 through 14. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

1 Formation s 0.00 5.80 1.00 

2 Water in borehole s 0.00 81.00 1.00 

3 Fiberglass cover of the sonde s 0.00 4.70 1.00 

5 Air behind the upper conductive sheets s 0.00 1.00 1.00 

6 Air near the driving point s 0.00 1.00 1.00 

7 Plastic cover of the driving point s 0.00 3.70 1.00 

8 Air behind the lower conductive sheets s 0.00 1.00 1.00 

10 Driving point and the cylindrical conductors pc ∞ ---

15 1st conductive sheet, upper Region of antenna 

2nd conductive sheet, upper Region of antenna 

cs 75.16 4.70 1.00 

16 cs 64.43 4.70 1.00 

17 3rd conductive sheet, upper Region of antenna 

4th conductive sheet, upper Region of antenna 

cs 52.44 4.70 1.00 

18 cs 41.00 4.70 1.00 

19 5th conductive sheet, upper Region of antenna 

6th conductive sheet, upper Region of antenna 

cs 25.05 4.70 1.00 

20 cs 14.09 4.70 1.00 

21 1st conductive sheet, lower Region of antenna cs 75.16 4.70 1.00 

22 2nd conductive sheet, lower Region of antenna 

3rd conductive sheet, lower Region of antenna 

cs 64.43 4.70 1.00 

23 cs 52.44 4.70 1.00 

24 4th conductive sheet, lower Region of antenna 

5th conductive sheet, lower Region of antenna 

cs 41.00 4.70 1.00 

25 cs 25.05 4.70 1.00 

26 6th conductive sheet, lower Region of antenna cs 14.09 4.70 1.00 

Table 11. Dimensions of regions 1, 2, 3, 5, and 6 in model 3 (Figure 3). Each region has a 

different shape, and so the number of coordinates needed to describe that shape generally 

varies. 

Region 1 Region 2 Region 3 Region 5 Region 6 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.07500 -30.00000 0.07500 -30.00000 0.00000 -0.48490 0.00000 0.21180 0.00200 -0.00510 

0.07500 30.00000 0.07500 30.00000 0.00000 -0.47980 0.03802 0.21180 0.00570 -0.00510 

30.00000 30.00000 0.00000 30.00000 0.03810 -0.47980 0.03802 0.47980 0.00570 0.00510 

30.00000 -30.00000 0.00000 0.48490 0.03810 0.47980 0.00000 0.47980 0.00200 0.00510 

0.04320 0.48490 0.00000 0.47980 

0.04320 -0.48490 0.00000 0.48490 

0.00000 -0.48490 0.04320 0.48490 

0.00000 -30.00000 0.04320 -0.48490 

9
--- 

--- 

Table 12. Dimensions of regions 7, 8, 10, 15, and 16 in model 3 (Figure 3). Each region 

has a different shape, and so the number of coordinates needed to describe that shape 

generally varies. 

Region 7 Region 8 Region 10 Region 15 Region 16 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.03810 0.08100 0.00000 -0.21180 0.00000 -0.21180 0.03802 0.21180 0.03802 0.25500 

0.00570 0.00510 0.03802 -0.21180 0.03810 -0.21180 0.03802 0.25500 0.03802 0.29820 

0.00570 -0.00510 0.03802 -0.47980 0.03810 -0.08100 0.03810 0.25500 0.03810 0.29820 

0.03810 -0.08100 0.00000 -0.47980 0.00570 -0.00510 0.03810 0.21180 0.03810 0.25500 

0.00200 -0.00510 

0.00200 0.00510 

0.00570 0.00510 

0.03810 0.08100 

0.03810 0.21180 

0.00000 0.21180 

Table 13. Dimensions of regions 17 to 21 in model 3 (Figure 3). 

Region 17 Region 18 Region 19 Region 20 Region 21 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.03802 0.29820 0.03802 0.34140 0.03802 0.38460 0.03802 0.42770 0.03802 -0.21180 

0.03802 0.34140 0.03802 0.38460 0.03802 0.42770 0.03802 0.47980 0.03802 -0.25500 

0.03810 0.34140 0.03810 0.38460 0.03810 0.42770 0.03810 0.47980 0.03810 -0.25500 

0.03810 0.29820 0.03810 0.34140 0.03810 0.38460 0.03810 0.42770 0.03810 -0.21180 

Table 14. Dimensions of regions 22 to 26 in model 3 (Figure 3). 

Region 22 Region 23 Region 24 Region 25 Region 26 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.03802 -0.25500 0.03802 -0.29820 0.03802 -0.34140 0.03802 -0.38460 0.03802 -0.42770 

0.03802 -0.29820 0.03802 -0.34140 0.03802 -0.38460 0.03802 -0.42770 0.03802 -0.47980 

0.03810 -0.29820 0.03810 -0.34140 0.03810 -0.38460 0.03810 -0.42770 0.03810 -0.47980 

0.03810 -0.25500 0.03810 -0.29820 0.03810 -0.34140 0.03810 -0.38460 0.03810 -0.42770 

Table 15. Coaxial cable used in model 3 (Figure 3). Type “s” refers to a region with 

standard or typical electromagnetic properties. Type “pc” refers to a region that is a 

perfect conductor. For such a region, both the relative dielectric permittivity and the 

relative magnetic permeability have no significance; consequently, the associated table 

entries are leaders (---). The dimensions are listed in Table 16. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

27 Inner Conductor pc ∞ ---

28 Dielectric Sheath s 0.00 1.30 1.00 

29 Outer Conductor pc ∞ ---

10
Table 16. Dimensions of the coaxial cable used for model 3 (Figure 3). 

Region 27 Region 28 Region 29 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 -0.02910 0.00200 -0.02910 0.00520 -0.02910 

0.00000 -0.00510 0.00200 -0.00510 0.00520 -0.00510 

0.00200 -0.00510 0.00520 -0.00510 0.00550 -0.00510 

0.00200 -0.02910 0.00520 -0.02910 0.00550 -0.02910 

11
MODEL 4 

Figure 4. Model 4. Both diagrams are to scale and may be compared to the diagrams in 

Figures 1, 2, and 3. Each region of the model is referenced by a number. The 

electromagnetic properties and the dimensions of each region are listed in Tables 17 

through 25. 

12
1 

2 

3 

4 

5 

6 

7 

8 

9 

10 --- 

11 --- 

12 --- 

13 --- 

14 --- 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

1

2

3

4

5

6

1

2

3

4

5

6

Table 17. Regions of model 4, except for the coaxial cable (Figure 4). Type “s” refers to a 

region with standard or typical electromagnetic properties. Type “pc” refers to a region 

that is a perfect conductor. For such a region, both the relative dielectric permittivity and 

the relative magnetic permeability have no significance; consequently, the associated 

table entries are leaders (---). Type “cs” refers to a conductive sheet that is used to 

simulate the resistive loading on the antenna. The dimensions of the regions are listed in 

Tables 18 through to 23. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

Formation s 0.00 5.80 1.00 

Water in borehole s 0.00 81.00 1.00 

Fiberglass cover of the sonde s 0.00 4.70 1.00 

Fiberglass tubing near the sonde head s 0.00 4.70 1.00 

Air behind the upper conductive sheets s 0.00 1.00 1.00 

Air near the driving point s 0.00 1.00 1.00 

Plastic cover of the driving point s 0.00 3.70 1.00 

Air behind the lower conductive sheets s 0.00 1.00 1.00 

Fiberglass tubing near the battery pack s 0.00 4.70 1.00 

Driving point and the cylindrical conductors pc ∞ ---

Wire braid for logging cable pc ∞ ---

Cable head pc ∞ ---

Sonde head pc ∞ ---

Battery pack pc ∞ -- st conductive sheet, upper Region of antenna cs 75.16 4.70 1.00 nd conductive sheet, upper Region of antenna

rd conductive sheet, upper Region of antenna 

cs 64.43 4.70 1.00 

cs 52.44 4.70 1.00 th conductive sheet, upper Region of antenna

th conductive sheet, upper Region of antenna 

cs 41.00 4.70 1.00 

cs 25.05 4.70 1.00 th conductive sheet, upper Region of antenna cs 14.09 4.70 1.00 st conductive sheet, lower Region of antenna

nd conductive sheet, lower Region of antenna 

cs 75.16 4.70 1.00 

cs 64.43 4.70 1.00 rd conductive sheet, lower Region of antenna

th conductive sheet, lower Region of antenna 

cs 52.44 4.70 1.00 

cs 41.00 4.70 1.00 th conductive sheet, lower Region of antenna

th conductive sheet, lower Region of antenna 

cs 25.05 4.70 1.00 

cs 14.09 4.70 1.00 

13
Table 18. Dimensions of regions 1 to 5 in model 4 (Figure 4). Each region has a different 

shape, and so the number of coordinates needed to describe that shape generally varies. 

Region 1 Region 2 Region 3 Region 4 Region 5 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.07500 -30.00000 0.07500 -30.00000 0.03810 0.53060 0.03560 0.47980 0.00000 0.21180 

0.07500 30.00000 0.07500 30.00000 0.04320 0.53060 0.03810 0.47980 0.03810 0.21180 

30.00000 30.00000 0.00000 30.00000 0.04320 -0.69370 0.03810 0.48230 0.03810 0.47980 

30.00000 -30.00000 0.00000 1.14020 0.03810 -0.69370 0.03560 0.48230 0.03560 0.47980 

0.00480 1.14020 0.03560 0.48230 

0.00480 0.73380 0.00000 0.48230 

0.02220 0.73380 

0.02860 0.56870 

0.04320 0.54330 

0.04320 -1.39550 

0.00000 -1.47370 

0.00000 -30.00000 

Table 19. Dimensions of regions 6 to 10 in model 4 (Figure 4). Each region has a 

different shape, and so the number of coordinates needed to describe that shape generally 

varies. 

Region 6 Region 7 Region 8 Region 9 Region 10 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00200 -0.00510 0.03810 0.08100 0.00000 -0.21180 0.03560 -0.47980 0.00000 -0.21180 

0.00570 -0.00510 0.00570 0.00510 0.00000 -0.64490 0.03810 -0.47980 0.03810 -0.21180 

0.00570 0.00510 0.00570 -0.00510 0.03560 -0.64490 0.03810 -0.64490 0.03810 -0.08100 

0.00200 0.00510 0.03810 -0.08100 0.03560 -0.47980 0.03560 -0.64490 0.00570 -0.00510 

0.03810 -0.47980 0.00200 -0.00510 

0.03810 -0.21180 0.00200 0.00510 

0.00570 0.00510 

0.03810 0.08100 

0.03810 0.21180 

0.00000 0.21180 

Table 20. Dimensions of regions 11 to 15 in model 4 (Figure 4). Each region has a 

different shape, and so the number of coordinates needed to describe that shape generally 

varies. 

Region 11 Region 12 Region 13 Region 14 Region 15 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 0.73380 0.00000 0.56870 0.00000 0.48230 0.00000 -1.47470 0.03802 0.21180 

0.00480 0.73380 0.02860 0.56870 0.03810 0.48230 0.04320 -1.39550 0.03802 0.25500 

0.00480 1.14020 0.02220 0.73380 0.03810 0.53060 0.04320 -0.69370 0.03810 0.25500 

0.00000 1.14020 0.00000 0.73380 0.04320 0.53060 0.03810 -0.69370 0.03810 0.21180 

0.04320 0.54330 0.03810 -0.64490 

0.02860 0.56870 0.00000 -0.64490 

0.00000 0.56870 

14
--- 

--- 

Table 21. Dimensions of regions 16 to 30 in model 4 (Figure 4). 

Region 16 Region 17 Region 18 Region 19 Region 20 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.03802 0.25500 0.03802 0.29820 0.03802 0.34140 0.03802 0.38460 0.03802 0.42770 

0.03802 0.29820 0.03802 0.34140 0.03802 0.38460 0.03802 0.42770 0.03802 0.47980 

0.03810 0.29820 0.03810 0.34140 0.03810 0.38460 0.03810 0.42770 0.03810 0.47980 

0.03810 0.25500 0.03810 0.29820 0.03810 0.34140 0.03810 0.38460 0.03810 0.42770 

Table 22. Dimensions of regions 21 to 25 in model 4 (Figure 4). 

Region 21 Region 22 Region 23 Region 24 Region 25 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.03802 -0.21180 0.03802 -0.25500 0.03802 -0.29820 0.03802 -0.34140 0.03802 -0.38460 

0.03802 -0.25500 0.03802 -0.29820 0.03802 -0.34140 0.03802 -0.38460 0.03802 -0.42770 

0.03810 -0.25500 0.03810 -0.29820 0.03810 -0.34140 0.03810 -0.38460 0.03810 -0.42770 

0.03810 -0.21180 0.03810 -0.25500 0.03810 -0.29820 0.03810 -0.34140 0.03810 -0.38460 

Table 23. Dimensions of region 26 in model 4 (Figure 4). 

Region 26 

ρ (m) z (m) 

0.03802 -0.42770 

0.03802 -0.47980 

0.03810 -0.47980 

0.03810 -0.42770 

Table 24. Coaxial cable used in model 4 (Figure 4). Type “s” refers to a region with 

standard or typical electromagnetic properties. Type “pc” refers to a region that is a 

perfect conductor. For such a region, both the relative dielectric permittivity and the 

relative magnetic permeability have no significance; consequently, the associated table 

entries are leaders (---). The dimensions are listed in Table 25. 

Region 

Number 

Description Type Electrical 

Conductivity 

(S/m) 

Relative 

Dielectric 

Permittivity 

Relative 

Magnetic 

Permeability 

27 Inner Conductor pc ∞ ---

28 Dielectric Sheath s 0.00 1.30 1.00 

29 Outer Conductor pc ∞ ---

Table 25. Dimensions of the coaxial cable used for model 4 (Figure 4). 

Region 27 Region 28 Region 29 

ρ (m) z (m) ρ (m) z (m) ρ (m) z (m) 

0.00000 -0.02910 0.00200 -0.02910 0.00520 -0.02910 

0.00000 -0.00510 0.00200 -0.00510 0.00520 -0.00510 

0.00200 -0.00510 0.00520 -0.00510 0.00550 -0.00510 

0.00200 -0.02910 0.00520 -0.02910 0.00550 -0.02910 

15