Embed Size (px)
Citation preview
AFWL-NTYE-TN-81 -15
I
I3
I
,
81-15., ...
‘“ $~ti 27?
INTERACTIONBEIWEENTHEDISCUSSIMULATORAND A BURIEDWIREOR PLATE
J. A. Marks
The Dikewood Corporation
1613 University Boulevard, N.E.
Albuquerque, New Mexico 87106.,
May 1981
.
Technical Note
tribution 1imited to US Gove
of mi1itary systems jequ~preport; Feb 80. r requests for th~s docuto AFWL/NTYE, Kirtlan Force Base, NM 87117.
AIF? FORCE WEAPONS LABC)RATC)RY
Air Force Systems Command ‘
Kirtland Air Force Base, NM 87117
‘,,
./...
.- —. . -. .-—
UNCLASSIFIED--------------- -------- ------- ------ ...”-. . . . .
becz.lul~y GLAs>lt-lcA1iur+ 9P i H[> i-~r.e rl~nrn u-ala cnr-real
REPORT DOCUMENTA~lON PAGEREAD INSTRUCTIONS
BEFORE COMPLETING FO11. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT’S CATALOG NUMBER
AFWL-NTYE-TN-81-15I.TITLE (md Subtlfle) 5. TYPEOF REPoRT& PERIOO CO\
INTERACTION BETWEEN THE DISCUS SIMULATOR Technical NoteAND A BURIED WIRE OR PLATE
6.PERFORMING O=lG. REPGaTNUt4
DC-TN-1508-71.AUTHOR(S) 8. CONTRACTOR GRANT NUMBER(A
J. A. Marks F29601-79-C-O036
1.PERFORMING ORGANIZATION NAME ANO ADDRESS 10. PROGRAh4 ELEMENT,PROJECT,
The Dikewood CorporationAREA& WORK UNIT NUMBERS
1613 University Boulevard, N.E.Albuquerque, New Mexico 87106
64312F/14DNE0716
1.CONTROLLING OFFICE NAhlE AND ADORESS‘2” !W;RW9A;E1981
Air Force Weapons Laboratory (NTYET)Air Force Systems Command 13. NuMBEROF PAGES
Kirtland AFB, New Mexico 87117.
14. MONITORING AGENCY NAME & ADD RESS(ff different from Controlling Office) 1S. SECURITY CLASS. (of this report)
UNCLASSIFIED
lSa. DECLASSIFICATION/DOWNGilAlSCHEDULE
6. DISTRIBUTION STATEMENT (ofthisReport)
Distribution limted to US Government agencies only, because test andevaluation of military systems/equipment are discussed in the report; Feb [Other requests for this document must be referred to AFUL/NTYE, Kirtland AiForce Base, NM 87117.
17. DISTRI BuTloN STATEMENT (of the abstract entered in Block 20, if different irom Repo:t)
18. SUPPLEMENTARY NOTES
9. KEY wOROS (Continue on reverse side if necessary and Identify by block number)
Electromagnetic ScatteringNumerical EMP SimulationRadiated EMPSource Region InteractionThree-Dimensional Finite Difference
!0, ABSTRACT (Continue on reverse side if nocossary and Identify by biock number)
This report describes the method and results for a three-dimensional finite difference study of the interaction and couing between a DISCUS type EMP simulator and various buriedconductors. The DISCUS arrangement of pulsers simulates thepassing EMP from a nuclear surface burst. Various pulserarrangements are considered.
-----DD ,;~~r.;,1473 EDITION OF 1 NOV6S IS OBSOLETE
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (Ilhen Data Enrorect}
—
Section
CONTENTS
Page
I INTRODUCTION
II GEOMETRY AND MESH 8
III SOURCE DESCRIPTION 10
IV RESULTS 11
1. CASE 1: u = 1, 37 m WIRE, 8 m SLATS,DX = 1, 19 PULSERS 12
2. CASE 2: a = 2, 29 mWIRE, 8 m SLATS,DX = 1, 19 PULSERS 13
3. COMPARISON 1: 2 m VS. 8 m LONG SLATS 134. COMPARISON 2: 9 PULSERS VS. 19 PULSERS 145. COMPARISON 3: PULSER AND WIRE CURRENTS
WITH/WITHOUT GROUND RODS ATTACHED TOEND PLATE 15
6. COMPARISON 4: 29 m BARE WIRE WITH OPENTERMINATION COMPARED TO 54 m BARE WIRESHORTED TO GROUND RODS 15
7. COARSE MESH DISCUS CALCULATIONS TO 3 l.lSFOR A BURIED UNINSULATED WIRE 16
a. Slat length variations and environmenteffects 18
b. Centered/off centered wire dirve andslat length effects 18
c. Ground conductivity and pulser positioneffects 18
v CONCLUSIONS 20
.-
1
..—
Figure
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
ILLUSTRATIONS
Page
DISCUS geometry with 1 m mesh 23
Source electric field 24
Top view (x,y) of Ex, E , and Ez mesh point
locations for DX slats ;ith slat length =2DY 25
Slat/pulser/wire mesh point locations (37 m wire,8 m siats, DX = 1) -
Pulser current and wire current along lengthof simulator
Currents at pulser no. 2 (source end, 9 m)
Currents at pulser no. 10 (center, 25 m)
Currents at pulser no. 18 (far end, 41 m)1?
26
27 ‘
28
29
30
Slat/pulser/wire mesh po{nt locations (29 m wire,8 m slats, DX = 1)
Electric fields normal to 29 m wire
Wire current and normal electric fields 2 mfrom source end
Wire current and normal electric fields at mid-point of 29 m wire
Wire current and normal electric fields 2 mfrom far end
Pulser current and wire current along lengthof simulator
= 2, 29 m wire, 8 m slats, DX = 1, 19 pulsers,~BS-1
= 2, 29 m wire, 8 m slats, DX = 1, 19 pulsers,~BS-4 (midpoint)
a = 2, 29 m wire, 8 m slats, DX = 1, 19 pulsers,OBS-7
Slat/pulser/plate mesh point locations (a = 1,29 m x 4 replate, 8 m or 2mslats, DX = 1)
31
32
33
34
35
36
37
38
39
40
2
. —-,,-—- -— ———-. —-..-—-—-,- -.. -.--— --,. ,—---- —..—...-
ILLUSTRATIONS (Continued)
Figure
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Page
Pulser 1, Z and plate I for source end 41
Pulser I, Z and plate I for center location 42
Pulser I, Z and plate I for far end location 43
Slat/pulser/plate mesh point locations (a = 1,29 m x 4 m plate, 9 pulsers, DX = 1) 44
Currents for source end observer 1, for casesa = 1, 29 m x 4 m plate, 8 m slats, DX = 1,19 pulsers; a = 1, 29 m x 4 m plate, 8 m slats,DX = 1, 9 pulsers 45
Currents for midpoint observer 4, for casesa.= 1, 29m x 4mplate, 8 m slats, DX= 1,19 pulsers; u = 1, 29 m x 4 m plate, 8 m slats,DX = 1, 9 pulsers 46
Ground rods connected to end plates 47
Pulser and wire currents w/wo ground rods(OBS 1, near source) 48
Pulser and wire currents w/wo ground rods(OBS 4, center) 49
Pulser and wire currents w/wo ground rods(OBS 7, far end) 50
Buried wire connected to ground rods 51
Pulser and wire current for 29 m wire open and54 m wire shorted to ground rods (OBS 1, nearsource) 52
Pulser and wire current for 29 m wire open and54 m wire shorted to ground rods (OBS 4, center) 53
Pulser and wire current for 29 m wire open and54 m wire shorted to ground rods (OBS 7, farend) 54
Coarse grid geometry for 4 m mesh 55
Source voltage for coarse mesh calculations 56
3
.—..—. . -. . . . . .. ... .. =. —-....- .“-.. ‘. -—-————— ..... -. —- - .- ‘– .-.-–.. .- -..
ILLUSTRATIONS (Concluded)
35 Coarse mesh, 4 m A’s, wire currents (center) 57
36 Coarse mesh, 4 m A’s, wire currents, 8 m and40 m long slats, center positioned wire andoff center wire 58
37 Coarse mesh, 4 m A’s, wire currents, 40 mlong slats, two ground conductivities (0.001and 0.01) 59
38 Coarse mesh, 4 m A’s, wire currents, 40 mlong slats, two ground conductivities (0.001and 0.01) 60
4
—. ---- ——-—-————— -T:- -—.—. .. . ..---— ~-—.-—-.— .-
I.
This note summarizes
to the interaction between
INTRODUCTION
several specific calculations relating
a DISCUS type simulator and buried
conductors. The DISCUS simulator is a serially arranged number
of pulsers positioned near the surface of the ground (e.g., Ref. 1).
In operation, the pulsers are sequentially fired to simulate the
passing EM.Pwave from a nuclear surface burst. Interacting objects
in these calculations are positioned below the ground surface.
Initial “late-time” DISCUS calculations were made to 3 us
using a uniform 4 m mesh in the A3D code (Ref. 2). Large time
steps could be taken, but at the expense of accurately describing
the fast rising source. More uncertainty must be attached to
these results because of the coarse mesh. The remainder of the
calculations were made using a uniform 1 m mesh. This provided a
compromise between the coarse mesh late-time model requiring rea-
sonable computer resources and a mesh less than 0.4 m useful for
early time but requiring excessive computer resources to go beyond
a few hundred nanoseconds. The 1 m mesh calculations cover from
0-720 ns. Interaction with two conductor types were considered--
a perfectly conducting wire (an antenna or cable) and a perfectly
conducting plate (a missile shelter perhaps).
1. Baum, C. E., “A Distributed-Source Conducting Medium Simulatorfor Structures Near and Below the Ground Surface,” EIMPSensorand Simulation Note 87, Air Force Weapons Laboratory, KirtlandAI?B,NM, 9 July 1969. .
2. Marks, J. A., “A User’s Manual for the Three-Dimensional A3DElectromagnetic Scattering Code,” DC-TN-1222-14, DikewoodIndustries, Inc.; November 1976 (also published as AFWL-TR-77-23).
— ..
5
..— ..... —
. ..._.. — ..—- -—- .. . .....--.~ .-.-. –..: .—. —---
Results show the
pulser impedances, and
plate as a function of
relationship between the pulser currents,
currents induced on the buried wire or
position along the DISCUS array. Electric
fields normal to the wire are given for some cases.
Computations are performed numerically using a double expo-
nential (over/under) source and a finite difference time domain
Maxwell solver, A3D. Typical mesh dimensions are shown in
Figure 1.
Section IV.I gives results for the 37 m and 29 m long wires
buried under a 19 pulser array. In addition to the pulser current,
pulser impedance, and wire current, the electric fields normal to
the wire are given as a function of position along the wire.
Section IV.2 describes problems encountered with defining
a faster source (a = 2) in the 1 m mesh. The results are more
ragged but illustrate the same general response characteristics
at the slower (a = 1) source.
Section IV.3 shows the effect of varying the pulser slat
length between 2 m and 8 m and the corresponding currents induced
on a 4 m wide plate buried 1 m.
Section IV.4 shows the variation in the pulser and buried
plate current when a 9 pulser array replaces the normal 19 pulser
array. This was modeled by replacing every other pulser location
with an additional conducting plate which filled the gap between
the original plates. The voltages of the remaining pulsers were
increased by the ratio of 19/9.
6
—.— ———.— . .. .. . . . . ,—. -— y-,--- . -,, . .. . .
Section IV.5 shows the effect of positioning ground rods
at the ends of the pulser array and actually shorting these rods
to the end plates of the DISCUS array. The buried wire remains
shorter overall than the array.
Section IV.6 shows the effect of positioning the ground
rods outside of the pulser array and then lengthening the buried
wire and connecting it to the ground rods.
Section IV.7 gives results form the coarse mesh calcula-
tions. These calculations indicate late time results to 3 vs.
—.
7
.-. .. —-.-
---- -: --— ... .- ‘ -. ---- ..—.
II. GEOMETRY AND MESH
The majority of these calculations were based on a uniform
1 m mesh in the A3D code. Table 1 gives meshing coordinates
and Figure 1 depicts the overall dimensions. Slight differences
in geometry are noted with each separate calculation.
8
—.———— —-——. . . . ,.—.._ .__,—- — —- .- . .-=..;.-~.. _—_ .—.— ._._,-.
TABLE 1. GEOMETRY AND MESH COORDINATES
Mesh Sizes
DX = 1, no. cells = 51; total X = 50 m
DY = 1, no. cells = 30; total Y = 29 m(symmetry plane)
DZ = 1, no. cells = 60; total Z = 59 m
X Components
Cable from 12-40 (mesh point locations)
Total Length = 29 m
20 plates (from 6 m to 44 m)
Y Components
Symmetry
Center of rods (or plates) at Y = O
Rod (or plates) length
2 m long (1 mesh + symmetry)
8 m long (4 meshes + symmetry)
Z Components
Air/ground at mesh point 31
Total ground depth = 30 m
Total air above ground = 29 m
Cable located 1 m below interface
Physical Constants
Dielectric constant of ground = 10 so
Ground conductivity, Og = 0.001 S/m
(some cases with ag = 0.01 S/m)
9
.- .... -.. .- .—
---—. — .—-. ___... ..— .-. —J. . —— . . . . . . —.___ ~,-- . . . . . ._ ___ ____ ____ ___
111. SOURCE DESCRIPTION
Sources used for the 1 m mesh calculations are defined by
an over/under exponential of the form
A. ea~V(T) = 2(T-TP)
I+e
a was set to 108 or 2 X108/s and referred to as a = 1 or a = 2.
Figure 2 shows difference in rate of rise. u = 1 rises 10 to
in 25 ns, a = 2 rises in 15 ns.
To simulate the surface burst conditions and the DISCUS
90%
simulator itself, the electric field at the mesh point between
two slats (plates) is set each time step using the double expo-
nential to determine the magnitude. These source mesh points are
defined in Figure 3a. Setting only the center-most Ex is referred
to as “center fire,” while “all fire” is defined as setting the Ex
field at all mesh positions to the end of the plate. Each source
point is separated by 2AX or 2 m for these cases. Four-hundred
time steps of 1.8 x1O-9
s for a total time of 0.72 us were used.
Each source mesh point relative time is retarded by 2AX/C to
simulate the surface burst source wave passing over the array at
the speed of light.
10
— —_;. ..-~-,——————- .-:-— ——— ..——---.. ...!. ..
Tables 2 and 3 list
DISCUS results to follow.
IV. RESULTS
the principal parameters varied for the
Specific differences between cases are
described under each subsection.
RunNo.
495496497498499500504505
TABLE 2. PARAMETERS USED IN
Source Wire/Plate Dimensions
a Length Widtha (m) (m)
12111111
WireWirePlatePlatePlateWireWireWire
3729292929292954
444
THE 1 m MESH CALCULATIONS
Slat GroundDX No. Length Rods(m) Pulsers (m) x
1 19 8 N1 19 8 N1 19 8 N1 19 2 N1 9 8 N1 19 8 N1 19 8 Y1 19 8 Y
aRise rate is given in units of inverse shakes (1 shake = 10 ns).
Run&
467468469470471472474475476
TABLE 3. PARAMETERS USED IN THE 4 m
Wire SourceLocation Definitiona
CenterCenterCenterCenterCenterOff centerOff centerCenterCenter
AFAFCFCFCFCFCF
EnvironmentAF
hlESHCALCULATIONS
Slat %Length (m) (S/m)
40 0.0140 0.00140 0.0140 0.0018 0.0018 0.001
40 0.0010.001
8 0.001
aAF for “all fire,” Ex set all meshes along slats.
CF for “center fire,” Ex set at center mesh point only.
-..—
11
— . ..—-.—..-
.—-— — —4— --- .—. — .. —.. —. — . .
1. CASE 1: a=l, 37 m WIRE, 8 m SLATS, DX = 1, 19 PULSERS
Stylized mesh point and observer numbering are depicted in
Figure 4. Results given in Figure 5 show the peak pulser current
and peak wire current along the simulation length. Pulser and
wire currents are largest at the midpoint of the length of wire.
The 37 m wire is overlapped at the ends by the slat structure.
Slats are 8 m long. Time domain results for three axial positions
are given in Figures 6-8. Each figure depicts the pulser current,
pulser impedance, and wire current for pulser numbers 2, 10, and
18. There are 19 pulsers altogether. Pulser number 10 is at the
center. Pulser number 1 is at the source end of the mesh.
cl = 1, 29 m WIRE, 8 m SLATS, DX = 1, 19 PULSERS
Electric fields normal to wire--This calculation differs
from the previous example by using a wire only 29 m long rather
than the 37 m length (see Fig. 9). Two electric field components
are used to estimate voltages at or near the wire, E the hori-Y’
zontal component, and Ez, the vertical component. Figure 10a
shows the maximum electric field observed at each observer posi-
tion along the wire and Figure 10b shows the late time (%0.7 I.IS)
electric fields along the wire. In both cases, the maximum fields
occur near the midpoint of the wire along with the largest cur-
rents. Figures 11-13 show time domain currents and E-fields for
near, center, and far locations along the 29 m wire.
12
2. CASE 2: u = 2, 29 m WIRE, 8 m SLATS, DX = 1, 19 PULSERS
Aria= 2 source in the 1 m mesh produces more oscillations
in the observed currents (due to the mesh cell size) than the
u = 1 source but only slightly less overall current than the
u = 1 source. I?ulserand wire current maximums along the length
of the DISCUS are given
ante, and
given for
corresponding
near, center,
in Figure 14. Pulser current, load imped-
wire current (i.e., directly below) are
and far locations in Figures 15-17.
3. COMPARISON 1: 2 m VS. 8 m LONG SLATS
u = 1, 29 m x 4 m plate, 8 m slats, DX = 1, 19 pulsersCY= 1, 29 m x 4 m plate, 2 m slats, DX = 1, 19 pulsers
For this comparison, a buried, thin, rectangular conducting
plate replaces the buried wire. Pulser currents and plate cur-
rents are compared when the slat lengths are either 8 m or 2 m.
The source time history is the a = 1 designation and the pulsers
continue to operate in the “center fire” mode.
The buried plate, 29 m x 4 m, is situated 1 m below the air/
ground interface, the same as for the wire cases. The 19 pulser
array is used. Figure 18 depicts the mesh point locations in the
longitudinal direction for pulser, plates, and observers. The
pulser array continues to overlap the plate by 5 m on each end.
In this comparison set, the 8 m slats overlap the buried
plate, while in the 2 m long slat case, the slats do not cover the
plate but are 1 m short on each side.
Figures 19-21 depict the pulser current, pulser impedance,
and plate surface current for three positions along the array.
Observers 1, 4, and 7 are located as seen in Figure 18.
13
.— .—.-
_— .._ . . . :.:i .. ..——’.. - ~—— . . A—. — . . . . ..—. —.——. . . ..-
We can note the following from these comparisons. The early
time rise portion of the induced plate current is unaffected by
the change in slat length as is expected. This result was shown
in the wire comparisons previously described. As time progresses,
the longer slat lengths require more current to maintain the
imposed pulser voltage. Corresponding increases occur in the plate
surface current. In Figures 19-21, we see only a twofold decrease
in currents when going from 8 m to 2 m slats. An inverse relation-
ship holds for the pulser impedance.
4. COMPARISON 2: 9 PULSERS VS. 19 PULSERS
a = 1, 29 m x 4 m plate, 8 m slats, DX = 1, 19 pulsersa = 1, 29 m x 4 m plate, 8 m slats, DX = 1, 9 pulsers
In this comparison, the simulator geometry is altered such
that only nine pulsers are fired and additional perfectly conduct-
ing slats are used to fill in the space between every other pair
of slats. This, in effect, makes the slats 3 m x 8 m. The
stylized mesh point locations are given in Figure 22. To compen-
sate for the “missing” pulsers and to maintain the same overall
source, the voltage impressed between the slats at the nine
pulsers is increased in the ratio of 19/9.
Comparisons of these two cases are given in Figures 23 and
24 for observer number 1, an end observer, and number 4, a mid-
point observer. Results are similar in shape to currents calcu-
lated in the buried wire case, as expected.
Early time results show an increase in the pulser and plate
current for the nine pulser array due to the increased local volt-
age source. In the nine pulser array, observer number 1 is
14
—. ..— .~–-.y .=7— — -- –,——,T-.—
.
located directly under pulser number 2, and observer number 4 is
located directly under the midpoint pulser, number 5. More oscil-
lations occur in the nine pulser arrangement also. At later times
approaching 1 ps, both pulser and plate current in the nine
pulser case appear to approach the same currents seen in the 19
pulser case.
5. COMPARISON 3: PULSER AND WIRE CURRENTS WITH/WITHOUT GROUiNDRODS ATTACHED TO END PLATE
(x = 1, 29 m wire, 8 m slats, DX = 1, 19 pulsersa = 1, 29 m wire, 8 m slats, DX = 1, 19 pulsers, ground
rods added and connected to last pulser plate
In this case, vertical ground rods are added to the calcula-
tion at the ends of the pulser array (Fig. 25). The vertical rods
are modeled by zeroing the vertical electric fields. The vertical
rods extend 24 m to the side and 20 m deep. The “a = 1“ source
is used in the “center fire” mode, a = 0.001 S/m.g
Figures 26-28 show the pulser and wire current (fat wire)
differences when adding the ground rods as depicted in Figure 29.
Little to no difference is seen in the wire currents and yet con-
siderably more pulser current is needed to drive the array with
the central ground rods connected to the end plates.
6. COMPARISON 4: 29 m BARE WIRE WITH OPEN TERMINATION COMPAREDTO 54 m BARE WIRE SHORTED TO GROUND RODS
c1 = 1, 29 m wire, 8 m slats, DX = 1, 19 pulsersa = 1, 54 m wire, 8 m slats, DX = 1, 19 pulsers, shorted
to ground rods
In this example, the pulser currents and wire currents are
compared when the 29 m wire (fat wire) is lengthened to 54 m and
shorted to the vertical ground rods at the ends of the mesh. The
15
. —.. . . ..
-.—— .. —- . .. . . . . .: ..-. - —-—— -—-- .. —— ..- .—. .—.
vertical rods are 54 m apart . The i~a= 1“ source is used with
pulsers in the “center fire” mode. Ground conductivity = 0.001
S/m.
Figures 30-32 compare the pulser and wire currents for
observers 1, 4, and 7 corresponding to near, center, and far ends
of the 29 m wire. Only slight increases are seen in the pulser
currents, while significant differences are noted in the wire cur-
rent. Wire current at the center of the wire is significantly
larger in the lengthened wire case and at the last calculated
time, 720 ns, is almost a
Currents are almost three
ends.
factor of 2 larger than the 29 m
times higher at observers nearer
case.
the
7. COARSE MESH DISCUS CALCULATIONS TO 3 ~S FOR A BURIEDUNINSULATED WIRE
Several coarse mesh DISCUS calculations were made using a
uniform 4 m space mesh to look at buried bare wire currents to
times to 3 us (Fig. 33). Clearly, mesh cells of this size are
too large to resolve a fast rising source, but larger time steps
can be taken so that a late time calculation
reasonable amount of computer time. In this
DISCUS is buried in a ground with dielectric
can be made in a
calculation, the
constant = 10 so so
that there is no air/ground interface. Table 4 gives the mesh
parameters for these runs. Figure 34 shows the electric field
used to drive the voltage between the rods. This source decreases
to 9.35 x 103 V/m at 2.4 x 10-6 s and was held constant after that.
Currents shown for these coarse mesh cases were observed at the
center of the buried wire.
16
—..——— ..— —.—. . ...—.——.——— ..——,—-=----- - “ --.-” . ...-...7. ., ,.
TABLE 4. PARAMETERS FOR 4 m MESH CASES
Mesh Sizes
AX = 4 m; 51 steps for 200 m length
AY = 4 m; 30 steps for 116 m width
AZ = 4 m; 60 steps for 236 m height*
X Components
Wire length = 52 m
..
Y Components
Symmetry at Y = O
Center of slats**
atY=O
Z Components
Source and pulser slats imposed at Z = 31
Wire located 1 mesh, i..e.,4 m below pulserslats
Dielectric constant = 10
*120 m below pulsers, 116 m above pulsers.
**Slats are wires of 0.04 m diameter using a thin wire model in
the 4 m mesh. Slat lengths of 8 m and 40 m used 1 mesh point for8 m wire using symmetry plane, 5 mesh points for 400 m wire usingsymmetry plane.
17
. .—
—.-. —.— ...- . .. . . .—-. - ... —— —.. —.—...- ..— .. -—.-.... -+-— .-
a. Slat length variations and environment effects--Figure 35
shows a comparison of the observed current for four cases using the
following parameter variations:
(1) 8 m long rods (slats), source is fired acrosscenter of rods only.
(2) 8 m long rods (slats), center and end fire.
(3) 40 m long rods (slats), center fire andevery 4 m along rods.
(4) Environment.
The environment case is modeled by removing the rods
(slats) and establishing the voltage source at all mesh points
across the grid. Center firing across the short 8 m slats gen-
erates 60% of the current on the wire generated by the environment
case.
b. Centered/off centered wire drive and slat length
effects--Figure 36 shows the effect on the wire currents for dif-
ferent length rods (slats) when the center fire mode is used in
both cases. Two wire positions are considered. In one case, the
wire is positioned directly under the simulator and the other case
has the wire positioned one mesh (4 m) to the side. Due to symme-
try, this is equivalent to having two wires present. Observed cur-
rent differences at early time due to changes in slat lengths are
extremely small and at late times, W3 us, the differences are less
than 10%. Slat length apparently has little to no effect, at
least for those cases where the voltage source is established
between the slats (or rods) as was done here.
c. Ground conductivity and pulser position effects--Figures
37 and 38 show results of varying the ambient conductivity between
18
-.-.———— —. —---- - — ——~..-— . .—_ . ——.:.. .... .”....?’.-’” .. . ,Y
,. ,
0.01 and 0.001 S/m for 40 m long slats in the “center fire” and
“fire all along” cases. The higher conductivity produces larger
currents since maintaining the voltage source across the higher
impedance ground conductivity requires more current. Interest-
ingly, for the lower conductivity cases, the late time currents
differ by only 20%, while the early time currents differ by closer
to 30%. The late time currents are less dependent on the actual
method of applying the source in the a = 0.001 case, but this is.. !3
not the case for the a = 0.01 case where the ratio remains fairlyg
constant throughout the time span. Figure 38 is Figure 37 redrawn
with the a = 0.01 cases normalized to the a = 0.001 cases byg g
reducing the currents by a factor of 10 to account for the differ-
ences in the source uE.
19
.—— — .. . . . ,. —-~ — .-. — . . . . . .. .
--—————.
v. CONCLUSIONS
Several interesting conclusions can be drawn from this
series of computer calculations. Modeling an EMP experiment with
a finite difference code proves to be a highly efficient means of
designing the experimental equipment required for system testing
and evaluation.
1. The source rise rate, a, is only important if the sys-
tem can respond to the faster rising currents induced along the
buried conductor. Once the pulse has passed through the region
the induced currents are not controlled by the rise rate.
2. A buried conductor initially responds to a single
row of DISCUS pulsers to within a factor of two of the result
seen for an infinite array of pulsers. The DISCUS pulser row can
simulate the real environment within a factor of two if the source
can be reproduced by the pulsers. After the pulse passes the
agreement is within 25%.
3. Altering the slat length has little to no effect
until the pulse peak has passed. Then the longer slat length
increases the pulser current and conductor current proportionately.
Short slats drive currents along the wire as well as long slats.
4. The DISCUS can be operated with fewer pulsers if the
source voltage can be increased proportionately. Comparisons
between 9 and 19 pulsers show good agreement for both early times
near peak and at times approaching 1 us.
20
.. ----- —:‘..- . .... --—-. —-- .—.-.-—.,
5. Ground rods added to the ends of the array have little
effect on the early peak response. Significant increases in
pulser current are required for the ground rod case, but only
slight changes are noted in the induced buried conductor currents.
6. Different length buried wires respond the same
initially until the pulse peak passes. Then the longer wire
begins to carry significantly more current with little to no dif-
ference in the actual pulser current...
21
...—. —..
—-—— ..—. . -—. –. -__— . .. .- _— ... ..-. ..— — . .
TABLE 5. SUMMARY OF BURIED CONDUCTOR RESPONSESTO PARAMETER VARIATIONS
Variable Parameter Near Pulse Peak Following Pulse Peak
Source Rise Rate Proportional Not Significant
Pulser Row(s) Single Row Simulates Single Row Simulates(Environment) Environment within Environment within
Factor of 2 30%
Slat Length Not Significant More Pulser DrawnMore Conductor CurrentSeen
Number of Pulsers Proportional Less Important
With/Without Not Significant Significant PulserGround Rods Current Increase to
Produce Same ConductorCurrent
Wire Length Not Significant Long Wire Picks UpMore Current
22
- ——. -—.:.. .,:,: -. —-----~ --- —— -— -———.-. .———. —‘> ,.
r- ———— ———— ———— —— —— ——
1m *
I I
I29 m
I
I
I------- —----- —..
20 slats Im wide, 1 m apart I1
/0 IAir I.—. .—. ------- I1
IGround
i
I
I
-1
I 30 mI
..
II !& = 10
Ir= 0.001
L‘g
——— ——— —
Buried wire or plate(various lengths )
—— — —— —— ——.
Side View
P—— ~—”—— ——— — ——— ——— ——
1>1m
I20 slats
wide, 2mor29 m
8 m longII
I
1
ElIm nr.— [
rL– —
Boundary
Top View
Figure 1. DISCUS geometry with 1 m mesh.
23
—-. . .
.—- .--.2 —. .:-. .:--, - --—.—- ,.- -, J..... --
200
150
100
50
0
0 20 40 60 80 100 120 140 160 180 200Time (ns)
Figure 2. Source electric field.
.
,,
-. — .—. ~ —— . . . . . -.. ...-.—-— ---—— ——— -—-—---—: --...-...--”
Source Ex set at
these mesh points
Elflif!il!tl1’x
(a) Ex locations (at 2.) >
mlml(b) Ey locations (at 2.)
mmll(c) Ez locations (at 20 t ~ AZ)
Figure 3. Top view (xjy) of Ex, E , and Ez mesh point
locations for DX slats ~ith slat length =
2 DY (slats are on 20 plane).
25
.... —— ..— . ---- .-
I “-
,i
,,,.
I
Midpoint
11 15 19 23 27 31
Wire ~ 8
35 39 43
44
Locations-
ObserverNumbers 1 2 3 4“5 6 7 8 9
Figure 4. Slat/pulser/wire mesh point locations(37 m wire, 8 m slats, DX = 1).
“
30
25
20
10
1
5
0
495= 1
L; = 37
Wire I
Pulser No. 2 4 6 8 10 12 14 16 18
0 Mesh Point 1.0 20 30 40
I?igure5. pul~er ~urrent anclwi.l$ecu]”rentalong length O-f simulator.
—— : —.. — .- -- —— .—.
280
210
140
0
Pulser Current 495101
90 180 270 360 450 540 630Time (ns)
1 I I I I I I
70
0
0 90 180 270 360 450 540 630
0
-2
-4
-6
-8
Pulser Impedance495101
Time (ns)
.
Wire Current
.
495101I I 1 I 1 1 I
’30 180 270 360‘ 450 540 630Time (ns)
.
Figure 6. Currents at pulser no. 2 (source end, 9 m).
28
.—. . . . . -,. —-, ~— ...— —— —- ——--.—--.- -,.”. .. .
.—-. — .
28
21
14
7
0
280
~ 210w
70
0
0
-4
-8
8-12
-16
.
.
Pulser Current 495105
I 90 180 270 360 450 540 630Time (ns)
I.
I
~
Pulser ImpedanceI 495105
0 90 180 270 360 450 540 630Time (ns)
I i I
Wire Current 495105I I I I I I
o 90 180 270 360 450 540 630Time (ns)
Figure 7. Currents at pulser no. 10 (center, 25 m).
. —.
..... -— —:. . - ._. —-— .- 1
16
12
8
4
0
280
210
140
70
0
0
-3
-6
-9
-12
I I
.
Pulser Current495109
0 90 180 270 360 450 540Time (ns)
630
I
L
Pulser Impedance495109
I I
) 90 180 270 360 450 540 630Time (ns)
Wire Current495109
I I 1 I Io 90 180 270 360 450 540 630
Time (ns)
Figure 8. Currents at pulser no. 18 (far end, 41 m).
30
——- —.- . —~—— —- —.- . .. -.,, .,.... . . .,. —.—. .-—
Midpoint
4Pulser No. +@@@@B@@@@@@@@@@@@@@
2
11 15 19 23 27 31 35 39 4312 40
Wire Locations .—~
Observer Nos. ~ 1 2 3 4 5 6 7
Figure 9. Slat/pulser/wire mesh point locations(29 mwire, 8 m slats, DX = 1 m).
.-.. A.. :—.=-=--l- —e .-— —--.—— . . _ ---- —.
5
4
x 2
E
:1u
‘a ol-lc).+h
-1
0.+ -2A
-5
Ez
496, I 1 I I t
— —123456
Observer Number
(a) Maximum electric fieldnormal to wire, E(horizontal) , Ez ~ver-tical) .
.
.
..
Ez
I 1 ! I I ! t
1234567Observer Number
(b) Electric fields normalto wire at t = 0.7 US..
Fibgure10. Electric fields normal to 29 m wire.
. . . ._-— — —-.,, . . .... --,,
2X105
4X105
6X105
8X105
o 90 180 270 360 450
0.7X105
1.4X105
2.1X105
2.8x105
0
2
4
6
8
Ez
.
Vertical Electric Field500101
540 630Time (ns)
E
Horizontal ElectricField
500101 -
I I 1 I t I Io 90 180 270 360 450 540 630
Time (ns)
\I
Uninsulated Wire Current500101
I t I 1 I I I
o 90 180 270 360 450 540Time (ns)
Figure 11. Wire current and normal electric2 m from source end.
630
fields
33
..- —
-. ...— . — -— ...-.”.””--- ——:— :“ —-
8x&
6X104
- 4X104E:- 2X104
2X104
4X104
6X104
8X104
b“ .,
.:I
1.I .iII EI ..
I , I !JY-\ I\, i“
“,,~~1
.
18*,1’@ .
500104
0 90 180 27.0 360 450 540 630Time (ns)
o
I24 -*
28 - .aEs 12 - -
Uninsulated Wire Current 50010416 “ f f I I I I Io 90 180 270 360 540 540 630
Time (rIs)
Figure 12. Wire current and normal electric fields atmidpoint of 29 m wire.
34
1.2X105
O.9X1O5
0.6x105
().3X105
0.3X105
().6x105
().9X105
1.2X105
——— —- — -.-— . . - — — — r..- -.——- . . . . . . . .
5X105
6X105
4X105
2X105E:
:+0
w-l
E(
c)+h*c1
2,8x105c)l-lH
2.IX105
1.4X105
0.7X105
o
3
6
9
I I [ I I 1 b
Ez
.
Vertical Electric
500107!
o 90 130 270 360 450 540 630Time (ns)
JHorizontal ElectricField
o 90 1s0 270 360 450 540 630Time (ns)
1
I\
Uninsulated Wire Current500107
I 1 I I I I I
o 90 1s0 270 360 450 540 630Time (ns)
Figure 13. Wire current and normal electric fields 2 mfrom far end.
35
—. —..
30 I I I I I I I I I
496 = 2L; = 29
25 -
20-
n4,Al
$ 15-um al
hAs
10-
5-
Pulser No. 2 4 6 8 10 12 14 16 1.80 I I I I 1 I I I 10 Mesh Point 10 20 30 40
l?igure14. Pulser current and wire current along length of simulator.
16
12
8
4
0
1000
100
10
1
0.1
0
-2
-4
-6
-8
a
,.
Pulser Current496101
I I I I I t Io 90 1s0 270 360 450 540 630
Time (ns)
Pulser Impedance
I I
496101 ~
o 90 1s0 270 360 450 540 630Time (ns)
.
Wire Current496101
0 90 180 270 360 450 540 630Time (ns)
Figure 15. a = 2, 29 m wire, 8 m19 pulsers, OBS-1.
slats, 1,
37
—. .—. -— .-—. ... —-. . . .
.—__— —— . -—. . : “—— __. —...-:- .——
n
..
a)v5‘-d
%E
H
u
24
18
12
6
0
1000
100
10
1
.0.1
0
-3
-6
-9
-12
I ,
Pulser Current496104
0
0 90 180 27o 360 450 540 630Time (ns)
1-
Pulser Impedance496104 1
0 90 180 270 360 450 540 630Time (ns)
I
Wire Current
496104
Io 90 180 270 360 450 540 630
Figure 16. a = 2, 29 m19 pulsers,
Time
wire,OBS-4
38
(ns)
8 m slats,(midpoint)
DX = 1,.
..; . ,- .,-. ... - —
16
12
8
4
0
1000
100
nc
10
1
0.1
0
-2
-4
-6
-8
I I I I I I I
Pulser
I Io 90 180 270 360 450 540 630
Current 496107 1
Time (ns)L I I I I I I I 3
Pulser Impedance496107
I I 1 I 1 I I
o 90 180 270 360 450 540 630Time (ns)
Wire Current 4961071 I 1 I I 1 1
—- --- --- --- .-.0 90 180 270 360 45LI 54U bsu
Time (ns)
Figure 17. a = 2, 29 m wire, 8 m19 pulsers, OBS-7
39
slats, DX = 1,
.— -— — .—
Midpoint
11Point
15 19 23 27 31 35
16
39
“!Plate
Location Buried Plate 4 mi
40
1
I)
I
ObserverLocations ~ 1 2 3 4 5 6 7
Figure 18. Slat/pulser/plate mesh point locations(a = 1, 29 m x 4m plate, 8 mor 2 m slats,DX = 1).
43
I
:,
“
20
15
10
5
0
240
180
120
60
0
0
-30
-60
-90
-120
8m
2m
Pulser Current 497101498101
0 90 1s0 270 360 450 540 630Time (ns)
o
497101498101
2m
I90 180 270 360 450
Time (ns)540 630
I I I I 1 I I
497101498101
Buried Plate CurrentI I I I I I
o 90 180 270 360 450 540 630Time (ns)
Figure 19. Pulser I, Z and plate I for source end.
41
-.. . -. —
-.. ——.- —.——._. — —.
36- I 1 1 I I I I
27 -
2m
18 - .
9 - .
Pulser Current 497104498104
00 90 180 270 360 450 540 630
120
60
0
Time (ns)
180
.L 2m
I
o
-7
-14
-21
0 90 180 270 360 450 540 630Time (ns)
-28
(
497104498104
T2m
8mBuried Plate
Current /
90 180 270 360 450 540 630Time (ns)
Figure 20. Pulser I, Z and plate I for center location.
42
..
.~ —. -- . ..,, .:...-—” - --~— ~ : ., -—-- -- —-—,—- -. .. .:
20
15
10
5
0
1 I I I 1 I I
2m/
I
o 90 180 270 360 450 540 630
24
18
12
6
00
0
-4
-8
-12
-16
8m
/“ —
Current 497107498107
Time (ns)
Pulser
L.
Impedance
2m8m/ 497107
I/./’ ~98107
90 180 270 360 450 540 630Time (ns)
\
. 497107Buried Plate Current 498107
0 90 180 270 360 450 540 630Time (ns)
Figure 21. Pulser I, Z and plate I for far end location.
43
s.=.-..-.=..—___ ,.__—_-.
I
Midpoint
,:
.,
II
[
,,I
t
Numbers
slat “Num~
1
I
Point
Pla”teLocation-
Observer
Locationsb
11 15 19 23 27 31 35 3!3
40
1 2 3 4 5 6 7
43Iii
Figure 22. Slat/pulser/plate mesh point locations(c%= 1, 29 m x 4 m plate, 9 pulsers, DX = 1).
,
24
18
12
6
0Pulser Current
497101499101
0 90 180 270 360 450 540 630Time (ns)
210
140
70
0
497101499101
I
o
-4
-8
-12
h 19 pulsers 9 pulsers
\ Pulser Impedance / 1,rf
o 90 180 270 360 450 540 630
-16
Time (ns)
Buried Plate Current
497101499101
1 t I I I I I
o 90 180 270 360 450 540 630Time (ns)
Figure 23. Currents for source end observer 1, for cases—a = 1, 29 m x 4 m plate, 8 m slats, DX = 1,19 pulsers; u =l,29mx4mplate, 8mslats, DX = 1, 9 pulsers.
—
45
--- -—
—----- . .-— — -=.- .—> —- —’. .-”: —-- —-. . . .. . . —.
+LA
w
80
60
QO
20
0
280
210
140
70
0
0
-9
Figure
-18
-27
-36
[ I 1 I I I I
497104499104
9 pulsers
19 pulsers -
Pulser Current
o 90 180 270 360 450 540 630Time (ns)
1 1 I I I 1 I
Pulser Impedance
1
.
.
9 pulsers
19 pulsers\ /
.
497104
0 90 180 270 360 450 540 630Time (ns)
Buried Plate Current497104499104
I 1 1 I I I 1 I 10 90 180 270 360 450 540 630
Time (ns)
24. Currents for midpoint observer 4, for cases a = 1,29 m x 4 m plate, 8 m slats, DX = 1, 19 pulsers;a = 1, 29 m x 4 m plate, 8 m slats, DX = 1, 9 pulsers.
43
.
------ .. :,:-...—-.-.,- -- —- --- ..—-- — .... .— .._—_—
20 m
I
Slats
Z2..i!’l!-Buried Wire
\ 1\ 24 m
\
\
\
\
\1
Air............Ground
\
Groundd- Rods
\
\
Side View Showing Ground RodsanclConnection to End Slat
lmT—
-44m
T------ -
9III81
I1 GroundII
/’Rods
ItI9II1a Slats
Symmetry----- ----
\
\
\
Plane
Top View Showing Ground Rodsand Connection to End Slat
- ..
l?igure25. Ground rods connected to end plates.
.—.—— ... .... —.- ~-.. .. —.....——— .... I
w
o
-2
-~
-6
-8
o
-8
500101504101
\ w/o ground rods “
. .
with ground rods
.
Pulser Current
o 90 180 270 360 450 540 630Time (ns)
1 1 I I 1 1 1
500101504101
.\ with ground rods
~ k“-J+-V
?VireCurrent
w/o ground rods
o 90 180 270 360 450 540 630Time (ns)
Figure 26. Pulser and wire currents w/wo ground rods(OBS 1, near source) .
48
-- —.- .- .-\_ ,,-— _ —— ,. -—— -- .- --- ->.,
,
0
-8
‘ba)“%k
8-9
-12
w/o ground rods
with ground rods
Pulser Current 500104504104
I i 1 ! I I f
o 90 1s0 270 360 450 540 630Time (ns)
.
with ground rods .
w/o ground rods
Wire Current500104504104
I I I ! I I
o 90 180 270 360 450 540 630Time (ns)
Figure 27. Pulser and wire currents w/wo ground rods(OBS 7, far end) .
49
-..
—-. —..-—- --4- —L. . .. . . ..>= —-. ---- ,.. .’— ~—-— -— —-. —,. -. —.—-e . .
0
w
+ -6
-12
0
-16
\
500107504107
.\
w/o ground rods
.
with ground rods
Pulser Currentt I I I I 1 I
o 90 180 270 360 450 540 630Time (ns)
with ground rods
w/o ground rods
Wire Current 500107504107
.
0 90 180 270 360 450 540 630Time (ns)
Figure 28. Pulser and wire currents w/*.voground rods(OBS 4, center) .
.
——— —— .. ...-—– —-. . .. . ..
CnP
1
slats
\
\
20 m
1
, J’L.L’1.-!?,.J-.---Ire
Ground
\Buried Wire
Side View Showing Ground Rodsand Connection to Buried Wire
: SlatsI8*b
~Lz_l fll_EkPlane
k—— 7m+
Top View Showing Ground Rods
\
and Connection to Buried Wire
\
\
\
Figure 2!)0 Buried wire connected to ground rods.
... ,. ..>.. . .. . . . ——— ..:..— . . ..- —.- . . ...’. .---L ----
0
-4
0
-12
Pulser Current 500101505101
54 m wire
o 90 1s0 270 360 450 540 630Time (ns)
Wire Current 500101505101 .
29 m wire
~1 54 m wire -
I I I I I I I
o 90 180 270 360 450 540 630Time (ns)
Figure 30. Pulser and wire current for 29 m wireopen and 54 m wire shorted to groundrods (OBS 1, near source) .
52
~—. - -. -.’. -v-— — –-. ——— —-- --- .:- . —..__ —
. . . . .
o
-8
0
.
500104Pulser Current 505104
29 m wire
4
54 m wire
I 1 I 1 I t 1
0 90 1s0 270 360 450 540 630Time (ns)
Wire Current
29 m wire
500104505104
54 m wire
-200 90 180 270 360 450 540 630
Time (ns)
Figure 31. Pulser and wire current for 29 m wireopen and 54 m wire shorted to groundrods (OBS 4, center).
53
. . ..—.
.... —..-.:— L -: -. ::... .L ”.- . .
0500107
29 m wire 505107
54 m wire
Pulser Current
-80 90 180 270 360 450 540 630
Time (ns)
o
-12
\
500107Wire Current 505107
54 m wire
o 90 180 270 360 450 540 630Time (ns)
Figure 32. Pulser and wire current for 29 m wireopen and 54 m wire shorted to groundrods (OBS 7, far end).
54
., ... . —,..-...-—~. ——— ~ . .-— _ .,,
l–-T–———————— ——— —
T
‘~ 200mI
*III I
I 116 m
i
IIIL_. —--
I16 rods of 0.04 m radius I
//
Hl4m
—— ——
\ I
t
[
4.
2;rm~ Symmet ryJ——
Plane
Top View
I 116 m II I ~~m--+ II
I -----------;------[-O<?/:< ‘“--F:;:”’!-----
Buried lYlre
i
I I120 m 16 rods of
I0.04 m radius
& = 10, Og = 0.001 or 0.01r
III
I—. A ——. —— —— —— —— — J
Side View
.
Figure 33. Coarse grid geometry for 4 m mesh.
55
..-. --- .. —- . .
-— —.. -—4. -.. —,: . .
270
180
90
0
-90
-180
_270
I 1 [ 1 1 I I
I
20 Q() 60 80 100 120 140Time (ns)
1 I I I I I I
Figure 34. Source voltage for coarse meshcalculations.
56
n=: —. - .—— ,. .- -.,.,
o
-4.5
n
‘P -9.0
I
-13.5
I
-18.00
1 471476468475
I
8 m long slats, center fire
T8 m long slats, center and end fire
— 40 m long slats, fire center and every 4 my!- l?mvironment
750 1500 2250 3( oTime (ns)
I?igure35. Coarse mesh, 4 m A’s, wire currents (center).
4
I
( Cnm“1
.1
I
t
o
-3
-6
-9
-12
1 I I b I 1 I I
470471472
40 m long slats
8 m long slats
40 m long slats
8 m long slats
Off center wires(Due to symmetry, two wires are incalculation. This is current on
Center positioned wire
o 750 1500 ~250 3000
Figure 36. Coarseslats,
Time (ns)
mesh, ~ m A’s, wire currents, 8 m and 40 m longcenter positioned wire and off center wire.
cmu)
0
-lo
-20
-30
-40
%= 0.001
469470
0 750 1500 2250 3000Time (ns)
Figure 37. Coarse mesh, 4 m A’s, wire currents, 40 m long slats, twoground concluctivites (0.001 and 0.01).
,,,.,,
,,?,,”:,,,,,,
. .
,.,“8‘1
0
-4.5
-13.s
I
-18.C
o
i
Center Fire 46746846’3470
= 0.01 cases
+~ AllI?ire
I I 1 I 1 I 4750 1500 2250 3000
Figure 38. Coarseground
l’ime (ns)
mesh, 4 m A’s, wire currents, 40 m long slats, twoconductivities (0.001 and 0.01).
.
![;Ti~;{'.i]W;;t ~~ 1, . . .- ',·';,)':1 I](https://img.pdfslide.us/doc/110x75/621a9acc6da7ac599a3e1ba4/tiiwt-1-1-i.jpg)
