ELECTROMAGNETIC PULSE (EMP) AND TEMPEST PROTECTION FOR FACILITIES

                  Table of Contents: http://cryptome.org/emp.htm

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                                   CHAPTER 2

                                EMP ENVIRONMENT


2-1. Outline. This chapter is organized as follows:

     2-1. Outline
     2-2. HEMP: detailed discussion
          a. HEMP generation
             (1) Gamma radiation
             (2) Compton scattering
             (3) Deposition region
             (4) Radiating magnetic field
          b. HEMP ground coverage
          c. Field strength vs ground location
          d. Electric field
          e. Transients
             (1) Transient definition
             (2) HEMP event time phases
             (3) Qualitative characteristics
          f. Magnetohydrodynamic EMP (MHD-EMP)
             (1) Early-phase generation
             (2) Late-phase generation
             (3) Electronic surge arresters
     2-3. Other EMP environments
          a. Surface burst EMP (SBEMP)
             (1) Source region
             (2) Electric and magnetic field relationship
             (3) Radiated region
          b. Air-burst EMP
             (1) Source region
             (2) Radiated region
          c. System-generated EMP (SGEMP)
             (1) Coupling modes
             (2) Transient radiation effects on electronics
          d. Summary
     2-4. Environment-to-facility coupling
          a. Modes of HEMP entry
             (1) Diffusion through the shield
             (2) Leakage through apertures
             (3) Intentional and inadvertent antennas
          b. Conductive penetrations
             (1) Basic coupling mechanisms
             (2) HEMP coupling analysis
             (3) Intrasite cables
     2-5. Equipment susceptibility
          a. Equipment response
             (1) Upset
             (2) Damage
          b. Equipment sensitivity
          c. Typical damage and upset levels
     2-6. Cited references
     2-7. Uncited references

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2-2. HEMP: detailed discussion.

   a. HEMP generation. HEMP is caused by a nuclear burst at high altitudes.
Prompt gamma rays following the nuclear detonation are the principal source of
HEMP. This gamma radiation causes bursts of electron flow from the Compton
effect, a photoelectric effect, and a "pair production" effect. Of these
three effects, however, the primary source of HEMP is the Compton effect. Due
to their low level of significance, the photoelectric and "pair production"
effects are not discussed.

      (1) Gamma radiation. At high altitudes (above 30 kilometers), the
atmosphere is thin and thus allows gamma radiation from the nuclear burst to
travel out radially for long distances (ref 2-1). Below the center of the
burst, however, the atmospheric density increases as the Earth's surface is
approached. The prompt gamma rays propogate toward the Earth in a thin
spherical shell, moving at the speed of light away from the burst..

      (2) Compton scattering. When the downward directed rays encounter the
upper regions of the atmosphere, they begin to interact with the atoms (or
molecules) of the atmosphere at a rate which is a function of atmospheric
density and burst conditions. The dominant interaction is Compton scattering,
in which the energy of a gamma ray is partially transferred to an electron of
an air atom (or molecule). The electron then begins traveling in
approximately the same direction as the gamma ray. The other product of
collision is a gamma ray of reduced energy. Figure 2-1 illustrates this
process (ref 2-1). The spherical shell of gamma rays is converted during
Compton scattering into a spherical shell of accelerated electrons.

      (3) Deposition region. The region in which Compton scattering occurs
is called the deposition region. The thickness and surface range of the
deposition region is a function of height-of-burst (HOB) and weapon size and
type. A representative thickness is from 20 kilometers to 40 kilometers, but
a deposition region may be as thick as 70 kilometers (10-kilometer to 80-
kilometer altitude) for a 300-kilometer HOB and a 10-megaton weapon.

      (4) Radiating magnetic field. In the spherical shell of Compton
electrons, the electrons are charged particles that rotate spirally around the
Earth's geomagnetic field lines (ref 2-2). The electrons thus have a velocity
component transverse to the direction of the gamma radiation. These
transverse currents give rise to a radiating magnetic field. This field
propagates through the atmosphere to the Earth's surface as if it were
contained in the same spherical shell as that formed by the original gamma ray
shell.

   b. HEMP ground coverage. Significant HEMP levels can occur at the Earth's
surface out to the tangent radius (and beyond, for frequencies below 100
kilohertz). The tangent radius is where the line of sight from the burst is
tangent with the Earth's surface. If one assumes a spherical Earth of radius
Re, the tangent radius Rt is given by--


                                     Re
                     Rt = Re cos-1(--------)
                                   Re + HOB
                                                                     (eq 2-1)


where HOB is the height of burst. For an approximate Earth radius of 6371
kilometers, an HOB of 100 kilometers corresponds to an Rt of 1121 kilometers,
an HOB of 300 kilometers corresponds to an Rt of 1920 kilometers, and an HOB
of 500 kilometers corresponds to an Rt of 2450 kilometers. Thus, the HEMP
generated by a nuclear explosion at an altitude of 500 kilometers would
illuminate the whole continental United States. If high-yield weapons are
used, the field strength will not vary much with HOB, so this large geographic
area can be covered with little reduction in peak field strength.

   c. Field strengths versus ground location. HEMP fields can be significant
out to the tangent radius, but the exact field strength as a function of
ground position depends on many factors. Burst-observer geometry is important
because HEMP is produced by electron motion transverse to the Earth's magnetic
field. Thus, electron moving along the field do not radiate. For a burst at
hlgh geomagnetic latitudes, as would be the case for Europe or North America,
the pattern shown in figure 2-3 results. There will be a region of near-zero
field strength north of the sub-burst point, where the magnetic field lines
from the burst site intersect the Earth. There will also be a broad arc of
maximum field strength that corresponds to electron trajectories perpendicular
to the geomagnetic field. The field amplitude is an appreciable fraction of
the peak amplitude (about 0.5 for most high-yield weapons) out to the tangent
radius. The EMP field strength will also vary as a function of HOB, weapon
yield (especially gamma yield), and geomagnetic field, which depends on geo-
magnetic latitude. Near the equator, the Earth's magnetic field strength is
weaker and the orientation is very different, so peak HEMP fields would be
smaller and the field strength pattern much different than that shown.

   d. Electric field. A commonly used unclassified time waveform of a HEMP
electric field E(t) in free space can be approximated by the analytical
expression--


                        kEpk ke a(t-ts)
                 E(t) = --------------- .(kV/m)
                        l+e(a+b) (t-ts)
                                                                     (eq 2-2)


where Epk = 50 kV/m (peak electric field in kilovolts per meter; k = 1.2 (a
normalization constant); a = 5 x 108 per second (exponential decay rate); ts =
10^-8 seconds (a time shift parameter); and t is the time of interest (in
seconds). This waveform is often called a "double exponential." Figure 2-4
is a graphic representation of the HEMP waveform; the frequency content of the
HEMP pulse also is depicted in figure 2-4. This waveform rises from 0.1 to
0.9 times its peak amplitude in about 5 nanoseconds (tr), and decays to one-
half its peak amplitude in about 200 nanoseconds (t1/2) (fig 2-4). The upper
left curve shows this waveform plotted on a linear time scale. The upper
right curve shows a logarithmic time scale that distorts the pulse shape but
gives the risetime more clearly. The Fourier transform of this transient
electric field is given by--

                 2.47 x 1013
E(u) = --------------------------------- volt second per meter
       (ju + 4 x 106)(Ju + 4.76 x 108)                                      
                                                                     (eq 2-3)

where j is the unit imaginary number and, u is the radian frequency. As the
lower curve shows (fig 2-4), the electric field strength stays fairly constant
in the 10-kilohertz to 1-megahertz frequency range, declines by a factor of
100 in the 1- to 100-megahertz range, and continues to decrease at a more
rapid rate for frequencies greater than 100 megahertz. HEMP energy generally
ranges from frequencies of 0.1 to 10 megahertz, with all but 1 percent falling
below 100 meqahertz.

      (1) Transients. The transient expected from HEMP has recently been
redefined analytically. Details of this new definition are classified and
thus cannot be presented here (DOD-STD-2169(C), ref 2-3).

      (2) Transient definition. In DOD-STD-2169, EMP experts have divided
the time representation of the HEMP event into three periods: early time,
intermediate time, and late time.

         (a) The early-time portion arrives at the Earth's surface quickly
and lasts about 1 microsecond. This is the portion caused by the first gamma
ray pulse. It is a fast spike and has its energy concentrated in the one to
several hundred megahertz frequency band.

         (b) Intermediate-time HEMP occurs between 1 microsecond and 0.1
second and has a frequency spectral content between 1 hertz and 100 kilohertz.
It is PrimarilY a hiqh-imPedance field.

         (c) Late-time HEMP is primarily the magnetohydrodynamic (MHD) EMP
occurring from 0.1 to 1000 or more seconds. MHD-EMP is discussed in paragraph
f below.

      (3) Qualitative characteristics. Figures 2-5 and 2-6 show unclassified
qualitative HEMP characteristics.

   f. Magnetohydrodynamic EMP (MHD-EMP). MHD-EMP is the late time (t > 0.1
second) component of EMP caused by a high-altitude nuclear burst. Two
distinct physical mechanisms are thought to produce different parts of the
MHD-EMP signal: an "early phase" from 0.1 to 10 seconds after the detonation,
and a "late phase" lasting from 0.1 to 1000 seconds. MHD-EMP fields have low
amplitudes, large spatial extent, and very low frequency. Such fields can
threaten very long landlines, including telephone cables and power lines, and
submarine cables.

      (1) MHD-EMP early-phase generation. A nuclear burst at high altitudes
gives rise to a rapidly expanding fireball of bomb debris and hot ionized gas.
This plasma tends to be diamagnetic in that it acts to exclude the Earth's
magnetic field from the inside of the fireball. Thus, as the fireball expands
and rises in early stages, it will deform the geomagnetic field lines and
thereby set up the early phases of the MHD-EMP, which can propagate worldwide.
The region on the ground immediately below the burst is shielded from early-
time MHD-EMP by a layer of ionized gas (the X-ray patch) produced by X-rays
from the nuclear burst.

      (2) MHD-EMP late-phase generation. Residual ionization and the bomb-
heated air under the rising fireball are mainly responsible for the late phase
of the MHD-EMP. As the bomb-heated air rises, residual ionization moves
across geomagnetic field lines and large current loops form in the ionosphere.
The ionospheric current loops then induce earth potentials. The late phase of
the MHD-EMP is seen in large sections of the Earth's surface, including
regions at the magnetic conjugate points. Though amplitudes are smaller than
for HEMP, the low-frequency fields can introduce damaging potential
differences on long cable systems.

      (3) Electronic surge arresters. The longer duration and greater energy
content coupled into electrical lines in the DOD-STD-2169 environment is an
important factor in the design and selection of electronic surqe arresters.

2-3. Other EMP environments. Of several different kinds of EMP environments,
HEMP is the one specified most often for system survivability. The discussion
of HEMP applies to all systems that must survive a nuclear event, even though
they are not targeted or even located close to a target. One reason is that
the peak field amplitudes are large enough to damage or upset most unprotected
electronic systems that use solid-state technology. Further, the frequency
band is broad and thus all types of electronic/electrical systems are
potentially susceptible. Third, as discussed previously, the HEMP area
coverage is large. The fact that HEMP occurs when other nuclear environments
are absent implies that systems with no defense against other nuclear effects
may need protection against HEMP. Although HEMP is a vital concern for
mission-critical systems and is the environment addressed in this manual,
other environments are briefly discussed for the sake of completeness. Table
2-1 lists some of the other EMP environments and compares their properties.

   a. Surface burst EMP (SBEMP). SBEMP is produced by a nuclear burst close
(less than 0.2 kilometer) to the Earth's surface (fig 2-7). The EMP is
generated in the source region, which extends out to a radius of 3 to 5
kilometers from the burst. EMP environments inside the source region can
affect systems such as ICBMs or command centers that have been hardened to
withstand nuclear blasts, thermal energy, and radiation inside the source
region. A surface burst also has fields radiating outside the source region,
with those field amplitudes significant (greater than 5 kilovolts per meter)
out to ranges of 10 kilometers and more. In this range, the radiated EMP is a
principal threat to systems that respond to very low frequencies or have very
large energy collectors such as long lines. Conducted EMP for these systems
is such that special attention must be given to surge protection to ensure
that the high currents can be dissipated.

      (1) Source region. The generation of EMP by a surface burst starts
when the gamma rays travel out radially from the burst. These rays scatter
Compton electrons radially, leaving behind relatively immobile positive ions
(fig 2-8). This charge separation produces radial electric fields (E~ with
amplitudes over 100 kilovolts per meter (amplitudes may approach 1 megavolt
per meter) and risetimes as short as a few nanoseconds. Since the-ground
conducts better than the air at early times, the strong radial electric field
causes a ground current to flow in a direction opposite to the radial Compton
current in the air. The resulting current loops produce azimuthal magnetic
fields. Magnetic fields are strongest at the Earth's surface and diffuse both
upward and downward from the interface. The discontinuity due to the air-
Earth interface also generates strong vertical electric fields in the source
region. Source region fields depend strongly on factors such as weapon yields
(gammas and neutrons), HOB, and distance from the burst. The interaction with
a system is very complex: besides the EM fields, the system may be exposed to
nuclear radiation, in addition to being located in a region of time-varying
currents and conductivity. In specifying a source region environment for a
system, then, the concept of balanced survivability is useful, as it is with
all EMP environments. If a facility is designed to withstand ionizing
radiation and other nuclear effects at a specified range from a given burst,
it should also be designed to withstand the EMP effects generated at that
range.

      (2) Electric and magnetic field relationship. The time-varying
currents and conductivity of the surface-burst source region imply a complex
relationship between electric and magnetic fields, which does not show the
simple magnitude and direction relationships of a plane wave. Determination
of these relationships is beyond the scope of this manual.

      (3) Radiated region. Outside the source region, the most important
feature of the charge distribution produced by a surface burst is the
asymmetry due to the air-earth interface (fig 2-8). In an infinite uniform
atmosphere, Compton electrons would travel out radially in all directions.
However, for SBEMP, the earth interferes with down-flowing electrons, which
results in a net vertical flow of Compton current. This produces a time-vary-
ing vertical dipole that radiates outside the source region. The main
components of the radiated field are the vertical electric field and the
azimuthal magnetic field.The field amplitude has a 1/R dependence with range,
as is typical of electric dipole radiation. The field rises quickly to its
first peak (electric field vector vertically upward), with a second peak of
opposite sign following some tens of microseconds later. More of the energy
occurs at lower frequencies than for HEMP. Figure 2-9 shows the calculated
electric field amplitude as a function of range for a large surface burst. As
the figure shows, radiated surface burst field amplitudes most often are
smaller than HEMP fields outside the source region. However, field amplitudes
can still be significant at ranges of 10 kilometers or more. The right
portion of the curve shows the inverse relationship between amplitude and
range beyond 5 kilometers. This is typical of electric dipole radiation in
the far-field region. There is no standard waveform as there is for HEMP.
Thus, the very concept of a standard waveform is less likely to be useful for
SBEMP because of the variation in amplitude and waveform with range and weapon
yield (output). Radiated SBEMP typically gives off most of its energy at
lower frequencies (below 100 kilohertz). The increase in low frequency
content and the vertical electric field orientation mean that the system
impact of radiated SBEMP may be more important than that of HEMP for some
systems, even though HEMP field magnitudes are qenerally larqer.

   b. Air-burst EMP.

      (1) Source region. Air-burst EMP results from a nuclear explosion at
intermediate altitudes--2 to 20 kilometers. The EMP produced by a burst at
heights between 0.2 and 2 kilometers will share characteristics of air and
surface bursts, and a burst between 20 and 40 kilometers will cause EMP
sharing characteristics of air-burst and high-altitude EMP. The source region
resembles the surface-burst source region in that weapon gammas scatter
Compton electrons radially outward (fig 2-10). Positive ions are left behind,
producing charge separation and radial electric fields. For air-burst EMP,
there is no return path through the ground. Due to ionization, however,
increased air conductivity enables a conduction current to flow opposite the
Compton current in the air. Still, no significant current loops are formed,
and the large azimuthal magnetic fields typical of a surface burst do not
result.

      (2) Radiated region. Outside the source region, the radial charge
separation resulting from the Compton current will produce some radiated
fields because a slight asymmetry exists. At intermediate altitudes, the
atmospheric density gradient permits Compton electrons to move farther up than
down. This asymmetry results in electric dipole radiation (fig 2-11). The
water vapor density will also vary with height, though this variation depends
on the weather. A typical decrease in water vapor density with altitude will
reinforce the asymmetry produced by the atmospheric density gradient. Even
with these two effects combined, the asymmetry is much weaker than for a
surface burst. The typical field strengths produced are on the order of 300
volts per meter at 5 kilometers from the burst. Pulse waveforms vary
significantly with burst altitude and assumed water vapor gradient, with
typical risetimes in the 1- to 5-microsecond range. The recoil Compton
electrons can also produce a radiated signal by the same geomagnetic turning
mechanism that gives rise to HEMP. This is called magnetic dipole radiation.
At low altitudes, electron paths are short so that peak amplitudes are limited
to hundreds of volts per meter, mainly to the east and west of the burst. The
peak amplitude increases with burst height until it reaches tens of kilovolts
per meter as the burst approaches the high-altitude region. Rise and decay
times are similar to those for HEMP--on the order of tens of nanoseconds.

   c. System generated EMP (SGEMP). SGEMP results from the direct
interaction of nuclear weapon gammas and X-rays with the system. Because
weapon gammas and X-rays are attenuated by the atmosphere at low altitudes,
SGEMP has special importance for systems outside the atmosphere, such as
satellites in space and missiles in flight. These can receive significant
gamma and X-ray exposures at considerable distances from a nuclear burst.
SGEMP involves complex modes of field and current generation that strongly
depend on the system's physical and electrical configuration. As a result,
there is no standard threat. The field amplitudes generated can be as large
as 100 kilovolts per meter, making SGEMP a significant threat to exposed
systems.

      (1) Coupling modes. The initial physical process is the generation of
energetic free electrons by Compton and photoelectric interactions of weapon
X-rays and gammas with the system materials. Emitted electrons produce space-
charge fields that turn back later electrons or, at higher gas pressures,
cause appreciable ionization. Emission of the electrons from internal walls
results in current generation and, hence, EM fields inside cavities. This
effect is termed internal EMP (IEMP). Coupling occurs both by electric and
magnetic field coupling directly onto signal cables and by induced current
flow on cable shields and ground systems. The asymmetric displacement of
electrons from a cable shield and from internal conductors and dielectrics
inside a single cable or cable bundle produces a distributed current generator
over the whole exposed region of the cable. Electron emission from the outer
skin of the subject system generates whole body interaction effects that
produce charge displacement and direct field coupling. These effects also can
influence internal EMP if there are penetrations or openings to the inside.

      (2) Transient radiation effects on electronics. The direct impingement
of radiation (e.g., X-rays, gamma rays, neutrons) can also change the
performance of semiconductor electronics through atomic interactions.
Operating thresholds, junction voltages, and the crystalline structure of
solid-state materials can be affected, thus changing the way devices and cir-
cuits using such materials operate. TREE normally is important only when
modern electronics might be exposed to the nuclear detonation source region
with a high in-flow of nuclear radiation.

   d. Summary. Table 2-2 outlines the EMP waveforms important for critical
systems. HEMP is the most difficult threat to harden against because of its
large spatial extent, high amplitude, and broad frequency coverage. It is
also the simplest threat to describe using the waveform definition in equation
2-2 and the plane wave approximation. The source region for an air or surface
burst combines intense fields with significant time-varying conductivities and
environments. Source-region EMP is important for systems that can withstand
other nuclear environments present in the source region. EMP radiated from a
surface burst usually has lower amplitude than HEMP and can affect systems
more due to the vertical field orientation and lower frequency. Air-burst
radiated fields have lower amplitudes and are less likely to be important (a
system hardened to survive HEMP will survive radiated air-burst EMP). SGEMP
is characterized by very high amplitudes, very fast risetimes, and importance
to systems outside the atmosphere. MHD-EMP has low amplitude but can damage
the interface circuits of long landlines or submarine cables.

2-4. Environment-to-facility coupling. To analyze how HEMP will affect
facilities and electronic equipment, the exterior free field threats must be
related to system, subsystem, and circuit responses. The functional
relationship between external causes and internal effects is often called a
"transfer function." The analysis involves learning how the system collects
energy from the incident HEMP field. The result is usually a matrix of
internal fields and transient voltages and currents that may flow in circuits
and subsystems. This is called a "determination of the coupling interactions
between the external threat and the system." Generally, HEMP enters shielded
enclosures by three different modes: diffusion through the shield; leakage
through apertures such as seams, joints, and windows; and coupling from inten-
tional or inadvertent antennas. These different modes are shown in figure 2-
12 and are discussed next.

   a. Modes of HEMP entry.

      (1) Diffusion through the shield. HEMP fields diffuse through
imperfectly conducting walls of shielded enclosures. The diffusion is
greatest for magnetic fields and is a low-pass filtering event, as shown by
the magnetic shielding effectiveness curve for an ideal enclosure (fig 2-13).
Thus, the field that reaches the inner region of a shielded enclosure is
basically a low-frequency magnetic field. This effect is greatest in an
enclosure with solid metal walls. It is also seen somewhat in enc]osures with
metal rebar or wire mesh reinforcement. The shielding effectiveness (SE) for
an enclosure with rebar is also shown in figure 2-13. The reduced SE at high
frequencies for rebar and wire mesh structures allows a significant fraction
of the incident HEMP environment to penetrate to electronics inside the
enclosure.

      (2) Leakage through apertures. Openings and other shielding
compromises include doors, windows, holes for adjustments and display units,
seams, improperly terminated cable shields, and poorly grounded cables.
Unless properly treated, each opening is a leak through which the HEMP field
can couple directly into the shielded enclosure. Leakage through an aperture
depends on its size, the type of structure housing it, and its location. The
aperture responds to both total magnetic and electric fields at the site of
the leak. The effect of apertures on the magnetic SE of an ideal enclosure is
shown in figure 2-14.

      (3) Intentional and inadvertent antennas. Intentional antennas are
designed to collect EM energy over specified frequency bands. However, there
will also be an out-of-band response to HEMP. Because the incident HEMP field
has a broad frequency spectrum and high field strength, the antenna response
must be considered both in and out of band. Analytical models are available
for determining the different antennas' responses to HEMP. These models,
along with the incident field, yield the HEMP energy that appears at the con-
necting cable. This energy later reaches the electronic systems inside the
enclosure at the other end of the connecting cable. Inadvertent antennas are
electrically conducting, penetrating external structures, cables, and pipes
that collect HEMP energy and allow its entry into the enclosure. As a rule,
the larger the inadvertent antenna, the more efficient energy collector it is
in producing large, transient levels in the enclosure. Figure 2-15 shows some
inadvertent antennas for a ground-based structure. The coupling for inadver-
tent antennas can be analyzed using transmission line and simple antenna
models. These analyses, however, are complex and beyond the scope of this
manual. The reader is directed to references 2-2 and 2-6 for guidance on
these analyses.

   b. Conductive penetrations. Many factors affect the coupling of EM energy
to penetrating conductors. The EMP waveform characteristics, such as
magnitude, rate of rise, duiation, and frequency, are each important.
Further, the observer's position with respect to the burst is a factor.
Because the interaction between fields and conductors is a vector process, the
direction of arrival and polarization is also important. Conductor character-
istics also affect HEMP coupling. These include conductor geometry (length,
path, terminations, distance above or below the earth's surface), physical and
electrical properties that determine series impedance per unit length
(including diameter, resistivity, and configuration), and the presence and
effectiveness of shielding. For overhead or buried conductors, the electrical
properties of soil affect coupling. Though dielectric permittivity and
magnetic permeability may be significant, soil conductivity is usually the
greatest determining factor for coupling. This is because both HEMP
attenuation in the ground and reflection from the ground increase with greater
soil conductivity. The soil skin effect also varies. An EM wave in a conduc-
tive medium ~ttenuates to 0.369 of its initial amplitude in a distance
d = (2/pwc) , where d is the skin depth, p is the magnetic permeability of
the medium, w is the angular frequency, and c is the conductivity. Because
the skin depth is greater at lower frequencies, lower frequency field
components attenuate less and the pulse risetime increases. Many elements of
a facility can act as efficient collectors and provide propagation paths for
EMP energy. As shown in figure 2-16, EMP can couple to structures such as
power and telephone lines, antenna towers, buried conduits, and the facility
grounding system. Actual antennas, nonelectrical penetrators such as
waterpipes, and any other conducive penetration can couple EMP energy into a
structure. In addition, if the structure is not shielded or is not shielded
well enough, EMP can couple to the cables between equipment inside.
Paragraphs (1) through (3) below briefly describe coupling mechanisms,
including theory, and give rough values for the currents and voltages that can
arise from a typical EMP event.

      (1) Basic coupling mechanisms. Figure 2-17 shows two basic modes by
which currents and voltages are induced in conductors. One mechanism shown is
that for inducing voltage in conductors by electric field. The electric field
exerts forces on the "mobile" electrons in the conductor, which results in a
current. The voltage associated with the force is the integral of the tangen-
tial component of E along the length of the wire. This assumes the electric
fieldis constant over the length of the wire and is parallel to it. The other
mechanism by which currents are induced on conductors is through changes in
the magnetic field, also shown in figure 2-17. Faraday's Law is the mathe-
matical expression that describes this phenomenon. This law relates the time
rate of change of the magnetic field to the production of an associated
electric field. This electric field "curls" around the changing magnetic
field and causes a voltage if a loop is present. The voltage for the loop of
area A in the figure is V = A(dB/dt), where B is normal to the loop and has
the same magnitude over the whole loop. This can give a good approximation
with HEMP when the magnetic field can be considered uniform over the area of
the loop. The fast rise rate of the magnetic field can produce large currents
and voltages. A sample calculation is helpful. Assume the following--

         A    = loop area = 0.1 meter squared (m2)

         E(t) = Ce-t/a where C = 50,000 volts/meter

         a    = 0.5 x 10-6 (time constant)

(Note: a simple exponential is used for this example.)

         H    = E/377 (a plane wave)

              = e-t/a(C/377)

         u    = uo (loop antenna in free space)

         uo   = 4(pi) x 10-7 Webers/amp-meter

Then:

         H   = 50,000/377 e-t/0.5 x 10^-6 amps/meter

             = 132.6 e-t/0.5 x 10^-6 amps/meter

         B   = uoH = 4(pi) x 10-7 x 132.6^e-t/0.5 x 10^-6 Webers/meter2

         Loop voltage VL = A (dB/dt)

                      d(4(pi) x 10-7 x 132.6 e-t/0.5 x 10^-6) Webers/meter2
      = 0.1 meters2 (-------------------------------------------------------- )
                                              dt

      = 0.1 (2 x 106 x 4(pi) x 10-7 x 132.6 e-t/0.5 x 10^-6) Webers/second

      = -33.3 e-t/0.5 x 10^-6 volts.

      (2) HEMP couplinq analysis. This section describes some of the more
important coupling interactions in the design and analysis of shielded
facilities.

         (a) Equivalent circuit for a small electric dipole. A small
electric dipole is one with a short length compared with the dominant
wavelengths incident on it. A HEMP contains 99 percent of its energy in
wavelengths longer than 3 meters. The analysis done here using a small dipole
model is significantly more accurate for dipoles less than 3 meters. The
model is fairly simple and serves to show how EMP coupling calculations are
done. Figure 2-18 shows a dipole and its equivalent circuit. The voltage is
induced by the EMP. The capacitance is caused by the two halves of the dipole
acting like two plates of a capacitor. For large resistance RL
(RL>>l/wCA), the capacitance has almost no effect and the voltage across the
equipment terminals is in phase with the incident electric field. For small
RL (RL<<wCA), the capacitance takes effect. Then--

        Q = CVoc = CA {-hEsin(theta)}                                 (eq 2-4)

                   dQ . RL                 dE
        VL = IRL = ----------- = RL{-hCA . ---- . sin(theta)}
                      dt                   dt

                                                                     (eq 2-5)

         (b) Equivalent circuit for a small loop (magnetic dipole). For
HEMP, a small loop is one with a radius less than 3 meters. Loop antennas can
be a major source of EMP-induced currents and voltages because of the EMP's
quickly changing magnetic field. Figure 2-19 shows a loop antenna and its
equivalent circuit. The voltage is induced by the EMP. The resistance, RL,
is the equipment or load resistance. The inductance, LA, is due to the loop.
For large RL (RL >>wLA), the inductance has almost no effect. Thus, the voltage
is proportioLnalL to the area of the loop and the rate of change of the
transverse magnetic field. For small RL (RL<<wLA), the inductance takes
effect and the current in the loop is proportional to the magnetic field. The
current will flow in a way that makes the magnetic flux through the loop due
to the current cancel the magnetic flux through the loop due to the field.

         (c) Typical coupling model. In actual coupling calculations, it is
often hard to depict a structure using the small dipole circuits just
described. For example, the microwave tower in figure 2-20 is not small
compared to a 3-meter wavelength, and it would be hard to represent it by
superimposing loops of different sizes, shapes, and orientations. Instead,
such a structure can be electrically approximated by a monopole of the same
height and of some effective radius, ae. An upper bound on the effective
radius is given by the tower dimensions at the base. The effect of ground is
approximated by assuming an infinitely conducting ground plane. For a worst-
case vertical orientation, the equivalent fat monopole over an infinitely
conducting ground plane is equal to a dipole of the same radius and twice the
height in free space. Models such as this can be used to find bounds or
orders of magnitude for coupling to large or complex structures. Model
validity or accuracy depends on the amount and kind of approximation used and
on how well results agree when compared empirically with experimental or
complex analYtical data.

         (d) Shielded cable coupling. To analyze the transients induced on
cables by EMP, two calculations usually are needed to find the coupling onto
the cable sheath and the voltage and resultant currents induced on the
internal wires. The calculation of coupling onto the cable sheath depends on
cable construction and location, and will be discussed for some typical cases
later. Figure 2-21 shows the calculated voltage induced on a wire inside a
shielded cable. The transfer impedance can be found theoretically, especially
for simple cable shields such as solid metallic conduits. For example, the
transfer impedance of a thin-walled tubular shield is given by--

                   1       (l+j)T/d
         ZT = ---------- . -----------                               (eq 2-6)
              2(pi)rcT     sinh(l+j)T/d

where r is the radius of the shield, c is its conductivity, T is the wall
thickness, j is the unit imaginary number, and d is the skin depth. Some
geometries, however, such as braided coaxial cables, are too complex for
theoretical treatment. Thus, it is often preferable to determine the transfer
impedance by experiment. For braided coaxial cables, the transfer impedance
is typically expressed as--

                    (l+j)s/d

         ZT = Ro ( ------------ ) = jwM12
                  sinh(l+j)s/d                                       (eq 2-7)

where Ro is the d.c. resistance per unit length, j is the unit imaginary
number, s is the shield wire diameter, d is the skin depth, w is the angular
frequency, and M12 is the leakage inductance per unit length. For typical
braided coaxial cables, Ro ranges from 1 to 25 milliohms per meter and M12
ranges from 0.1 to 1 nanohenry per meter. At low frequencies, s/d << 1 and
wM12 << Ro and ZT reduces to Ro. For example, for an RG-58 coaxial cable at
f = 104 hertz, d = 0.24 << 1 and wM12 = 0.01 milliohms per meter << Ro = 14.2
milliohms per meter so the transfer impedance is about equal to Ro. A 500-amp
current on a cable length of 100 meters will therefore induce a voltage drop
on the center conductor of 500 amps(100 meters)(14.2 milliohms per meter) =
710 volts.

         (e) Transmission line coupling. Transmission line theory is the
chief method used to calculate EMP coupling to aerial and buried conductors,
simple cables, and other long penetrators (e.g., pipes, ducts). A
transmission line picks up EMP from both the electric field and the changing
magnetic field. The loop formed by the line, its terminations, and the ground
behaves much like a loop antenna and picks up EMP from the transverse changing
magnetic field. The links between the line and ground behave much like dipole
antennas and pick up EMP from the vertical electrical field. The line also
picks up EMP from the longitudinal electric field. Though this last source
seems the most clearcut, it does not cause as much of the total current and
voltage as the other two. The transmission line theory involves many points
that were ignored in the analyses of small dipole and loop antennas. First,
the conductor is long compared to the incident wavelengths. This means that
currents and voltages will differ everywhere on the line. Also, there will be
reflection from the ground plane. With all such factors taken into account,
an analytical solution can be obtained, often with the help of a computer.
This solution usually involves the short circuit current and the open circuit
voltage at the line's termination. Figure 2-22 shows an approximate model of
this EM coupling. The transmission line is broken into N sections. N is
chosen based on the bandwidth needed in the model. One- to three-foot
sections are typical. Each inductor and capacitor in the model is chosen such
that L = ZoT/2 and C = T/Zo, where Zo is the characteristic impedance and T is
the transit time in each section. The voltage source in each section depends
on the incident fields. This theory also applies to transmission lines with
multiple cables. In this case, a source and load impedance will exist between
each cable and ground and between each cable and every other cable. Current
and voltages will be induced between the cables. This is caused by the
changing magnetic field component transverse to the loop formed by two cables
and by the electric field component pointing between them. This kind of EMP
pickup is called the differential mode. EMP pickup causing currents and
voltages between each cable and ground is called the common mode. These two
modes are often treated separately and both create a need for protection.

         (f) Aerial conductors. Long, straight, horizontal aerial conductors
include pole-mounted power distribution lines and signal-carrying cables.
Figure 2-23 shows how the peak coupled current and the time-to-peak depend on
the line length. The peak current and time-to-peak also depend on the line's
height above ground, its size and construction, the soil conductivity, and
other factors. The figure shows peak currents calculated for a pulse of the
form Eoe-t/x, where Eo is the peak field amplitude of 50 kilovolts per meter
and x is an exponential decay constant of 250 nanoseconds. This waveform
looks much like the standard double exponential discussed earlier. It is used
here to make calculations easier. Grazing, end-on incident is assumed with a
polarization of about 16 degrees from the horizontal. The vertical field
component for this polarization angle is 15 kilovolts per meter. The
horizontal field component is much larger (about 48 kilovolts per meter), but
it gives rise to a smaller induced current because of transmission line
behavior. This polarization is typical of that expected at latitudes in the
United States where the magnetic dip angle is more vertical than horizontal.
A worst-case angle of incidence is assumed. Figure 2-23 shows how peak
current as a function of the line length approaches a limiting value, in this
case about 10 kiloamps. The point at which the limiting value is reached is
called the critical line length. The time required for the current to reach
its peak value also increases with line length until a limiting value is
reached. Figure 2-23 also shows the bulk current that will be induced on the
aerial conductor. If the conductor is a shielded cable, the values shown will
correspond to the sheath current. The currents induced on conductors inside
the shield will depend on the transfer impedance.

         (g) Buried conductors. Buried conductors can be significant EMP
collectors because low-frequency components of EMP fields are not greatly
attenuated for typical soil conductivities and burial depths. The amplitude
of the induced current varies inversely with the square root of the soil
conductivity, which ranges from 10-4 to 10-2 mhos per meter. Figure 2-24
shows the variation in induced cable current with burial depth. The effect of
deeper burial is both to reduce the amplitude of the induced current and to
increase the risetime to peak current because of increased skin depth. (See
para 2-4b above.) Figure 2-24 is for a semi-infinite cable. A finite cable
will show a different response, especially near the cable ends. The
differences in response are related to the cable sheath material and the way
the cable is grounded. The cable's induced current also depends on the
amplitude, waveform, and direction of the incident pulse. It will be
proportional to the amplitude of the incident pulse (Eo). It will also be
proportional to the square root of the decay time constant (T) of the incident
pulse for an assumed exponential waveform E(t) = Eoe-t/T. This constant is
nearly the same as beta in the standard double exponential waveform. In the
figure, the pulse is incident from directly overhead with the electric field
parallel to the cable. This is a worst-case orientation. The current given
in the figure corresponds to the total current induced on the cable, mainly
sheath current, that can be related to the current on conductors inside the
shield in terms of the transfer impedance.

         (h) Ringing. As discussed earlier, the incident HEMP pulse is a
broadband signal with a time waveform approximated by very fast risetime and
exponential decay. If all coupling paths had broadband frequency responses,
EMP-induced transients would show similar waveforms. However, inductance,
capacitance, and resistance are inherent in any cable, cable shielding, and
grounding system, and give rise to frequency dependence. Any LRC system will
have characteristic resonant frequencies. EMP-induced transients thus will
tend to oscillate, or "ring," at these dominant frequencies, with the decay
rate of the oscillation ruled by the width of the resonance in the frequency
domain (fig 2-25). A very narrow resonance(*) can cause a long-lived
oscillation. This increased energy is added to the system and the likelihood
of damage increases. Typical ringing frequencies range from 1 to 15 mega-
hertz, depending on the physical and electrical details of the shielding and
grounding systems.
______________________

* The narrow resonance results from circuits of high Q (quality factor) which have
low resistive dissipation of energy.


         (i) Conductive penetrations. Pipes and other penetrators with
nonelectrical functions act very much like the shield of a shielded cable.
Most often such penetrators are buried. For these buried conductors,
transmission line theory can be used to calculate HEMP coupling, with the soil
acting as the return path. Both nonelectric penetrators and components with
an electrical function can couple EMP energy by acting in a mode other than
that for which they were designed. For example, waveguides usually are
designed to guide waves of a much higher frequency than HEMP; however,
currents can be coupled onto the exterior of waveguides and conducted to the
sensitive equipment. Conductive penetrations not only can collect HEMP
energy, they also can serve as low-impedance paths to ground for currents
induced elsewhere in a facility.

      (3) Intrasite cables. Intrasite or internal cables at a structure may
connect to mission-essential equipment. EMP-induced transients on these
cables result partly from direct interaction with EMP fields that reach the
structure's interior. These internal EMP fields couple to long, internal
cable runs and internal cable loops (fig 2-26). EMP-induced transients on
internal cables may also result from "cross talk." Typically, a cable that
penetrates a facility will branch into many smaller cables (e.g., low-current
power cables, individual telephone lines). These penetrators run alongside
other internal cables so that penetrating EMP-induced transients tend to be
shared. This especially occurs when cables run together in the same cable
tray or conduit, but it can also happen to some degree if the cables pass
within a few meters of each other. The result is that all cables linked to a
piece of mission-essential equipment must be seen as potential sources of
harmful voltage and currents. Figure 2-27 shows the distribution of currents
at equipment leads for a typical unshielded telephone communications facility
when subjected to a 50-kilovolt per meter EMP, polarized 16 degrees from the
horizontal and coming from a worst-case direction. The structure has an
incoming power line on which a peak current of 4 kiloamps is seen. Nineteen
waveguides with a total peak current of 5 kiloamps also penetrate the
structure. The waveguides come from a microwave tower and are grounded as
they enter the structure.

2-5. Equipment susceptibility. System damage or upset from EMP is caused by
currents and voltages induced in conductors exposed to a free-field or a
partly attenuated EM pulse coupled to circuits. External conductors,
structures, and internal conductors act as unintentional receiving antennas
and "coupling" paths. They can deliver the resulting EMP-induced currents and
voltages to sensitive components of electronic equipment. The HEMP-induced
currents on exterior long-line penetrators, such as power and telephone lines,
can have amplitudes as high as thousands of amperes. Currents induced on
internal cable runs can be as high as hundreds of amperes for most structures
and even higher in facilities with lower SE. It is important to note that
exterior voltage transients can be in the megavolt range, and it would be
normal to expect an order of thousands of volts from internal coupling.
Transients of these magnitudes can be delivered to electronic circuits, such
as integrated semiconductor circuits, which can be damaged by only a few tens
of volts, a few amperes, or less. These circuits also operate at relatively
low levels (e.g., 5 volts and tens of milliamperes) and can be upset by EMP
currents of similar values. If the large exterior coupled transients were
allowed to enter a structure that had no HEMP protection treatment, even
relatively "hard" devices, such as relay coils and radio frequency
interference (RFI) filters, would likely be damaged. Figure 2-28 shows this
potential EMP interaction leading to mission degradation.

   a. Equipment response. HEMP produces two distinct responses by equipment
and system components: upset and damage. Upset is a nonpermanent change in
system operation that is self-correcting or reversible by automatic or manual
means. Damage is an unacceptable permanent change in one or more system
parts. The spectrum of thresholds for some system components is shown in
figure 2-29. The figure clearly shows that semiconductors are highly
susceptible to HEMP and thus need protection.

      (1) Upset. Transient upset has a threshold about one order of
magnitude below the damage thresholds. It occurs when an induced HEMP
transient exceeds the operating signal level. It has a time scale that falls
within the circuit's time response. Figure 2-30 shows some examples of upset.
Figure 2-30(a) shows a flip-flop changing state due to a HEMP transient on the
trigger input. Figure 2-30(b) shows a NAND gate with a temporary change in
its output logic level from a HEMP transient on the power supply line. Figure
2-30(c) shows an amplifier driven to saturation by a HEMP transient
superimposed on its signal input.

      (2) Damage.

         (a) Semiconductors. Damage to semiconductors due to applied
transients is typically some form of thermal-related failure and therefore is
related to the total energy applied to the device. For discrete devices
(transistors, diodes), the predominant failure mode appears to be localized
melting across the junction. The melted regions form resistive paths across
the junction which short out the junction or mask any other junction action
(ref 2-7). Metallization burnout resulting in open circuits has also been
identified as a failure mode in inteqrated circuits (ref 2-8). A convenient
approach for failure analysis is the concept of the power failure threshold
(Pth) (ref 2-1). The power failure threshold is defined as--

                                 Pth = At-b                           (eq 2-8)

where A is the damage constant based on the device material and geometry, and
b is the time-dependence constant. The constants A and b can be determined
empirically for every device of interest by the least-squares curve fit to
experimental pulse test data. In general, it will be more convenient to use
the Wunsch model (ref 2-7) for the power failure threshold with previously
determined values of the Wunsch model damage constant for any analysis. This
theoretical model has a time-dependence constant of b = 1/2. Empirical data
for a wide range of devices fits the model within the experimental data spread
in the midrange of pulse widths, approximately 100 nanoseconds to 100
microseconds (ref 2-1). The Wunsch model theoretical equation is--

                            Pth = Kt-1/2 Kw/cm2                      (eq 2-9)

where t is the pulse width in microseconds and K is the Wunsch model damage
constant in kW - (microsecond)1/2. K is expressed in these units since the
numerical value of K is then equal to the power necessary for failure when a
1-microsecond pulse is applied to the junction. Figures 2-31 and 2-32 show
typical ranges for K for various semiconductors. Multiplication of this
factor by t-1/2 will yield the pulse power threshold.

         (b) Passive elements. The passive elements most susceptible to
damage from HEMP-induced currents are those with very low voltage or power
ratings and precision components for which a small change is significant.
Resistor failures due to high-level pulsed currents are caused by energy-
induced thermal overstress and voltage breakdown. Resistor failure threshold
can be calculated from the resistor's parameters and the empirical relation
given in reference 2-9. Exposure of capacitors to transient currents sets up
a voltage across the capacitor that increases with time. For nonelectrolytic
capacitors, this voltage keeps rising until the capacitor's dielectric
breakdown level is reached. That point is typically 10 times the d.c. voltage
rating. For electrolytic capacitors, the voltage relationship holds until the
zener level of the dielectric is reached. After that, damage can occur. The
damage threshold for electrolytic capacitors in the positive direction is 3 to
10 times their d.c. voltage rating. For the negative direction it is one-half
their positive failure voltage (ref 2-10). Transformer and coil damage due to
HEMP-induced currents results from electric breakdown of the insulation. The
pulse-breakdown voltage is typically 5500 volts for power supply transformers
and 2750 volts for small signal transformers (ref 2-11).

   b. Equipment sensitivity. Localizing responses of specific circuits or
components within equipment or a system often is not possible for complex
equipment. Therefore, when estimating system response, it is often more
realistic to deal with the thresholds at the equipment level instead of at the
circuit or component level. Using the equipment thresholds approach usually
requires that the applicable systems have had their thresholds analyzed or
measured. Measured thresholds for some types of communications equipment are
given in table 2-3.

   c. Typical damage and upset levels. Table 2-4 gives typical HEMP-induced
transient levels as observed in tests and analyses at operational facilities.
The largest voltage value is 2 megavolts and the largest current is 4
kiloamps. Much smaller values may also result. This is especially true for
the inner conductor of the coaxial line because of the shielding protection
provided by the outer conductor. The data in Table 2-4 were obtained with the
equipment under test in a parallel plate EMP simulator. The simulator
excitation approximated the 50-kilo- volt/meter double exponential waveform
with risetime of 5 to 10 nanoseconds and e-fold of approximately 0.5
microseconds. A current probe was then used to measure the peak-to-peak
current on a power supply lead. The current measured was typically a damped
sinusoid with frequency dependent on equipment type and lead length.

2-6. Cited references.

       2-1. DNA EMP Course Study Guide, draft prepared for Defense Nuclear
       Agency (The BDM Corporation, April 1983).

       2-2. Ghose, Rabindra N., EMP Environment and System Hardness Design,
       Library of Congress Catalog Card Number 83-51062 (Don White
       Consultants, Inc., Gainesville, VA, 1984).

       2-3. DOD-STD-2169, (U) Hiqh-Altitude Electromaqnetic Pulse (HEMP)
       Environment (DOD, June 1985) (5).

       2-4. Prototype HEMP Desiqn Practice Handbook, prepared for Defense
       Communications Agency, Contract No. DCA 100-77-C-0040 (IRT
       Corporation, 31 May 1978).

       2-5. EMP Awareness Course Notes, DNA 2772T (HQ, Defense Nuclear
       Agency, August 1971).

       2-6. Lee, K. S. H., EMP Interaction: Principles, Techniques, and
       Reference Data, AFWL-TR-80-402, (Dikewood Industries, Albuquerque,
       NM, December 1980).

       2-7. Wunsch, D. C., and R. R. Bell, "Determination of Threshold
       Failure Levels of Semiconductor Diodes and Transistors due to Pulse
       Voltages," IEEE Transactions on Nuclear Science, NS-15, No. 6
       (Institute of Electrical and Electronic Engineers, December 1968).

       2-8. Jenkins, C. R., and D. L. Durgin, "EMP Susceptibility of
       Integrated Circuits," IEEE Transactions on Nuclear Science, NS-22, No.
       6 (Institute of Electrical and Electronic Engineers, December 1975).

       2-9. Tasca, D. M., D. C. Wunsch, and H. Domingos, "Device Degradation
       by High Amplitude Currents and Response Characteristics of Discrete
       Resistors," IEEE Transactions on Nuclear Science, NS-22, No. 6
       (Institute of Electrical and Electronic Engineers, December 1975).

       2-10. Tasca, D. M., H. B. O'Donnell, and S. J. Stokes III, Pulse
       Power Responses and Damage Characteristics of Capacitors, Final
       Report, Contract F29601-75-C-0130 (General Electric, December 1976).

       2-11. Dunbar, W., and J. Lambert, "Power System Component EMP
       Malfunction/Damage Threshold," paper presented at DNA EMP Seminar
       IIRI. Chicaqo. IL, 14-16 MaY 1974.

2-7. Uncited references.

       DNA EMP Handbook, DNA 2114H-2, Vol 2 (Defense Nuclear Agency,
       November 1971).

       Lee, K. S. H., T. K. Liu, and L. Morins, "EMP Response of Aircraft
       Antennas," IEEE Transactions on Antenna Properties, AP-26, No. 1
       (Institute of Electrical and Electronic Engineers, January 1978).

       EMP Design Guidelines for Naval Ship Systems, ITTR NSWC/WOL/TR-75-
       193, Naval Surface Weapons Center, 22 August 1975.

       EMP Engineering and Design Principles, Bell Laboratories, PEM-37
       (Lawrence Livermore Laboratory, 1975).

       MIL-STD-461C, Electromagnetic Emission and Susceptibility
       Requirements for the Control of Electromagnetic Interference (DOD, 4
       August 1986).


               Table 2-1. Important features of EMP environments*

____________________________________________________________________________

Type                Features                     Systems impact
____________________________________________________________________________

HEMP                Large extent, high           Most widely specified threat
                    amplitude, broad frequency
                    band, plane wave

Surface-burst

  Source region     Large amplitude, limited     Important for systems which
                    extent includes varying      are hard to other nuclear
                    conductivity, currents       effects

  Radiated region   Large amplitude varies       Can supercede HEMP if
                    inversely with distance      vertical orientation or
                                                 low freqs. important

Air-burst

  Source region     Similar to surface-burst     See surface burst

  Radiated region   Amplitude less than HEMP     Superceded by HEMP

SGEMP               Very high amplitude          Important for exoatmospheric
                    and fast rise time           systems

MHD-EMP             Very low frequency, low      May affect long-land
                    amplitude, large extent      or submarine cables

_______________
*Source: ref 2-1, DNA EMP Course Study Guide, draft prepared fo Defense
Nuclear Agency (The BDM Corp., April 1983), p I-51.



                      Table 2-2. EMP waveform summary*

___________________________________________________________________________
                        Peak
Type                    amplitude               Timeframe
___________________________________________________________________________

HEMP                    50 kV/m                 Few nanosec to 200 nanosec

Surface-burst

  Source region         1 MV/m                  Few nanosec to 1 microsec

                        10 kV/m                 1 microsec to 0.1 sec

  Radiated region       10 kV/m                 1 microsec to 100 microsec

Air-burst

  Source region         Similar to surface-
                        burst

  Radiated region       300 V/m at 5 km,        10 nanosec to 5 microsec
                        typical (highly
                        dependent on HOB

SGEMP                   100 kV/m                Few nanosec to 100 nanosec

MHn-EMp                 30 V/km                 0.1 sec to 100 sec

______________
*Source: ref 2-1, DNA EMP Course Study Guide, draft prepared for
Defense Nuclear Agency (The BDM Corp., April 1983), p I-49.


[Tables 2-3 and 2-4 and Figures 2-1 to 2-32 not digitized here.]

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[End Chapter 2]