ELECTROMAGNETIC PULSE (EMP) AND TEMPEST PROTECTION FOR FACILITIES ------------------------------------------------------------------------------ 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 ------------------------------------------------------------------------------ 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 10^8 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 10^13 E(u) = --------------------------------- volt second per meter (ju + 4 x 10^6)(Ju + 4.76 x 10^8) (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 (m^2) 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/meter^2 Loop voltage VL = A (dB/dt) d(4(pi) x 10^-7 x 132.6 e^-t/0.5 x 10^-6) Webers/meter^2 = 0.1 meters^2 (-------------------------------------------------------- ) dt = 0.1 (2 x 10^6 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 couDlinq analvsis. 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<>wL ), the inductance has almost no effect. Thus, the voltage is proportioLnalL to ~he area of the loop and the rate of change of the transverse magnetic field. For small RL (RL<