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In this study, HPM theory and the general design principles introduced in the previous chapter are to define a notional e-bomb. Our e-bomb includes an HPM power source, appropriate waveguide, and an antenna/reflector. The pulse generated by the HPM source follows a rectangular wave shape.
Figure 14. E-Bomb major elements
Abstract
Hypothetical electromagnetic bomb
First, the theory behind HPM technology is defined. Next, the device radiated output is described and used to define the propagation pattern of generated electromagnetic field to ill be estimated as a function of range. Then, the coupling mechanisms between the HPM device output and the target system are defined. After defining the yield for the conception e-bomb from an HPM source, the impact on electronic systems is considered. The basis for consideration is according to the known, published threshold values of electronic systems. The possible effects are analyzed and the potential lethality range for different targets is estimated. A flow diagram of the described process is shown in Figure 15.
Figure 15. The e-bomb microwave flow from the power source to the damage/upset of target system.
To support the interaction assessment, a MATLAB model is used to simulate e-bomb effects using HPM theory. Published data for relevant systems is then used to validate the model.
For the simulation model, the frequency ( f ) and the duration of the
microwave pulse/pulsewidth ( τ ) will be decided by the user. For the purpose of this study, 100 nanoseconds (ns) is chosen as the default pulsewidth to make relevant but meaningful comparison between the different classes of e-bomb. For frequencies at or above 1 GHz frequency, 100 ns pulsewidth will contain 100 cycles and from an interaction viewpoint, 100 cycles should be adequate to ring up most system resonances, resulting in a steady-state maximum signal (voltage or current) at the failure port (Taylor and Giri, 1994).
Figure 17. Waveguide dimensions
As seen on Figure 17, let the inner dimensions of the waveguide be : a: larger dimension of the waveguide b: smaller dimension of the waveguide. Since a>b, the TE 10 mode has the lowest cutoff frequency, it is generally desirable to have only one propagating mode in the waveguide. This minimizes dispersion and allows more efficient operation of the waveguide (Taylor and Giri, 1994).
The model impedance for the rectangular waveguide that operates in TE 10 mode is
2 1 /^2 1 , (^0012)
− ⎥⎥⎦
Z = Z −⎜⎝⎛^ λ a^ ⎟⎠⎞ (1)
where
Z 0 : wave impedance of free space ( μ / ε= 120 π)
λ : operating wavelength ( λ = cf , where the c is the
speed of light in free space, 3x10^8 m/s) a : larger dimension of the waveguide (Taylor and Giri, 1994).
For our e-bomb simulation, the dimensions of the waveguide are entered by the user. Free space wave impedance will be reference impedance in the simulation as shown in equation (1).
Once the model impedance is determined, the peak electric field (E-field) in the waveguide is given by:
E (^) max waveguide abZ 1 , 0 P avg ( )= 4 (2)
where
Z 1 (^) , 0 : model impedance of waveguide
P avg : average power of HPM source a : larger dimension of the waveguide b : smaller dimension of the waveguide (Taylor and Giri,
- (Giri and Tesche, 2003) (Giri, 2004).
For the simulation, the average power will be entered by the user in terms of the classifications of e-bomb, which will be defined later in this chapter.
Another issue for HPM propagation is the atmospheric breakdown limitations. The upper limit of microwave power that can be transmitted in a waveguide and in the air is determined by the dielectric strength of the medium in which the microwave pulse propagates. As a rule of thumb, 3 MV/m maximum
For the standard atmospheric conditions (1013.25 hPa), the maximum field strength that can propagate in the atmosphere is around 3.10 MV/m for 100 ns. pulsewidth (the standard pulsewidth for the simulation).
The breakdown limitation formula shown in equation (3) is valid for air only. The waveguide may be filled with different inert gas, for example sulphur hexafluoride (SF 6 ), which has a critical field strength level of 3-4 times that of air at microwave frequencies (Larsson, Johansson, and Nyholm, 2006). Combinations of SF 6 and Nitrogen (N 2 ) have also proved valuable when working with pulse power technology at peak output.
If the waveguide is vacuumed and then filled with appropriate gas with a high dielectric strength, a field strength up to 74 MV/m can be sustained in the waveguide (Taylor and Giri, 1994).
As mentioned before, in HPM applications at GW power range, the waveguide and the horn are evacuated. But the dimensions of the horn aperture must have a minimum value at which the power density and the peak electric field at the aperture of the antenna enable the transition from the vacuum to 1 atm. SF 6 gas. This means that the peak electric field at the aperture of the antenna must also be below the breakdown electric field. For the simulation, this value is around 3.10 MV/m. As seen on Figure 19, if the aperture has dimensions a ' (^) (width of the aperture, larger dimension) and b ' (^) (height, smaller dimension), corresponding to the a and b of the waveguide, the peak electric field at the aperture is estimated by
( ) max ( ) a ' b ' E attheaperture E E waveguide ab peak =^ bd = × (4)
Figure 19. Aperture details of the proposed horn antenna
If it is assumed that (^) aa '^ = (^) bb ', the equation (4) becomes
E (^) peak ( attheaperture )= Ebd = E max ( waveguide )×⎜⎝⎛ bb ' ⎟⎠⎞ (5)
Once the minimum value for b 'is calculated, other dimension of the horn, a ' , can be calculated as well (Taylor and Giri, 1994) (Giri, 2004).
For example, at f = 1.2 GHz and Pavg^ = 2GW, the peak electric field in the
waveguide is found to be 14.3 MV/m, which means that (^) bb '^ should be about
0.2165 in order to keep the electric field below 3.10 MV/m at the aperture of the horn antenna. As a result, the minimum dimension of b 'is (97.79 mm/0.2165) = 45.17 cm. Using the same ratio for a ' , it is found to be that a ' is (195. mm/0.22) = 90.33 cm.
The other option can be the use of parabolic dish (see Figure 20) instead of horn antenna. If the focal length of the parabolic dish ( F ) is known, the peak electric field at the aperture can be estimated without using the dimensions of the antenna by
where
r : target distance (in meter) from the e-bomb E (^) peak ( farfield ): E-field strength from the e-bomb at the distance r area ofthe reflector : a ' × b 'for the horn antenna
d^2
π for the parabolic antenna where d is the
diameter of the parabolic dish p (^) avg ( farfield ) : average power density u : energy density (Taylor and Giri, 1994) (Giri and Tesche, 2003) (Giri, 2004).
The field strength at one meter from the antenna is called the figure of merit (FOM). According to the far field parameters, the E-field and range product gives the FOM of the e-bomb. FOM provides a convenient comparative performance measure for HPM device outputs that is conveniently and easily scaled to the device peak field output at ranges beyond far-field.
As the microwave signal propagates through the troposphere, it is attenuated through energy absorption by atmospheric gases and by rain. Rain droplets also scatter as well as absorb microwave transmissions; however, the scattering of energy out of a beam is small when compared to the absorption loss.
Figure 21. Atmospheric attenuation of microwave propagation at 0o^ C and 1 atm due to oxygen and water absorption (Taylor and Giri, 1994).
According to Figure 21, the attenuation due to the atmosphere is not significant below 1GHz. Consider the commonly used frequency at 2.45 GHz, where commercially available devices such as microwave ovens, cell phones etc. are operated. Among these devices, a microwave oven source can be used as a general HPM generator for an e-bomb. Any later HPM sources that will be defined as the source of e-bombs in this study will not be operated more than 2.45 GHz. Since the atmospheric attenuation increases by the frequency, the
Figure 22 shows the attenuation due to the rain for different rain rates at interested frequencies. The attenuation increases when the operating frequency increases. It also increases when the rain rate increases. For moderate rainfall, R = 5 mm/h, the corresponding path loss is 0.00038 dB/km at 1.2 GHz, 0. dB/km at 1.7 GHz, 0.0012 at 2 GHz, and 0.002 dB/km at 2.45 GHz.
(^0) 0.5 1 1.5 2 2.5 3
X: 2.45Y: 0.
The Attenuation of Microwave due to the Rain
frequency (GHz)
attenuation (dB/km)
0.5 mm/h 5 mm/h 25 mm/h 50 mm/h 100 mm/h
Figure 22. Attenuation of microwave due to the rain at different rain rates.
Up to this point, the basic theory for the hypothetical e-bomb is defined including the propagation features in the atmosphere. This theory as described will be used as the basis for MATLAB simulation calculation.
2. Classifications of the Source Elements
To show a wide range of different applications, source technologies and the range of effects on different targets, three types of e-bomb will be categorized an evaluated:
- Low-Tech (Small) E-Bomb
- Medium-Tech (Moderate) E-Bomb
- High-Tech (Powerful) E-Bomb
a. Low-Tech (Small) E-Bomb A low-tech e-bomb is characterized by marginal performance, minimal technical capabilities, and is easily assembled and deployed (Giri and Tesche, 2003).
For this thesis, it will be assumed that low-tech (small) e-bombs will be used against relatively small and unshielded systems. Unshielded systems are considered to be fully exposed by e-bomb electromagnetic waves.
Low power levels are generally in the kW levels (Giri, 2004). For the simulation, a microwave oven specifications will be used to define the low- tech e-bomb. There are commercially available magnetron microwaves in the range of 800-2000 watts, which makes for an easily procured HPM generator.
Though militarily not applicable, the purpose of using a microwave oven source is to show that low-tech e-bomb designed from commercially available sources with average power level between 800-2000 watts are possible to produce field strength levels at about kV/m level at km distances with a reasonable antenna.
A commercially available continuous wave (CW) microwave oven has the operating frequency of 2.45 GHz. From Table.1, corresponding rectangular waveguide can be either WR340 or WR430. For this study, both waveguides will be used. According to the outputs of each e-bomb (WR340 and
effectiveness is assumed for moderately shielded systems. Civil aviation aircraft provide a good example for moderately shielded systems that might have roughly 30 dB shielding.
It is known that sufficiently intense electromagnetic signals in the frequency range of 200 MHZ to 5 GHz can cause electronic damage in many systems. For the simulation of medium-tech e-bomb, 1.2 GHz and 1.7 GHz are chosen as the operating frequencies due to their common applicability to standard radar and communications technologies that are similar in form. Moderate power levels can be in the range of 1 to 20 MW (Giri, 2004). For the average power, a range between 1-20 MW will be analyzed to decide the most effective power source and operating frequency. There are also commercially available radar systems that operate around 1.2 GHZ and 1.7 GHz frequency level and radiate an average power up to 20 MW.
For the medium-tech e-bomb, corresponding rectangular waveguides are chosen to be WR770 for 1.2 GHz frequency and WR650 for 1. GHz frequency from Table.1. After comparing the outputs of each frequency option of the moderate e-bomb, a conservative estimate will be identified that covers the largest output from the two as the medium-tech (moderate) e-bomb for the analysis the potentially lethal effect on different systems.
Based on the initial work by Giri (Taylor and Giri, 1994), a parabolic (dish) antenna with 4.9 m 2 aperture area (d=2.5m) with 0.5m focal length (F) will be used for reflector of the medium-tech e-bomb. Focal length and aperture area are chosen arbitrarily. The pulsewidth is to be 100ns (as was done for low-tech e- bomb). Specifications for the “Medium-Tech (Moderate) E-Bomb” are shown in Table.3.
Operating frequency ( f ) 1.2 GHz and 1.7 GHz
Average power ( Pavg ) 1-20 MW
WR650 waveguide dimensions ( a × b ) 0.1651x0.08255 m
WR770 waveguide dimensions ( a × b ) 0.19558x0.09779 m
Aperture area of the reflector ( A ) 4.9 m 2 (d=2.2 m)
Focal length of the reflector ( F ) 0.5 m
Pulsewidth ( τ ) 100 ns
Table 3. Specifications of Medium-Tech (Moderate) E-Bomb
c. High-Tech (Powerful) E-Bomb More sophisticated high-tech and high-power electromagnetic systems would certainly require specialized and sophisticated technologies and perhaps even specifically tuned output to cause severe damage to a specific target (Giri, 2004).
For the e-bomb simulation, it will be assumed that high-tech (powerful) e-bombs will be used against fully shielded systems. A 40-50 dB shielding effectiveness is assumed for fully shielded systems. Military systems are a good example of fully shielded systems and are procured with shielding requirements in order to perform designed missions.
Following the initial work by Giri (Taylor and Giri, 1994), The operating frequency of high-tech (powerful) e-bomb is chosen to be 2 GHz. High power levels can be in the range of 100’s of MW to GW’s (Giri and Tesche, 2003). For the average power, a 20 GW source will be used to assess the effects of powerful e-bomb on target systems. A 20 GW vircator source has been reported by Benford in 1987 (Benford, 2004). Obviously, the technology has
produce joule heating to the extent that thermal damage occurs. (usually between 600 and 800 degrees Kelvin) (Benford, Swegle, and Schamiloglu, 2007).
No matter what kind of e-bomb is used or which power/frequency/mode is applied, two principal coupling modes are recognized in open literature in assessing how much power is coupled into target systems:
- Front Door Coupling
- Back Door Coupling Both coupling mechanisms are explained here, although, only the back door coupling will be used in the simulation in order to assess the lethality of three classes of hypothetical e-bombs. Considering that front door coupling inherently has more energy delivered into target systems than the energy delivered through back door coupling, it can be assumed that, in reality, more susceptibility can be achieved than the susceptibility shown in this study.
All the coupling estimates will assume that the target system is in the main lobe of the e-bomb antenna. Clearly, if the target is in the sidelobes or at random angles, the coupling efficiency will decrease, and less power will be delivered to the target.
1. Front Door Coupling
Front Door Coupling is typically observed when the power radiated from the e-bomb is directly coupled into the electronic systems, which involves an antenna such as radars, EW or communications equipments. The antenna subsystem is designed to couple power in and out of the equipment, and thus provides an efficient path for the power flow from the electromagnetic weapon to enter the equipment and cause damage (Kopp, 1996).
For front door coupling to gain entry through an antenna, it can be appropriate to operate the e-bomb at the in-band frequency of target system if it
is known (Benford, Swegle, and Schamiloglu, 2007). For this reason, most front door coupling is efficient for only a narrow band of frequency, and is inefficient outside the band.
2. Back Door Coupling
Back Door Coupling occurs when the electromagnetic field from the e- bomb produces large transient currents (termed spikes, when produced by a transient source) or electrical standing waves (when produced by a HPM weapon) thru cracks, small apertures and on fixed electrical wiring and cables interconnecting equipment, or providing connections to power mains or the telephone network. Equipment connected to exposed cables or wiring will experience either high voltage transient spikes or standing waves, which can damage power supplies and communications interfaces if not shielded or inherently robust. Moreover, should the transient penetrate into the equipment, other devices inside can be damaged through mutual coupling. Any cable can comprise multiple linear segments, which are typically at close to right angles; therefore, whatever the relative orientation of the e-bomb, one or more segments can provide very good coupling efficiency. Network cables use fast, low-loss dielectrics and are thus very efficient at propagating such transients with minimal loss (Kopp, 1996). Back door coupling can generally be described as wideband, but may have narrow-band characteristics because of resonance effects (coupling to cables for example).
Theory for the back door coupling is more complex than that for the front door coupling. Since the cross section of coupling is difficult to determine for the target system, the susceptibility results can be different from the expected (Benford, Swegle, and Schamiloglu, 2007).
For the validation of the hypothetical e-bomb model and the assessment of each e-bomb’s lethality, a basic theory relating field strength to coupled current will be used in the simulation.
