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Abstract
This paper investigates the effects of a nuclear-disturbed environment on the transmission of electromagnetic (EM) waves through the atmosphere. An atmospheric nuclear detonation can produce heightened free electron densities in the surrounding atmosphere that can disrupt EM waves that propagate through the disturbed region. Radiation transport models simulated the ionization and free electron densities created in the atmosphere from a 1 MT detonation at heights of burst of 5 km, 25 km, and 75 km. Recombination rates for the free electrons in the atmosphere were applied, from previous work in the literature, to determine the nuclear-induced electron densities as a function of time and space after the detonation. A ray-tracing algorithm was applied to determine the refraction and reflection of waves propagating in the different nuclear-disturbed environments. The simulation results show that the free electron plasma created from an atmospheric nuclear detonation depend on the height of burst of the weapon, the weapon yield, and the time after detonation. Detonations at higher altitudes produce higher free electron densities for greater durations and over larger ranges. The larger the free electron densities, the greater the impact on EM wavelengths in regards to refraction, reflection, and absorption in the atmosphere. An analysis of modern infrastructure and the effects of nuclear-disturbed atmospheres on different signal wavelengths and systems is discussed.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The transmission of radio frequencies through the atmosphere can be altered and degraded in the event of an atmospheric nuclear detonation. As modern society continues to rely increasingly on wireless communications, understanding the effects of a nuclear-disturbed atmosphere on these systems and their operational capabilities is critical. Experimental tests investigating nuclear-disturbed atmospheric conditions have not been carried out since the atmospheric nuclear testing period of the 1950s and early 1960s [1–3]; therefore, the effects on modern communication systems is relatively unknown. This manuscript models the effects of a nuclear-disturbed environment on various electromagnetic (EM) frequencies and analyzes the implications for modern infrastructure.
EM wave propagation in the atmosphere is affected by the number of free electrons that the wave encounters. Free electrons change the electric permittivity of the air, which causes the index of refraction to change for that air medium, and, as a result, refraction or reflection can occur to an EM wave. Nuclear detonations increase the number of free electrons in the atmosphere as a consequence of the immense amount of ionizing radiation (x-rays, gamma rays, beta particles, and neutrons) they emit. The free electrons generated in the atmosphere from a nuclear detonation form a cold plasma that can affect the propagation of EM waves through attenuation, refraction, or complete reflection (depending on the free electron levels and signal frequency) [2,4]. The number of free electrons that are persistent in the atmosphere from the detonation depends on the density of the surrounding air; lower altitudes with higher air densities tend to remove and recombine electrons at faster rates than those of higher altitudes. Understanding the effects a nuclear detonation has on the propagation of EM waves in the atmosphere is critical for understanding the operational capabilities of various communication systems, radar, and other equipment. The study of EM wave propagation from artificial plasmas created from the re-entry of space vehicles in the upper atmosphere has been a focus of increased study recently [5–7], but the spacecraft plasma studies occur on a spatial scale that is many orders of magnitude lower than that of a nuclear detonation. In this work, we model atmospheric nuclear detonations and the resulting free electron plasmas that they create in the atmosphere. Radiation transport codes are used to determine the level of free electrons in the surrounding atmosphere. A simple ray-tracing algorithm is used to model the propagation of different EM wavelengths as they encounter different nuclear-disturbed environments. This work quantifies the effects on EM wave propagation in the atmosphere from a nuclear detonation as a function of the height of burst (HOB) and time after the detonation.
2. Background
2.1 Index of refraction of air and plasma
The index of refraction for non-ionized air differs from that of air with a free electron content (air with a free electron content is also known as a plasma). The index of refraction (n) for a medium (air, plasma, etc.) is defined by the speed of light in a vacuum (c) over the speed of light in that particular medium (v) in Eqs. (1)–(4).
The speed of light in a medium depends on the magnetic permeability ($\mu$) and electric permittivity of the medium ($\epsilon$); in a vacuum, these values are labeled as $\mu _0$ and $\epsilon _0$. For EM waves propagating in Earth’s atmosphere, the magnetic permeability ($\mu _r$) will be 1 (non-magnetic media have a value of 1), but the electric permittivity ($\epsilon _r)$ will depend on whether the wave is in a plasma (like that of the ionosphere) or in the non-ionized air of lower altitudes. Free electrons in the air cause the electric permittivity ($\epsilon _r$) to be less than unity, resulting in an index of refraction below 1 for some wavelengths. This impacts only the phase velocity of the light ($v_p$); the group velocity ($v_g$) still remains at or below the speed of light (i.e., there are no superluminal effects). Nonetheless, with the index of refraction for the phase velocity dropping below unity, this causes a bending or refracting of the EM wave when it encounters a plasma. The index of refraction for the phase velocity of the EM wave is
Here, $N$ is equal to the free electron density of the plasma (electrons/$m^3$), $m$ is the mass of an electron, $e$ is the charge of an electron, $\omega$ is the frequency of the EM wave, and $\epsilon _0$ is the permittivity of a vacuum. For more information on the full derivation and in-depth explanation of the refractive index of a plasma, see the relevant Refs. [8–10]. From Eq. (5), one can see that the index of refraction for a plasma depends on the free electron density of the plasma and the frequency of the EM wave. These two variables are explored later in this work as we examine the increased electron density in the atmosphere from a nuclear detonation and how it subsequently affects various wavelengths.
2.2 Ionosphere
The ionosphere is a layer in the atmosphere (between an altitude of approximately 60 to 1,000 km) that contains high concentrations of free electrons, primarily from ionization by high-energy photons from the sun (UV and x-rays). The ionosphere is made up of three regions: the D-region (60–90 km), E-region (90–150 km), and F-region (150–1,000 km) [11]. The D-region appears only during the day as the rapid recombination rates of the free electrons at this altitude eliminate this region at nighttime (i.e., recombination processes in this region dominate over ionization processes without the sun overhead). In addition to diurnal changes, the electron levels of the different ionosphere layers can change with the seasons, solar activity, and geographical latitude. A graph of the electron density levels of the ionosphere as a function of altitude and diurnal solar levels can be seen in Fig. 1 (data obtained from the International Reference Ionosphere 2012 model [12,13], for an East Tennessee location in May of 2020). The D-region and a significant portion of the electrons in the E-region are eliminated during nighttime due to recombination and removal of the free electrons with the surrounding atmosphere. The values in Fig. 1 can experience an order of magnitude increase in the event of a large solar flare [11]. The index of refraction of the ionosphere can be less than 1 for specific wavelengths (see Eq. (5)), which can cause an EM wave to be refracted or reflected when it encounters the ionosphere.
The free electron density of the ionosphere forms a cold plasma that can reflect radio waves enabling non–line-of-sight communications. Radio frequencies are typically divided into bands, and different organizations delineate the bands with different nomenclature and frequency ranges; for this work, we use the International Telecommunications Union (ITU) designation for the different frequency bands [14]. Medium-frequency (MF) wavelengths (300–3,000 kHz or 1,000–100 m) and low-frequency (LF) wavelengths (30–300 kHz or 10–1 km) used for AM radio and navigation are totally reflected by the ionosphere (as well as frequency bands lower than LF). High-frequency (HF) wavelengths (3–30 MHz or 100–10 m) are also reflected by the ionosphere but not until the wave reaches the F-layer of the ionosphere. At this altitude, the wave can travel long distances, and this band is commonly used for “over the horizon” radar and communication. Wavelengths below HF are not reflected by the ionosphere and can escape into space. These wavelength bands include: very high frequency (VHF) wavelengths (30–300 MHZ or 10–1 m) used for line-of-sight communications, ultra high frequency (UHF) wavelengths (1–0.1 m) used for mobile phones, GPS and various other systems, and super high frequency (SHF) wavelengths (0.1–0.01 m) used in 5G communication and satellite communications systems (Fig. 2 depicts the wavelength band ranges and their relation to the rest of the EM spectrum). All of these wavelength bands (LF – SHF) can be affected by a change in the electron content of the atmosphere from a nuclear detonation. Thus, in Section 4, the impacts of a nuclear-disturbed environment on all of these wavelength bands are analyzed.
2.3 Nuclear-disturbed environment
During an atmospheric nuclear detonation, gamma rays, x-rays, and neutrons stream out of the exploding weapon and cause widespread ionization of the surrounding air. The electrons liberated from the surrounding air recombine at various rates depending on the HOB the weapon (electrons at higher altitudes recombine more slowly than at lower altitudes due to the lower density of air) and the weapon yield. In addition to the prompt radiation given off during the explosion, the weapon debris after the detonation emits high-energy beta particles and gammas that contribute to the continued ionization of air. Thus, the total free electron content of the atmosphere surrounding a nuclear detonation can be determined as a function of time by a differential equation that equates the initial ionization from the prompt radiation, the free electron removal rate via recombination and neutral particle attachment, and the continuing ionization rate from the weapon debris [2].
Free electron removal from the atmosphere occurs via two general processes: electron–ion recombination and electron–neutral particle elimination [15]. Electron–ion recombination involves electrons combining with positively charged ions to form neutral particles. There are three different kinds of recombination: (1) radiative recombination, (2) dissociative recombination, and (3) dielectric recombination [16] (for more information on these different recombination mechanisms, see the relevant references [10,11,15,16]). These recombination processes are dependent on electron densities ($N_e$), ion densities ($N_+$), and the recombination coefficient ($\alpha$), which is a function of air density and temperature. The differential equation for the electron–ion recombination effect is
Electron–neutral particle attachment involves attachment of an electron to a neutral particle to form a negative ion. This free electron removal process is dependent on electron densities, neutral particles densities ($\rho$), and the attachment coefficient ($\beta$), which is approximately equal to $4 \times 10^{13}$ cm$^6$ g$^{-2}$ s$^{-1}$ [2]. The differential equation for the electron–neutral particle elimination process is
To estimate the free electron generation rates in the atmosphere from prompt radiation and delayed radiation, we used the radiation transport code MCNP [17]. Glasstone and Dolan assumptions [2] were used for the prompt radiation fluxes (neutrons released per fission, prompt gamma rays per fission, ionizing radiation partition of the yield as a function of altitude, etc.) and the SCALE nuclear code suite [18] was used to produce the delayed gamma and beta particle fluxes (assumed pure U-235, fission only device). The radiation fluxes from SCALE and the Glasstone and Dolan assumptions were inputted into MCNP to obtain the total ionizations in the surrounding air as a function of time. An example of the electron generation rate using MCNP (recombination was not taken into account) at 15 s post-detonation for a 1 MT detonation can be seen in Fig. 3. The computational fluid dynamics (CFD) code COMSOL [19] was used to obtain the fireball size and subsequent nuclear debris cloud altitude as a function of time (see Ref. [20] for more information on the fireball modeling in COMSOL). A 3D mesh tally for the electron generation rates was used in MCNP to acquire the spatial profile. The electron generation rates from the delayed radiation outside of the fireball are primarily from the gamma rays, as the beta particles produced by the weapon debris do not travel very far (a few meters) in air. The bright white spot in Fig. 3 is caused by the short travel of beta particles in air. The weapon debris was approximated as a uniform source throughout the fireball.
Fig. 3. Simulation of the electron creation rate ($cm^{-3} s^{-1}$) in the atmosphere from a 1 MT detonation at a 5 km HOB, 15 seconds post detonation.
Combining the electron generation rate in the air from MCNP (Q(t)) with the electron recombination and electron elimination processes, we can get a differential equation for the total free electron density of the air as a function of time:
Solving this differential equation yields the total free electron density as a function of time (for more information on how the form of this approximate solution to this differential equation was solved, see reference [2]):
Equation (9), along with the MCNP ionization rates and other variables, are used in this work to obtain the electron densities in the atmosphere as a function of time and space. Detonations of a 1 MT yield device are modeled at 5, 25, and 75 km HOBs. The free electron densities from the detonations and the natural ionosphere electron densities are input into a ray-tracing model (see next section) to determine the effects on different wavelengths of EM waves.
2.4 Ray tracing model
A simple ray-tracing model was developed to predict the amount of refraction that photons of different wavelengths would experience when traveling through a nuclear-disturbed environment and the ionosphere regions. The ray-tracing algorithm consists of a discretized atmosphere from the Earth’s surface to an altitude of 400 km using 500 m discretized layers. The constituents and density of the atmosphere are from the US Standard Atmosphere [21]. The natural electron levels of the ionosphere were obtained from the International Reference Ionosphere 2012 model [12,13]. The ray-tracing algorithm simulates a ray propagating (starting at ground level) at a given inclination angle. Snell’s law (Eq. (10)) is applied every time the ray encounters a boundary between discretized layers.
The propagation and refraction of the wave as it transitions between atmospheric layers is simulated. As an example, a ray-tracing graph of signals with various wavelengths in a normal atmosphere (non-nuclear disturbed) with a starting inclination angle of 45 degrees can be seen in Fig. 4.
Fig. 4. Ray tracing schematic of photons with varied wavelengths launched at a 45 degree inclination angle into the atmosphere for an average daytime condition.
The 100 m wavelength actually reflects off of the E region of the ionosphere during normal conditions, whereas the 25 m wavelength (which is typically used for over-the-horizon communications) is significantly refracted and eventually reflected by the F-region. The remaining wavelengths are refracted some but still escape into outer space for normal ionospheric conditions. In the following section, we demonstrate the combination of this ray-tracing algorithm with the nuclear detonation–induced electrons in the atmosphere to evaluate the effects on a range of wavelengths in a nuclear disturbed ionosphere.
3. Results
The MCNP models for the electron generation rates in the atmosphere from a 1-MT detonation at 5, 25, and 75 km HOBs are integrated into Eq. (9) to determine the free electron content in the surrounding atmosphere as a function of time. The MCNP model includes the prompt gamma and neutron free electron generation and the delayed beta particle and delayed gamma-ray free electron generation. The free electron density contours for a 5 km HOB can be seen in Fig. 5 for 15 and 180 s after the detonation.
Fig. 5. Simulation of the free electron density levels ($cm^{-3}$) in the atmosphere from a 1 MT detonation at a 5 km HOB at times of 15 s (left) and 180 s (right) post-detonation.
The high density of the atmosphere at 5 km causes the gamma rays, neutrons, and beta particles to travel only short distances before causing an ionization and being absorbed. In Fig. 5, the extent of the range of the gamma rays is only around 5 km, whereas the beta particles never make it outside of the fireball (bright white spot in Fig. 5). As the fireball and debris cloud rise higher into the atmosphere, the air density decreases such that the gamma rays can travel tens of kilometers before depositing their energy and generating free electrons. Additionally, the higher air density of the low altitudes causes recombination and free electron loss at significantly higher rates than those at higher altitudes. The result is a free electron cold plasma of around $10^3-10^4 ~e/cm^3$ that surrounds the fireball out to a few kilometers at early times up to a minute. As the fireball and debris cloud rise higher in the atmosphere, the free electron plasma extends out to tens of kilometers. The time-dependent electron density 2 km horizontally away from the detonation origin, for a range of different altitudes, can be seen in Fig. 6.
Fig. 6. The time-dependent electron density levels of the atmosphere, 2 km horizontally away from the detonation origin for a 5 km HOB, for a range of different altitudes.
The free electron density in the atmosphere at low altitudes (<10 km) quickly dissipates as the dense lower atmosphere removes the free electrons at a faster rate than they can be produced by the weapon debris. Figure 6 shows that the higher altitudes can support a free electron density for longer times, but there is a time delay in the creation of the electrons. The fireball and weapon debris have to rise out of the dense lower atmosphere and into the low-density high atmosphere to have long-range electron creation and sustainable electron densities in the atmosphere. The high atmosphere (>10 km) experiences sustained electron densities around $10^2$ to $10^3 ~e/cm^3$ for time periods of an hour or more for tens of kilometers surrounding the weapon debris cloud. The sparsity of data points at early times in Fig. 6 is due to the long computation time of running both the CFD code to determine fireball evolution and then using that as input into the radiation transport and plasma models. The selected time steps in the models allow general trends of the data to be understood while reducing the large computing times involved with modeling each time iteration in the scenario. The effects of this atmospheric ionization on different wavelength transmissions, 15 s after detonation, can be seen in Fig. 7. The wavelength transmission was assumed to originate at a horizontal distance of 5 km away from the detonation origin and with a starting inclination angle of 45 degrees.
Fig. 7. Ray tracing schematic of photons with various wavelengths launched at a 45 degree inclination angle into a nuclear-disturbed atmospheric environment (15 s after a 1 MT detonation at a 5 km HOB.
The free electron levels of the cold plasma surrounding the fireball cause photons with wavelengths of 100 m or more to be refracted back to Earth, reducing the operational range of these wavelengths. The 25 m wavelength (over the horizon transmissions) encounters a significant refraction as it propagates through the cold plasma, which could cause range reduction and location error. The fireball region can sustain electron levels of 1$0^8$ or more due to the high temperatures of the air [2]; wavelengths on the order of a meter could be reflected if the transmission intersects with the fireball region.
As the HOB of a nuclear weapon increases, the extent and intensity of the free electron densities in the atmosphere increase. At 25 km HOB, the gamma rays from weapon detonation and the weapon debris travel long distances (hundreds of kilometers) in the atmosphere before dissipating their energy and ionizing the air. Additionally, the high atmosphere is less efficient at removing free electrons, causing elevated cold plasma levels over a wide swath of the upper atmosphere for long periods of time. The free electron densities of the atmosphere from a 25 km HOB detonation (1 MT) can be seen in Fig. 8 for times of 15 s and 180 seconds s the detonation.
Fig. 8. Simulation of the free electron density levels ($cm^{-3}$) in the atmosphere from a 1 MT detonation at a 25 km HOB at times of 15 s (left) and 180 s (right) post detonation.
The highest levels of electron density surrounding the weapon detonation occur in a mushroom shape above the weapon and reach up to around 75 km in altitude. This 60–75 km altitude appears to be a region of maximum free electron density, as the atmosphere density is relatively high enough for significant ionizations, yet the recombination and neutral particle elimination rates are relatively low. Figure 8 shows only the free electron densities created by the nuclear detonation; natural levels were excluded from this graph (the natural levels were added in for the ray tracing graphs) to illustrate the impact from the weapon detonation. Figure 9 shows the time-dependent electron density 10 km horizontally away from the detonation origin for a range of different altitudes.
Fig. 9. The time-dependent electron density levels of the atmosphere 10 km horizontally from the detonation origin for a 25 km HOB, for a range of different altitudes.
The free electrons at higher altitudes have a longer lifetime than at low altitudes due to the diminished recombination and attachment coefficients. The low air density of the upper atmosphere is less efficient at removing electrons via electron neutral particle elimination causing the dominant electron removal method to switch from attachment of electrons to neutral particles to electron-ion recombination. As a result, the free electron densities from 35 km to 75 km hover around the $10^4$ to $10^5 ~e/cm^3$ range for time periods of over an hour. In addition, the large swath of free electrons creates a much larger cross section of atmosphere that could affect the transmission of a wavelength. The effects of the free electron cold plasma created in the upper atmosphere are shown in Fig. 10 for photons with wavelengths ranging from 0.01 m to 100 m.
Fig. 10. Ray tracing schematic of photons with various wavelengths launched at a 45 degree inclination angle into a nuclear-disturbed atmospheric environment (15 s after a 1 MT detonation at a 25 km HOB).
The higher free electron density of the 25 km HOB cold plasma causes photons with wavelengths greater than 25 m to be refracted back to Earth. The 25 m wavelength is typically used for over-the-horizon communications; thus, this would disrupt these types of communications by prematurely reflecting the wave back to Earth. The 10 m signal wavelength is also significantly refracted by the cold plasma, which can cause location and operation errors. Figure 10 assumes that the transmission originates at a horizontal distance of 25 km away from the detonation origin and with a starting inclination angle of 45 degrees (transmission passes outside of the fireball region). If a signal wavelength were to intersect the fireball region, then the wavelengths reflected would be on the scale of 1 m as the fireball region typically has a couple orders of magnitude larger free electron densities due to the higher temperatures of the air and short travel range of the beta particles. Both Fig. 8 and 10 assumed a 45 degree inclination angle of propagation, but the inclination angle also has an impact on which signal wavelengths are refracted. This effect is discussed in more detail in the next section.
For a detonation at 75 km HOB, the low density of the surrounding atmosphere causes the free electron densities at altitudes lower than the detonation point to be the highest because the radiation emitted from the weapon must travel down toward the Earth to interact with the atmosphere. Consequently, the free electron levels are the highest for this HOB due to the high radiation flux in a zone that has just enough air to cause widespread ionization while also having a minimal amount of air to inhibit electron removal. The free electron densities of the atmosphere from a 75 km HOB detonation (1 MT) can be seen in Fig. 11 for a time of 15 s after the detonation. At the higher altitude, the weapon-induced cold plasma swath is also much larger as a result of increased gamma ray propagation than that at the 5 and 25 km HOBs. Electron densities on the order of $10^5-10^6 ~e/cm^3$ reach out in all directions for hundreds of kilometers and from an altitude of 50 to 100 km.
Fig. 11. Simulation of the free electron density levels ($cm^{-3}$) in the atmosphere from a 1 MT detonation at a 75 km HOB at a time of 15 s post detonation.
The higher density of electrons combined with the extremely large swaths of the atmosphere that they inhabit create a harsh environment for EM signal propagation. In Fig. 12, the effects of the free-electron cold plasma on the propagation of wavelengths ranging from 0.01 m to 100 m are shown. The cold plasma that surrounds the fireball and weapon debris is dense enough to reflect wavelengths of 10 m and larger while causing a large refraction for wavelengths around 1 m. Figure 12 is for a trajectory that originates 25 km horizontally out from the detonation origin and at an initial inclination angle of 45 degrees (ray passes underneath the fireball); propagating through the fireball would result in 10 cm wavelengths being reflected and a refraction of 1 cm wavelengths.
Fig. 12. Ray tracing schematic of photons with various wavelengths launched at a 45 degree inclination angle into a nuclear-disturbed atmospheric environment (15 s after a 1 MT detonation at a 75 km HOB.
The cold plasma from a 75 km HOB would have a longer duration than that from a 25 km HOB (see Fig. 10), but there is a unique phenomenon that occurs at bursts in the altitude region of 50–100 km that can change the free electron levels in a different way. Nuclear detonations with a HOB between 50 and 100 km create dense fireballs that rise ballistically into the upper atmosphere [22]. At low altitudes (<50 kms), the fireball is under-dense and rises buoyantly in the atmosphere (the buoyant rise of the fireball creates a toroidal cloud, or mushroom cloud). The ballistic fireball rise at higher altitudes creates a shockwave in the upper atmosphere as the debris cloud travels upward at supersonic speeds into the upper atmosphere [22,23]. This creates a shockwave that propagates through the upper atmosphere and was seen during an historic US nuclear test, Hardtack Teak (see Fig. 13). The Hardtack Teak test had a HOB of 76.8 km and the shockwave created a red aura around the fireball (the red airglow seen in Fig. 13) as it passed through the upper atmosphere of the Pacific and over the observers (who took the photo) in Hawaii over 700 miles away [1,24].
Fig. 13. (Left) COMSOL simulation of the thermal contours of a nuclear fireball for a 1 MT detonation at a HOB of 50 km (75 seconds post-detonation). (Right) Picture of the fireball and airglow from the historic nuclear detonation Teak from an observer 700 miles away on Hawaii (image is from public domain and not subject to copyright) [1,24].
COMSOL simulations of a 75 km HOB detonation show a similar trend in which a shockwave forms in the atmosphere from the ballistic rise of the fireball (Figs. 13 and 14). The momentum from the rising fireball draws air from the lower atmosphere upwards causing the atmosphere to “heave upward” [23]. In Fig. 14, the colder, denser air (the purple color) from lower altitudes is drawn upward to form this atmospheric “heave.” This impacts the ionosphere, as the free electrons and surrounding air are taken upward with the shockwave, with lower electron density air replacing it. Essentially, a detonation at this altitude blows a hole in the ionosphere, as the electron levels are reduced by the heaving upward of denser, lower electron content air. Communications systems that rely on ionospheric reflection are degraded or experience blackout due to this effect. This was reported in the Teak test: an initial increase in the ionosphere was initially detected, followed by a dramatic decrease in the electron density. This decrease in electron density caused a radio blackout over the Pacific that spanned over 1,000 miles and lasted until sunrise [1,2]. For bursts between 50 km and 100 km, the electron density is elevated initially (as seen in Fig. 11) but will become electron-depleted as the rising fireball heaves the lower, less electron-dense atmospheric air upward through the E and F Region of the ionosphere. Various photon wavelengths propagating near the detonation will initially be reflected by the nuclear-induced cold plasma; however, as the shockwave propagates upward, an instability in the ionosphere will develop, which will cause photon wavelengths that traditionally reflect off the ionosphere to be lost or reflected at a significantly higher altitude. For detonations above 100 km, the electron density levels will look similar to that of the 75 km HOB but the high-altitude shockwave will not be an issue. Thus, these nuclear-induced electron levels will remain elevated and for long periods of time before recombination and removal. In conclusion, the higher the altitude of the detonation, the higher the electron densities and larger swaths of atmosphere they will inhabit (except for detonations between 50 and 100 km).
Fig. 14. COMSOL simulation of the thermal contours (left) and temperature map (right) of the upper atmosphere from the ballistic shockwave caused by the rising fireball from a 1 MT detonation (180 seconds post-detonation).
The simulations in this section should be regarded as a first-order approximation. Experimental validation of these models is not possible due to the lack of experimental data on the free electron generation rates from a nuclear detonation in the literature. The atmospheric nuclear weapon test reports from the 1950s and 1960s [2] simply remarked on the effects on their equipment from the detonations; free electron generation rates were not physically measured. Nevertheless, even though our results constitute a first-order approximation, it is important for them to be documented in the peer-reviewed literature. Future work to improve on these models (aside from nuclear testing and adding more time steps in the models), should focus on better understanding the free electron recombination at all altitudes of the atmosphere.
4. Discussion
In the previous section, ray traces of photons with different wavelengths transmitted through the atmosphere at an inclination angle of 45 degrees were shown, but the angle of inclination also plays an important role in the refraction and reflection of EM signals in a nuclear-disturbed environment. The level of refraction a signal experiences is a function of not only the frequency-dependent indices of refraction of adjacent media, but the angle relative to normal at which the wave encounters the layer boundary (Snell’s Law, see Eq. (10)). In Fig. 15, a graph of the maximum usable wavelength for atmospheric transmission (the smallest wavelength that will not reflect off of the ionosphere) is shown as a function of the electron concentration and inclination angle.
Fig. 15. The maximum usable wavelength for atmospheric transmission (smallest wavelength that will not be reflected in units of meters) as a function of the electron concentration and inclination angle.
The incident angle is a measured relative to the horizon, with 90 degrees amounting to the zenith. For inclination angles of less than 15 degrees, wavelengths down to 0.1 m can be reflected by 25 and 75 km HOB detonations. In contrast, for inclination angles over 75 degrees, wavelengths of 100 m or more may not be reflected by the cold plasma formed by a lower altitude detonation (5 km HOB). This manuscript analyzes only the refractive index dependent behavior of EM signals propagating through a nuclear-disturbed environment. However, there are other effects on EM wave propagation from the nuclear-induced cold plasma such as attenuation, dispersion, group delay, and Faraday rotation that can occur to a propagating EM wave. We leave this as future work.
In systems that are affected by a nuclear-disturbed atmosphere, the VHF (1–10 m), HF (10–100 m), MF (100–1000 m), and LF bands (1–10 km) will be the most affected. For low-altitude detonations (5 km HOB), the LF band (AM longwave, navigation) and MF band (AM radio) could be affected from the low-altitude reflection of the wave off of the cold plasma surrounding the detonation, causing a degradation in the maximum transmission range of the signal. The extent of the cold plasma is limited to around 10 km at low altitudes (<5 km HOB), so this effect will be rather localized. For higher altitude bursts (25 km HOB) or after the fireball and debris cloud have risen to higher altitudes, the cold plasma is larger in both the vertical and horizontal directions, potentially extending up to hundreds of kilometers horizontally. This large swath of cold plasma can cause widespread communications degradation. In addition, at 25 km HOB, the HF frequency bands (over-the-horizon radio, radar, communications, etc.) are reflected by the cold plasma surrounding the detonation, causing location and range error for over-the-horizon signals. The VHF band (FM radio, television broadcasts, line-of-sight communications) can also experience significant refraction and reflection for bursts at 25 km HOB, causing communications to degrade for up to an hour or more. Detonations from 50 to 100 km will at first cause reflection of VHF waves, but as the shockwave creates an instability in the ionosphere, reflections of the MF and LF wavelengths will degrade, causing a blackout of these signals (duration depends on whether it is day time or night time, as solar activity will repopulate the ionosphere and atmospheric transport processes disperse and mix the cold plasma). For bursts above 100 km, the elevated electron densities will remain and will cause issues with VHF, along with severe refraction of UHF signals (television broadcasts, mobile phones, GPS). Finally, if a signal intercepts the fireball region, then UHF and even some SHF signals could be reflected or severely refracted. In summary, low-altitude detonations will cause localized effects to HF through MF bands for a few minutes, whereas higher altitude detonations can affect signals with wavelengths down to VHF and potentially UHF bands over large swaths of atmosphere (hundreds of kilometers), persisting for multiple hours.
5. Conclusions
An atmospheric nuclear detonation can produce heightened free electron densities in the surrounding atmosphere that can disrupt EM waves that propagate through the disturbed region. The free electron plasma surrounding the detonation depends on the HOB of the weapon, the weapon yield, and the time after detonation. Detonations at higher altitudes produce higher electron densities for greater durations and over larger ranges. For low-altitude bursts (5 km HOB), the cold plasma is localized within 10 km of the detonation point and will affect only MF and LF bands. Higher altitude bursts (25 km HOB) will create a cold plasma swath ranging from tens to hundreds of kilometers. The free electron levels induced by these high-altitude bursts can affect VHF and higher frequency bands. Bursts between 50 and 100 km will initially elevate the electron levels, but a decrease will soon follow due to atmospheric “heave” caused by the high-altitude shockwave. Finally, propagation through the actual fireball or weapon debris cloud can result in refraction and reflection of wavelengths down to 1 cm.
Funding
Defense Threat Reduction Agency (HDTRA1-93-1-201).
Acknowledgments
This work was supported by Defense Threat Reduction Agency Award HDTRA1-93-1-201.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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