The indirect effects of a nearby lightning strike on an airborne vehicle with its long trailing conducting plume is not well understood. Since airborne vehicles and its payload are expensive, their loss as a result of either a direct strike or due to the induced current and voltage of a nearby lightning strike is not desirable. The electromagnetic field generated due to the induced current on the skin of the vehicle may get coupled with the internal circuitry through the apertures on the vehicle body. If the coupled electromagnetic energy is more than the damage threshold level of the sensitive devices of the control circuit, they may fail which may lead to aborting the mission or a possible degradation in the vehicle performance. It has been reported that lightning induced phenomena was the cause of malfunctioning as well as aborting of some of the lunar missions. So in the present work, the computation of induced current and voltage on the skin of the vehicle body in the presence of an ionized long trailing exhaust plume has been attempted. The lightning channel is assumed to be vertical to the ground plane and extends up to a height of 7.5 km. The radiated electric and magnetic fields from the lightning channel at different heights from 10 m to 10 km and for lateral distances varying from 20 m to 10 km from the lightning channel are computed and the field waveforms are presented. For the computation of the radiated electric and magnetic fields from the lightning channel, modified transmission line with exponential current decay (MTLE) model for representing the lightning channel and the Heidler’s expression for the lightning channel base current are used. The peak amplitude of the lightning current used is 12 kA with a maximum current derivative of 40 kA/µs. It is seen that the vertical electric field in general, is bipolar in nature and that the height at which the change in polarity reversal takes place increases with increase of lateral distance from the lightning channel. The vertical electric field just above the ground is unipolar for all lateral distances from the channel and this is because the contribution due to the image of the lightning channel dominates the vertical electric field. The horizontal electric field is always unipolar for all heights and all lateral distances from the lightning channel studied. The effect of variation in the rate of rise of lightning current (di/dt) and the velocity of lightning current on the radiated electric and magnetic fields for the above heights and distances have also been studied. It is seen that the variation in maximum current derivative does not have a significant influence on the electric field when ground is assumed as a perfect conductor but it influences significantly the horizontal electric field when ground has finite conductivity. The velocity of propagation of lightning current on the other hand has a significant influence for both perfectly as well as finitely conducting ground conditions. For the computation of the induced current and voltage on the body of the airborne vehicle due to the coupling of the above mentioned electromagnetic fields radiated from a near by lightning discharge, the vehicle and its exhaust plume have been modeled as a transmission line and Finite Difference Time Domain (FDTD) numerical technique has been used for the computation. Regardless of the vehicle size, the structure can be modeled as a nonuniform transmission line consisting of a series of sections consisting of capacitive and inductive components. These components of the vehicle and its exhaust plume are computed using the Method of Moment (MoM) technique. The interaction of the electromagnetic wave with the plume depends on the electrical conductivity as well as the gas dynamic characteristics of the plume. Hence, in this research work an attempt has also been made to study the electrical conductivity (σe) and permittivity (εe) as well as the gas dynamic properties of the exhaust plume taking into consideration its turbulent nature. In general, the airborne vehicle can be considered as perfectly conducting (conductivity 3x107 S/m) where as the plume has finite conductivity. The electrical properties of an airborne vehicle exhaust plume such as electrical conductivity and the permittivity and their distribution along axial and radial directions depend on several factors. They are (i) propellant composition, (ii) impurity content in the propellants which generate ionic charge particles in the exhaust and (iii) the characteristics of the exhaust plume intensive parameters such as temperature, pressure, velocity and the presence of shock waves. These properties of the exhaust plume are computed in the two separate regions of interest as discussed next. The first region is inside the combustion chamber and up to the nozzle throat of the vehicle and the second region is from the throat to the exterior i.e., the ambient atmosphere or the downstream of the plume. In the first region where chemical reaction kinetics have to be considered, NASA Chemical Equilibrium with Application (CEA) software package has been used to compute the intensive parameters of the fluid at the throat of the nozzle. The pressure in the combustion chamber is taken as 4410 kPa and the back pressure at the exit plane is taken as 101.325 kPa. In the second region, FLUENT software package have been used for the fluid dynamic study of the exhaust plume from the vehicle nozzle throat to the exterior domain. The data obtained from the first region using CEA provides the parameters at the nozzle throat that are used as input parameters for the second region. In the study, a conical nozzle configuration of throat radius (rt) of 0.0185 m (nozzle exit plane radius is 0.05 m), half cone angle of 18º and nozzle expansion ratio (Ae/At) of 7.011 are used. The contour plot of the intensive parameters of the exhaust plume and the mass fraction of the charged particles are presented. The vehicle exhaust flow passes through different types of expansion and compression waves. In the present work, simulation is done for a slightly under expanded nozzle i.e. nozzle exit static pressure is slightly more than the ambient static pressure. Since the exit pressure is more than the ambient pressure, the exhaust gases expand to reach the ambient pressure. As the expansion waves reach the contact discontinuity (i.e. the boundary where the outer edge of the gas flow meets the free stream air), they again reflect back inward to create compression waves. These compression waves force the flow to turn back inward and increase its pressure. If the compression waves are strong enough, they will merge into an oblique shock wave. In the present work, more than eight such barrel shocks are captured. When the shock waves are generated, Mach number reduces sharply and static temperature and static pressure increases where as the total temperature of the exhaust remains constant in the shock wave formations. The characteristics of the plume such as pressure, temperature, velocity and concentration of the charged particles (i.e., e¯, Na+ and Cl¯) and neutral species such as CO, CO2 , Cl, H, HCl, H2O, H2 , N2, Na, NaCl, O, OH and O2 along axial and radial directions in the external domain have been studied. The above parameters are used to compute the collision frequencies and plasma frequencies of the charged particles as well as the number density of the species along axial and radial directions of the exhaust plume. These parameters are used to compute the effective conductivity distribution in the axial and radial directions for an incident electromagnetic field of frequency 1 MHz. The peak value of the conductivity computed is 0.12 S/m near the exit plane and it reduces to 0.02 S/m at an axial distance of 7.5 m from the exit plane which is well within the range suggested in the published literature. It has been observed that the oscillation in the conductivity along axial direction is a reflection of the shock wave formation in the exhaust plume. The electrical conductivity and the relative permittivity of the exhaust plume have been computed for three different radii of the nozzle at the exit plane i.e., 0.025 m, 0.05 m and 0.075 m. It is seen that the distribution of the conductivity and relative permittivity along the axial direction of the exhaust are independent of the nozzle exit plane radius. To study the coupling of lightning electromagnetic field with the vehicle and its exhaust plume two cases have been considered. These are (i) when the vehicle and its exhaust plume are at certain height above the ground and (ii) when the exhaust plume is touching the ground. The dimensions of the vehicle used in the study are as follows: length of the vehicle is 20 m and the length of its exhaust plume is 75 m. The radius of the vehicle is taken as 0.5 m. The vehicle and its exhaust plume are assumed to be at a lateral distance of 250 m from the lightning channel. In case one, when the vehicle and its inhomogeneous exhaust plume tip is at a height of 10 m above the ground, both the ends are open. So the reflection coefficients of the current wave and voltage wave at the end points are -1 and +1 respectively irrespective of the characteristic impedances of the vehicle and its exhaust plume. So when the reflected current propagates it will tend to reduce along the length of the object. Hence, the induced current at the end points are zero and the currents in the end segments are less than those in the intermediate segments. The spatial distribution of the peak magnitude of the time varying induced current, |Imax|, in each segment along the length of the vehicle without and with the exhaust plume are presented. In case of vehicle without plume, the maximum value of the induced current is at the middle segment of the vehicle and its value is 4.8 A. The presence of the inhomogeneous plume enhances the maximum value of the induced current to 33 A and its position is shifted to the exhaust plume side. When the voltage wave propagates, it will enhance the induced voltage in the vehicle body. The time varying potential difference between the end points of the vehicle without plume and the vehicle with its exhaust plume which drives the induced current are computed and it is seen that the potential difference for the vehicle without plume is unipolar whereas it is bipolar for the vehicle with exhaust plume. The lightning induced current on the skin of the vehicle will generate an electromagnetic field which may couple with the internal electronic devices and circuits through the apertures. The amount of electromagnetic energy that will be transmitted through an aperture on the vehicle skin and coupled with the internal electronic equipments depends on the characteristics of the induced current on the skin of the vehicle, the electrical size, shape, orientation and location of the aperture and the location of the internal electronic devices with respect to the aperture. So the time varying induced current and its di/dt at three different locations on the vehicle body i.e., tail of the vehicle, middle of the vehicle and vehicle nose are computed. It is seen that the induced current on the vehicle and its di/dt in the absence of the plume are oscillating in nature but they are critically damped in the presence of the trailing inhomogeneous exhaust plume. It also shows that the enhancement of induced current and its di/dt at the tail are much more than at the middle or at the nose of the vehicle which is true for an electrically short vehicle i.e., lv/λmin ≈ 0.067 as cited in the literature. So the presence of an aperture on the skin of the vehicle near to tail will transmit maximum electromagnetic energy into the inside of the vehicle. Therefore during design of the electrically short airborne vehicles, any aperture should be avoided near the tail of the vehicle or internal electronic devices should be placed away from the tail of the vehicle. In case 2, when the plume is touching the ground, the transient induced current in the plume will propagate into the soil. The effective impedance for smaller currents will be quite high (the inductance and capacitance effect are not taken into consideration for calculating the impedance. So the impedance of the soil is dominated by only the resistance). However, as soon as the current exceeds a certain value, the resulting soil gradient can reach the breakdown gradient of the soil i.e., 200-500 kV/m as cited in literature resulting in soil ionization. This will effectively lower the soil impedance. These dynamic characteristics of the soil resistance with induced current are incorporated by considering the expression for the soil resistance. To study the effect of soil resistivity on the time varying induced current and the voltage, computations have been done for various resistivities of the soil i.e., 0 Ωm, 100 Ωm and 200 Ωm. For soil resistivity of 0 Ωm, the reflection coefficients at the ground and at the open ends for the current wave are +1 and -1 respectively. So at the ground end, the reflected current wave will enhance and at the open end it will diminish as it propagates along the length of the vehicle and its exhaust. As the resistivity of the soil increases, the reflection coefficient of the current at the ground end decreases from +1, so the peak magnitude of the current reduces along the length till the length is half of the total length of the plume and the vehicle. Therefore, the peak magnitude of the induced current in the ground segment is much more than the peak magnitude of the current in the segment at the open end. For a finitely conducting plume, the peak value of the potential difference between the two ends of the vehicle and its exhaust plume are 92 kV, 91 kV and 90 kV for soil resistivities of 0 Ωm 100 Ωm and 200 Ωm respectively. Therefore the influence of the soil resistivity on the induced current is found to be not much significant. The spatial distribution of the peak magnitude of the time varying induced current in each segment along the length of the vehicle with inhomogeneous exhaust plume for the above three different soil resistivities are presented at a lateral distance of 250 m from the lightning channel. It is seen that when the plume is touching the ground, the induced current on the vehicle at the tail, middle and nose sections are marginally more than when the vehicle and its exhaust are at a height of 10 m above the ground. The effects of different parameters such as peak value and maximum di/dt of lightning current, velocity of lightning current, lateral distance of the vehicle from lightning channel and the height of the tip of the exhaust plume above the ground on the induced current and voltage on the airborne vehicle have also been studied. The peak amplitude of the lightning current used are 30 kA and 100 kA in addition to 12 kA mentioned earlier for the field computation. Also maximum di/dt values of 40 kA/µs and 120 kA/µs for the lightning current have been used for the computation. It is observed that the induced current increases with increase of the peak value, maximum di/dt as well as the velocity of propagation of the lightning current where as the induced current will reduce with increase of lateral distance and height of the tip of the exhaust plume above the ground. As an offshoot of the present work, the axial and radial distribution of the parameter, σe/ωεe (loss tangent of the exhaust plume) for an incident electromagnetic wave (lightning electromagnetic field) frequency of 1 MHz have been computed to study the conducting properties of the exhaust plume. σe/ωεe of the exhaust plume at 1 MHz frequency varies from 2324 to 365. Since σe/ωεe >>1, the plume behaves as a good conductor and the displacement currents can be neglected. In addition to this, the variation of parameter σe/ωεe for frequency ranges of 0.1 MHz to 5 GHz are also studied where σe and εe are the maximum effective conductivity and permittivity of the exhaust plume at the chosen frequency of an incident EM wave. It shows that the parameter σe/ωεe is 1.8x104 at 0.1 MHz and reduces to 0.45 for 5 GHz and its value is 1 at a frequency of 2.285 GHz. Therefore at lower EM wave frequency, the exhaust plume behaves as a good conductor and that conductivity reduces with increase of the frequency. The exhaust plume in the present study behaves as a good conductor below or at the EM wave frequency of 2.285 GHz. The microwave attenuation of electromagnetic wave through the ionized plume (the angle of incidence of microwave is 90o and transmission of microwave is always transverse to the exhaust plume) has also been studied using the above electrical characteristics computed and it is seen that the attenuation follows the axial variation in the conductivity of each cross section of the plume. In the present work, a theoretical model has also been developed to compute the microwave attenuation through the vehicle exhaust plume using the electrical conductivity computed earlier for any angle of incidence of the microwave. The thesis also lists some additional topics for further studies.

Society’s dependence on electronic and electrical systems has increased rapidly over the past few decades, and people are relying more and more on these gadgets in their daily life because of the efficiency in operation which these systems can offer. This has revolutionized many areas of electrical and electronics engineering including power sector, telecommunication sector, transportation and many other allied areas. With progress in time, the sophistication in the systems also increased. Also as the systems size reduced from micro level to nano level, the compactness of the systems increased. This paved the way for development in the digital electronics leading to new and efficient IC 0s that came into existence. Power sector also faced a resurge in its technology. Most of the analog meters are now replaced by digital meters. The increased sophistication and compactness in the digital system technology made it susceptible to electromagnetic interference especially from High Power Electromagnetic Sources. Communication, data processing, sensors, and similar electronic devices are vital parts of the modern technological environment. Damage or failures in these devices could lead to technical or financial disasters as well as injuries or the loss of life. Electromagnetic Interference (EMI) can be explained as any malicious generation of electromagnetic energy introducing noise or signals into electric and electronic systems, thus disrupting, confusing or damaging these systems. The disturbance may interrupt, obstruct, or otherwise degrade or limit the effective performance of the circuit. These effects can range from a simple degradation of data to a total loss of data. The source may be any object, artificial or natural, that carries rapidly changing electrical currents, such as an electrical circuit. The sources of electromagnetic interference can be either unintentional or intentional. The sources producing electromagnetic interference can be of different power levels, different frequency of operation and of different field strength. One such classification of these sources are the High Power Electromagnetic Sources (HPEM) High Power Electromagnetic environment refers to sources producing very high peak electromagnetic fields at very high power levels. These power levels coupled with the extremely high magnitude of the fields are sufficient to cause disastrous effects on the electrical and electronic systems. There has been a lot of developments in the field of the source technology of HPEM sources so that they are now one of the strongest sources of electromagnetic interference. High Power Electromagnetic environment refers to the sources producing very high peak electromagnetic fields at very high power levels. These power levels coupled with the extremely high magnitude of the fields are sufficient to cause disastrous effects on the electrical and electronic systems. HPEM environments are categorized based on the source characteristics such as the peak electric field, often called threat level, frequency coverage or bandwidth, average power density and energy content. The sources of electromagnetic interference can be either unintentional or intentional. Some examples of unintentional sources are the increased use of electromagnetic spectrum which generates disturbance to various systems operating in that frequency band, poor design of systems without taking care of other systems present nearby as well as lightning. Intentional sources are High altitude Electromagnetic Pulse (HEMP) or Nuclear Electromagnetic Pulse (NEMP) due to nuclear detonations, Ultra Wide Band (UWB) field from Impulse Radiating Antennas (IRA), Nar-row band fields like those coming from High Power Microwaves (HPM), High Intensity Radio Frequency (HIRF) sources. Of these the lightning is natural and all other sources are man-made. The significant progress in the Intentional High-Power Electromagnetic (HPEM) sources and antenna technologies and the easy access to simple HPEM systems for anyone entail the need to determine the susceptibility of electronic equipment as well as coupling of these fields with systems such as cables (buried as well as aerial), airborne vehicle etc. to these types of threats. Buried cables are widely used in the communication and power sectors due to their efficient functioning in urban cities and towns. These cables are more prone to electromagnetic interferences from HPEM sources. The buried communication cables or even the buried data cables are connected to sensitive equipments and hence even a slight rise in the voltage or the current at the terminals of the equipments can become a serious problem for the smooth operation of the system. In the first part of the thesis the effect of the electromagnetic field due to these sources on the cables laid underground has been studied. The second part of this thesis deals with the study of the interaction of the EM field from the above mentioned HPEM sources with an airborne vehicle. Airborne vehicle and its payload are extremely expensive so that any destruction to these as a result of the voltages and currents induced on the vehicle on account of the incoming HPEM fields can be quite undesirable. The incoming electromagnetic fields will illuminate the vehicle along its axis which results in the induction of currents and voltages. These currents and voltages will get coupled to the internal control circuits that are extremely sensitive. If the induced voltage/ current magnitude happen to be above the damage threshold level of these circuits then it will result in either a malfunction of the circuit or a permanent damage of it, with both of them being detrimental to the success of the mission. This will even result in the abortion of the mission or possible degradation of the vehicle performance. Hence it is worthwhile to see what will be the influence of an incoming HPEM electromagnetic field on the airborne vehicle with and without the presence of an exhaust plume. In this work, the HPEM sources considered are NEMP, IRA and HPM. The electromagnetic fields produced by the EMP can induce large voltage and current transients in electrical and electronic circuits which can lead to a possible malfunction or permanent damage of the systems. The electric field at the earth 0s surface can be modelled as a double exponential pulse as per the IEC standard 61000-2-9. The NEMP field incident on the earth’s surface is considered as that coming from a source at a distance far away from the earth’s surface; hence a plane wave approximation has been used. Impulse radiating antennas are the ones that are used as the major source of ultra wide band radiation. These are highly powerful antennas that use a pulsed power source as the input and this power source is conditioned to get an extremely sharp rise time pulse. These antennas are very high power antennas that are capable of producing a significant electromagnetic field. Impulse radiating antenna is a paraboloidal reflector and hence is an aperture antenna. Initially the radiated field due to this aperture needs to be found out at any observation point from the antenna. In this thesis, the aperture distribution method is used to accurately determine the field due to the aperture. In this method the field reflected from the surface of the reflector is first found on an imaginary plane through the focal point of the reflector that is normal to the axis of the reflector, by using the principles of geometrical optics, which then is extended to the observation point. The IRA considered for the present work is the one of the most powerful IRA as per the published literature available in the open domain. This has an input voltage of 1.025 MV. The far field electric field measured at the boresight (at r =85 m) being equal to 62 kV/m, and the uncorrected pulse rise time (10%-90%) is 180 ps for this IRA. HPM sources are usually electromagnetic radiators having a reflector with a horn antenna kept at their focal point for excitation. HPM sources generally operate in single mode or at tens or hundreds of Hz repetition rates. Many HPM radiators are developed in the world each with their own peculiar geometry and power levels. In the present thesis, a single waveguide (WR-975) fed HPM antenna assembly has been studied. The chosen waveguide has a cut-o_ frequency of 1 GHz and a power level of 10 GW. The wavelength associated with the waveguide is 0.3 m. The field pattern shows a definite peak in its response when the frequency is 1 GHz, the cut-off frequency of the waveguide. The electric field coming out of the HPEM sources travel through the medium that is either air alone or a combination of air and soil respectively depending upon whether the circuit on which the coupling is analysed is an airborne vehicle or an underground cable. The media plays a major role in the coupling, as the field magnitude is influenced by the characteristic properties of the media. As height increases the magnitude of the electric field decreases for all types of sources and also the time before which the field waveform starts is increased. The electric field in the soil is decided by the soil properties such as its conductivity and permittivity. The soil is modelled in frequency domain and the high frequency behaviour of soils is considered with its conductivity and permittivity taken as functions of frequency, as the incident field has high frequency components. A soil medium can be electromagnetically viewed as a four component dielectric mixture consisting of soil particles, air voids, bound water, and free water. When electric field is incident on the soil, it gets polarized. This is as a result of a wide variety of processes, including polarization of electrons in the orbits around atoms, distortion of molecules, reorientation of water molecules, accumulation of charge at interfaces, and electrochemical reactions. Whatever is the HPEM source, an increase in the soil conductivity results in an increased attenuation of the field. Also there is a significant loss of high frequency components in the GHz range in the field due to the selective absorption by the soil. This effect causes the percentage attenuation to be maximum for HPM and minimum for NEMP and IRA lying in between these two extremities. Increase in permittivity of the soil causes attenuation of the electric field for all HPEM sources. This is due to the relaxation mechanisms in the soil due to atomic- or molecular-scale resonances. The coupling of the electromagnetic fields due to HPEM sources is considered in the first phase. Two cables are considered (i) buried shielded and (ii) buried shielded twisted pair cables. The results are arrived at using the Enhanced Transmission Line model. The induced current is more for a shielded cable than a twisted pair cable of the same configuration. The induced current magnitude depends upon the type of the HPEM source, the depth of burial of the cable and the point on the cable where the current/ voltage is computed. Current is maximum at the centre of the cable for a matched termination and the voltage is the minimum at this point. The ratio of the induced current in the inner conductor with respect to the shield current of a shielded cable is the least for an HPM, and maximum for NEMP. This is due to the fact that higher frequencies are absorbed more by the shield of the cable. This affects HPM induced current the maximum and NEMP the least because of the presence of the lower frequency components in NEMP. Induced current in the twisted pair cable depends upon the number of pairs of the cable and the pitching of the cable. The electromagnetic field from the HPEM sources propagates with less attenuation in air due to the lower resistance this medium offers for electromagnetic wave propagation. Hence any system in air, be it electrical or electronic, will be under the strong illumination by these electromagnetic fields. As the second part of this thesis, the influence of the electromagnetic fields from all the three HPEM sources on an airborne vehicle in flight is analysed. For this part of study, the Electromagnetic (EM) fields radiated by all the three sources at different heights from the earth 0s surface have been computed. The coupling study has been done for the case of a vehicle with plume as well as without plume. For the second case, the electromagnetic modelling of the plume has been done taking into consideration its conductivity, which in turn depends on the different ionic species present in the plume. The species of the exhaust plume depends upon the chemical reactions taking place in the combustion chamber of the nozzle of the vehicle. The presence of the alkali metals as impurity in the airborne vehicle propellant will generate considerable ion particles such as Na+, Cl in addition to e- in the plume mixture during combustion which makes the plume electrically conducting. But it does not influence the pressure, temperature and velocity of the plume. After the nozzle throat, the exhaust plume regains the supersonic speed, so the flow of the exhaust plume is assumed as compressible flow in the second region. The electrons have high collision frequency, high number density, high plasma frequency and lower molecular mass and hence the highly mobile electrons dominate the heavy ion particle in the computation of the electrical conductivity of the plume. The plume conductivity decreases marginally from the axis till a distance equal to the nozzle radius but the peak value increases sharply towards the exit plane edge of the nozzle radius. The induced current is computed using Method of Moments. The induced current depends upon the type of interference source, its characteristics, whether the plume is present or not and the type of the plume. The HPM induces maximum current in the vehicle because of the fact that the plume has a tendency to become more conductive at these frequencies. The induced currents due to the EM fields from IRA and NEMP comes after the HPM. The presence of the plume enhances the magnitude of the induced current. If the plume is homogeneous then the current induced in it is more.