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Manipulating strong electromagnetic fields with the average transverse momentum of relativistic nuclear collisions
Abstract We show that an event-shape engineering based on the mean transverse momentum of charged hadrons, $$[p_t]$$ [ p t ] , provides an optimal handle on the strength of the magnetic field created in central heavy-ion collisions at high energy. This is established through quantitative evaluations of the correlation existing between the event-by-event magnetic field produced by the spectator protons in 5.02 TeV Pb + Pb collisions and the event-by-event $$[p_t]$$ [ p t ] at a given collision centrality. We argue that the event selection based on $$[p_t]$$ [ p t ] provides a better handle on the magnetic field than the more traditional selection based on the event ellipticities. Advantages brought by this new method for the experimental search of the chiral magnetic effect are discussed.
High-Density Signal Interface Electromagnetic Radiation Prediction for Electromagnetic Compatibility Evaluation
Radiated power calculation approaches for practical scenarios of incomplete high- density interface characterization information and incomplete incident power information are presented. The suggested approaches build upon a method that characterizes power losses through the definition of power loss constant matrices. Potential radiated power estimates include using total power loss information, partial radiated power loss information, worst case analysis, and statistical bounding analysis. A method is also proposed to calculate radiated power when incident power information is not fully known for non-periodic signals at the interface. Incident data signals are modeled from a two-state Markov chain where bit state probabilities are derived. The total spectrum for windowed signals is postulated as the superposition of spectra from individual pulses in a data sequence. Statistical bounding methods are proposed as a basis for the radiated power calculation due to the statistical calculation complexity to find a radiated power probability density function.
3D modeling of deep borehole electromagnetic measurements with energized casing source for fracture mapping at the Utah Frontier Observatory for Research in Geothermal Energy
Here, we present a 3D numerical modelling analysis evaluating the deployment of a borehole electromagnetic measurement tool to detect and image a stimulated zone at the Utah Frontier Observatory for Research in Geothermal Energy geothermal site. As the depth to the geothermal reservoir is several kilometres and the size of the stimulated zone is limited to several 100 m, surface-based controlled-source electromagnetic measurements lack the sensitivity for detecting changes in electrical resistivity caused by the stimulation. To overcome the limitation, the study evaluates the feasibility of using a three-component borehole magnetic receiver system at the Frontier Observatory for Research in Geothermal Energy site. To provide sufficient currents inside and around the enhanced geothermal reservoir, we use an injection well as an energized casing source. To efficiently simulate energizing the injection well in a realistic 3D resistivity model, we introduce a novel modelling workflow that leverages the strengths of both 3D cylindrical-mesh-based electromagnetic modelling code and 3D tetrahedral-mesh-based electromagnetic modelling code. The former is particularly well-suited for modelling hollow cylindrical objects like casings, whereas the latter excels at representing more complex 3D geological structures. In this workflow, our initial step involves computing current densities along a vertical steel-cased well using a 3D cylindrical electromagnetic modelling code. Subsequently, we distribute a series of equivalent current sources along the well's trajectory within a complex 3D resistivity model. We then discretize this model using a tetrahedral mesh and simulate the borehole electromagnetic responses excited by the casing source using a 3D finite-element electromagnetic code. This multi-step approach enables us to simulate 3D casing source electromagnetic responses within a complex 3D resistivity model, without the need for explicit discretization of the well using an excessive number of fine cells. We discuss the applicability and limitations of this proposed workflow within an electromagnetic modelling scenario where an energized well is deviated, such as at the Frontier Observatory for Research in Geothermal Energy site. Using the workflow, we demonstrate that the combined use of the energized casing source and the borehole electromagnetic receiver system offer measurable magnetic field amplitudes and sensitivity to the deep localized stimulated zone. The measurements can also distinguish between parallel-fracture anisotropic reservoirs and isotropic cases, providing valuable insights into the fracture system of the stimulated zone. Besides the magnetic field measurements, vertical electric field measurements in the open well sections are also highly sensitive to the stimulated zone and can be used as additional data for detecting and imaging the target. We can also acquire additional multiple-source data by grounding the surface electrode at various locations and repeating borehole electromagnetic measurements. This approach can increase the number of monitoring data by several factors, providing a more comprehensive dataset for analysing the deep-localized stimulated zone. The numerical analysis indicates that it is feasible to use the combination of the energized casing and downhole electromagnetic measurements in monitoring localized stimulated zone at large depths.
First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.
Correlated Electromagnetic Levitation Actuator: A Reaction Sphere Based Attitude Control System
To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at NASA’s Marshall Space Flight Center have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. The probe also includes the ability to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL Finite Element Analysis and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller thatmitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.
Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System
To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.
Improved Electromagnetic Brake
A proposed design for an electromagnetic brake would increase the reliability while reducing the number of parts and the weight, relative to a prior commercially available electromagnetic brake. The reductions of weight and the number of parts could also lead to a reduction of cost. A description of the commercial brake is prerequisite to a description of the proposed electromagnetic brake. The commercial brake (see upper part of figure) includes (1) a permanent magnet and an electromagnet coil on a stator and (2) a rotor that includes a steel contact plate mounted, with tension spring loading, on an aluminum hub. The stator is mounted securely on a stationary object, which would ordinarily be the housing of a gear drive or a motor. The rotor is mounted on the shaft of the gear drive or motor. The commercial brake nominally operates in a fail-safe (in the sense of normally braking) mode: In the absence of current in the electromagnet coil, the permanent magnet pulls the contact plate, against the spring tension, into contact with the stator. To release the brake, one excites the electromagnet with a current of the magnitude and polarity chosen to cancel the magnetic flux of the permanent magnet, thereby enabling the spring tension to pull the contact plate out of contact with the stator. The fail-safe operation of the commercial brake depends on careful mounting of the rotor in relation to the stator. The rotor/stator gap must be set with a tolerance between 10 and 15 mils (between about 0.25 and about 0.38 mm). If the gap or the contact pad is thicker than the maximum allowable value, then the permanent magnetic field will not be strong enough to pull the steel plate across the gap. (For this reason, any contact pad between the contact plate and the stator must also be correspondingly thin.) If the gap exceeds the maximum allowable value because of shaft end play, it becomes impossible to set the brake by turning off the electromagnet current. Although it may still be possible to set the brake by applying an electromagnet current to aid the permanent magnetic field instead of canceling it, this action can mask an out-of-tolerance condition in the brake and it does not restore the fail-safe function of setting the brake when current is lost.
Discriminating electromagnetic radiation based on angle of incidence
The present invention provides systems, articles, and methods for discriminating electromagnetic radiation based upon the angle of incidence of the electromagnetic radiation. In some cases, the materials and systems described herein can be capable of inhibiting reflection of electromagnetic radiation (e.g., the materials and systems can be capable of transmitting and/or absorbing electromagnetic radiation) within a given range of angles of incidence at a first incident surface, while substantially reflecting electromagnetic radiation outside the range of angles of incidence at a second incident surface (which can be the same as or different from the first incident surface). A photonic material comprising a plurality of periodically occurring separate domains can be used, in some cases, to selectively transmit and/or selectively absorb one portion of incoming electromagnetic radiation while reflecting another portion of incoming electromagnetic radiation, based upon the angle of incidence. In some embodiments, one domain of the photonic material can include an isotropic dielectric function, while another domain of the photonic material can include an anisotropic dielectric function. In some instances, one domain of the photonic material can include an isotropic magnetic permeability, while another domain of the photonic material can include an anisotropic magnetic permeability. In some embodiments, non-photonic materials (e.g., materials with relatively large scale features) can be used to selectively absorb incoming electromagnetic radiation based on angle of incidence.
Photon electrodynamics and photon structure as a bunch of one of many possible states of electromagnetic field
Fundamental laws of conservation are used to show that electromagnetic field is generally represented (even in vacuum at ρ = 0 and j = 0) using four vectors D, E, B, and H with different equations of state (material equations) that are linear for electromagnetic waves and nonlinear for photons and particles. An equation that describes different states of electromagnetic field (i.e., different but not arbitrary relationships of field vectors E, H, D, and B) is derived. It is shown that electromagnetic wave and photon are different states of electromagnetic field that exhibit different dependences of energy density on field vectors. Partial analytical solutions are obtained for a photon (spatially localized bunch of electromagnetic field energy) that propagates at a velocity of light along a single (as distinct from electromagnetic wave) direction.
Electromagnetic waveguide based thermal energy extraction with emissive materials and modifications
The method presented uses thermally emissive materials for the extraction of heat through the use of electromagnetic waveguides, wherein the emissive material comprises materials which emit electromagnetic radiation due to thermal excitation, wherein the electromagnetic radiation is coupled to electromagnetic waveguides; a receiver adapted to receive the electromagnetic radiation for utilization, wherein the extracted electromagnetic radiation may propagate arbitrary distances inside the waveguides before the need for processing, for example, to maximize the temperature differential between the emissive material and that of the receiver; and the exchange of the chemical composition of some portion of the environment the apparatus is housed in. The thermal energy extraction apparatus described herein has the purpose of removing heat from a source for conversion to other forms of energy such as electricity and for thermal management applications. Wherein for heat management, the benefit of waveguides would constitute reduced interference with electronics through electromagnetic coupling.
Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma
An exactly solvable one-dimensional model describing resonance tunneling (reflectionless transmission) of a transverse electromagnetic wave through wide layers of magnetoactive plasma is developed on the basis of the Helmholtz equation. The plasma layers include a set of spatially localized density structures the amplitudes and thicknesses of which are such that approximate methods are inapplicable for their analysis. The profiles of the plasma density structures strongly depend on the choice of the free parameters of the problem that determine the amplitudes of plasma density modulation, characteristic scale lengths of the density structures, their number, and the total thickness of the nonuniform plasma layer. The plasma layers can also include a set of random inhomogeneities. The propagation of electromagnetic waves through such complicated plasma inhomogeneities is analyzed numerically within the proposed exactly solvable model. According to calculations, there are a wide set of inhomogeneous structures for which an electromagnetic wave incident from vacuum can propagate through the plasma layer without reflection, i.e., the complete tunneling of thick plasma barriers takes place. The model also allows one to exactly solve a one-dimensional problem on the nonlinear transillumination of a nonuniform plasma layer in the presence of cubic nonlinearity. It is important that, due to nonlinearity, the thicknesses of the evanescent plasma regions can decrease substantially and, at a sufficiently strong nonlinearity, such regions will disappear completely. The problem of resonance tunneling of electromagnetic radiation through gradient wave barriers is of interest for various applications, such as efficient heating of dense plasma by electromagnetic radiation and transmission of electromagnetic signals from a source located in the near-Earth plasma or deep in the plasma of an astrophysical object through the surrounding evanescent regions.
Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite the continuous effort. Without such local conservation laws, energy and momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic fields reside on different manifolds. To overcome this difficulty, we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact, local conservation laws, in particular the energy-momentum conservation laws, for the electromagnetic gyrokinetic system. A weak Euler-Lagrange equation is established to replace the standard Euler-Lagrange equation for the particles. It is discovered that an induced weak Euler-Lagrange current enters the local conservation laws. And it is the new physics captured by the high-order field theory on heterogeneous manifolds. A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy-momentum conservation laws electromagnetic gauge-invariant.
Multiphysics and Multiscale Simulation Methods for Electromagnetic Energy Assisted Fossil Fuel to Hydrogen Conversion (Final Scientific/Technical Report)
This report summarizes the technical accomplishments of the four-year research project “Multiphysics and Multiscale Simulation Methods for Electromagnetic Energy Assisted Fossil Fuel to Hydrogen Conversion” (Award No. DE-FE0032092), conducted at Howard University and the University of Houston (subawardee) from September 2021 to August 2025. The project successfully achieved all four major objectives: 1. 3D Structural Characterization – Developed 3D optical imaging and mechanical sectioning methods to characterize catalyst distribution and support morphology in nickel foam substrates. Successfully reconstructed 3D geometries and imported them into COMSOL Multiphysics for electromagnetic simulations. 2. EM Hotspot Simulation – Created all-frequency stable electromagnetic formulations and 3D nodal discontinuous Galerkin (NDG) methods for coupled electromagnetic-thermal-fluid problems in multiscale catalytic media. Demonstrated stable solutions from DC to microwave frequencies. 3. Multiphysics Coupling – Developed multiscale simulation methods coupling FEM electromagnetic solvers with thermal transport equations. Reactive molecular dynamics (ReaxFF MD) simulations were performed to investigate catalytic reaction mechanisms at the atomistic level. Demonstrated electromagnetic-thermal co-simulation capabilities for porous catalyst structures. 4. System Optimization – Designed and optimized EM-assisted catalytic systems using nickel foam and carbon foam structures, demonstrating significant temperature increases due to microwave heating. Observed and characterized plasma generation in carbon fiber catalysts. Investigated multiple reaction chamber geometries for improved microwave energy deposition. The project produced significant scientific contributions including 15+ peer-reviewed publications, trained multiple Ph.D. students and undergraduate researchers, and advanced the understanding of microwave-assisted hydrogen production from fossil fuels.
Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations
There is considerable interest in the application of quantum information science to advance computations in plasma physics. A particular point of curiosity is whether it is possible to take advantage of quantum computers to speed up numerical simulations relative to conventional computers. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments to heat a plasma or to generate currents in the plasma. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers electromagnetic wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. Following an analytical formulation for the scattering of a Gaussian pulse, it is deduced that the maximum transmission coefficient for a pulse is $\sqrt{n_2/n_1}$ times that for a plane wave; the incident and transmitted pulses propagating in dielectric media with refractive indices $n_1$ and $n_2$, respectively. The analytical theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber representation of the electromagnetic fields and expressed in term of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses. Apart from their time-asymptotic forms, the simulations display an interplay between the incident, reflected, and transmitted pulses in the vicinity of the transition region between two dielectric media.
Real-time closed-loop simulation and upset evaluation of control systems in harsh electromagnetic environments
Digital control systems for applications such as aircraft avionics and multibody systems must maintain adequate control integrity in adverse as well as nominal operating conditions. For example, control systems for advanced aircraft, and especially those with relaxed static stability, will be critical to flight and will, therefore, have very high reliability specifications which must be met regardless of operating conditions. In addition, multibody systems such as robotic manipulators performing critical functions must have control systems capable of robust performance in any operating environment in order to complete the assigned task reliably. Severe operating conditions for electronic control systems can result from electromagnetic disturbances caused by lightning, high energy radio frequency (HERF) transmitters, and nuclear electromagnetic pulses (NEMP). For this reason, techniques must be developed to evaluate the integrity of the control system in adverse operating environments. The most difficult and illusive perturbations to computer-based control systems that can be caused by an electromagnetic environment (EME) are functional error modes that involve no component damage. These error modes are collectively known as upset, can occur simultaneously in all of the channels of a redundant control system, and are software dependent. Upset studies performed to date have not addressed the assessment of fault tolerant systems and do not involve the evaluation of a control system operating in a closed-loop with the plant. A methodology for performing a real-time simulation of the closed-loop dynamics of a fault tolerant control system with a simulated plant operating in an electromagnetically harsh environment is presented. In particular, considerations for performing upset tests on the controller are discussed. Some of these considerations are the generation and coupling of analog signals representative of electromagnetic disturbances to a control system under test, analog data acquisition, and digital data acquisition from fault tolerant systems. In addition, a case study of an upset test methodology for a fault tolerant electromagnetic aircraft engine control system is presented.