Coupling 1D Telegrapher Equations to 3D Maxwell's Equations with Applications to Pulsed Power.
Abstract not provided.
McGregor, Duncan Alisdair Odum↗
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An Investigation into High Voltage Spiral Generators Utilizing Thyristor Input Switches
High voltage nanosecond pulses are widely used in scientific research, but their wider adoption in industry requires compact, cost effective and easy to use generators to be developed. This paper presents modelling and experimental investigations into one method of producing such pulses – a spiral generator with a solid-state, thyristor-based input switch. It includes how the pulses are formed within the spiral, why a high speed input switch is required, how the geometry of the spiral dictates its output characteristics, and the effects of different loads. Using thyristors, often connected in series to increase the operating voltage of the spiral, enables the spiral generators to have low jitter, high repetition rate, and long lifetime. Modelling of the circuit used a combination of telegraph equations to account for the wave propagation along the spiral and a lumped circuit exchanging charge between the spiral, the input switch, and the load. The model is verified by detailed experimental results with the relative error being < 10% in most cases. Here, the output voltage pulse was often observed to have an initial peak of much lower magnitude than the subsequent peak(s) – which can only be fully explained by considering wave propagation effects. Lower input switch inductance, shorter switching time, larger mean diameter of the spiral, and increasing the width of the copper tape that makes up the spiral can all increase the voltage multiplication efficiency. Though increasing the number of turns that make up the spiral can increase the output voltage, it can also lower the multiplication efficiency. By understanding the effects of different geometries the spiral can be optimized to drive different loads - three applications of such spiral generators are then presented: pulses with 10 kV amplitude and 10 kHz repetition rate for driving DBD plasma, pulses with amplitude of 10 kV and 10 kV/ns rising rate for triggering of advanced solid state switches, and pulses with -50 kV amplitude and 50 ns rising time for triggering high current gas switches through field distortion.1 Index Terms—spiral generator, nanosecond pulses, telegraph equations, series-connected thyristor module, pulse forming process
42 ENGINEERING↗
Real-Time Fault Location Using the Retardation Method
A new method for short-circuit fault location is proposed. The method is based on instantaneous signal measurement and its first and second derivatives, which are the novel elements of the current approach. The derivatives allow associating a precise time stamp to the occurrence of the fault. Due to retardation phenomena, the difference between the times in which a signal is registered in two detectors can be used to locate the fault. We offer several mathematical models to describe the fault. Although a description of faults in terms of a lumped circuit is useful for elucidating the methods for detecting the fault, this description will not suffice to describe the fault signal propagation; hence, a distributed models is needed, which is given in terms of the telegraph equations. Those equations were used to derive a transmission line transfer function, and an exact analytical description of the fault signal propagating in the transmission line was obtained. The analytical solution was verified both by numerical simulations and experimentally.
42 ENGINEERING↗
Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain
This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Advection versus diffusion in Richtmyer-Meshkov mixing
The Richtmyer-Meshkov (RM) instability is one of the most severe degradation mechanisms for inertial confinement fusion (ICF), and mitigating it has been a priority for the global ICF effort. In this Letter, the instability's ability to atomically mix is linked to its background decay of residual turbulent energy. Here, we show how recently derived inequalities from the mathematical theory of PDEs constrain the evolution. A model RM process at leading order may diffusively mix or retain imprints of its initial structures indefinitely, depending on initial conditions, and there exists a theoretical range of zero-mixing for certain values of parameters. The results may apply to other systems resembling scalar transport in decaying turbulence.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗