Robert A. Marshall

Bio: Robert A. Marshall is an academic researcher from University of Colorado Boulder. The author has contributed to research in topics: Ionosphere & Electron precipitation. The author has an hindex of 21, co-authored 100 publications receiving 1731 citations. Previous affiliations of Robert A. Marshall include Boston University & Stanford University.

Numerical Electromagnetics: The FDTD Method

Abstract: Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.

A survey of ELF and VLF research on lightning-ionosphere interactions and causative discharges

Abstract: [1] Extremely low frequency (ELF) and very low frequency (VLF) observations have formed the cornerstone of measurement and interpretation of effects of lightning discharges on the overlying upper atmospheric regions, as well as near‐Earth space. ELF (0.3–3 kHz) and VLF (3–30 kHz) wave energy released by lightning discharges is often the agent of modification of the lower ionospheric medium that results in the conductivity changes and the excitation of optical emissions that constitute transient luminous events (TLEs). In addition, the resultant ionospheric changes are best (and often uniquely) observable as perturbations of subionospherically propagating VLF signals. In fact, some of the earliest evidence for direct disturbances of the lower ionosphere in association with lightning discharges was obtained in the course of the study of such VLF perturbations. Measurements of the detailed ELF and VLF waveforms of parent lightning discharges that produce TLEs and terrestrial gamma ray flashes (TGFs) have also been very fruitful, often revealing properties of such discharges that maximize ionospheric effects, such as generation of intense electromagnetic pulses (EMPs) or removal of large quantities of charge. In this paper, we provide a review of the development of ELF and VLF measurements, both from a historical point of view and from the point of view of their relationship to optical and other observations of ionospheric effects of lightning discharges.

An improved model of the lightning electromagnetic field interaction with the D‐region ionosphere

Abstract: [1] We present an improved time-domain model of the lightning electromagnetic pulse (EMP) interaction with the lower ionosphere. This improved model inherently accounts for the Earth's curvature, includes an arbitrary number of ion species, and uses a convolutional Perfectly Matched Layer (PML) boundary. We apply an improved model of electron heating due to the lightning EMP and electrostatic fields, and we include ionization, attachment, and detachment. In addition to modeling lightning, this model can be used for long-distance VLF wave propagation in the Earth-ionosphere waveguide, heating of the lower ionosphere by VLF transmitters, and heating in the F-region ionosphere by lightning. In this paper we present three initial results of this model. First, we compare results of ionospheric heating and electron density disturbances with and without electron detachment taken into account. We find that detachment is important only for the QE effects on time scales longer than 1 ms. Second, we find a simple explanation for the recently-reported “elve doublets”, which we find are an effect of the rise and fall times of the lightning waveform. In particular, we find that all elves are doublets, and the rise and fall times of the current pulse control the brightness and separation in time of the two successive halves of the elve. Third, we find a similar simple explanation for “ring” sprites, whole columns appear in a circle symmetric around the discharge axis. We find that ring sprites can be initiated for particular current waveforms, where the QE and EMP fields in the mesosphere produce a maximum reduced field away from the discharge axis.

Subionospheric early VLF signal perturbations observed in one‐to‐one association with sprites

Abstract: [1] Observations on the night of 21 July 2003 of the ionospheric effects of a thunderstorm in central France are reported. From 0200 to 0315 UT, a camera system in the Pyrenees Mountains captured 28 sprites, triggered by +CG lightning as observed by the French METEORAGE lightning detection system. A narrowband VLF receiver located on Crete, at ∼2200 km southeast of the storm, observed subionospheric VLF signals from six ground-based transmitters. The amplitude of one of the VLF signals, originating at a transmitter located ∼150 km west of the storm and passing through the storm region, exhibited rapid onset perturbations occurring in a nearly one-to-one relationship with the optical sprites. These “early” VLF events are consistent with a process of narrow-angle forward scattering from a volume of enhanced ionization above the storm with lateral sizes larger than the VLF radio wavelength. The many +CG and −CG discharges that did not produce sprites were also found to not be associated with detectable VLF amplitude perturbations, even though some of these discharges reached relatively large peak currents. The rapid onsets of several of the sprite-related VLF perturbations were followed by relatively long onset durations, ranging from ∼0.5 to 2.5 s, indicating that these events were early but not “fast.” These “early/slow” events may suggest a slow process of ionization build-up in the lower ionosphere, following intense lightning discharges that also lead to sprites. A limited number of early VLF perturbation events were also associated with whistler-induced electron precipitation events, or classic Trimpi perturbations, undoubtedly produced by the precipitation of electrons due to whistler-mode waves injected into the magnetosphere by the same lightning flash that led to the production of the sprite.

Theory and Design of Charged Particle Beams

Abstract: Review of Charged Particle Dynamics. Beam Optics and Focusing Systems Without Space Charge. Linear Beam Optics with Space Charge. Self-Consistent Theory of Beams. Emittance Variation. Beam Physics Research from 1993 to 2007. Appendices. List of Frequently Used Symbols. Bibliography. Index.

Terrestrial laser scanning in forest inventories

Abstract: Decision making on forest resources relies on the precise information that is collected using inventory. There are many different kinds of forest inventory techniques that can be applied depending on the goal, scale, resources and the required accuracy. Most of the forest inventories are based on field sample. Therefore, the accuracy of the forest inventories depends on the quality and quantity of the field sample. Conventionally, field sample has been measured using simple tools. When map is required, remote sensing materials are needed. Terrestrial laser scanning (TLS) provides a measurement technique that can acquire millimeter-level of detail from the surrounding area, which allows rapid, automatic and periodical estimates of many important forest inventory attributes. It is expected that TLS will be operationally used in forest inventories as soon as the appropriate software becomes available, best practices become known and general knowledge of these findings becomes more wide spread. Meanwhile, mobile laser scanning, personal laser scanning, and image-based point clouds became capable of capturing similar terrestrial point cloud data as TLS. This paper reviews the advances of applying TLS in forest inventories, discusses its properties with reference to other related techniques and discusses the future prospects of this technique.

Monte Carlo model for analysis of thermal runaway electrons in streamer tips in transient luminous events and streamer zones of lightning leaders

Abstract: [1] Streamers are thin filamentary plasmas that can initiate spark discharges in relatively short (several centimeters) gaps at near ground pressures and are also known to act as the building blocks of streamer zones of lightning leaders. These streamers at ground pressure, after 1/N scaling with atmospheric air density N, appear to be fully analogous to those documented using telescopic imagers in transient luminous events (TLEs) termed sprites, which occur in the altitude range 40–90 km in the Earth's atmosphere above thunderstorms. It is also believed that the filamentary plasma structures observed in some other types of TLEs, which emanate from the tops of thunderclouds and are termed blue jets and gigantic jets, are directly linked to the processes in streamer zones of lightning leaders. Acceleration, expansion, and branching of streamers are commonly observed for a wide range of applied electric fields. Recent analysis of photoionization effects on the propagation of streamers indicates that very high electric field magnitudes ∼10 Ek, where Ek is the conventional breakdown threshold field defined by the equality of the ionization and dissociative attachment coefficients in air, are generated around the tips of streamers at the stage immediately preceding their branching. This paper describes the formulation of a Monte Carlo model, which is capable of describing electron dynamics in air, including the thermal runaway phenomena, under the influence of an external electric field of an arbitrary strength. Monte Carlo modeling results indicate that the ∼10 Ek fields are able to accelerate a fraction of low-energy (several eV) streamer tip electrons to energies of ∼2–8 keV. With total potential differences on the order of tens of MV available in streamer zones of lightning leaders, it is proposed that during a highly transient negative corona flash stage of the development of negative stepped leader, electrons with energies 2–8 keV ejected from streamer tips near the leader head can be further accelerated to energies of hundreds of keV and possibly to several tens of MeV, depending on the particular magnitude of the leader head potential. It is proposed that these energetic electrons may be responsible (through the “bremsstrahlung” process) for the generation of hard X rays observed from ground and satellites preceding lightning discharges or with no association with lightning discharges in cases when the leader process does not culminate in a return stroke. For a lightning leader carrying a current of 100 A, an initial flux of ∼2–8 keV thermal runaway electrons integrated over the cross-sectional area of the leader is estimated to be ∼1018 s−1, with the number of electrons accelerated to relativistic energies depending on the particular field magnitude and configuration in the leader streamer zone during the negative corona flash stage of the leader development. These thermal runaway electrons could provide an alternate source of relativistic seed electrons which were previously thought to require galactic cosmic rays. The duration of the negative corona flash and associated energetic radiation is estimated to be in the range from ∼1 μs to ∼1 ms depending mostly on the pressure-dependent size of the leader streamer zone.