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NASA NTRS2018

Ion Injection Triggered EMIC Waves in the Earth's Magnetosphere

We present Van Allen Probe observations of electromagnetic ion cyclotron (EMIC) waves triggered solely due to individual substorm-injected ions in the absence of storms or compressions of the magnetosphere during 9 August 2015. The time at which the injected ions are observed directly corresponds to the onset of EMIC waves at the location of Van Allen Probe A (L = 5.5 and 18:06 magnetic local time). The injection was also seen at geosynchronous orbit by the Geostationary Operational Environmental Satellite and Los Alamos National Laboratory spacecraft, and the westward(eastward) drift of ions(electrons) was monitored by Los Alamos National Laboratory spacecraft at different local times. The azimuthal location of the injection was determined by tracing the injection signatures backward intime to their origin assuming a dipolar magnetic field of Earth. The center of this injection location wasdetermined to be close to 20:00 magnetic local time. Geostationary Operational Environmental Satelliteand ground magnetometer responses confirm substorm onset at approximately the same local time.The observed EMIC wave onsets at Van Allen Probe were also associated with a magnetic field decrease.The arrival of anisotropic ions along with the decrease in the magnetic field favors the growth of the EMICwave instability based on linear theory analysis.

Van Allen Probes↗

DOE OSTI2025

Neutron stars and the dense matter equation of state

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Here, theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas , vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci. , vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Physics↗

DOE OSTI2022

Interaction of radio frequency waves with cylindrical density filaments -- scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗

DOE OSTI2024

The kinetic analog of the pressure–strain interaction

Energy transport in weakly collisional plasma systems is often studied with fluid models and diagnostics. However, the applicability of fluid models is limited when collisions are weak or absent, and using a fluid approach can obscure kinetic processes that provide key insights into the physics of energy transport. Kinetic diagnostics retain all of the information in 3D-3V phase space and thereby reach beyond the insights of fluid models to elucidate the mechanisms responsible for collisionless energy transport. In this work, we derive the Kinetic Pressure–Strain (KPS): a kinetic analog of the pressure–strain interaction, which is the channel between flow energy density and internal energy density in fluid models. Through two case studies of electron Landau damping, we demonstrate that the KPS diagnostic can elucidate kinetic mechanisms that are responsible for energy transport in this channel, just as the related field–particle correlation is known to identify kinetic mechanisms of transport between electromagnetic field energy density and kinetic energy density in particle flows. In addition, we show that resonant electrons play a major role in transferring energy between fluid flows and internal energy during the process of Landau damping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy α-α scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD θ-angle. As a first step, we recalculate α-α scattering in our Universe utilizing various improvements in the adiabatic projection method, which leads to an improved, parameter-free prediction of the S- and D-wave phase shifts for laboratory energies below 10 MeV. We find that positive shifts in the pion mass have a small effect on the S-wave phase shift, whereas lowering the pion mass adds some repulsion in the two-alpha system. The effect on the D-wave phase shift turns out to be more pronounced as signaled by the D-wave resonance parameters. Variations of the fine-structure constant have almost no effect on the low-energy α-α phase shifts. We further show that up-to-and-including next-to-leading order in the chiral expansion, variations of these phase shifts with respect to the QCD θ-angle can be expressed in terms of the θ-dependent pion mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius

Meaningful predictions for electric quadrupole (E2) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown E2 observables. However, converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) approaches. Matrix elements of the E2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. We demonstrate that the convergence patterns of the E2 and radius observables are strongly correlated, and that meaningful predictions for the absolute scale of E2 observables may be made by calibrating to the experimentally-known ground-state charge radius. Here, we illustrate by providing robust ab initio predictions for several E2 transition strengths and quadrupole moments in p-shell nuclei, in cases where experimental results are available for comparison.

6 ≤ A ≤ 19↗

DOE OSTI2024

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice—such as (p x , p y )-wave and (d x 2 –y 2 , d xy )-wave superconductors. Such a system has two possible superconducting states: the chiral state (e.g., p + ip or d + id), which breaks time-reversal symmetry, and the nematic state (e.g., p + p or d + d), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A nonanalytic cubic term arises, as in the case of a conventional s -wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. Here, we analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Generalized slab universal instability and its appearance in pair plasma

In this work, a generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron–ion plasma, while Debye shielding strongly stabilizes this instability when λ D approaches ρ i (λ D is the Debye length and ρi is the ion gyroradius). In particular, we examine the stability criterion for this instability in electron–positron pair plasmas and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value n c = B 2 /(8πm e c 2 ).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

Burkholder, R. J.↗

DOE OSTI2022

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Massive twistor worldline in electromagnetic fields

We study the (ambi-)twistor model for spinning particles interacting via electromagnetic field, as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. We compute the momentum kick and spin kick up to one-loop order and show precisely how they are encoded in the classical eikonal. The all-orders-in-spin effects are encoded as a dynamical implementation of the Newman-Janis shift, and we find that the expansion in both spins can be resummed to simple expressions in special kinematic configurations, at least up to one-loop order. We confirm that the classical eikonal can be understood as the generator of canonical transformations that map the in-states of a scattering process to the out-states. We also remark that cut contributions for converting worldline propagators from time-symmetric to retarded amount to the iterated action of the leading eikonal at one-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Non-Thermal Solar Wind Electron Velocity Distribution Function

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1999

Progress of Cometary Science in the Past 100 Years

Enormous strides made by cometary science during the 20th century defy any meaningful comparison of its state 100 years ago and now. The great majority of the subfields enjoying much attention nowadays did not exist in the year 1900. Dramatic developments, especially in the past 30-50 years, have equally affected observational and theoretical studies of comets. The profound diversification of observing techniques has been documented by the ever widening limits on the electromagnetic spectrum covered. While the time around 1900 marked an early period of slow and painful experimentation with photographic methods in cometary studies, observations of comets from the x-ray region to the radio waves have by now become routine. Many of the new techniques, and all those involved with the wavelengths shorter than about 300 nm, were made possible by another major breakthrough of this century - observing from space. Experiments on dedicated Earth-orbiting satellites as well as several deep-space probes have provided fascinating new information on the nature and makeup of comets. In broader terms, much of the progress has been achieved thanks to fundamental discoveries and major advances in electronics, whose applications resulted in qualitatively new instruments (e.g. radiotelescopes) and sensors or detectors (e.g. CCD arrays). The most universal effect on the entire cometary science, from observing to data handling to quantitative interpretations, has been, as in any other branch of science, due to the introduction of electronic computers, with their processing capabilities not only unheard of, but literally unimaginable, in the age of classical desk calculators. As if all this should not be enough, the today's generations of comet scientists have, in addition, been blessed with nature's highly appreciated cooperation. Indeed, in the span of a dozen years, between 1985 and 1997, we were privileged to witness four remarkable cometary events: (i) a return of Halley's celebrated comet; (ii) the impact of an extensively fragmented comet Shoemaker-Levy 9 into Jupiter - a once-in-a-millenium episode; (iii) a closeup, appearance of a small but very active Earth-approaching comet Hyakutake; and (iv) an unforgettable celestial show of comet Hale-Bopp, one of the brightest and the most massive comets ever observed. We have been - and for many years to come will be - harvesting scientifically lucrative findings based on the flood of data accumulated during observational campaigns organized for these and other recent objects. Our understanding of cometary phenomena will continue to grow as observing techniques are further being improved and as more sophisticated theories are being developed. Recent accomplishments achieved in the rapidly expanding field of comets are certain to stimulate the members of this astronomical community in their quest for new discoveries in the 21st century!

Sekanina, Zdenek↗