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On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. Furthermore, the second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. Additionally, this solution will be useful for a beam of particles that all move in one direction with a small angular divergence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Relaxation mechanisms in a disordered system with Poisson-level statistics

Here we discuss the interplay between many-body localization and spin symmetry. To this end, we study the time evolution of several observables in the anisotropic t- j model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the $\mathbb{Z}_2$ spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the $\mathbb{Z}_2$ spin transformation relax towards the equilibrium value at relatively short timescales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry-preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.

36 MATERIALS SCIENCE↗

The Axisymmetric Pulsar Magnetosphere

We present the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, E (raised dot) B = 0, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely when either the force-free and/or the ideal MHD condition E (raised dot) B = 0 are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.

Contopoulos, J.↗

Numerical simulation of a relativistic magnetron using a fluid electron model

An approach to numerically modeling relativistic magnetrons, in which the electrons are represented with a relativistic fluid, is described. A principal effect in the operation of a magnetron is space-charge-limited (SCL) emission of electrons from the cathode. We have developed an approximate SCL emission boundary condition for the fluid electron model. This boundary condition prescribes the flux of electrons as a function of the normal component of the electric field on the boundary. Here we show the results of a benchmarking activity that applies the fluid SCL boundary condition to the one-dimensional Child–Langmuir diode problem and a canonical two-dimensional diode problem. Simulation results for a two-dimensional A6 magnetron are then presented. Computed bunching of the electron cloud occurs and coincides with significant microwave power generation. Numerical convergence of the solution is considered. Sharp gradients in the solution quantities at the diocotron resonance, spanning an interval of three to four grid cells in the most well-resolved case, are present and likely affect convergence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of ionization waves on dust chain formation in a DC discharge

An interesting aspect of complex plasma is its ability to self-organize into a variety of structural configurations and undergo transitions between these states. A striking phenomenon is the isotropic-to-string transition observed in electrorheological complex plasma under the influence of a symmetric ion wake field. Such transitions have been investigated using the Plasma Kristall-4 (PK-4) microgravity laboratory on the International Space Station. Recent experiments and numerical simulations have shown that, under PK-4-relevant discharge conditions, the seemingly homogeneous direct current discharge column is highly inhomogeneous, with large axial electric field oscillations associated with ionization waves occurring on microsecond time scales. here, a multi-scale numerical model of the dust–plasma interactions is employed to investigate the role of the electric field in the charge of individual dust grains, the ion wake field and the order of string-like structures. Results are compared with those for dust strings formed in similar conditions in the PK-4 experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advanced Closures for Nonlinear Fluid Simulations of Plasmas (Final Report)

Advanced Closures for Nonlinear Fluid Simulations of Plasmas E. Held, Utah State University (Principal Investigator) J.-Y. Ji, Utah State University (Co-Investigator) Utah State University (USU) continued to develop and apply closures for hybrid fluid/kinetic simulations of magnetized fusion plasmas. The closures developed by USU's fusion theory and computation group use the drift ordering and are referred to as "continuum" and "general moment" approaches. They differ in their representation for the distribution functions which probabilistically describe the density of particles in 5 dimensional phase space. The two chosen velocity variables, needed in studies of kinetic physics for magnetized plasmas, are the speed and the component of a particle's velocity along the magnetic field. In magnetized plasmas, the charged particle trajectories are tied closely to the magnetic field lines. Both approaches account for binary interactions between particles using the Coulomb collision operator. Theoretical and computational development along both lines provided avenues for verification between the two approaches. This funding allowed USU to further develop physically accurate and numerically efficient models that advance our understanding of kinetic physics in experiments like the International Thermonuclear Experimental Reactor (ITER). The ITER device will likely prove the physical practicality of thermonuclear fusion by producing 500 megawatts of clean, abundant fusion power. This work helped to realize this goal by advancing our simulation capability using hybrid fluid/kinetic models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Resurgence, conformal blocks, and the sum over geometries in quantum gravity

In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, R) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electron Flow to a Satellite at High Positive Potential

The Tethered Satellite System (TSS) is designed to deploy a 1.6 m diameter spherical satellite a distance of 20 km above the space shuttle orbiter on an insulated conducting tether. Because of the passage of the conducting tether through the earth's magnetic field, an emf is generated producing a positive satellite potential of about 5000 V. Electron flow under the influence of this high positive potential is the focus of the present analysis. The ionospheric parameters at TSS orbit altitude are; thermal velocity of electrons, 1.9 x 10(exp 5) M/S, thermal velocity of the ions, 1.1 x 10(exp 3) m/s, velocity of the satellite 8 x 10(exp 3) m/s. The electrons, with a Debye length, lambda(D) = 0.49 cm, spiral about the earth's magnetic field lines (0.4 Gauss) with a radius of about 3 cm and the ions spiral with a radius of 5 m. Under these conditions, the electron thermal energy, kT is 0.17 eV. The TSS satellite radius, r(p) is 163 Debye lengths. There is an extensive literature on the interaction of satellites with the near-earth ionospheric plasma. The space charge limitation to the electron current collected by a sphere at positive electrical potential was calculated by Langmuir and Blodgett (1924). Parker and Murphy (1967) recognized the importance of the influence of the earth's magnetic field and used the guiding center approximation to calculate the electron current collected by a positive charged satellite. More recently Ma and Schunk (1989) have calculated the time dependent flow of electrons to a spherical satellite at positive potential utilizing numerical methods and Sheldon (1994) used similar methods to solve this problem for the steady state. In order to analyze some of the phenomena that occurred in the ionosphere during the TSS flights, it would be useful to have analytic expressions for these electron flows. The governing equations are very complex and an exact analytical solution is not likely. An approximate analytical solution is feasible however, and the results of one attempt are presented herein.

Sheldon, John W.↗

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Schaffer, L.↗

Overview of Results from the Cassini Magnetospheric Imaging Instrument (MIMI) During the First Year of Operations

The MIMI investigation comprises three sensors covering the indicated energy ranges: the Ion and Neutral Camera (INCA) -- 7 keV/nuc 3 Mev) and protons (1.6 < E < 160 Mev) from the back end of the dual field-of-view telescope. The Saturn observation sequences began in January, 2004 and culminated in Saturn Orbit Insertion on July 1, 2004. The MIMI sensors observed substantial activity in interplanetary space for several months prior to SOI, including several interplanetary shocks associated with corotating interaction regions, numerous increases most likely originating from particle streams in the vicinity of the Saturnian bow shock and energetic neutral atoms (ENA) emanating from Saturn s magnetosphere. Results following SOI revealed: a dynamical magnetosphere with a day-night asymmetry and an 11-hour periodicity; several water-product ions (O+, OH+, H2O+), but little N+; inferred quantities of neutral gas sufficient to cause major losses in the trapped ions and electrons in the middle and inner magnetosphere; a Titan exosphere that is a copious source of ENA; INCA imaging through ENA has also revealed a previously unknown radiation belt residing inward of the D-ring that is most likely the result of double charge-exchange between the main radiation belt and the upper layers of Saturn s exosphere. Finally, there is ample evidence for the presence of substorm-like injections of plasma that subsequently corotates for a number of days before dissipating on the night-side magnetotail. The observations will be presented and discussed in the context of current theoretical models.

Krimigis, S. M.↗

Mapping and probing Froggatt-Nielsen solutions to the quark flavor puzzle

The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. In its minimal application to the quark sector, the different quark types and generations have different charges under a 𝑈⁢(1)𝑋 flavor symmetry. The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. Only a handful of charge assignments are generally considered in the literature. We analyze the complete space of possible charge assignments with |𝑋 𝑞𝑖 | ≤ 4 and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. Future precision measurement of Δ⁢𝐹 = 2 observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hybrid-Vlasov Simulation of Soft X-Ray Emissions at the Earth’S Dayside Magnetospheric Boundaries

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause, the magnetosheath and the polar cusps by remote sensing techniques. The Solar wind–Magnetosphere–Ionosphere Link Explorer (SMILE) and Lunar Environment heliospheric X-ray Imager (LEXI) missions aim to obtain soft X-ray images of near-Earth space thanks to their Soft X-ray Imager (SXI) instruments. While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission, the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma. To investigate the possible signatures of ion-kinetic-scale processes in soft X-ray images, we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model. The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field. We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations, providing meridional and equatorial views. We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirror mode wave structures in the magnetosheath and flux transfer events (FTEs) at the magnetopause. Our results suggest that, although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers, mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images. For instance, a local increase by 30% in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12% enhancement in the line-of-sight- and time integrated soft X-ray emissivity originating from this region. Likewise, a proton density increase by 14% in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%. These are likely conservative estimates, given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind. These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale, transient phenomena occurring on the dayside.

magnetosphere↗

Investigation of powertrain system decarbonization using electrically assisted turbocharging and hybridization in off-road vehicles

In recent years, the causes, effects, and existential threat of a global anthropogenic climate shift have drawn significant attention and stimulated mitigation efforts from all genres of scientific, political, and industrial bodies. The greenhouse effect and the detrimental environmental impact of excess greenhouse gas (GHG) emissions, like carbon dioxide, is well studied and targeted as the primary culprit for aversive action. However, some fields exist where reducing GHG emissions is met by considerable challenges. One such field is the production and operations of off-road vehicles. Applications of these vehicles are highly diverse and are often characterized by rugged, especially transient, and power intensive duty cycles that make one-fits-all vehicle configuration solutions impractical. This research surveys existing literature to identify the modern technologies packages and challenges that face development and configuration of powertrain systems which currently navigate the regulated emissions and unique duty cycle requirements of this market space. A novel powertrain concept is proposed and evaluated with respect to the pinnacle objectives of load performance improvement, criteria pollutant reduction, and reducing the life cycle GHG intensity of its operation. A sure-fire path to vehicular GHG reduction is through improving the fuel efficiency of internal combustion engines (ICEs), an entrenched component of the off-road vehicle sector. Unfortunately, this is more easily said than done. An approach that has proven successful in this endeavor is engine downsizing and turbocharging, where a larger engine is replaced with a smaller one with added air system boosting via turbocharger to reduce frictional and pumping losses while also enabling access to additional fuel energy. However, practical realization of these potential benefits is often impeded by the transient response capability of the smaller engine across the operating space. For this reason, downsized ICE powertrains have turned to electrified forced induction systems (EFISs) for a decoupling of exhaust energy and engine speed from boost capability. Platformed on 48V hybrid technology, these systems introduce the need for more sophisticated controls around the engine gas-exchange process for the management of boost performance and exhaust gas emissions. On this account, simulation studies utilizing a GT-POWER model of a turbocharged 4.5 L engine outfit with an EFIS using an electrically driven compressor (eBooster®) are conducted to provide insight into the performance of this air handling architecture on an off-road engine. The results show that improvement in transient torque response time in sync with reduction in engine-out soot and NOx emissions are possible with an engine recalibration that leverages the transient air-fuel ratio authority of the eBooster®. Benefits are further demonstrated when duty cycle simulations of the 48V mild-hybrid engine concept are exercised, showing an acute decrease in cumulative fuel usage and soot production. Powertrain hybridization is another technological pathway achieving pronounced GHG reduction successes in modern on-road vehicle applications through integration of Li-ion battery technology. In the off-road vehicle segment, a review of available literature concludes that hybridized architectures are present but generally lack the depth of technologies that have both high specific energy and power capabilities, and thus are limited in their inclusion of Li-ion batteries for ICE assistance and enhanced energy storage capability. Therefore, building on the mild-hybrid engine results, the downsized and eBoosted engine concept was integrated into a larger high-voltage battery-hybrid series-electric powertrain system. Hybrid powertrain parameter sensitivity studies were carried out in a numerical charge-sustaining framework, providing novel insights into power flows between the battery and the engine and how their respective capabilities and operation contribute to GHG and criteria pollutant emissions of diverse duty cycles. Application of supervisory power management introduced robustness into the power sourcing and battery SOC control process and showed that optimum specification of battery properties can yield synergies between GHG emissions and battery energy capacity. Furthermore, examination of recent literature on Li-ion batteries has shown that pack manufacturing is a highly energy intensive process, thereby producing considerable quantities of GHGs that scale with energy storage capacity. Also scaling with a battery’s energy storage capacity is its investment cost. In consideration of these factors, an inclusive technoeconomic and GHG life cycle analysis is conducted. This analysis systematically compares the carbon footprint and total cost of ownership associated with the proposed hybrid powertrain concept to reference and alternative powertrain configurations, facilitating a thorough evaluation of the decarbonization effectiveness and economic viability.

99 GENERAL AND MISCELLANEOUS↗