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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Maximizing TDRS Command Load Lifetime

The GNC software onboard ISS utilizes TORS command loads, and a simplistic model of TORS orbital motion to generate onboard TORS state vectors. Each TORS command load contains five "invariant" orbital elements which serve as inputs to the onboard propagation algorithm. These elements include semi-major axis, inclination, time of last ascending node crossing, right ascension of ascending node, and mean motion. Running parallel to the onboard software is the TORS Command Builder Tool application, located in the JSC Mission Control Center. The TORS Command Builder Tool is responsible for building the TORS command loads using a ground TORS state vector, mirroring the onboard propagation algorithm, and assessing the fidelity of current TORS command loads onboard ISS. The tool works by extracting a ground state vector at a given time from a current TORS ephemeris, and then calculating the corresponding "onboard" TORS state vector at the same time using the current onboard TORS command load. The tool then performs a comparison between these two vectors and displays the relative differences in the command builder tool GUI. If the RSS position difference between these two vectors exceeds the tolerable lim its, a new command load is built using the ground state vector and uplinked to ISS. A command load's lifetime is therefore defined as the time from when a command load is built to the time the RSS position difference exceeds the tolerable limit. From the outset of TORS command load operations (STS-98), command load lifetime was limited to approximately one week due to the simplicity of both the onboard propagation algorithm, and the algorithm used by the command builder tool to generate the invariant orbital elements. It was soon desired to extend command load lifetime in order to minimize potential risk due to frequent ISS commanding. Initial studies indicated that command load lifetime was most sensitive to changes in mean motion. Finding a suitable value for mean motion was therefore the key to achieving this goal. This goal was eventually realized through development of an Excel spreadsheet tool called EMMIE (Excel Mean Motion Interactive Estimation). EMMIE utilizes ground ephemeris nodal data to perform a least-squares fit to inferred mean anomaly as a function of time, thus generating an initial estimate for mean motion. This mean motion in turn drives a plot of estimated downtrack position difference versus time. The user can then manually iterate the mean motion, and determine an optimal value that will maximize command load lifetime. Once this optimal value is determined, the mean motion initially calculated by the command builder tool is overwritten with the new optimal value, and the command load is built for uplink to ISS. EMMIE also provides the capability for command load lifetime to be tracked through multiple TORS ephemeris updates. Using EMMIE, TORS command load lifetimes of approximately 30 days have been achieved.

Brown, Aaron J.↗

The Zero Boil-Off Tank Experiment Ground Testing and Verification of Fluid and Thermal Performance

The Zero Boil-Off Technology (ZBOT) Experiment involves performing a small scale International Space Station (ISS) experiment to study tank pressurization and pressure control in microgravity. The ZBOT experiment consists of a vacuum jacketed test tank filled with an inert fluorocarbon simulant liquid. Heaters and thermo-electric coolers are used in conjunction with an axial jet mixer flow loop to study a range of thermal conditions within the tank. The objective is to provide a high quality database of low gravity fluid motions and thermal transients which will be used to validate Computational Fluid Dynamic (CFD) modeling. This CFD can then be used in turn to predict behavior in larger systems with cryogens. This paper will discuss the work that has been done to demonstrate that the ZBOT experiment is capable of performing the functions required to produce a meaningful and accurate results, prior to its launch to the International Space Station. Main systems discussed are expected to include the thermal control system, the optical imaging system, and the tank filling system.This work is sponsored by NASAs Human Exploration Mission Directorates Physical Sciences Research program.

Fluid management↗

Electromagnetic ion cyclotron waves stimulated by modest magnetospheric compressions

AMPTE/CCE magnetic field and particle data are used to test the suggestion that increased hot proton temperature anisotropy resulting from convection during magnetospheric compression is responsible for the enhancement in Pc 1 emission via generation of electromagnetic ion cyclotron (EMIC) waves in the dayside outer equatorial magnetosphere. The relative increase in magnetic field is used to gauge the strength of the compression, and an image dipole model is used to estimate the motion of the plasma during compression. Proton data are used to analyze the evolution of the proton distribution and the corresponding changes in EMIC wave activity expected during the compression. It is suggested that enhancements in dynamic pressure pump the energetic proton distributions in the outer magnetosphere, driving EMIC waves. Waves are expected to be generated most readily close to the magnetopause, and transient pressure pulses may be associated with bursts of EMIC waves, which would be observed on the ground in association with ionospheric transient signatures.

Anderson, B. J.↗

Concept Design of Active Shielding for Dynamic Wireless Charging of Light-duty EV

Dynamic wireless charging of electric vehicles is a flexible and state of the art charging technology with the potential capability of enabling fully automated in-motion charging. With charging power increasing to more than 100 kW for light duty vehicles, electromagnetic field (EMF) emission becomes a critical challenge. Due to the high costs of ferrite materials, this paper proposes an active shielding solution with multiple canceling coils installed on the ground side to supplement ferrite passive shielding to ensure electromagnetic safety. Two canceling coils are designed on two sides of the ground side coil. The canceling coils are small in size and 180 degree opposite in phase to the ground coil. Simulation and modeling shows that the canceling coils can reduce EMF emission from 37.2 µT to 18.2 µT at 0.8 m during 100 kW operation with only 2.5% of ground side current flowing in the canceling coils. These results have been preliminarily verified by inductance measurements and magnetic field measurement at 1.1 m distance without canceling coils. By further increasing the canceling coils’ currents to 4%, EMF emission can also be mitigated at 200 kW, although the canceling coils’ shape, position, and phase angle can be further optimized to improve the three-dimensional field distribution.

25 ENERGY STORAGE↗

Energy transport and dynamics

We report findings concerning energy transport and dynamics in flares during the impulsive and gradual phases based on new ground-based and space observations (notably from Yohkoh). A preheating sometimes occurs during the impulsive phase. Ca XIX line shifts are confirmed to be good tracers of bulk plasma motions, although strong blue shifts are not as frequent as previously claimed. They often appear correlated with hard X-rays but, for some events, the concept that electron beams provide the whole energy input to the thermal component seems not to apply. Theory now yields: new diagnostics of low-energy proton and electric beams; accurate hydrodynamical modeling of pulse beam heating of the atmosphere; possible diagnostics of microflares (based on X-ray line ratio or on loop variability); and simulated images of chromospheric evaporation fronts. For the gradual phase, the continual reorganization of magnetic field lines over active regions determines where and when magnetic reconnection, the mechanism favored for energy release, will occur. Spatial and temporal fragmentation of the energy release, observed at different wavelengths, is considered to be a factor as well in energy transport and plasma dynamics.

Schmieder, Brigitte↗

Structure and Dynamics of the Quiet Solar Chromosphere

The grant supported research on the structure of the quiet, nonmagnetic chromosphere and on wave excitation and propagation in both the nonmagnetic chromosphere and the magnetic network. The work on the structure of the chromosphere culminated in the recognition that between two competing views of the solar chromosphere, older models by Avrett and collaborators (referred to as VAL) and the newer, dynamical model by Carlsson & Stein (referred to as CS), the clear decision is in favor of the older models, and this in spite of the evident lack of physics, which does not include wave motion and oscillations. The contrast between the static VAL models and the dynamical CS model can be stated most succinctly by comparing the temperature variation implied by the VAL models and the temperature fluctuations of the CS model, which are, respectively, of the order of 10% for the VAL model (at heights where hydrogen is 50% ionized) and a factor of 10 (at the upper boundary of their chromospheric model). The huge fluctuations of the CS model have never been observed, whereas the smaller temperature variations of the VAL models are consistent with ground-based and space-based observations. While it should be obvious which model describes the Sun and which one fails, the case is far from settled in the minds of solar physicists. Thus, much educational work remains to be done and, of course, more research to develop arguments that make the case more convincing. The research on waves and oscillations has been based on a unified theory of excitation of acoustic waves in the field-free atmosphere and of transverse and longitudinal waves in magnetic flux tubes located in the magnetic network by noting, first, that impulsive excitation of all these waves in gravitationally stratified media leads to oscillations at the respective cutoff frequencies and, second, that the observed oscillation frequencies in the nonmagnetic and magnetic parts of the chromosphere match corresponding cutoff frequencies in the upper solar photosphere. The dynamical simulations by Carlsson and Stein have been most instructive and of fundamental importance for understanding wave propagation in a stratified medium by their "flaws", the most important of which is an intensity excess at the H2v emission peak in the H line of Ca II, which is surprising since the observed intensity should have been an upper limit to the simulated intensity. The only plausible explanation for a predicted intensity that is higher than observed is that energy is spread horizontally in upward propagation in the Sun, but not in the plane-wave modeling of CS (as well as by almost everyone else). Investigations of the horizontal size of the region disturbed by the upward-propagating shock in the acoustic-wave propagation implies that the waves in H2v bright-point oscillations emanate from a point source with a diameter corresponding to the width of an intergranular lane, about 100 km, and reach a size of about 4000 km in the upper layers of the chromosphere. Linear, analytic modeling of waves emanating from a point source in a stratified atmosphere shows that the upward-expanding propagation channel does not have sharp boundaries and that the shape of the wave front depends on the order of the wave behind the initial pulse. Otherwise, the behavior of the linear waves resembles that of the nonlinear shock waves observed in the Sun. Research that needs to be done to firm up the conclusions reached above concerns the numerical simulations of nonlinear waves and oscillations in a three-dimensional stratified atmosphere with impulsive excitation, and observations linking directly the horizontal size of the disturbed area in upward propagation to individual waves.

Kalkofen, Wolfgang↗

A Theory of Ultrafast Charge Transfer Relaxation with Non-Innocent Solvent Molecules

In this work we revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE- HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797–4810, 1994] that has long challenged the applicability of Marcus’s theory of elec- tron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TD- DFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the sol- vent relaxation time); for non-polar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge trans- fer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environ- ments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetospheric substorms.

A proposed model of the substorm growth phase describes a gradual development of internal magnetospheric convection driven by enhanced field-line reconnection at the front-side magnetopause. The observed increased tail magnetic field, inward motion of the tail current system, and inward displacement of the plasma sheet inner edge are shown to follow from a line-tied inward motion of the dayside magnetopause and a slow development of magnetospheric convection. Resulting changes in the nightside auroral oval ionosphere lead to the formation of the auroral electrojet which is the ground signature (magnetically) of substorm breakup.

Coroniti, F. V.↗

Observations and seismoacoustic simulations of earthquake-generated infrasound waves in non-epicentral regions

We analysed infrasound waves associated with the Gyeongju earthquake (ML 5.8) that occurred on 2016 September 12, in the southeastern Korean Peninsula. For infrasound wave detection, the Progressive Multichannel Correlation method was applied to the infrasound data set recorded at seven arrays operating in South Korea at epicentral distances ranging from 178 to 472 km. Based on the back-projection method constrained by array-dependent celerity and azimuth deviation models, the source regions were identified in both the epicentral and non-epicentral regions. Remarkably, the non-epicentral secondary sources of this earthquake were located in regions with shallow water depths: (i) the western coastal area in the Yellow Sea and (ii) the shallow ocean basin and bank in the East Sea. The location results obtained from the earthquake could be corroborated through its foreshock (ML 5.1), yielding location results consistent with those of the main shock. The generation of infrasound waves over shallow water depths was fortuitously validated by direct recordings of dominant single-frequency (~0.3 Hz) infrasound waves at close range via temporary sensors near the ocean basin and bank. We interpreted that low-frequency infrasound signals could be generated from interactions among the ocean floor, shallow seawater and atmosphere. We performed numerical simulations of seismoacoustic fields to predict ground motions on the seafloor and acoustic transmission efficiency between the water and air interface. The simulations quantified the energy transfer through different media and clarified our observational results. We found that because this solid Earth‒water‒atmosphere coupled air wave has a relatively low frequency (~0.3 Hz), it can survive propagation over long distances compared with high-frequency infrasound waves generated in inland and mountain regions. In this study, we extend our understanding of water‒atmosphere coupling and the monitoring framework for earthquake-associated non-epicentral infrasound waves, encompassing not only inland ground shaking but also shallow sea regions located far from the epicentre.

Earthquake monitoring and test-ban treaty verifica↗

A guidance and navigation system for continuous low-thrust vehicles

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

Jack-Chingtse, C.↗

Scanning Backscatter Lidar Observations for Characterizing 4-D Cloud and Aerosol Fields to Improve Radiative Transfer Parameterizations

Clouds have a powerful influence on atmospheric radiative transfer and hence are crucial to understanding and interpreting the exchange of radiation between the Earth's surface, the atmosphere, and space. Because clouds are highly variable in space, time and physical makeup, it is important to be able to observe them in three dimensions (3-D) with sufficient resolution that the data can be used to generate and validate parameterizations of cloud fields at the resolution scale of global climate models (GCMs). Simulation of photon transport in three dimensionally inhomogeneous cloud fields show that spatial inhomogeneities tend to decrease cloud reflection and absorption and increase direct and diffuse transmission, Therefore it is an important task to characterize cloud spatial structures in three dimensions on the scale of GCM grid elements. In order to validate cloud parameterizations that represent the ensemble, or mean and variance of cloud properties within a GCM grid element, measurements of the parameters must be obtained on a much finer scale so that the statistics on those measurements are truly representative. High spatial sampling resolution is required, on the order of 1 km or less. Since the radiation fields respond almost instantaneously to changes in the cloud field, and clouds changes occur on scales of seconds and less when viewed on scales of approximately 100m, the temporal resolution of cloud properties should be measured and characterized on second time scales. GCM time steps are typically on the order of an hour, but in order to obtain sufficient statistical representations of cloud properties in the parameterizations that are used as model inputs, averaged values of cloud properties should be calculated on time scales on the order of 10-100 s. The Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE) provides exceptional temporal (100 ms) and spatial (30 m) resolution measurements of aerosol and cloud backscatter in three dimensions. HARLIE was used in a ground-based configuration in several recent field campaigns. Principal data products include aerosol backscatter profiles, boundary layer heights, entrainment zone thickness, cloud fraction as a function of altitude and horizontal wind vector profiles based on correlating the motions of clouds and aerosol structures across portions of the scan. Comparisons will be made between various cloud detecting instruments to develop a baseline performance metric.

Schwemmer, Geary K.↗

Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation

TerraSAR-X (TSX) and TanDEM-X (TDX) are two advanced synthetic aperture radar (SAR) satellites flying in formation. SAR interferometry allows a high resolution imaging of the Earth by processing SAR images obtained from two slightly different orbits. TSX operates as a repeat-pass interferometer in the first phase of its lifetime and will be supplemented after two years by TDX in order to produce digital elevation models (DEM) with unprecedented accuracy. Such a flying formation makes indeed possible a simultaneous interferometric data acquisition characterized by highly flexible baselines with range of variations between a few hundreds meters and several kilometers [1]. TSX has been successfully launched on the 15th of June, 2007. TDX is expected to be launched on the 31st of May, 2009. A safe and robust maintenance of the formation is based on the concept of relative eccentricity/inclination (e/i) vector separation whose efficiency has already been demonstrated during the Gravity Recovery and Climate Experiment (GRACE) [2]. Here, the satellite relative motion is parameterized by mean of relative orbit elements and the key idea is to align the relative eccentricity and inclination vectors to minimize the hazard of a collision. Previous studies have already shown the pertinence of this concept and have described the way of controlling the formation using an impulsive deterministic control law [3]. Despite the completely different relative orbit control requirements, the same approach can be applied to the TSX/TDX formation. The task of TDX is to maintain the close formation configuration by actively controlling its relative motion with respect to TSX, the leader of the formation. TDX must replicate the absolute orbit keeping maneuvers executed by TSX and also compensate the natural deviation of the relative e/i vectors. In fact the relative orbital elements of the formation tend to drift because of the secular non-keplerian perturbations acting on both satellites. The goal of the ground segment is thus to regularly correct this configuration by performing small orbit correction maneuvers on TDX. The ground station contacts are limited due to the geographic position of the station and the costs for contact time. Only with a polar ground station a contact visibility is possible every orbit for LEO satellites. TSX and TDX use only the Weilheim ground station (in the southern part of Germany) during routine operations. This station allows two scheduled contact per day for the nominal orbit configuration, meaning that the satellite conditions can be checked with an interval of 12 hours. While this limitation is usually not critical for single satellite operations, the visibility constraints drive the achievable orbit control accuracy for a LEO formation if a ground based approach is chosen. Along-track position uncertainties and maneuver execution errors affect the relative motion and can be compensated only after a ground station contact.

Ardaens, J. S.↗

Linear Seismic Source Equivalents in 3D Nonlinear Models: Effects of Embedded Small-Scale, Near-Source Structures

Gaining a proper understanding of how Earth structure and other near-source properties affect estimates of explosion yield is important to the nonproliferation mission. The yields of explosion sources are often based on seismic moment or waveform amplitudes. Quantifying how the seismic waveforms or estimates of the source characteristics derived from those waveforms are influenced by natural or man-made structures within the near-source region, where the wavefield behaves nonlinearly, is required to understand the full range of uncertainty in those yield estimates. We simulate tamped chemical explosions using a nonlinear, shock physics code and couple the ground motions beyond the elastic radius to a linear elastic, full waveform seismic simulation algorithm through 3D media. In order to isolate the effects of simple small-scale 3D structures on the seismic wavefield and linear seismic source estimates, we embed spheres and cylinders close to the fully- tamped source location within an otherwise homogenous half-space. The 3 m diameters spheres, given their small size compared to the predominate wavelengths investigated, not surprisingly are virtually invisible with only negligible perturbations to the far-field waveforms and resultant seismic source time functions. Similarly, the 11 m diameter basalt sphere has a larger, but still relatively minor impact on the wavefield. However, the 11 m diameter air-filled sphere has the largest impact on both waveforms and the estimated seismic moment of any of the investigated cases with a reduction of ~25% compared to the tamped moment. This significant reduction is likely due in large part to the cavity collapsing from the shock instead of being solely due to diffraction effects . Although the cylinders have the same diameters as the 3 m spheres, their length of interaction with the wavefield produces noticeable changes to the seismic waveforms and estimated source terms with reductions in the peak seismic moment on the order of 10%. Both the cylinders and 11 m diameter spheres generate strong shear waves that appear to emanate from body force sources.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure

We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin–orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction—even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson–Fischer point (which can lead to numerical instabilities). Here, we do not address magnetic fields here.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluation of total energy-rate feedback for glidescope tracking in wind shear

Low-altitude wind shear is recognized as an infrequent but significant hazard to all aircraft during take-off and landing. A total energy-rate sensor, which is potentially applicable to this problem, has been developed for measuring specific total energy-rate of an airplane with respect to the air mass. This paper presents control system designs, with and without energy-rate feedback, for the approach to landing of a transport airplane through severe wind shear and gusts to evaluate application of this sensor. A system model is developed which incorporates wind shear dynamics equations with the airplance equations of motion, thus allowing the control systems to be analyzed under various wind shears. The control systems are designed using optimal output feedback and are analyzed using frequency domain control theory techniques. Control system performance is evaluated using a complete nonlinear simulation of the airplane and a severe wind shear and gust data package. The analysis and simulation results indicate very similar stability and performance characteristics for the two designs. An implementation technique for distributing the velocity gains between airspeed and ground speed in the simulation is also presented, and this technique is shown to improve the performance characteristics of both designs.

Belcastro, C. M.↗

Advances and trends in structural and solid mechanics; Proceedings of the Symposium, Washington, DC, October 4-7, 1982

The mechanics of materials and material characterization are considered, taking into account micromechanics, the behavior of steel structures at elevated temperatures, and an anisotropic plasticity model for inelastic multiaxial cyclic deformation. Other topics explored are related to advances and trends in finite element technology, classical analytical techniques and their computer implementation, interactive computing and computational strategies for nonlinear problems, advances and trends in numerical analysis, database management systems and CAD/CAM, space structures and vehicle crashworthiness, beams, plates and fibrous composite structures, design-oriented analysis, artificial intelligence and optimization, contact problems, random waves, and lifetime prediction. Earthquake-resistant structures and other advanced structural applications are also discussed, giving attention to cumulative damage in steel structures subjected to earthquake ground motions, and a mixed domain analysis of nuclear containment structures using impulse functions.

Noor, A. K.↗

SHIVA: Spaceflight Holography Investigation in a Virtual Apparatus

SHIVA, a NASA spaceflight program, will exploit a unique, holography-based, diagnostics tool to test and apply a new, more general analytical solution to a fundamental equation of motion. The equation describes particle dynamics in fluids in a microgravity environment, and our solution represents the first analytical solution of it. When gravity is removed the equation becomes much more complex and had been solved previously only by numerical means. After our analytical solution has been validated it will be used as a tool for making additional measurements of the gravity environment. Our experiment will be optimized for testing the model, measuring g, g-jitter, and other microgravity phenomena. We will also collect data for which no current theory exists, This paper describes ground experiments and analysis that have been conducted by the investigator team to support the flight experiment.

Trolinger, James D.↗

A three-step model of high harmonic generation using complex classical trajectories

Highlights: • Rigorous trajectory formulation of strong field physics and high harmonic generation. • The Coulomb ground state is represented by an ensemble of complex trajectories. • Trajectories transition seamlessly from the ground state to ionization or recollision. • The ionized wavepacket is reproduced well from the complex trajectories. • Classically allowed and forbidden processes are treated in a single framework. We present a new trajectory formulation of high harmonic generation that treats classically allowed and classically forbidden processes within a single dynamical framework. Complex trajectories orbit the nucleus, producing the stationary Coulomb ground state. When the field is turned on, these complex trajectories continue their motion in the field-dressed Coulomb potential and therefore tunnel ionization, unbound evolution and recollision are described within a single, seamless framework. The new formulation can bring mechanistic understanding to a broad range of strong field physics effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗