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NASA NTRS1995

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Isar, Aurelian↗
NASA NTRS1994

Charged-particle motion in multidimensional magnetic-field turbulence

We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.

Giacalone, J.↗
NASA NTRS1994

Adiabatic invariants in stellar dynamics, 3: Application to globular cluster evolution

The previous two companion papers demonstrate that slowly varying perturbations may not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with R(sub g) less than or approximately 8 kpc: a concentration c = 1.5 cluster with R(sub g) kpc loses up to 95% of its initial mass in 15 Gyr. Only those with concentration c greater than or approximately 1.3 survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will decrease this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, x, which may be considerably larger than their initial values.

Weinberg, Martin D.↗
NASA NTRS1994

The onset of gravothermal oscillations in globular cluster evolution

We have carried out an extensive set of Fokker-Planck simulations of the evolution of globular clusters on very long timescales, up to 600 times the initial core collapse time t(sub cc). We consider an idealized equal mass star cluster, with a wide range of values for the total number of stars, 7000 less than N less than 2 x 10(exp 6). Our models include the heating effect of compact binaries formed in three-body encounters, which halts the initial core collapse and drives a core reexpansion. Postcollapse gravothermal oscillations of the cluster core are found to occur for all N approximately greater than or equal to 8000. For 8000 approximately less than or equal to N approximately less than or equal to 11,000, the oscillation has a simple, regular waveform with a single, well-defined period. For N approximately equals 12,000, the oscillations become nonlinear in a process resembling a period doubling. For N approximately greater than or equal to 14,000, the waveform of the oscillations becomes increasingly more irregular with increasing N, resembling chaotic behavior for N approximately greater than or equal to 15,000. During the oscillations, the core radius and core mass vary dramatically: by more than a factor of 10 for N greater than 15,000, by more than a factor of 100 for N greater than 5 x 10(exp 4), and by more than a factor of 1000 for N greater than 5 x 10(exp 5). However, even during the times of maximum expansion, the core contains only a small fraction of the cluster mass. For most N values, the maximum core mass at any time after core collapse is less than 1% of the cluster mass. The exceptions lie in the range 5 x 10(exp 4) approximately less than or equal to N approximately equal to or less than 2 x 10(exp 5), where the maximum post-collapse core mass reaches approximately 2% of the cluster mass. We discuss the observational implications of these predictions.

Breeden, Joseph L.↗
NASA NTRS1995

Stochastic charging of dust grains in planetary rings: Diffusion rates and their effects on Lorentz resonances

Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.

Schaffer, L.↗
NASA NTRS1995

A kinetic study of solar wind electrons in the transition region from collision dominated to collisionless flow

We have studied the evolution of the velocity distribution function of a test population of electrons in the solar corona and inner solar wind region, using a recently developed kinetic model. The model solves the time dependent, linear transport equation, with a Fokker-Planck collision operator to describe Coulomb collisions between the 'test population' and a thermal background of charged particles, using a finite differencing scheme. The model provides information on how non-Maxwellian features develop in the distribution function in the transition region from collision dominated to collisionless flow. By taking moments of the distribution the evolution of higher order moments, such as the heat flow, can be studied.

Lie-Svendsen, O.↗
NASA NTRS1996

Study of Nonclassical Fields in Phase-Sensitive Reservoirs

We show that the reservoir influence can be modeled by an infinite array of beam splitters. The superposition of the input fields in the beam splitter is discussed with the convolution laws for their quasiprobabilities. We derive the Fokker-Planck equation for the cavity field coupled with a phase-sensitive reservoir using the convolution law. We also analyze the amplification in the phase-sensitive reservoir with use of the modified beam splitter model. We show the similarities and differences between the dissipation and amplification models. We show that a super-Poissonian input field cannot become sub-Poissonian by the phase-sensitive amplification.

Kim, Myung Shik↗
NASA NTRS1998

Modeling Electric Field Influences on Plasmaspheric Refilling

We have a new model of ion transport that we have applied to the problem of plasmaspheric flux tube refilling after a geomagnetic disturbance. This model solves the Fokker-Planck kinetic equation by applying discrete difference numerical schemes to the various operators. Features of the model include a time-varying ionospheric source, self-consistent Coulomb collisions, field-aligned electric field, hot plasma interactions, and ion cyclotron wave heating. We see refilling rates similar to those of earlier observations and models, except when the electric field is included. In this case, the refilling rates can be quite different that previously predicted. Depending on the populations included and the values of relevant parameters, trap zone densities can increase or decrease. In particular, the inclusion of hot populations near the equatorial region (specifically warm pancake distributions and ring current ions) can dramatically alter the refilling rate. Results are compared with observations as well as previous hydrodynamic and kinetic particle model simulations.

Liemohn, M. W.↗
NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗
DOE OSTI2026

Formation and Redshift Evolution of Dark Matter Spikes

Dark matter density spikes forming around adiabatically growing black holes can dramatically enhance indirect and direct detection signals. Canonical predictions, however, assume a zero-mass seed in a purely dark matter environment and do not track the long-term dynamical impact of surrounding stars. We present a semi-analytic framework that first generalizes adiabatic spike formation to include finite seed masses, stellar cusps, and non-circular orbits, and then studies the subsequent cosmic evolution by solving coupled Fokker-Planck equations for the dark matter and stellar phase-space distributions, with a heating rate modulated by the cosmic star formation rate. Starting conservatively from canonical Gondolo-Silk spikes and marginalizing over astrophysical uncertainties, we find that stellar gravitational heating drives the inner slope towards $γ_χ\simeq 1.5$ within a few Gyrs (e.g by $z \lesssim 2$ for spikes formed at $z\simeq 10$), yielding overdensities two to four orders of magnitude below canonical expectations but still well above an NFW-like cusp. We provide redshift-dependent benchmarks for the column density and $J$-factor relevant to scattering, decay and annihilation signatures. Any robust interpretation of indirect dark matter signals from galactic nuclei must account for this evolution.

Herrera, Gonzalo [MIT, LNS; MIT, MKI; Harvard U.]↗
DOE OSTI2025

Nonequilibrium effects in high-gain inertial confinement fusion

Recent experimental demonstrations of ignition and target gain in inertial confinement fusion (ICF) have stimulated interest in exploring the fundamental physics of violent deuterium-tritium (DT) burn in high-gain ICF targets. A significant DT-burn fraction is a necessary condition for high energy gain and large neutron yields (>100MJ). Using classical molecular-dynamics (MD) simulations and a hybrid fluid-kinetic model, we examine how a large fraction of low-energy 𝛼 particles can kick D and T ions out of equilibrium in high-gain ICF targets. The MD results suggest that (1) temperatures of 𝑇 𝐷 and 𝑇 𝑇 can differ by as much as ∼20% of their mean temperature and (2) the deviation of the DT energy distribution from the Maxwell-Boltzmann function can exceed ∼30%. Some of these MD observations, such as the preferential heating of D ions by low-energy 𝛼 particles and the temperature separation, can be explained by a proposed hybrid fluid-kinetic model. Furthermore, the implication of such nonequilibrium effects on the DT reactivity is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1966

Cosmic-ray propagation. I.

Charged particle motion in random magnetic field, describing time evolution of particle distribution in pitch angle and position in terms of Fokker- Planck coefficients

INTERPLANETARY MAGNETIC FIELD↗
NASA NTRS1967

Dynamical friction.

Chandrasekhar dynamical friction theory for star in cluster adapted to Fokker-Plank electron in two-component plasma theory and including multiple encounters

STAR CLUSTER↗