Nonlocal Energy Transport Research Articles

Analytic insights into nonlocal energy transport: Steady state Fokker Planck theory in arbitrary Z plasmas

The generation of energetic electrons in laser fusion in an important issue. The electrons may either arise from a laser plasma instability, or from the uncoupled high temperature tail of a Maxwellian distribution. To study these in a laser fusion context, it is important to find a method accurate enough to be useful, and simple enough to be incorporated into a radiation hydrodynamics numerical simulation, the main workhorse for studying the laser fusion target. That is why analytic insights become important, they allow one to simplify the Fokker Planck theory so that a solution of it can be incorporated into a radiation hydrodynamic simulation. This work develops and analyzes a steady state Fokker Planck theory for plasmas of arbitrary Z. It develops a method of solving the simplified Fokker Planck method with a technique called sparse eigenfunction analysis. This method appears to work reasonably well when compared to the experimental results from the Rochester/NIF on plastic spherical targets with and without a silicon layer.

Analytic insights into nonlocal energy transport. III. steady state Fokker Planck theory in spherical and planar geometry

This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.

Tunneling and Filtering of Degenerate Microwave Modes in a Polarization-Dependent Waveguide Containing Index Gradient Barriers

The drastic difference between complex transmission coefficients for TE11 and TH11 GHz modes prop- agating through subwavelength gradient barriers in a metallic waveguide is examined. Amplitude-phase structures of the transmitted TE11 and TH11 modes are described in the framework of an exactly solvable model of these barriers. A sharp contrast in transmission is found between degenerate TE 11 and TH11 modes distinguished by their polarization structures due to polarization-dependent tunneling and nonlocal energy transport through thin gradient dielectric barriers.

Wave-based laser absorption method for high-order transport–hydrodynamic codes

Models of the laser propagation and absorption are a crucial part of the laser–plasma interaction models. Hydrodynamic codes are afflicted by usage of the simplified, not self-consistent, models of the geometrical optics, limiting their physical accuracy. A robust and efficient method is presented for computing the stationary wave solution, not restricted to this field of application exclusively. The method combines the semi-analytic and high-order differential approaches to benefit from both. Flexibility of the discretization is maintained, including the discontinuous methods. Performance of the model is evaluated for the problem of a transition layer by comparison with the analytic solution. Reliable results on coarse computational meshes and high convergence rates on fine meshes are obtained. The relevance to the current fusion research and non-local energy transport is pointed out.

Analytic insights into nonlocal energy transport. I. Krook models

In direct drive laser fusion, nonlocal transport of the more energetic electrons can have at least two potentially important effects. First, the most energetic electrons, furthest out on the tail of the distribution function, can cause preheat of the fuel deep inside the target. Second, nearby the nonlocal deposition of less energetic electrons can spread out the ablation layer, possibly having a stabilizing effect on the Rayleigh Taylor instability. This sequence of two papers treats two different methods of modeling nonlocal transport. For about 20 years, these phenomena have been treated with a Krook model for the electron collisions. However, different versions have given different results, especially as regards preheat. Our first paper attempts to analyze the various reasons for discrepancies and correct errors and derives a variety of simple formulas to evaluate preheat. The second paper offers, for the first time, a steady state, nonlocal method of using the Fokker Planck equation to evaluate the nonlocal transport and deposition of energetic electrons deposited by some mechanism, at some particular point in the plasma. Regarding ablation surface broadening, the two models are not very different; but regarding preheat, the Fokker Planck model gives orders of magnitude less. This is a very optimistic result for a direct drive laser fusion.

Analytic insights into nonlocal energy transport. II. Combined steady state Fokker Planck and Krook theory

In a direct drive laser fusion, nonlocal transport of the more energetic electrons can have at least two potentially important effects. First, the most energetic electrons, furthest out on the tail of the distribution function can cause preheat of the fuel deep inside the target. Second, nearby the nonlocal deposition of less energetic electrons can spread out the ablation layer, possibly having a stabilizing effect on the Rayleigh Taylor instability. This sequence of two papers treats two different methods of modeling nonlocal transport. For about 20 years, these phenomena have been treated with a Krook model for the electron collisions. However, different versions have given different results, especially as regards preheat. Our first paper attempts to analyze the various reasons for discrepancies, correct errors, and derives a variety of simple formula to evaluate preheat. The second paper offers, for the first time, a steady state, nonlocal method of using the Fokker Planck equation to evaluate the nonlocal transport and deposition of energetic electrons deposited by some mechanism, at some particular point in the plasma. Regarding ablation surface broadening, the two models are not very different; but regarding preheat, the Fokker Planck model gives orders of magnitude less. This is a very optimistic result for the direct drive laser fusion.

Extended Subadiabatic Layer in Simulations of Overshooting Convection

Abstract We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.

Group velocity and nonlocal energy transport velocity in finite photonic structures

We have derived an explicit relation between the group delay velocity vgd(ω), determined by the slope of the dispersion curves, and the nonlocal energy transport velocity vE(ω) in a lossless, finite, one-dimensional photonic crystal. Using this relation, we find a simple link between vgd(ω) and the group velocity vg(ω)(ω) defined in terms of the electromagnetic dwell time. It is shown that vE(ω)≤vgd(ω) for any frequency and vE(ω)=vgd(ω)=vg(ω)(ω) at the resonance frequencies of the transmission coefficient. It was established that the band structure of a finite periodic crystal is of great importance to describe and understand the properties of these velocities. In particular, it was shown that the occurrence of superluminal group delay velocities in these structures is closely related to the existence of null gaps in their dispersion relation. Calculations performed for a half-wave-quarter-wave stack show that the energy velocity remains always subluminal.

The development and experimental evaluation of a simple analytical model for the TPR in the build-up region of megavoltage photon beams

The purpose of this work was to develop a simple analytical model for the tissue phantom ratio (TPR) in the build-up region of megavoltage photon beams and to experimentally evaluate the model under a variety of clinically relevant field configurations. Considering electron contamination and primary photons as the main components of the absorbed dose in the build-up region, an analytic expression for the TPR was derived. The electron contamination component was addressed with a biexponential function; the primary photon component was treated as nonlocal energy transport, i.e., assuming the energy deposited by secondary electrons can be described by a biexponential mode similar to that of contaminating electrons. The model contains five independent constants, which were fitted experimentally. The accuracy of the model was evaluated by comparing its results with in-phantom measurements taken on square, rectangular, irregular, and wedged fields, for 6 and 15 MV photon beams on a GE-Saturne 41 accelerator. More specifically, the accuracy of the model was quantified using the gamma index with 2% dose and 2 mm spatial tolerances as described by Low et al. [Med. Phys. 25, 656-661 (1998)]. For square cerrobende blocked fields, the maximum recorded gamma indices were 0.42 and 0.54 for 6 and 15 MV beams, respectively. For "I" shaped fields, the corresponding maxima were 0.64 and 0.52, respectively, while for "cross" shaped fields they were 0.42 and 0.76. For rectangular 10 × 30 cm fields, the corresponding maxima were 0.32 and 0.42, and for 7 × 20 cm fields, they were 0.70 and 0.35, respectively. For square 10 × 10 cm and 15 × 15 cm fields with an acrylic tray, the maxima were 0.57 and 0.45 for 6 MV and 0.32 and 0.77 for 15 MV beams, respectively. For a 10 × 10 cm 60° wedged field, the maxima were 0.53 and 0.33 for 6 and 15 MV beams, respectively. In all examined cases of irregular, rectangular, square (with and without tray), and wedged fields, the gamma index was less than unity. Thus, the model correctly predicted TPR in all cases, using the defined criteria. A simple analytical model for the TPR in the build-up region was developed and evaluated experimentally. The model's predicted TPR values were compared with physical measurements for irregular, square (with and without tray), rectangular, and wedged fields, for 6 and 15 MV photon beams. In every case examined, the results of the model agreed with the experimental measurements based on specific quantitative agreement criteria. The model appears useful for predicting the TPR in the build-up region of megavoltage beams for different types of fields, in different configurations.

Non-local energy transport in tunneling and plasmonic structures

Various definitions of the velocity of propagation of the electromagnetic field have been adopted in experimental and theoretical studies of tunneling and plasmonic systems. Tunneling problems are often analyzed by invoking the group delay (or dwell time) velocities. On the other hand, slow light and plasmonic systems are considered by using the wave packet group velocity. This paper discusses various definitions for the velocity of the electromagnetic wave propagation and compares them in applications to the problems of slow light and superluminality in resonant and tunneling structures. Energy propagation is, in general, a nonlocal quantity and depends on the global properties of the system, rather than being simply a local quantity. The energy propagation velocity takes into account the non-local characteristics of the wave propagation and offers a natural generalization for those situations when the group velocity is ill defined or gives unphysical results. It is shown that the group delay velocity, which may be superluminal away from the resonance, becomes equal to the energy velocity at the resonant point.

Femtosecond microscopy of radial energy transport in a micrometer-scale aluminum plasma excited at relativistic intensity

Using femtosecond microscopy, we observe subpicosecond transport of thermal energy radially outward from a micrometer-sized spot of an aluminum target following P-polarized excitation at >10(18) W/cm2 with a 24 fs pulse. The rapid expansion coincides with the onset of nonlocal energy transport dominated by radiation and hot electrons.

Excitation of kinetic Alfvén turbulence by MHD waves and energization of space plasmas

Abstract. There is abundant observational evidence that the energization of plasma particles in space is correlated with an enhanced activity of large-scale MHD waves. Since these waves cannot interact with particles, we need to find ways for these MHD waves to transport energy in the dissipation range formed by small-scale or high-frequency waves, which are able to interact with particles. In this paper we consider the dissipation range formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field irrespectively of their frequency. We study a nonlocal nonlinear mechanism for the excitation of KAWs by MHD waves via resonant decay AW(FW)→KAW1+KAW2, where the MHD wave can be either an Alfvén wave (AW), or a fast magneto-acoustic wave (FW). The resonant decay thus provides a non-local energy transport from large scales directly in the dissipation range. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0~10-2. In turn, KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and acceleration in a variety of space plasmas. An anisotropic energy deposition in the field-aligned degree of freedom for the electrons, and in the cross-field degrees of freedom for the ions, is typical for KAWs. A few relevant examples are discussed concerning nonlinear excitation of KAWs by the MHD wave flux and consequent plasma energization in the solar corona and terrestrial magnetosphere.

Solar models with energy transport by weakly interacting particles

view Abstract Citations (111) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solar Models with Energy Transport by Weakly Interacting Particles Gilliland, R. L. ; Faulkner, J. ; Press, W. H. ; Spergel, D. N. Abstract Accretion by the sun of weakly interacting massive particles (WIMPs or cosmions) from a background population leads to efficient nonlocal energy transport in the solar core. At concentrations as low as 10 to the -11th by number, such particles, with ideal scattering cross sections, can lower the central temperature sufficiently to bring the predicted neutrino detection rate into agreement with observations. Since the perturbation is restricted to a small core, only small adjustments to the free parameters (initial hydrogen abundance and convection mixing length) are required to produce standard solar models with significantly lower (high-energy) neutrino fluxes. Publication: The Astrophysical Journal Pub Date: July 1986 DOI: 10.1086/164380 Bibcode: 1986ApJ...306..703G Keywords: Energy Transfer; Solar Neutrinos; Stellar Structure; Weak Interactions (Field Theory); Energy Distribution; Flux (Rate); Stellar Evolution; Stellar Models; Temperature Distribution; Solar Physics; ELEMENTARY PARTICLES; NEUTRINOS; SUN: INTERIOR full text sources ADS |