Free-streaming Limit Research Articles

SLOW SHOCKS AND CONDUCTION FRONTS FROM PETSCHEK RECONNECTION OF SKEWED MAGNETIC FIELDS: TWO-FLUID EFFECTS

In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not perfectly anti-parallel, i.e. they are skewed, magnetic energy is first converted to bulk kinetic energy and then thermalized in slow magnetosonic shocks. We show that the latter resemble parallel shocks or hydrodynamic shocks for all skew angles except those very near the anti-parallel limit. As for parallel shocks, the structures of reconnection-driven slow shocks are best studied using two-fluid equations in which ions and electrons have independent temperature. Time-dependent solutions of these equations can be used to predict and understand the shocks from reconnection of skewed magnetic fields. The results differ from those found using a single-fluid model such as magnetohydrodynamics. In the two-fluid model electrons are heated indirectly and thus carry a heat flux always well below the free-streaming limit. The viscous stress of the ions is, however, typically near the fluid-treatable limit. We find that for a wide range of skew angles and small plasma beta an electron conduction front extends ahead of the slow shock but remains within the outflow jet. In such cases conduction will play a more limited role in driving chromospheric evaporation than has been predicted based on single-fluid, anti-parallel models.

A hybrid Godunov method for radiation hydrodynamics

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density E r and flux F r as well as a modified Godunov scheme for the material density ρ, momentum density m, and energy density E. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel’s principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati and Colella (2007) [41]. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.

A higher-order Godunov method for radiation hydrodynamics: Radiation subsystem

A higher order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second order accurate in both time and space, unsplit, asymptotically preserving, and uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Numerical tests demonstrate second order convergence across various parameter regimes.

The Wouthuysen-Field effect in a clumpy intergalactic medium

We show that, due to the high optical depth of the intergalactic medium to Lyman-alpha photons before the Epoch of Reionization, the Lyman-alpha scattering rate responsible for the Wouthuysen-Field effect from an isolated source will be negligible unless (1) there is sufficient time for the scattering photons to establish a steady state, or (2) the scattering gas is undergoing internal expansion or has a peculiar motion of tens to hundreds of km/s away from the source. We present steady-state solutions in the radiative diffusion approximation for the radiation field trapped in a clump of gas and show that this may result in an enhancement, by a factor of up to 10^6, of the strength of the Wouthuysen-Field effect over that obtained from the free-streaming limit. Solutions to the time-dependent diffusion equation, however, suggest that the timescales required to reach such a steady state will generally exceed the source lifetimes. In the presence of internal expansion, a steady state may be established as photons are redshifted into the red wing, and significant enhancement in the scattering rate may again be produced. Alternatively, a substantial scattering rate may arise in systems with a peculiar motion away from the source that redshifts the received radiation into the resonance line centre. As a consequence, at epochs z<30, when collisional decoupling is small except in dense regions, and prior to the establishment of any large-scale diffuse radiation field of resonance line photons, the 21cm signature from the Intergalactic Medium produced by the Wouthuysen-Field effect will in general trace the peculiar velocity field of the gas in addition to its density structure.

An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

Flux limited diffusion theory in a moving fluid

We extend the flux limited diffusion theory in a moving fluid to be able to treat any combination of absoption and scattering.The extended flux limited diffusion theory is fully flux limited and displays the correct behavior in the free streaming limit and in the near thermodynamic equilibrium limit.

Electron plasma oscillations at arbitrary Debye lengths

A solution is presented for electron plasma oscillations in a thermalized plasma, at arbitrary ratios of the Debye length AλD and the perturbation wavelength λ. The limit λD≪λ corresponds to the conventional fluid-like theory of small particle excursions, whereas λD≫λ corresponds to the free-streaming limit of strong kinetic phase mixing due to large particle excursions. A strong large-Debye-distance (LDD) effect already appears when λD ≳ λ. The initial amplitude of the fluid-like contribution to the macroscopic density perturbation then becomes small compared with the contribution from the free-streaming part. As a consequence, only a small fraction of the density perturbation remains after a limited number of kinetic damping times of the free-streaming part. The present analysis can be considered as a first exercise in an attempt to tackle the far more difficult problem of large-Larmor-radius (LLR) effects in a magnetized plasma. The analysis further shows that a representation in terms of normal modes of the form exp (— iωt) leads to amplitude factors of these modes that are related to each other and that depend on the combined free-streaming and fluid behaviour of the plasma. Consequently, these modes are coupled and cannot be treated as independent of each other.

Measurements of the heat flux, inverse bremsstrahlung absorption and equilibration in an under-dense laser heated plasma

A fully ionised hydrogen plasma of initial density approximately=5*1017 cm-3 and temperature approximately=12 eV is heated using a 1.053 mu m laser beam focussed to a spot of 200 mu m diameter with an irradiance of 5*1013 W cm-2. The resulting evolution of the plasma is monitored by Thomson scattering of a second laser beam at 5265 AA. Comparison with a one-dimensional two fluid hydrodynamic simulation shows that the inverse bremsstrahlung absorption coefficient should be modified to include the strong field correction and that the maximum heat flux is about 0.1 of the free streaming limit. The ratio of the electron mean free path to the temperature scale length is about 0.1 and Te/Ti approximately=5. The level of ion acoustic turbulence is observed to be small, close to thermal. The ion-electron equilibration rate is found to agree with the usual classical value.

Ion front and ablation in a freely expanding two-ion, two-temperature, noncollisional plasma

The equations for the free expansion of a two-ion, two-temperature, noncollisional, isothermal, and quasineutral plasma are derived and solved using a self-similar technique. The hydrodynamic variables are determined by four independent parameters, viz., α, the relative charge to mass ratio of the two ions; N10, the initial concentration of the main ion; τ, the temperature ratio of the hot and cold electrons; and ρ, the initial concentration ratio of the cold and hot electrons. The formation of an ion front in the numerically dominant species is predicted for the first time even under the quasineutral and isothermal assumptions. A necessary condition for the breakdown of the self-similar solution is derived. The location of the ion front and the point where the solution breaks down are tabulated as a function of the four parameters and the results are discussed. The expression for the normalized ion current, taking into account the flux limitation under the free-streaming limit, is derived. The expressions for the mass, momentum, and energy ablation are also derived and the relevant data are discussed with reference to laser–plasma interaction.

A Flux-Limited Diffusion Model for Charged-Particle Transport

AbstractA new algorithm for modeling charged-particle transport in a fully ionized plasma is presented. A standard multigroup discretization of the Fokker-Planck-Boltzmann equation is transport-corrected to implicitly include the anisotropic effects of both coulomb scattering and nuclear reactions. This allows the subsequent application of the Levermore flux-limited diffusion theory, which was originally developed for isotropic radiative transfer calculations. A finite differencing of the resulting spatial transport operator is constructed so as to yield centered and upwinded operators in the diffusion and free-streaming limits, respectively. The time integration is performed by the general purpose ordinary differential equation solver TORANAGA. This approach results in a highly vectorizable algorithm that has been implemented on the CRAY-1. Some numerical results are presented that compare this algorithm to the corresponding, but far more expensive, Monte Carlo calculations.

An observation of a high heat flux in a laser-heated plasma

A small volume of an initially uniform plasma is heated with a CO2 laser focused to an intensity of 1.3*1011 W cm-2. The evolving thermal and rarefaction wave is measured by Thomson scattering. Comparison of these measurements with a one-dimensional simulation shows that the heat flux reaches 15% of the free-streaming limit.

Thermal Instability and Magnetic Field Generated by Large Heat Flow in a Plasma, Especially under Laser-Fusion Conditions

Representing a large heat flow in a plasma as a flow of hot relatively collisionless electrons balanced by an opposing current of cold collisional electrons, it can be shown that an electrothermal instability can be induced in the cold resistive plasma when the heat flow exceeds about 3% of the free-streaming limit. This is nonconvective if the temperature of the cold plasma is less than $0.2{{n}_{e}}^{\frac{1}{4}}{Z}^{\frac{1}{2}}$\ifmmode^\circ\else\textdegree\fi{}K, with ${n}_{e}$ in ${\mathrm{m}}^{\ensuremath{-}3}$. The instability will lead to filamentary magentic structures with a typical growth time of a few picoseconds and wavelength about 10 \ensuremath{\mu}m.

The measurement of ion acoustic turbulence and reduced thermal conductivity caused by a large temperature gradient in a laser heated plasma

An extensive account is given of experiments in which an homogeneous preformed plasma of density 6*1016 cm-3 was heated by 10.6 mu m radiation focused on 1011 W cm-2. Ruby laser scattering gave space and time resolved measurements of the resultant density and temperature, showing large temperature gradients up to lambda e mod Delta T mod /T=0.5. Enhanced low frequency turbulence was observed. When compared with a one dimensional computer code, the observed temperature gradients imply that the heat flux was limited to 4+or-2% of the free streaming limit but that the absorption was 1.1+or-0.5 times the classical inverse bremsstrahlung absorption rate. The observed Te/Ti and lambda e mod Delta T mod /T were sufficient to excite heat flux driven ion acoustic turbulence, which explains the observed low frequency turbulence. This turbulence level is shown to be large enough to account for the observed thermal conductivity.

Observation of Severe Heat-Flux Limitation and Ion-Acoustic Turbulence in a Laser-Heated Plasma

The thermal conductivity of a plasma of density of 6 x 10/sup 16/ cm/sup -3/ is measured when it is heated by a 300-MW, 3-ns CO/sub 2/ laser pulse. The data are best represented using a heat flux which is limited to approx. 4% of the free-streaming limit. Low-frequency turbulence is observed of sufficient intensity to cause this flux limit.

Laser Fusion Hydrodynamics Calculations

Laser fusion hydrodynamics calculations include both the solution of the plasma hydrodynamics equations and transport equations for various nonthermal particles. The solution of the hydrodynamics equations is usually a combination of an explicit technique for the hyperbolic equation-of-motion and an implicit method for parabolic temperature equations. Transport equations are solved using fully implicit techniques to allow their time step to be as large as the time step used in the solution of the hydrodynamics equations.Multigroup flux-limited diffusion theory is often used to model the time-dependent transport problem. In this method, the diffusion coefficient is “adjusted” to provide a physically plausible result in the free streaming limit. The energy dependence of the distribution function is modeled using multigroup theory. Another method of solving the transport problem, time-dependent particle tracking, approximates the trajectory of the charged particles as straight lines, from creation to thermalization. This simple method accurately describes the slowing down of thermonuclear reaction products, while the flux-limited diffusion technique is more applicable to the transport of electrons and photons.

On the optimum laser power for maximum thermonuclear yield with deuterium-tritium pellets

Reports the results obtained in a parametric investigation of the thermonuclear yield of deuterium-tritium pellets as a function of the initial laser power. The hydrodynamic equations used to describe the pellet-laser interaction and subsequent evolution include the following physical processes: heat conduction with modifications due to the so-called free-streaming limit, energy exchange among the various particle species, ion viscosity, bremsstrahlung emission, classical absorption of laser power via inverse bremsstrahlung at densities below the critical density, rho c and phenomenological anomalous absorption at densities rho > rho c, and thermonuclear reactions. Spherical symmetry is assumed.