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The classical work of Braginskii [Zh. Eksp. Teor. Fiz. 33, 459 (1957)] published almost 65 years ago was the first to provide a complete, closed fluid description of a weakly coupled, fully ionized, collisional plasma immersed in a magnetic field. While this fact is not widely known or appreciated, the Braginskii expressions for the electron transport coefficients can under- or overestimate the said coefficients by up to a factor of two for the electron Hall parameter of order unity (with the Hall parameter being proportional to the electron gyro-frequency over the electron–ion collision frequency) and can provide incorrect Hall-parameter scalings for its large values. Starting with the work of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], several papers attempted to correct the Braginskii electron results with varying degrees of success. Herein, we present our own effort with a hope to finally put this problem to rest. [ABSTRACT FROM AUTHOR]

Hydrodynamic properties of a turbulent two-phase flow (water droplets in the air) produced by a mechanical jet sprayer were studied experimentally and the drag force on the droplets was found to be anomalously weak; the drag coefficient is four to seven times smaller than predicted by standard expressions. Several hypotheses are suggested in this article and discussed in an attempt to explain the phenomenon. A two-dimensional model of the flow with the drag anomaly is proposed, which provides excellent agreement between the numerical and experimental results. Taking the drag anomaly into account allows an explanation of a number of features of the two-phase flow that are hard to explain otherwise, in particular, the fact that only about one-half of the initial water jet momentum was transferred to the gas during the experiment. [ABSTRACT FROM AUTHOR]

Revolver and Double Shell Inertial Confinement Fusion capsule designs hope to achieve a robust volumetric thermonuclear burn via the use of a high-Z pusher shell filled with a cryogenic D–T fuel. Unfortunately, mix of the pusher material into the fuel (gas) may adversely impact the burn performance. Hydrodynamic instability of the metal/gas interface as the mix source is an obvious concern, but 1D effects may also be detrimental. Such effects include plasma diffusion at material interfaces, which has been the subject of numerous theoretical, computational, and experimental investigations. However, other 1D mix mechanisms may exist, which have yet to be thoroughly explored. In particular, plasma kinetic effects may drive the mix when a shock breaks out of the metal/gas interface. Using the state-of-the-art, hybrid (kinetic-ion/fluid electron), multi-ion Vlasov–Fokker–Planck code, iFP, we show that shock-driven kinetic effects can reconfigure the interface and the interfacial width subsequently grows diffusively. Finally, we consider any implications for high-Z pusher designs. [ABSTRACT FROM AUTHOR]

A multi-species plasma ion transport model has been added to the adaptive mesh refinement radiation hydrodynamics code, xRage, to include kinetic transport effects when the particle distributions are near Maxwellian, with deviations proportional to a Knudsen number smaller than one. The model is first verified against self-similar solutions reported previously for the pressure equilibrium case, and next shown to be relatively insensitive to the choice of equation of state for the ions. Simulations are then used to examine Inertial Confinement Fusion dynamics in a 1D spherical geometry characteristic of an Omega implosion with a plastic (CH) shell containing a deuterium-tritium (DT) fuel, and with an added heavy ion impurity, argon. Even in this simplified 1D geometry, several interesting results are apparent. Ion stratification occurs similarly to that reported previously in purely kinetic simulations. The hydrogen in the plastic shell is transported radially inward, carried with the main drive shock, and thus migrates away from the C ions. The fuel D and T ions show the expected stratification with an increase in the lighter species concentration during the shock implosion and a reversal, with heavier species concentrations enhanced after shock expansion from the center. This stratification during burn yields different burn weighted ion temperatures, Ti, for the reactions, Ti[DD] < Ti[DT] < Ti[TT], consistent in their ordering with experiments. The mix widths per ion, measured where concentrations fall to 10% of their interfacial value, are evaluated as a function of time, and these are seen to be significant (of order 10 μm) even at early times, well before the main shock converges and before the shell deceleration. The 1D geometry may be a reasonable approximation for this early time mix and implies that this transport may play a role in reducing or modifying the instabilities driven by initial perturbations, ablation, and Rayleigh-Taylor unstable deceleration. An apparent depletion of the heavier ions seen at the incoming ion shock front warrants further investigation. [ABSTRACT FROM AUTHOR]

Double shell capsules are predicted to ignite and burn at relatively low temperature (∼3 keV) via volume ignition and are a potential low-convergence path to substantial α-heating and possibly ignition at the National Ignition Facility. Double shells consist of a dense, high-Z pusher, which first shock heats and then performs work due to changes in pressure and volume (PdV work) on deuterium-tritium gas, bringing the entire fuel volume to high pressure thermonuclear conditions near implosion stagnation. The high-Z pusher is accelerated via a shock and subsequent compression of an intervening foam cushion by an ablatively driven low-Z outer shell. A broad capsule design parameter space exists due to the inherent flexibility of potential materials for the outer and inner shells and foam cushion. This is narrowed down by design physics choices and the ability to fabricate and assemble the separate pieces forming a double shell capsule. We describe the key physics for good double shell performance, the trade-offs in various design choices, and the challenges for capsule fabrication. Both 1D and 2D calculations from radiation-hydrodynamic simulations are presented. [ABSTRACT FROM AUTHOR]

Anomalous thermonuclear yield degradation (i.e., that not describable by single-fluid radiation hydrodynamics) in Inertial Confinement Fusion (ICF) implosions is ubiquitously observed in both Omega and National Ignition experiments. Multiple experimental and theoretical studies have been carried out to investigate the origin of such a degradation. Relative concentration changes of fuel-ion species, as well as kinetically enhanced viscous heating, have been among possible explanations proposed for certain classes of ICF experiments. In this study, we investigate the role of such kinetic plasma effects in detail. To this end, we use the iFP code to perform multi-species ion Vlasov-Fokker-Planck simulations of ICF capsule implosions with the fuel comprising various hydrodynamically equivalent mixtures of deuterium (D) and helium-3 (3He), as in the original Rygg experiments [J. R. Rygg et al., Phys. Plasmas 13, 052702 (2006)]. We employ the same computational setup as in O. Larroche [Phys. Plasmas 19, 122706 (2012)], which was the first to simulate the experiments kinetically. However, unlike the Larroche study, and in partial agreement with experimental data, we find a systematic yield degradation in multi-species simulations versus averaged-ion simulations when the D-fuel fraction is decreased. This yield degradation originates in the fuel-ion species stratification induced by plasma shocks, which imprints the imploding system and results in the relocation of the D ions from the core of the capsule to its periphery, thereby reducing the yield relative to a non-separable averaged-ion case. By comparing yields from the averaged-ion kinetic simulations and from the hydrodynamic scaling, we also observe yield variations associated with ion kinetic effects other than fuel-ion stratification, such as ion viscous heating, which is typically neglected in hydrodynamic implosions' simulations. Since our kinetic simulations are driven by hydrodynamic boundary conditions at the fuel-ablator interface, they cannot capture the effects of ion viscosity on the capsule compression, or effects associated with the interface, which are expected to be important. Studies of such effects are left for future work. [ABSTRACT FROM AUTHOR]

The ion velocity structure of a strong collisional shock front in a plasma with multiple ion species is directly probed in laser-driven shock-tube experiments. Thomson scattering of a 263.25 nm probe beam is used to diagnose ion composition, temperature, and flow velocity in strong shocks ( M ∼ 6 ) propagating through low-density ( ρ ∼ 0.1 mg/cc) plasmas composed of mixtures of hydrogen (98%) and neon (2%). Within the preheat region of the shock front, two velocity populations of ions are observed, a characteristic feature of strong plasma shocks. The ionization state of the Ne is observed to change within the shock front, demonstrating an ionization-timescale effect on the shock front structure. The forward-streaming proton feature is shown to be unexpectedly cool compared to predictions from ion Fokker-Planck simulations; the neon ionization gradient is evaluated as a possible cause. [ABSTRACT FROM AUTHOR]

We derive fluid equations for describing steady-state planar shocks of a moderate strength (0 < M - 1≲1 with M being the shock Mach number) propagating through an unmagnetized quasineutral collisional plasma comprising two separate ion species. In addition to the standard fluid shock quantities, such as the total mass density, mass-flow velocity, and electron and average ion temperatures, the equations describe shock stratification in terms of variations in the relative concentrations and temperatures of the two ion species along the shock propagation direction. We have solved these equations analytically for weak shocks (0 < M - 1 ≪ 1), with the results depending on M, ratios of the ion masses and charges, and the upstream mass fraction of one of the ion species. These analytical results are instrumental for gaining understanding of the behavior of weak shocks, and they have been used to verify kinetic simulations of shocks in multi-ion plasmas. [ABSTRACT FROM AUTHOR]

A plasma transport model has been implemented in an Eulerian AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 lm and smaller for viscous effects to appear and 10 lm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more Lagrangian-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an Eulerian computation of complex and dynamically evolving mix regions. [ABSTRACT FROM AUTHOR]

For the first time, 41Ar produced by the (n,Y) reaction trom 40Ar in the beryllium shell ot a DT filled Inertial Confinement Fusion capsule has been measured. 41Ar is co-deposited with beryllium in the sputter deposition ot the capsule shell. Combined with a measurement ot the neutron yield, the radioactive 41Ar then quantifies the areal density of beryllium during the DT neutron production. The measured 1.15 ± 0.17 × 10+8 atoms of 41Ar are 2.5 times that from the best post-shot calculation, suggesting that the 41Ar and Be areal densities are correspondingly higher than those calculated. Possible explanations are that (1) the beryllium shell is compressed more than calculated, (2) beryllium has mixed into the cold DT ice, or more likely (3) less beryllium is ablated than calculated. Since only one DT filled beryllium capsule has been fielded at NIF, these results can be confirmed and expanded in the future. [ABSTRACT FROM AUTHOR]

A number of studies have considered how the rate of magnetic reconnection scales in large and weakly collisional systems by the modelling of long reconnecting current sheets. However, this setup neglects both the formation of the current sheet and the coupling between the diffusion region and a larger system that supplies the magnetic flux. Recent studies of magnetic island merging, which naturally include these features, have found that ion kinetic physics is crucial to describe the reconnection rate and global evolution of such systems. In this paper, the effect of a guide field on reconnection during island merging is considered. In contrast to the earlier current sheet studies, we identify a limited range of guide fields for which the reconnection rate, outflow velocity, and pile-up magnetic field increase in magnitude as the guide field increases. The Hall-MHD fluid model is found to reproduce kinetic reconnection rates only for a sufficiently strong guide field, for which ion inertia breaks the frozen-in condition and the outflow becomes Alfvóenic in the kinetic system. The merging of large islands occurs on a longer timescale in the zero guide field limit, which may in part be due to a mirror-like instability that occurs upstream of the reconnection region. [ABSTRACT FROM AUTHOR]

A Particle X-ray Temporal Diagnostic (PXTD) has been implemented on OMEGA for simultaneous time-resolved measurements of several nuclear products as well as the x-ray continuum produced in High Energy Density Plasmas and Inertial Confinement Fusion implosions. The PXTD removes systematic timing uncertainties typically introduced by using multiple instruments, and it has been used to measure DD, DT, D3He, and T3He reaction histories and the emission history of the x-ray core continuum with relative timing uncertainties within ±10-20 ps. This enables, for the first time, accurate and simultaneous measurements of the x-ray emission histories, nuclear reaction histories, their time differences, and measurements of Ti(t) and Te(t) from which an assessment of multiple-ion-fluid effects, kinetic effects during the shock-burn phase, and ion-electron equilibration rates can be made. [ABSTRACT FROM AUTHOR]

Mixing at interfaces in dense plasma media is a problem central to inertial confinement fusion and high energy density laboratory experiments. In this work, collisional particle-in-cell simulations are used to explore kinetic effects arising during the mixing of unmagnetized plasma media. Comparisons are made to the results of recent analytical theory in the small Knudsen number limit and while the bulk mixing properties of interfaces are in general agreement, some differences arise. In particular, "super-diffusive" behavior, large diffusion velocity, and large Knudsen number are observed in the low density regions of the species mixing fronts during the early evolution of a sharp interface prior to the transition to a slow diffusive process in the small-Knudsen-number limit predicted by analytical theory. A center-of-mass velocity profile develops as a result of the diffusion process and conservation of momentum. [ABSTRACT FROM AUTHOR]

The first indirect drive implosion experiments using Beryllium (Be) capsules at the National Ignition Facility confirm the superior ablation properties and elucidate possible Be-ablator issues such as hohlraum filling by ablator material. Since the 1990s, Be has been the preferred Inertial Confinement Fusion (ICF) ablator because of its higher mass ablation rate compared to that of carbon-based ablators. This enables ICF target designs with higher implosion velocities at lower radiation temperatures and improved hydrodynamic stability through greater ablative stabilization. Recent experiments to demonstrate the viability of Be ablator target designs measured the backscattered laser energy, capsule implosion velocity, core implosion shape from self-emission, and in-flight capsule shape from backlit imaging. The laser backscatter is similar to that from comparable plastic (CH) targets under the same hohlraum conditions. Implosion velocity measurements from backlit streaked radiography show that laser energy coupling to the hohlraum wall is comparable to plastic ablators. The measured implosion shape indicates no significant reduction of laser energy from the inner laser cone beams reaching the hohlraum wall as compared with plastic and high-density carbon ablators. These results indicate that the high mass ablation rate for beryllium capsules does not significantly alter hohlraum energetics. In addition, these data, together with data for low fill-density hohlraum performance, indicate that laser power multipliers, required to reconcile simulations with experimental observations, are likely due to our limited understanding of the hohlraum rather than the capsule physics since similar multipliers are needed for both Be and CH capsules as seen in experiments. [ABSTRACT FROM AUTHOR]

Paper I [A. N. Simakov and K. Molvig, Phys. Plasmas 23, 032115 (2016)] obtained a fluid description for an unmagnetized collisional plasma with multiple ion species. To evaluate collisional plasma transport fluxes, required for such a description, two linear systems of equations need to be solved to obtain corresponding transport coefficients. In general, this should be done numerically. Herein, the general formalism is used to obtain analytical expressions for such fluxes for several specific cases of interest: a deuterium-tritium plasma; a plasma containing two ion species with strongly disparate masses, which agrees with previously obtained results; and a three ion species plasma made of deuterium, tritium, and gold. These results can be used for understanding the behavior of the aforementioned plasmas, or for verifying a code implementation of the general multi-ion formalism. [ABSTRACT FROM AUTHOR]

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. - JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produce two systems of linear equations (for "vector" and "tensor" portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in Paper II [A. N. Simakov and K. Molvig, Phys. Plasmas 23, 032116 (2016)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas. [ABSTRACT FROM AUTHOR]

The fast rates of magnetic reconnection found in both nature and experiments are important to understand theoretically. Recently, it was demonstrated that two-fluid magnetic reconnection remains fast in the strong guide field regime, regardless of the presence of fast-dispersive waves. This conclusion is in agreement with recent results from kinetic simulations, and is in contradiction to the findings in an earlier two-fluid study, where it was suggested that fast-dispersive waves are necessary for fast reconnection. In this paper, we give a more detailed derivation of the analytic model presented in a recent letter and present additional simulation results to support the conclusions that the magnetic reconnection rate in this regime is independent of both collisional dissipation and system-size. In particular, we present a detailed comparison between fluid and kinetic simulations, finding good agreement in both the reconnection rate and overall length of the current layer. Finally, we revisit the earlier two-fluid study, which arrived at different conclusions, and suggest an alternative interpretation for the numerical results presented therein. [ABSTRACT FROM AUTHOR]

"Reduced" (i.e., simplified or approximate) ion-kinetic (RIK) models in radiation-hydrodynamic simulations permit a useful description of inertial-confinement-fusion (ICF) implosions where kinetic deviations from hydrodynamic behavior are important. For implosions in or near the kinetic regime (i.e., when ion mean free paths are comparable to the capsule size), simulations using a RIK model give a detailed picture of the time- and space-dependent structure of imploding capsules, allow an assessment of the relative importance of various kinetic processes during the implosion, enable explanations of past and current observations, and permit predictions of the results of future experiments. The RIK simulation method described here uses moment-based reduced kinetic models for transport of mass, momentum, and energy by long-mean-free-path ions, a model for the decrease of fusion reactivity owing to the associated modification of the ion distribution function, and a model of hydrodynamic turbulent mixing. The transport models are based on local gradientdiffusion approximations for the transport of moments of the ion distribution functions, with coefficients to impose flux limiting or account for transport modification. After calibration against a reference set of ICF implosions spanning the hydrodynamic-to-kinetic transition, the method has useful, quantifiable predictive ability over a broad range of capsule parameter space. Calibrated RIK simulations show that an important contributor to ion species separation in ICF capsule implosions is the preferential flux of longer-mean-free-path species out of the fuel and into the shell, leaving the fuel relatively enriched in species with shorter mean free paths. Also, the transport of ion thermal energy is enhanced in the kinetic regime, causing the fuel region to have a more uniform, lower ion temperature, extending over a larger volume, than implied by clean simulations. We expect that the success of our simple approach will motivate continued theoretical research into the development of first-principles-based, comprehensive, self-consistent, yet useable models of kinetic multispecies ion behavior in ICF plasmas. [ABSTRACT FROM AUTHOR]

In this letter, it is demonstrated using two-fluid simulations that low-β magnetic reconnection remains fast, regardless of the presence of fast dispersive waves, which have been previously suggested to play a critical role. To understand these results, a discrete model is constructed that offers scaling relationships for the reconnection rate and dissipation region (DR) thickness in terms of the upstream magnetic field and DR length. We verify these scalings numerically and show how the DR self-adjusts to process magnetic flux at the same rate that it is supplied to a larger region where two-fluid effects become important. The rate is therefore independent of the DR physics and is in good agreement with kinetic results. [ABSTRACT FROM AUTHOR]

Thermonuclear inertial confinement fusion plasmas confined by a heavy metal shell may be subject to the mixing of metal into the gas with a resulting degradation of fusion yield. Classical plasma diffusion driven by a number of gradients can provide a physical mechanism to produce atomic mix, possibly in concert with complex hydrodynamic structures and/or turbulence. This paper gives a derivation of the complete dissipative plasma hydrodynamics equations from kinetic theory, for a binary ionic mixture plasma consisting of electrons, e, a light (hydrogenic gas) ion species, i, and a heavy, high Z¡ plasma metal species, ¡. A single mean ionization state for the heavy metal, Z¡, is assumed to be provided by some independent thermodynamic model of the heavy metal Z¡ = Z¡ (ni, n¡, Te). The kinetic equations are solved by a generalized Chapman-Enskog expansion that assumes small Knudsen numbers for all species: NKe = ke/L 1, NKi = ki/L 1. The small electron to ion mass ratio, me/mi 1, is utilized to account for electron-ion temperature separation, Te = Ti, and to decouple the electron and ion transport coefficient calculations. This produces a well ordered perturbation theory for the electrons, resulting in the well known "Spitzer" problem of Spitzer and collaborators and solved independently by Braginskii. The formulation in this paper makes clear the inherent symmetry of the transport and gives an analytic solution for all values of the effective charge Zeff, including Zeff < 1. The electron problem also determines the ambipolar electric field and the "thermal forces" on both ion species that are needed for the ion kinetic solution. The ion transport problem makes use of the small mass ratio between ion species, mi/m¡ 1, to identify an "ion Spitzer problem" that is mathematically identical to that for the electrons but with different thermodynamic forces. The ionic scattering parameter, A¡ = n¡Z/ni, replaces the Ze¡¡ of the electron problem, but has an extended domain, 0 < A¡ < i, to cover all mixture fractions from the pure gas to the pure metal plasma. The extension of the Spitzer problem to include this extended domain is given in this work. The resulting transport equations for the binary gas-metal plasma mixture are complete and accurate through second order. All transport coefficients are provided in analytic form. [ABSTRACT FROM AUTHOR]

Beryllium ablators offer higher ablation velocity, rate, and pressure than their carbon-based counterparts, with the potential to increase the probability of achieving ignition at the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. We present here a detailed hydrodynamic stability analysis of low (NIF Revision 6.1) and high adiabat NIF beryllium target designs. Our targets are optimized to fully utilize the advantages of beryllium in order to suppress the growth of hydrodynamic instabilities. This results in an implosion that resists breakup of the capsule, and simultaneously minimizes the amount of ablator material mixed into the fuel. We quantify the improvement in stability of beryllium targets relative to plastic ones, and show that a low adiabat beryllium capsule can be at least as stable at the ablation front as a high adiabat plastic target. [ABSTRACT FROM AUTHOR]

For indirect drive inertial confinement fusion, Beryllium (Be) ablators offer a number of important advantages as compared with other ablator materials, e.g., plastic and high density carbon. In particular, the low opacity and relatively high density of Be lead to higher rocket efficiencies giving a higher fuel implosion velocity for a given X-ray drive; and to higher ablation velocities providing more ablative stabilization and reducing the effect of hydrodynamic instabilities on the implosion performance. Be ablator advantages provide a larger target design optimization space and can significantly improve the National Ignition Facility (NIF) [J. D. Lindl et al., Phys. Plasmas 11, 339 (2004)] ignition margin. Herein, we summarize the Be advantages, briefly review NIF Be target history, and present a modern, optimized, low adiabat, Revision 6 NIF Be target design. This design takes advantage of knowledge gained from recent NIF experiments, including more realistic levels of laser-plasma energy backscatter, degraded hohlraum-capsule coupling, and the presence of cross-beam energy transfer. [ABSTRACT FROM AUTHOR]

Recent work by Molvig et al. [Phys. Rev. Lett. 109, 095001 (2012)] examined how fusion reactivity may be reduced from losses of fast ions in finite assemblies of fuel. In this paper, this problem is revisited with the addition of an asymptotic boundary-layer treatment of ion kinetic losses. This boundary solution, reminiscent of the classical Milne problem from linear transport theory, obtains a free-streaming limit of fast ion losses near the boundary, where the diffusion approximation is invalid. Thermonuclear reaction rates have been obtained for the ion distribution functions predicted by this improved model. It is found that while Molvig's 'Knudsen distribution function' bounds from above the magnitude of the reactivity reduction, this more accurate treatment leads to less dramatic losses of tail ions and associated reduction of thermonuclear reaction rates for finite fuel volumes. [ABSTRACT FROM AUTHOR]

The use of the standard approaches for evaluating a neoclassical radial electric field Er, i.e., the Ampere (or gyro-Poisson) equation, requires accurate calculation of the difference between the gyroaveraged electron and ion particle fluxes (or densities). In the core of a tokamak, the nontrivial difference appears only in high-order corrections to a local Maxwellian distribution due to the intrinsic ambipolarity of particle transport. The evaluation of such high-order corrections may be inconsistent with the accuracy of the standard long wavelength gyrokinetic equation (GKE), thus imposing limitations on the applicability of the standard approaches. However, in the edge of a tokamak, charge-exchange collisions with neutrals and prompt ion orbit losses can drive non-intrinsically ambipolar particle fluxes for which a nontrivial (Er-dependent) difference between the electron and ion fluxes appears already in a low order and can be accurately predicted by the long wavelength GKE. The parameter regimes, where the radial electric field dynamics in the tokamak edge region is dominated by the non-intrinsically ambipolar processes, thus allowing for the use of the standard approaches, are discussed. [ABSTRACT FROM AUTHOR]

Nonlinear analytical theory of magnetic reconnection with a large guide field is presented for the first time. We confirm that two distinct steady-state reconnection regimes are possible depending on the relative size of the diffusion region thickness δ versus the sound gyroradius ρs. The reconnection is slow (Sweet–Parker-like) for δ>=ρs, and fast otherwise. However, unlike earlier work, we find that ion viscosity μ plays a fundamental role in the fast regime. In particular, for δ<ρs we obtain δ∝Ha-1, with Ha∝1/ημ as the Hartmann number, and the reconnection rate Ez∝Pr-1/2, with Pr=μ/η as the Prandtl number and η as the resistivity. If the perpendicular ion viscosity is employed for μ, the reconnection rate becomes independent of plasma β and collision frequencies, and therefore potentially fast. [ABSTRACT FROM AUTHOR]

Inertial effects in nonlinear magnetic reconnection are studied within the context of two-dimensional electron magnetohydrodynamics with resistive and viscous dissipation. Families of nonlinear solutions for relevant current sheet parameters are predicted and confirmed numerically in all regimes of interest. Electron inertia becomes important for current sheet thicknesses δ below the inertial length de. In this case, in the absence of electron viscosity, the sheet thickness experiences a nonlinear collapse to arbitrarily small scales. Viscosity regularizes solutions at small scales. The transition between resistive and viscous regimes features a hysteresis bifurcation that describes suitable current sheet solutions and reconnection rates. Away from transition, the nonlinear reconnection rate is found not to be explicitly dependent on the electron inertia or dissipation coefficients. [ABSTRACT FROM AUTHOR]

Magnetic reconnection is of fundamental importance for laboratory and naturally occurring plasmas. Reconnection usually develops on time scales which are much shorter than those associated with classical collisional dissipation processes, and which are not fully understood. While such dissipation-independent (or “fast”) reconnection rates have been observed in particle and Hall magnetohydrodynamics (MHD) simulations and predicted analytically in electron MHD, a quantitative analytical theory of fast reconnection valid for arbitrary ion inertial lengths di has been lacking. Here we propose such a theory without a guide field. The theory describes two-dimensional magnetic field diffusion regions, provides expressions for the reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and di. It also demonstrates that both open X-point and elongated diffusion regions allow dissipation-independent reconnection and reveals a possibility of strong dependence of the reconnection rates on di. [ABSTRACT FROM AUTHOR]

Short mean-free path two-fluid equations are employed to evaluate the lowest order nonambipolar radial current in plasma confined by a three-dimensional toroidal magnetic field. The result is used to obtain a necessary condition for intrinsic ambipolarity of plasma transport in such a field and to derive a criterion for the importance of the toroidal field ripple for collisional tokamak plasma rotation. The ripple effects on toroidal plasma rotation are found to be negligible if the characteristic perpendicular length scale is determined by the pedestal width of order the poloidal ion gyroradius (as may be the case in the H-mode regime), but may conceivably become important for more shallow plasma gradients. [ABSTRACT FROM AUTHOR]

Collisional plasma confined by magnetic fields in a screw-pinch and any axisymmetric, up-down symmetric closed magnetic field line configuration (such as a dipole or a field reversed configuration) is considered, and equations governing the evolution of the self-consistent radial electric field and flow are derived for each case, provided that effects of plasma fluctuations are negligible. [ABSTRACT FROM AUTHOR]

A simple zero-dimensional model is proposed that synthesizes the complex dynamics of driven, two-dimensional, magnetically reconnecting systems within the resistive magnetohydrodynamics (MHD) framework. The model applies to the so-called asymptotic regime of the well-known magnetic island coalescence problem, where well-separated macroscopic “ideal” and microscopic “resistive” regions are assumed to exist. The dynamics of the ideal region is described in terms of the Lorentz and pressure gradient forces on current filaments, and conservation of magnetic flux; that of the resistive region is described in terms of plasma flow and magnetic field magnitudes at the current sheet boundaries. Matching of the two regions provides the evolution equation for the current sheet thickness. The results for the O-point position versus time, reconnection rate, current sheet thickness, etc., at different resistivities obtained from the model agree well with those from the fully nonlinear two-dimensional reduced MHD simulation. [ABSTRACT FROM AUTHOR]

The effect of magnetic topology on ion and impurity flows in a tokamak is considered by investigating the consequences of (i) the reversal of toroidal and poloidal magnetic fields and currents; (ii) a switch from lower to upper X-point operation; (iii) poloidal magnetic field or plasma current reversal, and (iv) toroidal magnetic field reversal. The general symmetries associated with magnetic topology changes in tokamaks are employed to demonstrate that the flux surface flows inside and outside the separatrix observed in Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] can be used to determine the flow features, including neoclassical and turbulent effects and in the presence of charge exchange. [ABSTRACT FROM AUTHOR]

An additional contribution to the ion viscosity for a collisional plasma is evaluated and found to be the same order as other temperature gradient terms in the collisional perpendicular viscosity. The new contribution arises because of an explicitly collisional portion of the ion distribution function. The evaluation of the Pfirsch-Schlüter radial electric field in a collisional tokamak of arbitrary cross section is extended to retain the new contribution. In a spherical tokamak this new contribution must be retained in determining the radial electric field, while in a conventional tokamak it is small by 1/q2, where q is the safety factor. [ABSTRACT FROM AUTHOR]

The drift kinetic equation of Hazeltine [R. D. Hazeltine, Plasma Phys. 15, 77 (1973)] for a magnetized plasma of arbitrary collisionality is widely believed to be exact through the second order in the gyroradius expansion. It is demonstrated that this equation is only exact through the first order. The reason is that when evaluating the second-order gyrophase dependent distribution function, Hazeltine neglected contributions from the first-order gyrophase dependent distribution function, and then used this incomplete expression to derive the equation for the gyrophase independent distribution function. Consequently, the second-order distribution function and the stress tensor derived by this approach are incomplete. By relaxing slightly Hazeltine’s orderings one is able to obtain a drift kinetic equation accurate through the second order in the gyroradius expansion. In addition, the gyroviscous stress tensor for plasmas of arbitrary collisionality is obtained. [ABSTRACT FROM AUTHOR]

The neoclassical electric field in a tokamak is determined by the conservation of toroidal angular momentum. In the steady state in the absence of momentum sources and sinks it is explicitly evaluated by the condition that radial flux of toroidal angular momentum vanishes. For a collisional or Pfirsch-Schlüter short mean-free path ordering with subsonic plasma flows we find that there are two limiting cases of interest. The first is the simpler case of a strongly up-down asymmetric tokamak for which the lowest order gyroviscosity does not vanish and must be balanced by the leading order collisional viscosity in order to determine the radial electric field. The second case is the more complicated case of an up-down symmetric tokamak for which the gyroviscosity must be evaluated to higher order and again balanced by the lowest order collisional viscosity to determine the radial electric field. In general, both the lowest and the next order contributions from the gyroviscosity must be retained. [ABSTRACT FROM AUTHOR]

Short mean free path descriptions of magnetized plasmas have existed for almost 50 years so it is surprising to find that further modifications are necessary. The earliest work adopted an ordering in which the flow velocity is assumed to be comparable to the ion thermal speed. Later, less well-known studies extended the short mean free path treatment to the normally more interesting drift ordering in which the pressure times the mean flow velocity is comparable to the diamagnetic heat flow. Such an ordering is required to properly retain the temperature gradient terms in the viscosity that arise from the gyrophase dependent and independent portions of the distribution function. The treatment herein corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which use an approximate truncated polynomial expression for the distribution function and neglect the nonlinear piece of the collision operator due to its bilinear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, the electron parallel and gyroviscosities, which were not considered by previous drift ordered treatments, are evaluated. As in all drift orderings, the collision frequency is assumed small compared to the cyclotron frequency. However, the perpendicular scale lengths are permitted to be much less than (as well as comparable to) the parallel ones; as is the case in many magnetic confinement applications. As a result, the description is valid for turbulent and collisional transport, and also allows stronger poloidal density, temperature, and electrostatic potential variation in a tokamak than the standard Pfirsch–Schlüter ordering. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Starting from the complete short mean-free path fluid equations describing magnetized plasmas, assuming that plasma pressure is small compared to magnetic pressure, considering field-aligned plasma fluctuations, and adopting an ordering in which the plasma species flow velocities are much smaller than the ion thermal speed, a system of nonlinear equations for plasma density, electron and ion temperatures, parallel ion flow velocity, parallel current, electrostatic potential, perturbed parallel electromagnetic potential, and a perturbed magnetic field is derived. The equations obtained allow sharp equilibrium radial gradients of plasma quantities, and are shown to contain the neoclassical (Pfirsch–Schlüter) results for plasma current, parallel ion flow velocity (with the correct temperature gradient terms), and parallel gradients of equilibrium electron and ion temperatures. Special care is taken to ensure the divergence-free character of perturbed magnetic field and total plasma current, as well as local particle number and total energy conservation. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Effects of neutral particles on plasma flows and radial transport in a collision-dominated plasma are discussed, with a particular attention given to the modifications due to a poloidal variation of the neutral density. It is found that neutrals are of no importance if the radial particle transport is on a Pfirsch-Schlüter level. If, on the other hand, anomalous effects increase this transport to the Pfirsch-Schlüter radial heat transport level or higher, neutral effects become important in determining the radial heat transport, radial electric field, and the ion parallel flow velocity. [ABSTRACT FROM AUTHOR]

The stability of axisymmetric plasmas confined by a closed poloidal magnetic field is investigated using magnetohydrodynamic equations with anisotropic resistivity and sound waves retained. It is shown that when the system is axially and up-down symmetric and the plasma beta =(plasmapressure/magneticpressure) is finite, a resistive instability with a growth rate proportional to the cube root of the resistivity exists at the ideal stability boundary for up-down antisymmetric modes. Both the ideal and resistive stability of a Z-pinch equilibrium and the point dipole equilibrium of Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. 82, 2689 (1999)] are studied in detail. For a Z pinch, ideal instabilities are found to always dominate over resistive instabilities. For the point dipole, ideal up-down antisymmetric modes are always stable, and the only resistive instabilities permitted have a growth rate proportional to the resistivity times the square of the azimuthal mode number. [ABSTRACT FROM AUTHOR]

An axially symmetric plasma confined by a poloidal magnetic field with closed field lines is considered. A kinetic analysis of electromagnetic modes is performed for an “intermediate collisionality” ordering in which the particle collision frequency is much smaller than the transit or bounce frequency, but much larger than the mode, magnetic drift, and diamagnetic drift frequencies. A second order integrodifferential ballooning equation for electromagnetic modes is derived, which describes “high-frequency” ideal magnetohydrodynamic (MHD) and “low-frequency” entropy modes. The equation recovers the corresponding ideal MHD ballooning equation for the mode frequency greater than the magnetic drift and diamagnetic drift frequencies, and generalizes the results of an earlier electrostatic treatment of the entropy mode to arbitrary plasma beta. Ion gyrorelaxation collisional modifications to the entropy mode are also evaluated for arbitrary plasma beta and specific results are presented for both a point dipole and Z pinch. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Strong collisional shocks in multi-ion plasmas are featured in many environments, with Inertial Confinement Fusion (ICF) experiments being one prominent example. Recent work [Keenan et al., Phys. Rev. E 96, 053203 (2017)] answered in detail a number of outstanding questions concerning the kinetic structure of steady-state, planar plasma shocks, e.g., the shock width scaling by the Mach number, M. However, it did not discuss shock-driven ion-species stratification (e.g., relative concentration modification and temperature separation). These are important effects since many recent ICF experiments have evaded explanation by standard, single-fluid, radiation-hydrodynamic (rad-hydro) numerical simulations, and shock-driven fuel stratification likely contributes to this discrepancy. Employing the state-of-the-art Vlasov-Fokker-Planck code, iFP, along with multi-ion hydro simulations and semi-analytics, we quantify the ion stratification by planar shocks with the arbitrary Mach number and the relative species concentration for two-ion plasmas in terms of ion mass and charge ratios. In particular, for strong shocks, we find that the structure of the ion temperature separation has a nearly universal character across ion mass and charge ratios. Additionally, we find that the shock fronts are enriched with the lighter ion species and the enrichment scales as M4 for M ≫ 1. [ABSTRACT FROM AUTHOR]

A concise and complete differential equation determining the Pfirsch–Schlüter radial electric field in an up-down symmetric tokamak is presented in the limit of weak poloidal magnetic field. [ABSTRACT FROM AUTHOR]

A correction to the article "Magnetic topology effects on Alcator C-Mod flows" that was published in the 2006 issue is presented.

A correction to the article "A new, explicitly collisional contribution to the gyroviscosity and the radial electric field in a collisional tokamak," that was published in the 2005 issue is presented.

© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An axially symmetric plasma immersed in a poloidal magnetic field with closed lines is considered. Low-frequency electrostatic modes are studied kinetically for an “intermediate collisionality” ordering, in which the particle collision frequency is much smaller than the transit or bounce frequency, but much larger than the mode, magnetic drift, and diamagnetic drift frequencies. This ordering is appropriate for the Levitated Dipole Experiment (LDX) [J. Kesner et al., 17th IAEA Fusion Energy Conference, Yokahama, Japan (IAEA, Vienna, 1999)] and some other closed field line devices. “High-frequency” magnetohydrodynamic-like and “low-frequency” entropy modes are found and stability boundaries are determined. Collisional effects are considered and the corresponding ion gyro-relaxation effects are evaluated. These effects introduce dissipation (or inverse dissipation) and are shown to modify the stability picture considerably, while leaving large stability regions in the d, η parametric space, where η is the ratio of the gradients of temperature and density and d is the ratio of the diamagnetic and magnetic drift frequencies. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The interchange and ballooning stability of general anisotropic pressure plasma equilibria in a dipolar magnetic field are investigated. Starting with the Kruskal-Oberman form of the energy principle and using a Schwarz inequality, a fluid form of the anisotropic pressure energy principle is derived, which, after appropriate minimization, gives an interchange stability condition and an integro-differential ballooning equation. These results are applied to the case of an anisotropic pressure equilibrium having the perpendicular pressure equal to the parallel pressure times a constant and, in particular, to a model point dipole equilibrium. It is found that the model equilibrium is interchange stable for all plasma betas = (plasma pressure/magnetic pressure) and ballooning stable for all betas up to some critical value. The interesting planetary case of "tied" field lines is also considered. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The energy principle is employed to show that the equilibrium confined by the magnetic field of a point dipole is stable to ballooning modes. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recent experimental studies of MARFEs (Multifaceted Asymmetric Radiation From the Edge) in the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] and TEXTOR-94 (upgraded Torus Experiment for Technology Oriented Research) [A. M. Messiaen et al., Phys. Plasmas 4, 1690 (1997)] tokamaks reveal low plasma temperature T∼0.7 eV, strong hydrogen radiation, and plasma recombination in the MARFE region. These results contradict a well-accepted model, based on low-Z impurity radiation, and can be better explained by a nonlinear stage of an ionization-recombination instability, discussed recently in the literature. In this paper, a qualitative analysis of the instability is performed, and its growth rate γ and the range of wavelengths of unstable perturbations are estimated. It is found that the instability exists for plasma temperatures near the wall T≲10 eV; and for lower temperatures, T∼1 eV, volumetric recombination becomes important and can increase γ considerably compared to the case without the volumetric recombination. The results of the qualitative analysis are confirmed by a numerical solution of the linearized fluid equations with recombination and ionization describing MARFEs. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]