Erik L. Vold

Classical transport equations for burning gas-metal plasmas

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 ZI plasma metal species, I. A single mean ionization state for the heavy metal, ZI, is assumed to be provided by some independent thermodynamic model of the heavy metal ZI=ZI(ni,nI,Te). The kinetic equations are solved by a generalized Chapman-Enskog expansion that assumes small Knudsen numbers for all species: NKe≡λe/L≪1,NKi≡λi/L≪1. The small electron to ion mass ratio, me/mi≪1, is utilized to account for electron-...

Fluid model equations for the tokamak plasma edge

Increasing evidence that the edge plasma plays a crucial role in global tokamak confinement motivates this study of two‐dimensional (2‐D) (θ,r) computational models of fluid transport in the edge plasma region. Fluid plasma equations, boundary conditions, and a coupled neutral–plasma model are developed assuming toroidal symmetry. A plasma potential equation is presented for consistent drift flow solution in the nonambipolar case. Simplified plasma equations are implemented in a 2‐D computational model. Results show large poloidal flux dominated by drift flow near the separatrix and parallel flow near the tokamak divertor target. Simultaneously large poloidal gradients in plasma potential and electric fields are seen. These may play a role in driving observed turbulent fluctuations in the edge plasma.

The effects of plasma diffusion and viscosity on turbulent instability growth

We perform two-dimensional simulations of strongly–driven compressible Rayleigh–Taylor and Kelvin–Helmholtz instabilities with and without plasma transport phenomena, modeling plasma species diffusion, and plasma viscosity in order to determine their effects on the growth of the hydrodynamic instabilities. Simulations are performed in hydrodynamically similar boxes of varying sizes, ranging from 1 μm to 1 cm in order to determine the scale at which plasma effects become important. Our results suggest that these plasma effects become noticeable when the box size is approximately 100 μm, they become significant in the 10 μm box, and dominate when the box size is 1 μm. Results suggest that plasma transport may be important at scales and conditions relevant to inertial confinement fusion, and that a plasma fluid model is capable of representing some of the kinetic transport effects.

The neutral diffusion approximation in a consistent tokamak edge plasma-neutral computation

Abstract A diffusion approximation for neutral transport in a plasma is developed for incorporation in a finite difference 2-D coupled plasma-neutral fluid computation model (EPIC). One energy group neutrals are assumed in thermal equilibrium locally with the plasma ions. Validity criteria for the model: λ 0 L T i is discussed where λ 0 is the neutral mean free path and L T i is the scale length for the ion temperature. Boundary conditions are derived to include particle recycling at the edge-core plasma interface, and neutral particle reflection from the pumping duct. The neutral diffusion model is incorporated in the 2-D computational code coupling the plasma-neutrals and compared extensively to Monte Carlo (DEGAS) calculations, showing that the neutral diffusion results are realistic over a wide range of limiter and divertor edge plasma conditions. Examples of the time dependent flux and the steady state density and temperature contours are shown for the ASDEX diverted tokamak, and are consistent with experimental data. The flux across the separatrix is seen to be dominated by recycled particles from the edge plasma. The neutral interaction source terms in the plasma density, parallel momentum and temperature equations are each seen to influence the plasma solution.

Visualization of expanding warm dense gold and diamond heated rapidly by laser-generated ion beams.

With the development of several novel heating sources, scientists can now heat a small sample isochorically above 10,000 K. Although matter at such an extreme state, known as warm dense matter, is commonly found in astrophysics (e.g., in planetary cores) as well as in high energy density physics experiments, its properties are not well understood and are difficult to predict theoretically. This is because the approximations made to describe condensed matter or high-temperature plasmas are invalid in this intermediate regime. A sufficiently large warm dense matter sample that is uniformly heated would be ideal for these studies, but has been unavailable to date. Here we have used a beam of quasi-monoenergetic aluminum ions to heat gold and diamond foils uniformly and isochorically. For the first time, we visualized directly the expanding warm dense gold and diamond with an optical streak camera. Furthermore, we present a new technique to determine the initial temperature of these heated samples from the measured expansion speeds of gold and diamond into vacuum. We anticipate the uniformly heated solid density target will allow for direct quantitative measurements of equation-of-state, conductivity, opacity, and stopping power of warm dense matter, benefiting plasma physics, astrophysics, and nuclear physics.

Uniform heating of materials into the warm dense matter regime with laser-driven quasimonoenergetic ion beams

In a recent experiment at the Trident laser facility, a laser-driven beam of quasimonoenergetic aluminum ions was used to heat solid gold and diamond foils isochorically to 5.5 and 1.7 eV, respectively. Here theoretical calculations are presented that suggest the gold and diamond were heated uniformly by these laser-driven ion beams. According to calculations and SESAME equation-of-state tables, laser-driven aluminum ion beams achievable at Trident, with a finite energy spread of ΔE/E∼20%, are expected to heat the targets more uniformly than a beam of 140-MeV aluminum ions with zero energy spread. The robustness of the expected heating uniformity relative to the changes in the incident ion energy spectra is evaluated, and expected plasma temperatures of various target materials achievable with the current experimental platform are presented.

Introduction and synopsis of the TITAN reversed-field-pinch fusion-reactor study

Abstract The TITAN reversed-field-pinch (RFP) fusion-reactor study has two objectives: to determine the technical feasibility and key developmental issues for an RFP fusion reactor operating at high power density: and to determine the potential economic (cost of electricity), operational (maintenance and availability), safety and environmental features of high mass-power-density fusion-reactor systems. Mass power density (MPD) is defined as the ratio of net electric output to the mass of the fusion power core (FPC). The FPC includes the plasma chamber, first wall, blanket, shield, magnets, and related structure. Two different detailed designs TITAN-I and TITAN-II, have been produced to demonstrate the possibility of multiple engineering-design approaches to high-MPD reactors. TITAN-I is a self-cooled lithium design with a vanadium-alloy structure. TITAN-II is a self-cooled aqueous loop-in-pool design with 9-C ferritic steel as the structural material. Both designs use RFP plasmas operating with essentially the same parameters. Both conceptual reactors are based on the DT fuel cycle, have a net electric output of about 1000 MWe, are compact, and have a high MPD of 800 kWe per tonne of FPC. The inherent physical characteristics of the RFP confinement concept make possible compact fusion reactors with such a high MPD. The TITAN designs would meet the U.S. criteria for the near-surface disposal of radioactive waste (Class C, IOCFR61) and would achieve a high Level of Safety Assurance with respect to FPC damage by decay afterheat and radioactivity release caused by accidents. Very importantly, a “single-piece” FPC maintenance procedure has been worked out and appears feasible for both designs. Parametric system studies have been used to find cost-optimized designs. to determine the parametric design window associated with each approach, and to assess the sensitivity of the designs to a wide range of physics and engineering requirements and assumptions. The design window for such compact RFP reactors would include machines with neutron wall loadings in the range of 10–20 MW/m 2 with a shallow minimum COE at about 18 MW/m 2 . Even though operation at the lower end of the this range of wall loading (10–12 MW/m 2 ) is possible, and may be preferable, the TITAN study adopted the design point at the upper end (18 MW/m 2 ) in order to quantify and assess the technical feasibility and physics limits for such high-MPD reactors. From this work, key physics and engineering issues central to achieving reactors with the features of TITAN-I and TITAN-II have emerged.

Overview of the TITAN-I fusion-power core

The TITAN reactor is a compact (major radius of 3.9 m and plasma minor radius of 0.6 m), high neutron wall loading (~18 MW/m 2 ) fusion energy system based on the reversed-field pinch (RFP) confinement concept. The reactor thermal power is 2918 MWt resulting in net electric output of 960 MWe and a mass power density of 700 kWe/tonne. The TITAN-I fusion power core (FPC) is a lithium, self-cooled design with vanadium alloy (V-3Ti-1Si) structural material. The surface heat flux incident on the first wall is ~4.5 MW/m 2 . The magnetic field topology of the RFP is favorable for liquid metal cooling. In the TITAN-I design, the first wall and blanket consist of single pass, poloidal flow loops aligned with the dominant poloidal magnetic field. A unique feature of the TITAN-I design is the use of the integrated-blanket-coil (IBC) concept. With the IBC concept the poloidal flow lithium circuit is also the electrical conductor of the toroidal-field and divertor coils. Three dimensional neutronics analysis yields a tritium breeding ratio of 1.18 and a molten salt extraction technique is employed for the tritium extraction system. Almost every FPC component would qualify for Class C waste disposal. The compactness of the design allows the use of single-piece maintenance of the FPC. This maintenance procedure is expected to increase the plant availability. The entire FPC operates inside a vacuum tank, which is surrounded by an atmosphere of inert argon gas to impede the flow of air in the system in case of an accident. The top-side coolant supply and return virtually eliminate the possibility of a complete LOCA occurring in the FPC. The peak temperature during a LOFA is 991 °C.

Plasma viscosity with mass transport in spherical inertial confinement fusion implosion simulations

The effects of viscosity and small-scale atomic-level mixing on plasmas in inertial confinement fusion (ICF) currently represent challenges in ICF research. Many current ICF hydrodynamic codes ignore the effects of viscosity though recent research indicates viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. We have implemented a Lagrangian hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diffusion approximation. The code is used to study ICF implosion differences with and without plasma viscosity and to determine the impacts of viscosity on temperature histories and neutron yield. It was found that plasma viscosity has substantial impacts on ICF shock dynamics characterized by shock burn timing, maximum burn temperatures, convergence ratio, and time history of neutron production rates. Plasma viscosity reduces the need for artificial viscosity to maintain numerical stability in the Lagrangian formulation and also modifies the flux-limiting needed for electron thermal conduction.

COMPUTATIONAL SIMULATIONS OF VORTICITY ENHANCED DIFFUSION

Computer simulations are used to investigate a phenomenon of vorticity enhanced diffusion (VED), a net transport and mixing of a passive scalar across a prescribed vortex flow field driven by a background gradient in the scalar quantity. The central issue under study here is the increase in scalar flux down the gradient and across the vortex field. The numerical scheme uses cylindrical coordinates centered with the vortex flow which allows an exact advective solution and 1D or 2D diffusion using simple numerical methods. In the results, the ratio of transport across a localized vortex region in the presence of the vortex flow over that expected for diffusion alone is evaluated as a measure of VED. This ratio is seen to increase dramatically while the absolute flux across the vortex decreases slowly as the diffusion coefficient is decreased. Similar results are found and compared for varying diffusion coefficient, D, or vortex rotation time, τv, for a constant background gradient in the transported scalar ...