The question of how to proceed toward ever more realistic plasma simulation studies using ever increasing computing power is addressed. The answer presented here is the M3D ͑Multilevel 3D͒ project, which has developed a code package with a hierarchy of physics levels that resolve increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale for the multilevel physics models is given. Each physics level is described and examples of its application are given. The existing physics levels are fluid models ͑3D configuration space͒, namely magnetohydrodynamic ͑MHD͒ and two-fluids; and hybrid models, namely gyrokinetic-energetic-particle/MHD ͑5D energetic particle phase-space͒, gyrokinetic-particle-ion/ fluid-electron ͑5D ion phase-space͒, and full-kinetic-particle-ion/fluid-electron level ͑6D ion phase-space͒. Resolving electron phase-space ͑5D or 6D͒ remains a future project.Phase-space-fluid models are not used in favor of ␦ f particle models. A practical and accurate nonlinear fluid closure for noncollisional plasmas seems not likely in the near future.

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In a plasma of multiple ion species, thermodynamic forces such as pressure and temperature gradients can drive ion species separation via inter-species diffusion. Unlike its neutral mix counterpart, plasma thermo-diffusion is found comparable to, or even much larger than, baro-diffusion. It is shown that such a strong effect is due to the long-range nature of the Coulomb potential, as opposed to short-range interactions in neutral gases. A special composition of the tritium and 3 He fuel is identified to have vanishing net diffusion during adiabatic compression, and hence provides an experimental test in which yield degradation is minimized during ICF implosions.In inertial confinement fusion (ICF), the central "hotspot" plasma, assembled by laser-driven spherical implosion [1], contains multiple ion species. Common combinations include low-Z fuel mixtures such as deuterium (D)/tritium (T) and D 3 He with possible addition of high-Z pusher ions, such as carbon or silicon, due to plastic or glass shell mixing [2,3] into the gas fill. Sometimes high-Z gas dopants such as Ar [4] or Kr [5] are intentionally introduced for diagnostic purposes, as well as to specifically study the pre-mix effects [6,7]. The powerful thermodynamic forces (e.g. pressure [8][9][10] and temperature gradients [9,10]) in an imploding target can drive ion species separation via inter-species diffusion. Observation of the resulting fuel stratification in the DT implosion, which upsets the initially optimal arrangement of equal number densities of D and T, in experiments [11] and kinetic simulations [12][13][14][15] have recently been reported. The targets with high-Z dopants show a particularly strong yield anomaly [6,7,16], suggesting that even stronger fuel stratification may take place.Perhaps the most intriguing physics aspect of interion-species diffusion in a collisional plasma is the role of thermo-diffusion, which, as its name suggests, is driven by the gradients of ion and electron temperatures. The novelty comes through as a sharp contrast to the better-known case of a neutral mixture, where thermo-diffusion is substantially less important than baro-diffusion, though often counteracts it [9]. According to statistical physics, thermo-diffusion strongly depends on the details of the collisional exchange between and within the species [10]. Due to the long range nature of Coulomb collisions in plasmas, as opposed to short range collisions between neutral particles, one may expect thermo-diffusion in plasmas and neutral mixtures to be fundamentally different. This difference becomes particularly striking with the observation that plasma baro-diffusion ratio k p is identical to its neutral counterpart [17].

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Electric field is a thermodynamic force that can drive collisional inter-ion-species transport in a multicomponent plasma. In an inertial confinement fusion (ICF) capsule, such transport causes fuel ion separation even with a target initially prepared to have equal number densities for the two fuel ion species. Unlike the baro-diffusion driven by ion pressure gradient and the thermo-diffusion driven by ion and electron temperature gradients, electro-diffusion has a critical dependence on the charge-to-mass ratio of the ion species. Specifically, it is shown here that electro-diffusion vanishes if the ion species have the same charge-to-mass ratio. An explicit expression for the electro-diffusion ratio is obtained and used to investigate the relative importance of electro- and baro-diffusion mechanisms. In particular, it is found that electro-diffusion reinforces baro-diffusion in the deuterium and tritium mix, but tends to cancel it in the deuterium and helium-3 mix.Comment: Submitted to Phys. Plasmas on 2012-03-06 (revised version 05/13/2012

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

Research on the National Spherical Torus Experiment, NSTX, targets physics understanding needed for extrapolation to a steady-state ST Fusion Nuclear Science Facility, pilot plant, or DEMO. The unique ST operational space is leveraged to test physics theories for next-step tokamak operation, including ITER. Present research also examines implications for the coming device upgrade, NSTX-U. An energy confinement time, τ E , scaling unified for varied wall conditions exhibits a strong improvement of B T τ E with decreased electron collisionality, accentuated by lithium (Li) wall conditioning. This result is consistent with nonlinear microtearing simulations that match the experimental electron diffusivity quantitatively and predict reduced electron heat transport at lower collisionality. Beam-emission spectroscopy measurements in the steep gradient region of the pedestal indicate the poloidal correlation length of turbulence of about ten ion gyroradii increases at higher electron density gradient and lower T i gradient, consistent with turbulence caused by trapped electron instabilities. Density fluctuations in the pedestal top region indicate ion-scale microturbulence compatible with ion temperature gradient and/or kinetic ballooning mode instabilities. Plasma characteristics change nearly continuously with increasing Li evaporation and edge localized modes (ELMs) stabilize due to edge density gradient alteration. Global mode stability studies show stabilizing resonant kinetic effects are enhanced at lower collisionality, but in stark contrast have almost no dependence on collisionality when the plasma is off-resonance. Combined resistive wall mode radial and poloidal field sensor feedback was used to control n = 1 perturbations and improve stability. The disruption probability due to unstable resistive wall modes (RWMs) was surprisingly reduced at very high β N /l i > 10 consistent with low frequency magnetohydrodynamic spectroscopy measurements of mode stability. Greater instability seen at intermediate β N is consistent with decreased kinetic RWM stabilization. A model-based RWM state-space controller produced long-pulse discharges exceeding β N = 6.4 and β N /l i = 13. Precursor analysis shows 96.3% of disruptions can be predicted with 10 ms warning and a false positive rate of only 2.8%. Disruption halo currents rotate toroidally and can have significant toroidal asymmetry. of this phenomenon in designing future RF systems. The snowflake divertor configuration enhanced by radiative detachment showed large reductions in both steady-state and ELM heat fluxes (ELMing peak values down from 19 MW m −2 to less than 1.5 MW m −2 ). Toroidal asymmetry of heat deposition was observed during ELMs or by 3D fields. The heating power required for accessing H-mode decreased by 30% as the triangularity was decreased by moving the X-point to larger radius, consistent with calculations of the dependence of E × B shear in the edge region on ion heat flux and X-point radius. Co-axial helicity injection reduced the induct...

Dynamics of runaway electrons in magnetic fields are governed by the competition of three dominant physics: parallel electric field acceleration, Coulomb collision, and synchrotron radiation. Examination of the energy and pitch-angle flows reveals that the presence of local vortex structure and global circulation is crucial to the saturation of primary runaway electrons. Models for the vortex structure, which has an O-point to X-point connection, and the bump of runaway electron distribution in energy space have been developed and compared against the simulation data. Identification of these velocity-space structures opens a new venue to reexamine the conventional understanding of runaway electron dynamics in magnetic fields.