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We consider the treatment of electrons in kinetic simulations of edge plasmas. A fully kinetic treatment of electrons is expensive because of the short timescales associated with rapid streaming along field lines. Hence we survey a number of reduced options, of varying complexity, with particular attention to the “adiabatic model” commonly used for core plasmas. We note that the adiabatic model is the linear limit of a Boltzmann model, whose nonlinear form is more appropriate for the large potential variations in edge plasmas, and then consider extensions to the Boltzmann model which render it applicable to a plasma which includes end-loss in the scrape-off layer (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

With the next generation of high-power laser facilities for inertial fusion coming online1,2, ensuring laser beam propagation through centimetre-scale plasmas is a key physics issue for reaching ignition. Existing experimental results3,4,5 including the most recent one6 are limited to small laser spots, low-interaction laser beam energies and small plasma volumes of 1–2 mm. Here, we demonstrate the propagation of an intense, high-energy, ignition-size laser beam through fusion-size plasmas on the National Ignition Facility (NIF) and find the experimental measurements to agree with full-scale modelling. Previous attempts to apply computer modelling as a predictive capability have been limited by the inherently multiscale description of the full laser–plasma interaction processes7,8,9,10,11. The findings of this study validate supercomputer modelling as an essential tool for the design of future ignition experiments.

The numerical simulation of plasmas is a critical tool for inertial confinement fusion (ICF). We have been working to improve the predictive capability of a continuum laser plasma interaction code pF3d, which couples a continuum hydrodynamic model of an unmagnetized plasma to paraxial wave equations modeling the laser light. Advanced numerical techniques such as local mesh refinement, multigrid, and multifluid Godunov methods have been adapted and applied to nonlinear heat conduction and to multifluid plasma models. We describe these algorithms and briefly demonstrate their capabilities.

A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.

We investigate the use of adaptive mesh refinement in the simulation of laser plasma filamentation. A numerical algorithm is constructed to solve model equations consisting of a fluid approximation of a quasineutral plasma combined with a paraxial light propagation model. The algorithm involves high-resolution plasma and light model discretizations on a block-structured, locally refined grid hierarchy, which is dynamically modified during the time integration to follow evolving fine-scale solution features. Comparisons of the efficiency of this approach to that of uniform grid calculations are presented.

The first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalous radial transport.

Summary form only given. Experiments on the National Ignition Facility (NIF) have employed the first four beams to measure propagation and laser backscattering losses in large ignition-size plasmas. Gas-filled targets between 2 mm and 7 mm length have been heated from one side by overlapping the focal spots of the four beams from one quad operated at 351 nm with a total intensity of 2times1015 W cm-2. The targets were filled with 1 atm of CO2 producing of up to 7 mm long homogeneously heated plasmas with densities of ne = 5times1020 cm-3 and temperatures of Te = 2 keV. The high energy in a NIF quad of beams of 16 kJ, illuminating the target from one direction, creates unique conditions for the study of laser plasma interactions at scale lengths not previously accessible. The propagation through the large-scale plasma was measured with a gated X-ray imager that was filtered for 3.5 keV X-rays. These data indicate that the beams interact with the full length of this ignition-scale plasma during the last ~1 ns of the experiment when applying full laser beam smoothing consisting of phase plates, smoothing by spectral dispersion and polarization smoothing. Measurements that only apply phase plates show, laser beam filamentation and reduced propagation speed. These results demonstrate the NIF experimental capabilities and further provide a benchmark for three-dimensional modeling of the laser-plasma interactions at ignition-size scale lengths

Experiments demonstrate energy and power transfer between copropagating, same frequency, beams crossing at a small angle in a plasma with a Mach 1 flow. The process is interpreted as amplification of the low intensity probe beam by the stimulated scatter of the high intensity pump beam. The observed probe amplification increases slowly with pump intensity and decreases with probe intensity, indicative of saturation limiting the energy and power transfer due to ion-wave nonlinearities and localized pump depletion. The results are consistent with numerical modeling including ion-wave nonlinearities.

Geodesic acoustic modes (GAMs) are an important phenomenon in a tokamak edge plasma. They regulate turbulence in a low confinement (L-mode) regime and can play an important role in the low to high (L–H) mode transition. It is therefore of considerable importance to develop a detailed theoretical understanding of their dynamics and relaxation processes. The present work reports on the numerical modelling of collisionless GAM relaxation, including the effects of a strong radial electric field characteristic of a tokamak pedestal in a high confinement (H-mode) regime. The simulations demonstrate that the presence of a strong radial electric field enhances the GAM decay rate, and heuristic arguments elucidating this finding are provided. The numerical modelling is performed by making use of the continuum gyrokinetic code COGENT.

We present edge gyrokinetic simulations of tokamak plasmas using the fully non-linear (full-f) continuum code TEMPEST. A non-linear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson equation. We demonstrate the following. (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high q (tokamak safety factor), and are necessary to explain the damping observed in our TEMPEST q-scans and consistent with the experimental measurements of the scaling of the GAM amplitude with edge q 95 in the absence of obvious evidence that there is a strong q-dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and parallel flow characteristics qualitatively like those observed in experiments.

Experiments show that power is transferred between two copropagating 351nm laser beams crossing in an Al plasma when the frequency of the driven ion wave is shifted by a Mach 1 flow. The resonant amplification of a low-intensity (⩽2.5×1014W∕cm2) beam intersected by a high-intensity (7.0×1014W∕cm2) pump beam is determined by comparing the transmitted beam power to that measured in experiments where the plasma flow direction is reversed and the ion wave is evidently detuned. The polarization of the amplified light is also observed to align to the pump polarization consistent with ion-wave scattering. The amplification is found to reduce with probe-beam intensity demonstrating a nonlinear saturation mechanism that is effective when the ion-wave damping is weak, which is modeled with a calculation including both the nonlinear ion-wave frequency shifts due to ion trapping and whole-beam pump depletion.