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Cohen, R. H.

Publications and source records attributed to Cohen, R. H..

Verification of 5D continuum gyrokinetic code COGENT: Studies of kinetic drift wave instability

COGENT (Continuum Gyrokinetic Edge New Technology) is a kinetic plasma simulation code that is being developed by the edge simulation laboratory (ESL) collaboration. The original version of the code has been developed in a 4D phase space (2D configuration space and 2D velocity space) to address kinetic plasma phenomena in a complex magnetic field geometry including the core, magnetic separatrix, and scrape-off layer regions. This paper is focused on extending the original 4D phase space to a 5D phase space (3D2V) to address full kinetic turbulences in a tokamak edge region. Here, we report on the current status of 5D COGENT, which presently operates in a shear-less, simple slab geometry. As a verification study, we use the problems of collision-less drift wave instability (universal instability) including its modification in the presence of collisional effects. The simulation model includes the gyrokinetic equations for ion and electron species coupled to the long-wavelength limit of the gyro-Poisson equation. Collisional effects are represented by the Krook collision model. Linear analytical results for the drift mode growth rate and real frequency are recovered, and the non-linear stage is modelled and analysed as well. In addition, extensive 5D runs have been performed to address the effects of the drift wave instability on blob/filamentary structures characteristic of a tokamak edge. Finally, a helical-shaped potential perturbation is observed to grow exponentially in time while spinning around the filament axis with electron drift frequency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Continuum kinetic modeling of the tokamak plasma edge

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas. The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comment on “Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake” [Phys. Plasmas 20, 102507 (2013)]

In the recently published paper “Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake” [Phys. Plasmas 20, 102507 (2013)], the authors raise interesting and important issues concerning divertor physics and design. However, the paper contains significant errors: (a) The conceptual framework used in it for the evaluation of divertor “quality” is reduced to the assessment of the magnetic field structure in the outer Scrape-Off Layer. This framework is incorrect because processes affecting the pedestal, the private flux region and all of the divertor legs (four, in the case of a snowflake) are an inseparable part of divertor operation. (b) The concept of the divertor index focuses on only one feature of the magnetic field structure and can be quite misleading when applied to divertor design. (c) The suggestion to rename the divertor configurations experimentally realized on NSTX (National Spherical Torus Experiment) and DIII-D (Doublet III-D) from snowflakes to X-divertors is not justified: it is not based on comparison of these configurations with the prototypical X-divertor, and it ignores the fact that the NSTX and DIII-D poloidal magnetic field geometries fit very well into the snowflake “two-null” prescription.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the applicability of the standard approaches for evaluating a neoclassical radial electric field in a tokamak edge region

The use of the standard approaches for evaluating a neoclassical radial electric field E r , 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 (E r -dependent) difference between the electron and ion fluxes appears already in a low order and can be accurately predicted by the long wavelength GKE. As a result, 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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Initial experimental evidence of self-collimation of target-normal-sheath-accelerated proton beam in a stack of conducting foils

Phenomena consistent with self-collimation (or weak self-focusing) of laser target-normal-sheath-accelerated protons was experimentally observed for the first time, in a specially engineered structure (“lens”) consisting of a stack of 300 thin aluminum foils separated by 50 μm vacuum gaps. The experiments were carried out in a “passive environment,” i.e., no external fields applied, neutralization plasma or injection of secondary charged particles was imposed. Experiments were performed at the petawatt “PHELIX” laser user facility (E = 100 J, Δt = 400 fs, λ = 1062 nm) at the “Helmholtzzentrum für Schwerionenforschung–GSI” in Darmstadt, Germany. The observed rms beam spot reduction depends inversely on energy, with a focusing degree decreasing monotonically from 2 at 5.4 MeV to 1.5 at 18.7 MeV. The physics inside the lens is complex, resulting in a number of different mechanisms that can potentially affect the particle dynamics within the structure. We present a plausible simple interpretation of the experiment in which the combination of magnetic self-pinch forces generated by the beam current together with the simultaneous reduction of the repulsive electrostatic forces due to the foils are the dominant mechanisms responsible for the observed focusing/collimation. This focusing technique could be applied to a wide variety of space-charge dominated proton and heavy ion beams and impact fields and applications, such as HEDP science, inertial confinement fusion in both fast ignition and heavy ion fusion approaches, compact laser-driven injectors for a Linear Accelerator (LINAC) or synchrotron, medical therapy, materials processing, etc.

43 PARTICLE ACCELERATORS↗

Electron cloud considerations for HIF drivers

Here, we review some previous results on electron-cloud dynamics and accumulation and the impact of electron clouds on ion beam dynamics, and assess these in the context of a magnetic-quadrupole-based heavy-ion fusion driver. We present a new analysis which exploits analytic solution of linearized envelope equations between accelerating gaps to derive a set of mapping equations which we use to extrapolate from previously obtained particle-simulation results for a beam transport system to an HIF driver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗