Comment on "Paleoclassical Transport in Low-Collisionality Toroidal Plasmas"

Paleoclassical transport [1] is a recently proposed fundamental process that is claimed to occur in resistive plasmas and to be missing in the collisional drift-kinetic equations (DKE) in standard use. In this Comment we raise three puzzles presented by paleoclassical transport as developed in [1], one to do with conservation and two concerning uniqueness

Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations

One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is that the inherent fluctuations in the turbulence, which limit the convergence achievable in the transport solver. In this article, we investigate the performance of one numerical coupling method in the presence of turbulent fluctuations. To test a particular numerical coupling method for the transport solver, we use an autoregressive-moving-average model to efficiently generate stochastic fluctuations with statistical properties resembling those of a gyrokinetic simulation. These fluctuations are then added to a simple, solvable problem, and we examine the behavior of the coupling method. We find that monitoring the residual as a proxy for the error can be misleading. From a pragmatic point of view, this study aids us in the full problem of transport coupled to DNS by predicting the amount of averaging required to reduce the fluctuation error and obtain a specific level of accuracy.Comment: 18 pages, 9 figure

Exact solution of the envelope equations for a matched quadrupole-focused beam in the low space-charged limit

The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)]in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant focusing function and neglects space charge. There are solutions in an infinite number of bands as the focus strength is increased. We show that all these bands are stable. Our explicit results for the phase advance sigma and the envelope a(z) are exact for all phase advances except multiples of 180o, where the behavior is singular. We find that the peak envelope size is minimized at sigma = 90o. Actual operation in the higher bands would require very large, very accurate field strengths and would produce significantly larger envelope excursions

Bringing global gyrokinetic turbulence simulations to the transport timescale using a multiscale approach

The vast separation dividing the characteristic times of energy confinement and turbulence in the core of toroidal plasmas makes first-principles prediction on long timescales extremely challenging. Here we report the demonstration of a multiple-timescale method that enables coupling global gyrokinetic simulations with a transport solver to calculate the evolution of the self-consistent temperature profile. This method, which exhibits resiliency to the intrinsic fluctuations arising in turbulence simulations, holds potential for integrating nonlocal gyrokinetic turbulence simulations into predictive, whole-device models.Comment: 7 pages, 3 figure

Comments on ECH current drive by asymmetric heating around the median plane (GA Technologies report No. GA-A18656, October 1986) by Tihiro Ohkawa

In a recent GA report Ohkawa describes a novel electron cyclotron current-drive (ECCD) scheme. Ohkawa finds a net toroidal plasma current driven by ''up-down'' asymmetries in the electron pressure anisotropy, i.e., differences in p/sub perpendicular/ - p/sub parallel/ evaluated at the same absolute value of B between the top and bottom half of the poloidal cross-section. Such up-down asymmetries are associated with the s-dependent, first order in nu/..omega../sub b/ part of the electron distribution function (s is distance along a magnetic field line). The current-drive efficiency estimated by Ohkawa is competitive with other rf current-drive schemes. Ohkawa's scheme is attractive because it appears that this scheme can produce an rf-driven current even when the electron-cyclotron power is dissipated on trapped electrons; and the scheme requires no selectivity in the sign of the parallel velocity of the electrons heated by the electron cyclotron wave. In sections I through III of this memo we analyze the current-drive calculation presented by Ohkawa. We conclude that, in the limit of long mean-free-path appropriate to current tokamak experiments and tokamak reactors, the current Ohkawa attempts to compute from a fluid model is a neoclassical correction to the Fisch-Boozer current. Neoclassical effects that give rise to corrections of this sort were first pointed out by Ohkawa in an earlier paper on ECH current drive. These neoclassical effects (which are associated with magnetic field variations and trapped particles) have been treated more accurately by using a kinetic rather than fluid theory in several recent papers. They are important because they can reduce the ECCD efficiency below the level computed by Fisch and Boozer

Millennial-scale deep ocean ventilation and sea-surface variability during the last four glacial cycles : a new assessment for the Northern Hemisphere ice-sheet growth

AGU Fall Meeting, S. Francisco (USA), 19-14 December 2007, Suppl., Abstract PP44B-0

First-principles based plasma profile predictions for optimized stellarators

In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators -- while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources -- are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein 7-X stellarator, where the central ion temperature was "clamped" to $T_i \approx 1.5$ keV regardless of the external heating power. By performing first-principles based simulations, the key mechanism leading to this effect is identified and guidelines for improving the plasma performance in future experimental campaigns are put forth. This work paves the way towards the use of high-fidelity models for the development of the next generation of stellarators, in which neoclassical and turbulent transport are optimized simultaneously

Calculation of Neutral Beam Injection into SSPX

The SSPX spheromak experiment has achieved electron temperatures of 350eV and confinement consistent with closed magnetic surfaces. In addition, there is evidence that the experiment may be up against an operational beta limit for Ohmic heating. To test this barrier, there are firm plans to add two 0.9MW Neutral Beam (NB) sources to the experiment. A question is whether the limit is due to instability. Since the deposited Ohmic power in the core is relatively small the additional power from the beams is sufficient to significantly increase the electron temperature. Here we present results of computations that will support this contention. We have developed a new NB module to calculate the orbits of the injected fast fast-ions. The previous computation made heavy use of tokamak ordering which fails for a tight-aspect-ratio device, where B{sub tor} {approx} B{sub pol}. The model calculates the deposition from the NFREYA package [1]. The neutral from the CX deposition is assumed to be ionized in place, a high-density approximation. The fast ions are then assumed to fill a constant angular momentum orbit. And finally, the fast ions immediately assume the form of a dragged down distribution. Transfer rates are then calculated from this distribution function [2]. The differential times are computed from the orbit times and the particle weights in each flux zone (the sampling bin) are proportional to the time spent in the zone. From this information the flux-surface-averaged profiles are obtained and fed into the appropriate transport equation. This procedure is clearly approximate, but accurate enough to help guide experiments. A major advantage is speed: 5000 particles can be processed in under 4s on our fastest LINUX box. This speed adds flexibility by enabling a ''large'' number of predictive studies. Similar approximations, without the accurate orbit calculation presented here, had some success comparing with experiment and TRANSP [3]. Since our procedure does not have multiple CX and relies on disparate time scales, more detailed understanding requires a ''complete'' NB package such as the NUBEAM [4] module, which follows injected fast ions along with their generations until they enter the main thermal distribution

The Search for Reconnection and Helicity During Formation of a Bounded Spheromak

Recent results from investigations using insertable magnetic probes at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] are presented. Experiments were carried out during pre-programmed, constant amplitude coaxial gun current pulses, where magnetic field increases stepwise with every pulse, but eventually saturates. Magnetic traces from the probe, which is electrically isolated from the plasma and spans the flux conserver radius, indicate there is a time lag at every pulse between the response to the current rise in the open flux surfaces (intercepting the electrodes) and the closed flux surfaces (linked around the open ones). This is interpreted as the time to buildup enough helicity in the open flux surfaces before reconnecting and merging with the closed ones. Future experimental and diagnostic plans to directly estimate the helicity in the open flux surfaces and measure reconnection are briefly discussed