arXiv subjects

G. W. Hammett

Publications and source records attributed to G. W. Hammett.

34 records · Page 2Linked to original sources

arXiv2012

Gyrokinetic studies of the effect of beta on drift-wave stability in NCSX

The gyrokinetic turbulence code GS2 was used to investigate the effects of plasma beta on linear, collisionless ion temperature gradient (ITG) modes and trapped electron modes (TEM) in National Compact Stellarator Experiment (NCSX) geometry. Plasma beta affects stability in two ways: through the equilibrium and through magnetic fluctuations. The first was studied here by comparing ITG and TEM stability in two NCSX equilibria of differing beta values, revealing that the high beta equilibrium was marginally more stable than the low beta equilibrium in the adiabatic-electron ITG mode case. However, the high beta case had a lower kinetic-electron ITG mode critical gradient. Electrostatic and electromagnetic ITG and TEM mode growth rate dependencies on temperature gradient and density gradient were qualitatively similar. The second beta effect is demonstrated via electromagnetic ITG growth rates' dependency on GS2's beta input parameter. A linear benchmark with gyrokinetic codes GENE and GKV-X is also presented.

physics.plasm-ph↗

arXiv2011

Simulating Gyrokinetic Microinstabilities in Stellarator Geometry with GS2

The nonlinear gyrokinetic code GS2 has been extended to treat non-axisymmetric stellarator geometry. Electromagnetic perturbations and multiple trapped particle regions are allowed. Here, linear, collisionless, electrostatic simulations of the quasi-axisymmetric, three-field period National Compact Stellarator Experiment (NCSX) design QAS3-C82 have been successfully benchmarked against the eigenvalue code FULL. Quantitatively, the linear stability calculations of GS2 and FULL agree to within ~10%.

physics.plasm-ph↗

arXiv2011

An Enhanced Nonlinear Critical Gradient for Electron Turbulent Transport due to Reversed Magnetic Shear

The first nonlinear gyrokinetic simulations of electron internal transport barriers (e-ITBs) in the National Spherical Torus Experiment show that reversed magnetic shear can suppress thermal transport by increasing the nonlinear critical gradient for electron-temperature-gradient-driven turbulence to three times its linear critical value. An interesting feature of this turbulence is nonlinearly driven off-midplane radial streamers. This work reinforces the experimental observation that magnetic shear is likely an effective way of triggering and sustaining e-ITBs in magnetic fusion devices.

physics.plasm-ph↗

arXiv2009

Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Direct coupling between a transport solver and local, nonlinear gyrokinetic calculations using the multiscale gyrokinetic code TRINITY [M. Barnes, Ph.D. thesis, arxiv:0901.2868] is described. The coupling of the microscopic and macroscopic physics is done within the framework of multiscale gyrokinetic theory, of which we present the assumptions and key results. An assumption of scale separation in space and time allows for the simulation of turbulence in small regions of the space-time grid, which are embedded in a coarse grid on which the transport equations are implicitly evolved. This leads to a reduction in computational expense of several orders of magnitude, making first-principles simulations of the full fusion device volume over the confinement time feasible on current computing resources. Numerical results from TRINITY simulations are presented and compared with experimental data from JET and ASDEX Upgrade plasmas.

physics.plasm-ph↗

arXiv2009

Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas

We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations. In each of the physically distinct scale ranges, the kinetic problem is systematically reduced to a more tractable set of equations. In the "inertial range" above the ion gyroscale, the kinetic cascade splits into a cascade of Alfvenic fluctuations, which are governed by the RMHD equations at both the collisional and collisionless scales, and a passive cascade of compressive fluctuations, which obey a linear kinetic equation along the moving field lines associated with the Alfvenic component. In the "dissipation range" between the ion and electron gyroscales, there are again two cascades: the kinetic-Alfven-wave (KAW) cascade governed by two fluid-like Electron RMHD equations and a passive phase-space cascade of ion entropy fluctuations. The latter cascade brings the energy of the inertial-range fluctuations that was damped by collisionless wave-particle interaction at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for these cascades. Astrophysical and space-physical applications are discussed in detail.

astro-ph↗

arXiv2008

Howes et al. Reply

Howes et al. Reply to Comment on "Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas" arXiv:0711.4355

astro-ph↗

arXiv2008

Gyrokinetic turbulence: a nonlinear route to dissipation through phase space

This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring at spatial scales smaller than the ion gyroscale and in velocity space. Scaling relations for the resulting fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The importance of adequately modeling and resolving collisions in gyrokinetic simulations is biefly discussed, as well as the relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas.

physics.plasm-ph↗

arXiv2008

Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests

A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-Theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2 is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.

physics.plasm-ph↗

arXiv2008

An iterative semi-implicit scheme with robust damping

An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the monitoring and control of the error introduced by the SI operator. This iteration essentially turns a semi-implicit method into a fully implicit method. Accuracy, rather than stability, determines the timestep. The scheme is second-order accurate and shown to be equivalent to a simple preconditioning method. We show how the diffusion operators can be handled so as to yield the property of robust damping, i.e., dissipating the solution at all values of the parameter $\mathcal D\dt$, where $\mathcal D$ is a diffusion operator and $\dt$ the timestep. The overall scheme remains second-order accurate even if the advection and diffusion operators do not commute. In the limit of no physical dissipation, and for a linear test wave problem, the method is shown to be symplectic. The method is tested on the problem of Kinetic Alfvén wave mediated magnetic reconnection. A Fourier (pseudo-spectral) representation is used. A 2-field gyrofluid model is used and an efficacious k-space SI operator for this problem is demonstrated. CPU speed-up factors over a CFL-limited explicit algorithm ranging from $\sim20$ to several hundreds are obtained, while accurately capturing the results of an explicit integration. Possible extension of these results to a real-space (grid) discretization is discussed.

physics.comp-ph↗

arXiv2007

Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas

This letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.

astro-ph↗

arXiv2005

Plasma instabilities and magnetic-field growth in clusters of galaxies

We show that under very general conditions, cluster plasmas threaded by weak magnetic fields are subject to very fast growing plasma instabilities driven by the anisotropy of the plasma pressure (viscous stress) with respect to the local direction of the magnetic field. Such an anisotropy will naturally arise in any weakly magnetized plasma that has low collisionality and is subject to stirring. The magnetic field must be sufficiently weak for the instabilities to occur, viz., beta>Re^{1/2}. The instabilities are captured by the extended MHD model with Braginskii viscosity. However, their growth rates are proportional to the wavenumber down to the ion gyroscale, so MHD equations with Braginskii viscosity are not well posed and a fully kinetic treatment is necessary. The instabilities can lead to magnetic fields in clusters being amplified from seed strength of ~10^{-18} G to dynamically important strengths of ~10 microG on cosmologically trivial time scales (~10^8 yr). The fields produced during the amplification stage are at scales much smaller than observed. Predicting the saturated field scale and structure will require a kinetic theory of magnetized cluster turbulence.

astro-ph↗

arXiv2004

Magnetised plasma turbulence in clusters of galaxies

Cluster plasmas are magnetised already at very low magnetic field strength. Low collisionality implies that conservation of the first adiabatic invariant results in an anisotropic viscous stress (Braginskii viscosity) or, equivalently, anisotropic plasma pressure. This triggers firehose and mirror instabilities, which have growth rates proportional to the wavenumber down to scales of the order of ion Larmor radius. This means that MHD equations with Braginskii viscosity are not well posed and fully kinetic description is necessary. In this paper, we review the basic picture of small-scale dynamo in the cluster plasma and attempt to reconcile it with the existence of plasma instabilities at collisionless scales.

astro-ph↗

arXiv2004

Saturated State of the Nonlinear Small-Scale Dynamo

We consider the problem of incompressible, forced, nonhelical, homogeneous and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.

astro-ph↗

arXiv2003

Non-existence of normal tokamak equilibria with negative central current

Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.

physics.plasm-ph↗

arXiv2002

A model of nonlinear evolution and saturation of the turbulent MHD dynamo

The growth and saturation of magnetic field in conducting turbulent media with large magnetic Prandtl numbers are investigated. This regime is very common in low-density hot astrophysical plasmas. During the early (kinematic) stage, weak magnetic fluctuations grow exponentially and concentrate at the resistive scale, which lies far below the hydrodynamic viscous scale. The evolution becomes nonlinear when the magnetic energy is comparable to the kinetic energy of the viscous-scale eddies. A physical picture of the ensuing nonlinear evolution of the MHD dynamo is proposed. Phenomenological considerations are supplemented with a simple Fokker--Planck model of the nonlinear evolution of the magnetic-energy spectrum. It is found that, while the shift of the bulk of the magnetic energy from the subviscous scales to the velocity scales may be possible, it occurs very slowly -- at the resistive, rather than dynamical, time scale (for galaxies, this means that generation of large-scale magnetic fields cannot be explained by this mechanism). The role of Alfvenic motions and the implications for the fully developed isotropic MHD turbulence are discussed.

astro-ph↗

arXiv2002

The nonlinear small-scale dynamo and isotropic MHD turbulence

This is a brief review of the main results of our recent studies of the nonlinear evolution of the small-scale MHD dynamo in the high-Prandtl-number regime and of the structure of the resulting saturated state of the isotropic homogeneous MHD turbulence. It is emphasized that the MHD regime without a uniform mean field (as is the case in our studies) is fundamentally different from the one in which such a field is externally imposed. The ability of the turbulence to bend and fold the magnetic-field lines leads to the emergence of a distinctive small-scale structure. The fields are organized in folds of characteristic length comparable to the size of the largest turbulent eddies with spatial-direction reversals at the resistive scale. These folds are very hard to destroy. In the nonlinear regime, the folding structure coexists with Alfven waves propagating along the folds. The turbulent energy injected by the forcing is dissipated in part resistively via the small-scale magnetic fields, and in part viscously via the Alfven waves.

astro-ph↗