801 research outputs found
A gyrokinetic model for the plasma periphery of tokamak devices
A gyrokinetic model is presented that can properly describe strong flows,
large and small amplitude electromagnetic fluctuations occurring on scale
lengths ranging from the electron Larmor radius to the equilibrium
perpendicular pressure gradient scale length, and large deviations from thermal
equilibrium. The formulation of the gyrokinetic model is based on a second
order description of the single charged particle dynamics, derived from Lie
perturbation theory, where the fast particle gyromotion is decoupled from the
slow drifts, assuming that the ratio of the ion sound Larmor radius to the
perpendicular equilibrium pressure scale length is small. The collective
behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that
describes the evolution of the gyroaveraged distribution function and includes
a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is
then developed into a set of coupled fluid equations referred to as the
gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged
distribution function is expanded onto a velocity-space Hermite-Laguerre
polynomial basis and the gyrokinetic equation is projected onto the same basis,
obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion
coefficients. The Hermite-Laguerre projection is performed accurately at
arbitrary perpendicular wavenumber values. Finally, the self-consistent
evolution of the electromagnetic fields is described by a set of gyrokinetic
Maxwell's equations derived from a variational principle, with the velocity
integrals of the gyroaveraged distribution function explicitly evaluated
Validating modelling assumptions of alpha particles in electrostatic turbulence
To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium
distribution must be used. In the work, the response of high-energy alpha
particles to electrostatic turbulence has been analyzed for several different
tokamak parameters. Our results are consistent with known scalings and
experimental evidence that alpha particles are generally well-confined: on the
order of several seconds. It is also confirmed that the effect of alphas on the
turbulence is negligible at realistically low concentrations, consistent with
linear theory. It is demonstrated that the usual practice of using a
high-temperature Maxwellian gives incorrect estimates for the radial alpha
particle flux, and a method of correcting it is provided. Furthermore, we see
that the timescales associated with collisions and transport compete at
moderate energies, calling into question the assumption that alpha particles
remain confined to a flux surface that is used in the derivation of the
slowing-down distribution.Comment: 23 pages, 13 figures, submitted to the Journal of Plasma Physic
ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry
This paper presents the current state of the global gyrokinetic code ORB5 as
an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177
409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of
equations using a PIC scheme and also includes collisions and strong flows. The
code assumes multiple gyrokinetic ion species at all wavelengths for the
polarization density and drift-kinetic electrons. Variants of the physical
model can be selected for electrons such as assuming an adiabatic response or a
``hybrid'' model in which passing electrons are assumed adiabatic and trapped
electrons are drift-kinetic. A Fourier filter as well as various control
variates and noise reduction techniques enable simulations with good
signal-to-noise ratios at a limited numerical cost. They are completed with
different momentum and zonal flow-conserving heat sources allowing for
temperature-gradient and flux-driven simulations. The code, which runs on both
CPUs and GPUs, is well benchmarked against other similar codes and analytical
predictions, and shows good scalability up to thousands of nodes
Validation of gyrokinetic modelling of light impurity transport including rotation in ASDEX Upgrade
Upgraded spectroscopic hardware and an improved impurity concentration
calculation allow accurate determination of boron density in the ASDEX Upgrade
tokamak. A database of boron measurements is compared to quasilinear and
nonlinear gyrokinetic simulations including Coriolis and centrifugal rotational
effects over a range of H-mode plasma regimes. The peaking of the measured
boron profiles shows a strong anti-correlation with the plasma rotation
gradient, via a relationship explained and reproduced by the theory. It is
demonstrated that the rotodiffusive impurity flux driven by the rotation
gradient is required for the modelling to reproduce the hollow boron profiles
at higher rotation gradients. The nonlinear simulations validate the
quasilinear approach, and, with the addition of perpendicular flow shear,
demonstrate that each symmetry breaking mechanism that causes momentum
transport also couples to rotodiffusion. At lower rotation gradients, the
parallel compressive convection is required to match the most peaked boron
profiles. The sensitivities of both datasets to possible errors is
investigated, and quantitative agreement is found within the estimated
uncertainties. The approach used can be considered a template for mitigating
uncertainty in quantitative comparisons between simulation and experiment.Comment: 19 pages, 11 figures, accepted in Nuclear Fusio
Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows
This paper presents a complete theoretical framework for plasma turbulence
and transport in tokamak plasmas. The fundamental scale separations present in
plasma turbulence are codified as an asymptotic expansion in the ratio of the
gyroradius to the equilibrium scale length. Proceeding order-by-order in this
expansion, a framework for plasma turbulence is developed. It comprises an
instantaneous equilibrium, the fluctuations driven by gradients in the
equilibrium quantities, and the transport-timescale evolution of mean profiles
of these quantities driven by the fluctuations. The equilibrium distribution
functions are local Maxwellians with each flux surface rotating toroidally as a
rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov
equation for a rotating plasma and the slow (resistive) evolution of the
magnetic field is given by an evolution equation for the safety factor q.
Large-scale deviations of the distribution function from a Maxwellian are given
by neoclassical theory. The fluctuations are determined by the high-flow
gyrokinetic equation, from which we derive the governing principle for
gyrokinetic turbulence in tokamaks: the conservation and local cascade of free
energy. Transport equations for the evolution of the mean density, temperature
and flow velocity profiles are derived. These transport equations show how the
neoclassical corrections and the fluctuations act back upon the mean profiles
through fluxes and heating. The energy and entropy conservation laws for the
mean profiles are derived. Total energy is conserved and there is no net
turbulent heating. Entropy is produced by the action of fluxes flattening
gradients, Ohmic heating, and the equilibration of mean temperatures. Finally,
this framework is condensed, in the low-Mach-number limit, to a concise set of
equations suitable for numerical implementation.Comment: 113 pages, 3 figure
Effects of the equilibrium model on impurity transport in tokamaks
Gyrokinetic simulations of ion temperature gradient mode and trapped electron
mode driven impurity transport in a realistic tokamak geometry are presented
and compared with results using simplified geometries. The gyrokinetic results,
obtained with the GENE code in both linear and non-linear modes are compared
with data and analysis for a dedicated impurity injection discharge at JET. The
impact of several factors on heat and particle transport is discussed, lending
special focus to tokamak geometry and rotational shear. To this end, results
using s-alpha and concentric circular equilibria are compared with results with
magnetic geometry from a JET experiment. To further approach experimental
conditions, non-linear gyrokinetic simulations are performed with collisions
and a carbon background included.
The impurity peaking factors, computed by finding local density gradients
corresponding to zero particle flux, are discussed. The impurity peaking
factors are seen to be reduced by a factor of ~2 in realistic geometry compared
with the simplified geometries, due to a reduction of the convective pinch. It
is also seen that collisions reduce the peaking factor for low-Z impurities,
while increasing it for high charge numbers, which is attributed to a shift in
the transport spectra towards higher wavenumbers with the addition of
collisions. With the addition of roto-diffusion, an overall reduction of the
peaking factors is observed, but this decrease is not sufficient to explain the
flat carbon profiles seen at JET.Comment: 19 pages, 9 figures (17 subfigures
Optimisation of confinement in a fusion reactor using a nonlinear turbulence model
The confinement of heat in the core of a magnetic fusion reactor is optimised
using a multidimensional optimisation algorithm. For the first time in such a
study, the loss of heat due to turbulence is modelled at every stage using
first-principles nonlinear simulations which accurately capture the turbulent
cascade and large-scale zonal flows. The simulations utilise a novel approach,
with gyrofluid treatment of the small-scale drift waves and gyrokinetic
treatment of the large-scale zonal flows. A simple near-circular equilibrium
with standard parameters is chosen as the initial condition. The figure of
merit, fusion power per unit volume, is calculated, and then two control
parameters, the elongation and triangularity of the outer flux surface, are
varied, with the algorithm seeking to optimise the chosen figure of merit. A
two-fold increase in the plasma power per unit volume is achieved by moving to
higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP
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