99 research outputs found
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
Comparison of BES measurements of ion-scale turbulence with direct, gyrokinetic simulations of MAST L-mode plasmas
Observations of ion-scale (k_y*rho_i <= 1) density turbulence of relative
amplitude dn_e/n_e <= 0.2% are available on the Mega Amp Spherical Tokamak
(MAST) using a 2D (8 radial x 4 poloidal channel) imaging Beam Emission
Spectroscopy (BES) diagnostic. Spatial and temporal characteristics of this
turbulence, i.e., amplitudes, correlation times, radial and perpendicular
correlation lengths and apparent phase velocities of the density contours, are
determined by means of correlation analysis. For a low-density, L-mode
discharge with strong equilibrium flow shear exhibiting an internal transport
barrier (ITB) in the ion channel, the observed turbulence characteristics are
compared with synthetic density turbulence data generated from global,
non-linear, gyro-kinetic simulations using the particle-in-cell (PIC) code
NEMORB. This validation exercise highlights the need to include increasingly
sophisticated physics, e.g., kinetic treatment of trapped electrons,
equilibrium flow shear and collisions, to reproduce most of the characteristics
of the observed turbulence. Even so, significant discrepancies remain: an
underprediction by the simulations of the turbulence amplituide and heat flux
at plasma periphery and the finding that the correlation times of the
numerically simulated turbulence are typically two orders of magnitude longer
than those measured in MAST. Comparison of these correlation times with various
linear timescales suggests that, while the measured turbulence is strong and
may be `critically balanced', the simulated turbulence is weak.Comment: 27 pages, 11 figure
Dispersion of ion gyrocenters in models of anisotropic plasma turbulence
Turbulent dispersion of ion gyrocenters in a magnetized plasma is studied in the context of a stochastic Hamiltonian transport model and nonlinear, self-consistent gyrokinetic simulations. The Hamiltonian model consists of a superposition of drift waves derived from the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. Finite Larmor radius (FLR) effects are included. Because there is no particle transport in the direction of the density gradient, the focus is on transport parallel to the shear flow. The prescribed flow produces strongly asymmetric non-Gaussian probability distribution functions (PDFs) of particle displacements, as was previously known. For kρ=0, where k is the characteristic wavelength of the flow and ρ is the thermal Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. The transition separates nearly ballistic superdiffusive dispersion from weaker superdiffusion at later times. FLR effects eliminate this transition. Important features of the PDFs of displacements are reproduced accurately with a fractional diffusion model. The gyroaveraged ExB drift dispersion of a sample of tracer ions is also examined in a two-dimensional, nonlinear, self-consistent gyrokinetic particle-in-cell (PIC) simulation. Turbulence in the simulation is driven by a density gradient and magnetic curvature, resulting in the unstable ρ scale kinetic entropy mode. The dependence of dispersion in both the axial and radial directions is characterized by displacement and velocity increment distributions. The strength of the density gradient is varied, using the local approximation, in three separate trials. A filtering procedure is used to separate trajectories according to whether they were caught in an eddy during a set observation time. Axial displacements are compared to results from the Hasegawa-Mima model. Superdiffusion and ballistic transport are found, depending on filtering and strength of the gradient. The radial dispersion of particles, as measured by the variance of tracer displacements, is diffusive. The dependence of the running diffusion coefficient on ρ for each value of the density gradient is considered
Recommended from our members
Mini-Workshop: Innovative Trends in the Numerical Analysis and Simulation of Kinetic Equations
In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations
Recommended from our members
Gyrokinetic Simulations of ETG and ITG Turbulence
Published gyrokinetic continuum-code simulations indicated levels of the electron thermal conductivity {chi}{sub e} due to electron-temperature-gradient (ETG) turbulence large enough to be significant in some tokamaks, while subsequent global particle-in-cell (PIC) simulations gave significantly lower values. We have carried out an investigation of this discrepancy. We have reproduced the key features of the aforementioned PIC simulations using the flux-tube gyrokinetic PIC code, PG3EQ, thereby eliminating global effects and as the cause of the discrepancy. We show that the late-time low-transport state in both of these sets of PIC simulations is a result of discrete particle noise, which is a numerical artifact. Thus, the low value of {chi}{sub e} along with conclusions about anomalous transport drawn from these particular PIC simulations are unjustified. In our attempts to benchmark PIC and continuum codes for ETG turbulence at the plasma parameters used above, both produce very large intermittent transport. We have therefore undertaken benchmarks at an alternate reference point, magnetic shear s=0.1 instead of s=0.796, and have found that PIC and continuum codes reproduce the same transport levels. Scans in the magnetic shear show an abrupt transition to a high-{chi}{sub e} state as the shear is increased above s=0.4. When nonadiabatic ions are used, this abrupt transition is absent, and {chi}{sub e} increases gradually reaching values consistent with transport analyses of DIII-D, JET, and JT60-U discharges. New results on the balances of zonal-flow driving and damping terms in late-time quasi-steady ITG turbulence and on real-geometry gyrokinetic simulations of shaped DIII-D discharges are also reported
The effect of toroidal flows on the stability of ITGs in MAST
The free energy in the large temperature and density gradients in tokamaks
can drive microinstabilities, which in turn drive turbulence. This turbulence is
responsible for the transport of energy and particles over and above that predicted
by neoclassical theory. Sheared toroidal rotation can suppress the turbulence and
stabilise the underlying microinstabilities, thereby reducing the transport. This
thesis investigates how variation of the equilibrium temperature and density profiles,
over the same scales associated with the microinstabilities, affects how the
ow shear
stabilises the linear modes and suppresses the turbulence. A global gyrokinetic code
is employed in this investigation, which retains the profile variation and simulates
the full 3D domain of a tokamak plasma.
How much
ow shear is needed to stabilise the linear ion temperature gradient
(ITG) mode is found to be dependent on its poloidal wavenumber, with longer
wavelength modes needing more
ow shear than the fastest growing mode. This
dependence is present whether the
ow shear is constant across the radius or if it
has the variation typical in an experimental rotation profile. There is an asymmetry
with respect to the sign of the
ow shear in the effectiveness of the stabilisation,
with the maximum linear growth rate occurring at finite negative shearing rates for
the plasma studied here. This asymmetry arises from the profile variation, and is
found to be significant in simulations of MAST L-mode plasmas, especially when
the effects of kinetic trapped electrons are included in the simulations.
Flow shear asymmetry is still present in nonlinear simulations, and the suppression
of fully-developed turbulence depends on the sign of the shearing rate.
With the experimental rotation profile, the heat
ux arising from ITG turbulence
is reduced by an amount comparable to the reduction in the linear growth rates.
When the direction of the rotation profile is reversed, such that the sign of the
ow
shear is
ipped while the magnitude remains the same, the turbulence is almost
completely suppressed. A new diagnostic on MAST, beam emission spectroscopy
(BES), is used to make a direct comparison between density
fluctuations from simulation,
and from experiment. Collisionless, electrostatic simulations with rotation
are found to disagree significantly with experiment in the level of ITG turbulence
activity and the correlation times and lengths of the turbulence. The inclusion
of electron-electron and electron-ion collisions into static simulations is enough to
bring the level of turbulent density
uctuations down to within a factor two of the
experimental levels, with the correlation lengths becoming comparable, while the
correlation times remain an order of magnitude too large
- âŠ