411 research outputs found
The Zero Turbulence Manifold in Fusion Plasmas
The transport of heat that results from turbulence is a major factor limiting
the temperature gradient, and thus the performance, of fusion devices. We use
nonlinear simulations to show that a toroidal equilibrium scale sheared flow
can completely suppress the turbulence across a wide range of flow gradient and
temperature gradient values. We demonstrate the existence of a bifurcation
across this range whereby the plasma may transition from a low flow gradient
and temperature gradient state to a higher flow gradient and temperature gra-
dient state. We show further that the maximum temperature gradient that can be
reached by such a transition is limited by the existence, at high flow
gradient, of subcritical turbulence driven by the parallel velocity gradient
(PVG). We use linear simulations and analytic calculations to examine the
properties of the transiently growing modes which give rise to this subcritical
turbulence, and conclude that there may be a critical value of the ratio of the
PVG to the suppressing perpendicular gradient of the velocity (in a tokamak
this ratio is equal to q/{\epsilon} where q is the magnetic safety factor and
{\epsilon} the inverse aspect ratio) below which the PVG is unable to drive
subcritical turbulence. In light of this, we use nonlinear simulations to
calculate, as a function of three parameters (the perpendicular flow shear,
q/{\epsilon} and the temperature gradient), the surface within that parameter
space which divides the regions where turbulence can and cannot be sustained:
the zero- turbulence manifold. We are unable to conclude that there is in fact
a critical value of q/{\epsilon} below which PVG-driven turbulence is
eliminated. Nevertheless, we demonstrate that at low values of q/{\epsilon},
the maximum critical temperature gradient that can be reached without
generating turbulence is dramatically increased.Comment: Doctoral Thesis, University of Oxford, 151 Page
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
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
A scaling theory of long-wavelength electrostatic turbulence in a magnetised,
weakly collisional plasma (e.g., ITG turbulence) is proposed, with account
taken both of the nonlinear advection of the perturbed particle distribution by
fluctuating ExB flows and of its phase mixing, which is caused by the streaming
of the particles along the mean magnetic field and, in a linear problem, would
lead to Landau damping. It is found that it is possible to construct a
consistent theory in which very little free energy leaks into high velocity
moments of the distribution function, rendering the turbulent cascade in the
energetically relevant part of the wave-number space essentially fluid-like.
The velocity-space spectra of free energy expressed in terms of Hermite-moment
orders are steep power laws and so the free-energy content of the phase space
does not diverge at infinitesimal collisionality (while it does for a linear
problem); collisional heating due to long-wavelength perturbations vanishes in
this limit (also in contrast with the linear problem, in which it occurs at the
finite rate equal to the Landau-damping rate). The ability of the free energy
to stay in the low velocity moments of the distribution function is facilitated
by the "anti-phase-mixing" effect, whose presence in the nonlinear system is
due to the stochastic version of the plasma echo (the advecting velocity
couples the phase-mixing and anti-phase-mixing perturbations). The partitioning
of the wave-number space between the (energetically dominant) region where this
is the case and the region where linear phase mixing wins its competition with
nonlinear advection is governed by the "critical balance" between linear and
nonlinear timescales (which for high Hermite moments splits into two
thresholds, one demarcating the wave-number region where phase mixing
predominates, the other where plasma echo does).Comment: 45 pages (single-column), 3 figures, replaced with version published
in JP
Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST
Experimental data from the Mega Amp Spherical Tokamak (MAST) is used to show
that the inverse gradient scale length of the ion temperature R/LTi (normalized
to the major radius R) has its strongest local correlation with the rotational
shear and the pitch angle of the magnetic field (or, equivalently, an inverse
correlation with q/{\epsilon}, the safety factor/the inverse aspect ratio).
Furthermore, R/LTi is found to be inversely correlated with the
gyro-Bohm-normalized local turbulent heat flux estimated from the density
fluctuation level measured using a 2D Beam Emission Spectroscopy (BES)
diagnostic. These results can be explained in terms of the conjecture that the
turbulent system adjusts to keep R/LTi close to a certain critical value
(marginal for the excitation of turbulence) determined by local equilibrium
parameters (although not necessarily by linear stability).Comment: 6 pages, 3 figures, submitted to PR
Turbulent transport in tokamak plasmas with rotational shear
Nonlinear gyrokinetic simulations have been conducted to investigate
turbulent transport in tokamak plasmas with rotational shear. At sufficiently
large flow shears, linear instabilities are suppressed, but transiently growing
modes drive subcritical turbulence whose amplitude increases with flow shear.
This leads to a local minimum in the heat flux, indicating an optimal E x B
shear value for plasma confinement. Local maxima in the momentum fluxes are
also observed, allowing for the possibility of bifurcations in the E x B shear.
The sensitive dependence of heat flux on temperature gradient is relaxed for
large flow shear values, with the critical temperature gradient increasing at
lower flow shear values. The turbulent Prandtl number is found to be largely
independent of temperature and flow gradients, with a value close to unity.Comment: 4 pages, 5 figures, submitted to PR
Transition to subcritical turbulence in a tokamak plasma
Tokamak turbulence, driven by the ion-temperature gradient and occurring in
the presence of flow shear, is investigated by means of local, ion-scale,
electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of
the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A
parameter scan in the local values of the ion-temperature gradient and flow
shear is performed. It is demonstrated that the experimentally observed state
is near the stability threshold and that this stability threshold is nonlinear:
sheared turbulence is subcritical, i.e. the system is formally stable to small
perturbations, but, given a large enough initial perturbation, it transitions
to a turbulent state. A scenario for such a transition is proposed and
supported by numerical results: close to threshold, the nonlinear saturated
state and the associated anomalous heat transport are dominated by long-lived
coherent structures, which drift across the domain, have finite amplitudes, but
are not volume filling; as the system is taken away from the threshold into the
more unstable regime, the number of these structures increases until they
overlap and a more conventional chaotic state emerges. Whereas this appears to
represent a new scenario for transition to turbulence in tokamak plasmas, it is
reminiscent of the behaviour of other subcritically turbulent systems, e.g.
pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic
Zero-Turbulence Manifold in a Toroidal Plasma
Sheared toroidal flows can cause bifurcations to zero-turbulent-transport
states in tokamak plasmas. The maximum temperature gradients that can be
reached are limited by subcritical turbulence driven by the parallel velocity
gradient. Here it is shown that q/\epsilon (magnetic field pitch/inverse aspect
ratio) is a critical control parameter for sheared tokamak turbulence. By
reducing q/\epsilon, far higher temperature gradients can be achieved without
triggering turbulence, in some instances comparable to those found
experimentally in transport barriers. The zero-turbulence manifold is mapped
out, in the zero-magnetic-shear limit, over the parameter space (\gamma_E,
q/\epsilon, R/L_T), where \gamma_E is the perpendicular flow shear and R/L_T is
the normalised inverse temperature gradient scale. The extent to which it can
be constructed from linear theory is discussed.Comment: 5 Pages, 4 Figures, Submitted to PR
Transport Bifurcation in a Rotating Tokamak Plasma
The effect of flow shear on turbulent transport in tokamaks is studied
numerically in the experimentally relevant limit of zero magnetic shear. It is
found that the plasma is linearly stable for all non-zero flow shear values,
but that subcritical turbulence can be sustained nonlinearly at a wide range of
temperature gradients. Flow shear increases the nonlinear temperature gradient
threshold for turbulence but also increases the sensitivity of the heat flux to
changes in the temperature gradient, except over a small range near the
threshold where the sensitivity is decreased. A bifurcation in the equilibrium
gradients is found: for a given input of heat, it is possible, by varying the
applied torque, to trigger a transition to significantly higher temperature and
flow gradients.Comment: 4 pages, 4 figures, submitted to PR
Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements
We investigate the effect of varying the ion temperature gradient (ITG) and
toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer
core of MAST by means of local gyrokinetic simulations. We show that nonlinear
simulations reproduce the experimental ion heat flux and that the
experimentally measured values of the ITG and the flow shear lie close to the
turbulence threshold. We demonstrate that the system is subcritical in the
presence of flow shear, i.e., the system is formally stable to small
perturbations, but transitions to a turbulent state given a large enough
initial perturbation. We propose that the transition to subcritical turbulence
occurs via an intermediate state dominated by low number of coherent long-lived
structures, close to threshold, which increase in number as the system is taken
away from the threshold into the more strongly turbulent regime, until they
fill the domain and a more conventional turbulence emerges. We show that the
properties of turbulence are effectively functions of the distance to
threshold, as quantified by the ion heat flux. We make quantitative comparisons
of correlation lengths, times, and amplitudes between our simulations and
experimental measurements using the MAST BES diagnostic. We find reasonable
agreement of the correlation properties, most notably of the correlation time,
for which significant discrepancies were found in previous numerical studies of
MAST turbulence.Comment: 67 pages, 37 figures. Submitted to PPC
Suppression of turbulence and subcritical fluctuations in differentially rotating gyrokinetic plasmas
Differential rotation is known to suppress linear instabilities in fusion
plasmas. However, even in the absence of growing eigenmodes, subcritical
fluctuations that grow transiently can lead to sustained turbulence. Here
transient growth of electrostatic fluctuations driven by the parallel velocity
gradient (PVG) and the ion temperature gradient (ITG) in the presence of a
perpendicular ExB velocity shear is considered. The maximally simplified case
of zero magnetic shear is treated in the framework of a local shearing box.
There are no linearly growing eigenmodes, so all excitations are transient. The
maximal amplification factor of initial perturbations and the corresponding
wavenumbers are calculated as functions of q/\epsilon (=safety factor/aspect
ratio), temperature gradient and velocity shear. Analytical results are
corroborated and supplemented by linear gyrokinetic numerical tests. For
sufficiently low values of q/\epsilon (<7 in our model), regimes with fully
suppressed ion-scale turbulence are possible. For cases when turbulence is not
suppressed, an elementary heuristic theory of subcritical PVG turbulence
leading to a scaling of the associated ion heat flux with q, \epsilon, velocity
shear and temperature gradient is proposed; it is argued that the transport is
much less stiff than in the ITG regime.Comment: 36 pages in IOP latex style; 12 figures; submitted to PPC
- …