3,710 research outputs found
Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity
Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates
have been computed to order in general magnetic geometry. Here
is the gyrokinetic expansion parameter, the gyroradius over the
macroscopic scale length. Starting from these results, the long-wavelength
limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken
for tokamak geometry. Employing the set of equations derived in the present
article, it is possible to calculate the long-wavelength components of the
distribution functions and of the poloidal electric field to order
. These higher-order pieces contain both neoclassical and turbulent
contributions, and constitute one of the necessary ingredients (the other is
given by the short-wavelength components up to second order) that will
eventually enter a complete model for the radial transport of toroidal angular
momentum in a tokamak in the low flow ordering. Finally, we provide an explicit
and detailed proof that the system consisting of second-order gyrokinetic
Fokker-Planck and quasineutrality equations leaves the long-wavelength radial
electric field undetermined; that is, the turbulent tokamak is intrinsically
ambipolar.Comment: 70 pages. Typos in equations (63), (90), (91), (92) and (129)
correcte
Stellarator bootstrap current and plasma flow velocity at low collisionality
The bootstrap current and flow velocity of a low-collisionality stellarator
plasma are calculated. As far as possible, the analysis is carried out in a
uniform way across all low-collisionality regimes in general stellarator
geometry, assuming only that the confinement is good enough that the plasma is
approximately in local thermodynamic equilibrium. It is found that conventional
expressions for the ion flow speed and bootstrap current in the
low-collisionality limit are accurate only in the -collisionality regime
and need to be modified in the -regime. The correction due to
finite collisionality is also discussed and is found to scale as
Conditions for up-down asymmetry in the core of tokamak equilibria
A local magnetic equilibrium solution is sought around the magnetic axis in
order to identify the key parameters defining the magnetic-surface's up-down
asymmetry in the core of tokamak plasmas. The asymmetry is found to be
determined essentially by the ratio of the toroidal current density flowing on
axis to the fraction of the external field's odd perturbation that manages to
propagate from the plasma boundary into the core. The predictions are tested
and illustrated first with an analytical Solovev equilibrium and then using
experimentally relevant numerical equilibria. Hollow current-density
distributions, and hence reverse magnetic shear, are seen to be crucial to
bring into the core asymmetry values that are usually found only near the
plasma edge.Comment: 6 pages, 2 figures, submitted for publicatio
Symmetry breaking in MAST plasma turbulence due to toroidal flow shear
The flow shear associated with the differential toroidal rotation of tokamak
plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by
the up-down symmetry of the magnetic equilibrium. Using experimental
Beam-Emission-Spectroscopy (BES) measurements and gyrokinetic simulations, this
symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself
as a tilt of the spatial correlation function and a finite skew in the
distribution of the fluctuating density field. The tilt is a statistical
expression of the "shearing" of the turbulent structures by the mean flow. The
skewness of the distribution is related to the emergence of long-lived density
structures in sheared, near-marginal plasma turbulence. The extent to which
these effects are pronounced is argued (with the aid of the simulations) to
depend on the distance from the nonlinear stability threshold. Away from the
threshold, the symmetry is effectively restored
Turbulent transport and heating of trace heavy ions in hot, magnetized plasmas
Scaling laws for the transport and heating of trace heavy ions in
low-frequency, magnetized plasma turbulence are derived and compared with
direct numerical simulations. The predicted dependences of turbulent fluxes and
heating on ion charge and mass number are found to agree with numerical results
for both stationary and differentially rotating plasmas. Heavy ion momentum
transport is found to increase with mass, and heavy ions are found to be
preferentially heated, implying a mass-dependent ion temperature for very
weakly collisional plasmas and for partially-ionized heavy ions in strongly
rotating plasmas.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
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
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
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