24,777 research outputs found
Intrinsic rotation in tokamaks: theory
Self-consistent equations for intrinsic rotation in tokamaks with small
poloidal magnetic field compared to the total magnetic field are
derived. The model gives the momentum redistribution due to turbulence,
collisional transport and energy injection. Intrinsic rotation is determined by
the balance between the momentum redistribution and the turbulent diffusion and
convection. Two different turbulence regimes are considered: turbulence with
characteristic perpendicular lengths of the order of the ion gyroradius,
, and turbulence with characteristic lengths of the order of the
poloidal gyroradius, . Intrinsic rotation driven by gyroradius
scale turbulence is mainly due to the effect of neoclassical corrections and of
finite orbit widths on turbulent momentum transport, whereas for the intrinsic
rotation driven by poloidal gyroradius scale turbulence, the slow variation of
turbulence characteristics in the radial and poloidal directions and the
turbulent particle acceleration can be become as important as the neoclassical
and finite orbit width effects. The magnetic drift is shown to be indispensable
for the intrinsic rotation driven by the slow variation of turbulence
characteristics and the turbulent particle acceleration. The equations are
written in a form conducive to implementation in a flux tube code, and the
effect of the radial variation of the turbulence is included in a novel way
that does not require a global gyrokinetic formalism.Comment: 88 pages, 4 figure
Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials
The current paradigm for understanding galaxy formation in the universe
depends on the existence of self-gravitating collisionless dark matter.
Modeling such dark matter systems has been a major focus of astrophysicists,
with much of that effort directed at computational techniques. Not
surprisingly, a comprehensive understanding of the evolution of these
self-gravitating systems still eludes us, since it involves the collective
nonlinear dynamics of many-particle systems interacting via long-range forces
described by the Vlasov equation. As a step towards developing a clearer
picture of collisionless self-gravitating relaxation, we analyze the linearized
dynamics of isolated one-dimensional systems near thermal equilibrium by
expanding their phase space distribution functions f(x,v) in terms of Hermite
functions in the velocity variable, and Legendre functions involving the
position variable. This approach produces a picture of phase-space evolution in
terms of expansion coefficients, rather than spatial and velocity variables. We
obtain equations of motion for the expansion coefficients for both
test-particle distributions and self-gravitating linear perturbations of
thermal equilibrium. N-body simulations of perturbed equilibria are performed
and found to be in excellent agreement with the expansion coefficient approach
over a time duration that depends on the size of the expansion series used.Comment: 12 pages, accepted for publication in MNRA
Turbulent momentum pinch of diamagnetic flows in a tokamak
The ion toroidal rotation in a tokamak consists of an flow due to
the radial electric field and a diamagnetic flow due to the radial pressure
gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis
force studied in previous work is only applicable to the flow. In
this Letter, the momentum pinch for the rotation generated by the radial
pressure gradient is calculated and is compared with the Coriolis pinch. This
distinction is important for subsonic flows or the flow in the pedestal where
the two types of flows are similar in size and opposite in direction. In the
edge, the different pinches due to the opposite rotations can result in
intrinsic momentum transport that gives significant rotation peaking.Comment: 5 pages and 3 figure
Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks
Two symmetries of the local nonlinear delta-f gyrokinetic system of equations
in tokamaks in the high flow regime are presented. The turbulent transport of
toroidal angular momentum changes sign under an up-down reflection of the
tokamak and a sign change of both the rotation and the rotation shear. Thus,
the turbulent transport of toroidal angular momentum must vanish for up-down
symmetric tokamaks in the absence of both rotation and rotation shear. This has
important implications for the modeling of spontaneous rotation.Comment: 15 pages, 2 figure
Ferromagnetic resonance with a magnetic Josephson junction
We show experimentally and theoretically that there is a coupling via the
Aharonov-Bohm phase between the order parameter of a ferromagnet and a singlet,
s-wave, Josephson supercurrent. We have investigated the possibility of
measuring the dispersion of such spin waves by varying the magnetic field
applied in the plane of the junction and demonstrated the electromagnetic
nature of the coupling by the observation of magnetic resonance side-bands to
microwave induced Shapiro steps.Comment: 6 pages, 5 figure
Optimized up-down asymmetry to drive fast intrinsic rotation in tokamaks
Breaking the up-down symmetry of the tokamak poloidal cross-section can
significantly increase the spontaneous rotation due to turbulent momentum
transport. In this work, we optimize the shape of flux surfaces with both
tilted elongation and tilted triangularity in order to maximize this drive of
intrinsic rotation. Nonlinear gyrokinetic simulations demonstrate that adding
optimally-tilted triangularity can double the momentum transport of a tilted
elliptical shape. This work indicates that tilting the elongation and
triangularity in an ITER-like device can reduce the energy transport and drive
intrinsic rotation with an Alfv\'{e}n Mach number on the order of . This
rotation is four times larger than the rotation expected in ITER and is
sufficient to stabilize MHD instabilities. It is shown that this optimal shape
can be created using the shaping coils of several experiments.Comment: 16 pages, 5 figure
Intrinsic rotation with gyrokinetic models
The generation of intrinsic rotation by turbulence and neoclassical effects
in tokamaks is considered. To obtain the complex dependences observed in
experiments, it is necessary to have a model of the radial flux of momentum
that redistributes the momentum within the tokamak in the absence of a
preexisting velocity. When the lowest order gyrokinetic formulation is used, a
symmetry of the model precludes this possibility, making small effects in the
gyroradius over scale length expansion necessary. These effects that are
usually small become important for momentum transport because the symmetry of
the lowest order gyrokinetic formulation leads to the cancellation of the
lowest order momentum flux. The accuracy to which the gyrokinetic equation
needs to be obtained to retain all the physically relevant effects is
discussed
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