180 research outputs found
On the nonlinear stability of a quasi-two-dimensional drift kinetic model for ion temperature gradient turbulence
We study a quasi-two-dimensional electrostatic drift kinetic system as a
model for near-marginal ion temperature gradient (ITG) driven turbulence. A
proof is given of the nonlinear stability of this system under conditions of
linear stability. This proof is achieved using a transformation that
diagonalizes the linear dynamics and also commutes with nonlinear
advection. For the case when linear instability is present, a corollary is
found that forbids nonlinear energy transfer between appropriately defined sets
of stable and unstable modes. It is speculated that this may explain the
preservation of linear eigenmodes in nonlinear gyrokinetic simulations. Based
on this property, a dimensionally reduced ()
system is derived that may be useful for understanding dynamics around the
critical gradient of Dimits
Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator
It is demonstrated that finite-pressure, approximately quasi-axisymmetric
stellarator equilibria can be directly constructed (without numerical
optimization) via perturbations of given axisymmetric equilibria. The size of
such perturbations is measured in two ways, via the fractional external
rotation and, alternatively, via the relative magnetic field strength, i.e. the
average size of the perturbed magnetic field, divided by the unperturbed field
strength. It is found that significant fractional external rotational transform
can be generated by quasi-axisymmetric perturbations, with a similar value of
the relative field strength, despite the fact that the former scales more
weakly with the perturbation size. High mode number perturbations are
identified as a candidate for generating such transform with local current
distributions. Implications for the development of a general non-perturbative
solver for optimal stellarator equilibria is discussed
On the scaling of ion and electron temperature gradient driven turbulence in slab geometry
We demonstrate that the scaling properties of slab ion and electron
temperature gradient driven turbulence may be derived by dimensional analysis
of a drift kinetic system with one kinetic species. These properties have
previously been observed in gyrokinetic simulations of turbulence in magnetic
fusion devices.Comment: To be published, Phys. Plasmas (2017
The universal instability in general geometry
The "universal" instability has recently been revived by Landreman, Antonsen
and Dorland [1], who showed that it indeed exists in plasma geometries with
straight (but sheared) magnetic field lines. Here it is demonstrated
analytically that this instability can be present in more general sheared and
toroidal geometries. In a torus, the universal instability is shown to be
closely related to the trapped-electron mode, although the trapped-electron
drive is usually dominant. However, this drive can be weakened or eliminated,
as in the case in stellarators with the maximum- property, leaving the
parallel Landau resonance to drive a residual mode, which is identified as the
universal instability
Irreversible energy flow in forced Vlasov dynamics
A recent paper [Phys. Plasmas 20, 032304 (2013)] considered the forced linear
Vlasov equation as a model for the quasi-steady state of a single stable plasma
wavenumber interacting with a bath of turbulent fluctuations. This approach
gives some insight into possible energy flows without solving for nonlinear
dynamics. The central result of the present work is that the forced linear
Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all
orders under a detuning of the forcing frequency and the characteristic
frequency associated with particle streaming. We first prove this by direct
calculation, tracking energy flow in terms of certain exact conservation laws
of the linear (collisionless) Vlasov equation. Then we analyze the steady-state
solutions in detail using a weakly collisional Hermite-moment formulation, and
compare with numerical solution. This leads to a detailed description of the
Hermite energy spectrum, and a proof of no dissipation at all orders,
complementing the collisionless Vlasov result.Comment: Small changes for clarit
Nonlinear growth of zonal flows by secondary instability in general magnetic geometry
We present a theory of the nonlinear growth of zonal flows in magnetized
plasma turbulence, by the mechanism of secondary instability. The theory is
derived for general magnetic geometry, and is thus applicable to both tokamaks
and stellarators. The predicted growth rate is shown to compare favorably with
nonlinear gyrokinetic simulations, with the error scaling as expected with the
small parameter of the theory.Comment: New J. Phys. 201
Distinct turbulence saturation regimes in stellarators
In the complex 3D magnetic fields of stellarators, ion-temperature-gradient
turbulence is shown to have two distinct saturation regimes, as revealed by
petascale numerical simulations, and explained by a simple turbulence theory.
The first regime is marked by strong zonal flows, and matches previous
observations in tokamaks. The newly observed second regime, in contrast,
exhibits small- scale quasi-two-dimensional turbulence, negligible zonal flows,
and, surprisingly, a weaker heat flux scaling. Our findings suggest that key
details of the magnetic geometry control turbulence in stellarators.Comment: Erratum added to en
Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence
We propose a quantitative model of ion temperature gradient driven turbulence
in toroidal magnetized plasmas. In this model, the turbulence is regulated by
zonal flows, i.e. mode saturation occurs by a zonal-flow-mediated energy
cascade ("shearing"), and zonal flow amplitude is controlled by nonlinear
decay. Our model is tested in detail against numerical simulations to confirm
that both its assumptions and predictions are satisfied. Key results include
(1) a sensitivity of the nonlinear zonal flow response to the energy content of
the linear instability, (2) a persistence of zonal-flow-regulated saturation at
high temperature gradients, (3) a physical explanation of the nonlinear
saturation process in terms of secondary and tertiary instabilities, and (4)
dependence of heat flux in terms of dimensionless parameters.Comment: Final journal version. Some clarifications and a new Fig.
Enstrophy non-conservation and the forward cascade of energy in two-dimensional electrostatic magnetized plasma turbulence
A fluid system is derived to describe electrostatic magnetized plasma
turbulence at scales somewhat larger than the Larmor radius of a given species.
It is related to the Hasegawa- Mima equation, but does not conserve enstrophy,
and, as a result, exhibits a forward cascade of energy, to small scales. The
inertial-range energy spectrum is argued to be shallower than a -11/3 power
law, as compared to the -5 law of the Hasegawa-Mima enstrophy cascade. This
property, confirmed here by direct numerical simulations of the fluid system,
may help explain the fluctuation spectrum observed in gyrokinetic simulations
of streamer-dominated electron-temperature-gradient driven turbulence [Plunk et
al., 2019], and also possibly some cases of ion-temperature-gradient driven
turbulence where zonal flows are suppressed [Plunk et al., 2017]
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