723 research outputs found
Transport in chaotic systems
This dissertation addresses the general problem of transport in chaotic systems. Typical fluid problem of the kind is the advection and diffusion of a passive scalar. The magnetic field evolution in a chaotic conducting media is an example of the chaotic transport of a vector field. In kinetic theory, the collisional relaxation of a distribution function in phase space is also an advection-diffusion problem, but in a higher dimensional space.;In a chaotic flow neighboring points tend to separate exponentially in time, exp({dollar}\omega t{dollar}) with {dollar}\omega{dollar} the Liapunov exponent. The characteristic parameter for the transport of a scalar in a chaotic flow is {dollar}\Omega\ \equiv\ \omega L\sp2/D{dollar} where L is the spatial scale and D is the diffusivity. For {dollar}\Omega\ \gg\ 1{dollar}, the scalar is advected with the flow for a time {dollar}t\sb{lcub}a{rcub}\ \equiv{dollar} ln(2{dollar}\Omega{dollar})/2{dollar}\omega{dollar} and then diffuses during the relatively short period 1/{dollar}\omega{dollar} centered on the time {dollar}t\sb{lcub}a{rcub}{dollar}. This rapid diffusion occurs only along the field line of the {dollar}\rm \ s\sb\infty{dollar} vector, which defines the stable direction for neighboring streamlines to converge. Diffusion is impeded at the sharp bends of an {dollar}\rm \ s{dollar} line because of a peculiarly small finite time Lyapunov exponent, hence a class of diffusion barriers is created inside a chaotic sea. This result comes from a fundamental relationship between the finite time Lyapunov exponent and the geometry of the {dollar}\rm \ s{dollar} lines, which we rigorously show in 2D and numerically validated for 3D flows.;The evolution of a general 3D magnetic field in a highly conducting chaotic media is also related to the spatial-temporal dependence of the finite time Lyapunov exponent. The Ohmic dissipation in a chaotic plasma will become a dominate process despite a small plasma resistivity. We show that the Ohmic heating in a chaotic plasma occurs in current filaments or current sheets. The particular form is determined by the time dependence of spatial gradient of the finite time Lyapunov exponent along a direction in which neighboring point neither diverge nor converge
On the collisional damping of plasma velocity space instabilities
For plasma velocity space instabilities driven by particle distributions
significantly deviated from a Maxwellian, weak collisions can damp the
instabilities by an amount that is significantly beyond the collisional rate
itself. This is attributed to the dual role of collisions that tend to relax
the plasma distribution toward a Maxwellian and to suppress the linearly
perturbed distribution function. The former effect can dominate in cases where
the unstable non-Maxwellian distribution is driven by collisionless transport
on a time scale much shorter than that of collisions, and the growth rate of
the ideal instability has a sensitive dependence on the distribution function.
The whistler instability driven by electrostatically trapped electrons is used
as an example to elucidate such a strong collisional damping effect of plasma
velocity space instabilities, which is confirmed by first-principles kinetic
simulations
Runaway electron current reconstitution after a non-axisymmetric magnetohydrodynamic flush
Benign termination of mega-ampere (MA) level runaway current has been
convincingly demonstrated in recent JET and DIII-D experiments, establishing it
as a leading candidate for runaway mitigation on ITER. This comes in the form
of a runaway flush by parallel streaming loss along stochastic magnetic field
lines formed by global magnetohydrodynamic instabilities, which are found to
correlate with a low-Z injection that purges the high-Z impurities from a
post-thermal-quench plasma. Here we show the competing physics that govern the
post-flush reconstitution of the runaway current in a ITER-like reactor where
significantly higher current is expected. The trapped ``runaways'' are found to
dominate the seeding for runaway reconstitution, and the incomplete purge of
high-Z impurities helps drain the seed but produces a more efficient avalanche,
two of which compete to produce a 2-3~MA step in current drop before runaway
reconstitution of the plasma current
Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench
The edge plasma turbulence and transport dynamics, as well as the divertor
power loads during the thermal quench phase of tokamak disruptions are
numerically investigated with BOUT++'s flux-driven, six-field electromagnetic
turbulence model. Here a transient yet intense particle and energy sources are
applied at the pedestal top to mimic the plasma power drive at the edge induced
by a core thermal collapse, which flattens core temperature profile.
Interesting features such as surging of divertor heat load (up to 50 times),
and broadening of heat flux width (up to 4 times) on the outer divertor target
plate, are observed in the simulation, in qualitative agreement with
experimental observations. The dramatic changes of divertor heat load and width
are due to the enhanced plasma turbulence activities inside the separatrix. Two
cross-field transport mechanisms, namely the turbulent convection
and the stochastic parallel advection/conduction, are identified to play
important roles in this process. Firstly, elevated edge pressure gradient
drives instabilities and subsequent turbulence in the entire pedestal region.
The enhanced turbulence not only transports particles and energy radially
across the separatrix via convection which causes the initial
divertor heat load burst, but also induces an amplified magnetic fluctuation
. Once the magnetic fluctuation is large enough to break the
magnetic flux surface, magnetic flutter effect provides an additional radial
transport channel. In the late stage of our simulation,
reaches to level that completely breaks magnetic flux surfaces such
that stochastic field-lines are directly connecting pedestal top plasma to the
divertor target plates or first wall, further contributing to the divertor heat
flux width broadening.Comment: 20 pages, 12 figure
A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions
Force-free plasmas are a good approximation where the plasma pressure is tiny
compared with the magnetic pressure, which is the case during the cold vertical
displacement event (VDE) of a major disruption in a tokamak. On time scales
long compared with the transit time of Alfven waves, the evolution of a
force-free plasma is most efficiently described by the quasi-static
magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we
consider a regularized quasi-static MHD model for force-free plasmas in tokamak
disruptions and propose a mimetic finite difference (MFD) algorithm. The full
geometry of an ITER-like tokamak reactor is treated, with a blanket module
region, a vacuum vessel region, and the plasma region. Specifically, we develop
a parallel, fully implicit, and scalable MFD solver based on PETSc and its
DMStag data structure for the discretization of the five-field quasi-static
perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial
discretization is coupled with a fully implicit DIRK scheme. The algorithm
exactly preserves the divergence-free condition of the magnetic field under the
resistive Ohm's law. The preconditioner employed is a four-level fieldsplit
preconditioner, which is created by combining separate preconditioners for
individual fields, that calls multigrid or direct solvers for sub-blocks or
exact factorization on the separate fields. The numerical results confirm the
divergence-free constraint is strongly satisfied and demonstrate the
performance of the fieldsplit preconditioner and overall algorithm. The
simulation of ITER VDE cases over the actual plasma current diffusion time is
also presented.Comment: 43 page
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