204 research outputs found
Modeling the effect of anisotropic pressure on tokamak plasmas normal modes and continuum using fluid approaches
Extending the ideal MHD stability code MISHKA, a new code, MISHKA-A, is
developed to study the impact of pressure anisotropy on plasma stability. Based
on full anisotropic equilibrium and geometry, the code can provide normal mode
analysis with three fluid closure models: the single adiabatic model (SA), the
double adiabatic model (CGL) and the incompressible model. A study on the
plasma continuous spectrum shows that in low beta, large aspect ratio plasma,
the main impact of anisotropy lies in the modification of the BAE gap and the
sound frequency, if the q profile is conserved. The SA model preserves the BAE
gap structure as ideal MHD, while in CGL the lowest frequency branch does not
touch zero frequency at the resonant flux surface where , inducing a
gap at very low frequency. Also, the BAE gap frequency with bi-Maxwellian
distribution in both model becomes higher if with a q
profile dependency. As a benchmark of the code, we study the m/n=1/1 internal
kink mode. Numerical calculation of the marginal stability boundary with
bi-Maxwellian distribution shows a good agreement with the generalized
incompressible Bussac criterion [A. B. Mikhailovskii, Sov. J. Plasma Phys 9,
190 (1983)]: the mode is stabilized(destabilized) if
Analysing the impact of anisotropy pressure on tokamak equilibria
Neutral beam injection or ion cyclotron resonance heating induces pressure
anisotropy. The axisymmetric plasma equilibrium code HELENA has been upgraded
to include anisotropy and toroidal flow. With both analytical and numerical
methods, we have studied the determinant factors in anisotropic equilibria and
their impact on flux surfaces, magnetic axis shift, the displacement of
pressures and density contours from flux surface. With , can vary 20% on flux surface, in a MAST like
equilibrium. We have also re-evaluated the widely applied approximation to
anisotropy in which , the average of parallel
and perpendicular pressure, is taken as the approximate isotropic pressure. We
find the reconstructions of the same MAST discharge with , using isotropic and anisotropic model respectively, to have a 3%
difference in toroidal field but a 66% difference in poloidal current
Sparse Bayesian information filters for localization and mapping
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and
Mapping (SLAM) that addresses the problem of scalability in large environments.
We describe an estimation-theoretic algorithm that achieves significant gains in computational
efficiency while maintaining consistent estimates for the vehicle pose and
the map of the environment.
We specifically address the feature-based SLAM problem in which the robot represents
the environment as a collection of landmarks. The thesis takes a Bayesian
approach whereby we maintain a joint posterior over the vehicle pose and feature
states, conditioned upon measurement data. We model the distribution as Gaussian
and parametrize the posterior in the canonical form, in terms of the information
(inverse covariance) matrix. When sparse, this representation is amenable to computationally
efficient Bayesian SLAM filtering. However, while a large majority of the
elements within the normalized information matrix are very small in magnitude, it is
fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability
benefits of a sparse parametrization by explicitly pruning these weak links in an effort
to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information
Filter (SEIF), which has laid much of the groundwork concerning the computational
benefits of the sparse canonical form. The thesis performs a detailed analysis of the
process by which the SEIF approximates the sparsity of the information matrix and
reveals key insights into the consequences of different sparsification strategies. We
demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent,
suffering from exaggerated confidence estimates. This overconfidence has
detrimental effects on important aspects of the SLAM process and affects the higher
level goal of producing accurate maps for subsequent localization and path planning.
This thesis proposes an alternative scalable filter that maintains sparsity while
preserving the consistency of the distribution. We leverage insights into the natural
structure of the feature-based canonical parametrization and derive a method that
actively maintains an exactly sparse posterior. Our algorithm exploits the structure
of the parametrization to achieve gains in efficiency, with a computational cost that
scales linearly with the size of the map. Unlike similar techniques that sacrifice
consistency for improved scalability, our algorithm performs inference over a posterior
that is conservative relative to the nominal Gaussian distribution. Consequently, we
preserve the consistency of the pose and map estimates and avoid the effects of an
overconfident posterior.
We demonstrate our filter alongside the SEIF and the standard EKF both in simulation
as well as on two real-world datasets. While we maintain the computational
advantages of an exactly sparse representation, the results show convincingly that
our method yields conservative estimates for the robot pose and map that are nearly
identical to those of the original Gaussian distribution as produced by the EKF, but
at much less computational expense.
The thesis concludes with an extension of our SLAM filter to a complex underwater
environment. We describe a systems-level framework for localization and mapping
relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped
with a forward-looking sonar. The approach utilizes our filter to fuse measurements
of vehicle attitude and motion from onboard sensors with data from sonar images of
the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a
ship hull
Comparison of methods for numerical calculation of continuum damping
Continuum resonance damping is an important factor in determining the
stability of certain global modes in fusion plasmas. A number of analytic and
numerical approaches have been developed to compute this damping, particularly
in the case of the toroidicity-induced shear Alfv\'en eigenmode. This paper
compares results obtained using an analytical perturbative approach with those
found using resistive and complex contour numerical approaches. It is found
that the perturbative method does not provide accurate agreement with reliable
numerical methods for the range of parameters examined. This discrepancy exists
even in the limit where damping approaches zero. When the perturbative
technique is implemented using a standard finite element method, the damping
estimate fails to converge with radial grid resolution. The finite elements
used cannot accurately represent the eigenmode in the region of the continuum
resonance, regardless of the number of radial grid points used.Comment: 19 pages, 9 figure
The shear Alfv\'en continuum with a magnetic island chain in tokamak plasmas
The shear Alfv\'en continuum spectrum is studied for a tokamak with a single
island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken
into account the toroidal geometry and toroidal mode coupling with the island
considered as a highly-shaped stellarator. Various new frequency gaps open up
inside the island due to its asymmetry both poloidally and toroidally, such as
the Mirror-induced Alfv\'en Eigenmode (MAE) gap and the Helicity-induced
Alfv\'en Eigenmode (HAE) gap. We have shown that the MAE gap acts as the
continuation of the outside Toroidal Alfv\'en Eigenmode (TAE) gap into the
island. However, the combined TAE/MAE gap is getting narrower as the island
grows, leaving only half of its original width with a moderate island size as
much as 3.2% of the minor radius. In addition, the two-dimensional
eigenfunction of the continuum mode on the lower tip of the MAE gap now has
highly localised structures around the island's long axis, contrary to the
usual oscillatory global solutions found with no or a low level of toroidal
asymmetry - an indication of the continuous spectrum becoming discrete and
dense. These results have implications for the frequency, mode structure and
continuum damping of global TAEs residing in the gap
Relaxed plasma equilibria and entropy-related plasma self-organization principles
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed
Multi-region relaxed magnetohydrodynamics with anisotropy and flow
We present an extension of the multi-region relaxed magnetohydrodynamics
(MRxMHD) equilibrium model that includes pressure anisotropy and general plasma
flows. This anisotropic extension to our previous isotropic model is motivated
by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria.
We prove that as the number of plasma regions becomes infinite, our anisotropic
extension of MRxMHD reduces to anisotropic ideal MHD with flow. The
continuously nested flux surface limit of our MRxMHD model is the first
variational principle for anisotropic plasma equilibria with general flow
fields.Comment: 11 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1401.307
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