Analytical calculation of the orbital spectrum of the guiding centre motion in axisymmetric magnetic fields

Charged particle motion in axisymmetric toroidal magnetic fields is analysed within the context of the canonical Hamiltonian guiding centre theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic field line is introduced and an analytical transformation to action-angle variables is obtained, under a zero drift width approximation. The latter is used to provide compact formulas for the orbital spectrum of the drift motion, namely the bounce/transit frequencies as well as the bounce/transit averaged toroidal precession and gyration frequencies. These formulas are shown to have a remarkable agreement with numerically calculated full drift width frequencies and significant differences from standard analytical formulas based on a pendulum-like Hamiltonian description. The analytical knowledge of the orbital spectrum is crucial for the formulation of particle resonance conditions with symmetry-breaking perturbations and the study of the resulting particle, energy and momentum transport.

Estimation of Atmospheric Duct Structure Using Radar Sea Clutter

Retrieving atmospheric refractivity profiles from the sea surface backscattered radar clutter is known as the refractivity-from-clutter (RFC) technique. Because the relationship between refractivity and radar sea clutter is clearly nonlinear and ill posed, it is difficult to get analytical solutions according to current theories. Previous works treat this problem as a model parameter estimation issue and some optimization algorithms are selected to get approximate solutions. Two main factors that limit the accuracy of the estimation are that 1) the refractive environments are described by using some idealized refractivity parameter models that cannot describe the exact information of the refractivity profile, and 2) accurate modeling of the sea surface radar cross section (RCS) is very difficult. Rather than estimating a few model parameters, this paper puts forward possibilities of using the variational adjoint approach to jointly retrieve the every-height refractivity values and sea surface RCS using radar clutter data. The derivation of the adjoint model is accomplished by an analytical transformation of the parabolic equation (PE) in the continuous domain. Numerical simulations including range-independent and range-dependent RCS cases are presented to demonstrate the ability of this method for RFC estimations. Making use of the refractivity retrievals, propagation loss predictions are also presented.

Flow factors for non-Gaussian roughness in hydrodynamic lubrication: An analytical interpolation

By extending the stochastic averaging techniques for lubricated rough surface contacts, as developed by Christensen and Tønder, a simple analytical transformation is derived to obtain the pressure flow factors for a non-Gaussian roughness whenever the corresponding Gaussian factors are known. The method is compared with results from numerical solutions available in the literature and it shows good agreement.