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Register a new userA Generalization of Abel Inversion to non axisymmetric density distribution
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Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $delta phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources.
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An asymptotic expansion is performed to obtain quasi-axisymmetric magnetic configurations that are weakly non-axisymmetric. A large space of solutions is identified, which satisfy the condition of quasi-axisymmetry on a single magnetic flux surface, while (non-axisymmetric) globally quasi-axisymmetric solutions are shown to not exist, agreeing with the conclusions of previous theoretical work. The solutions found are shown to be geometrically constrained at low aspect ratio or high toroidal period number. Solutions satisfying the more general condition of omnigeneity (generalized quasi-axisymmetry) are also shown to exist, and it is found that quasi-axisymmetric deformations can be superposed with an omnigenous solution, while preserving the property of omnigeneity, effectively extending the space of good configurations. A numerical solution of the first order quasi-axisymmetry problem is demonstrated and compared with solutions found with a widely used MHD equilibrium solver, independently verifying that quasi-axisymmetry is satisfied at the appropriate order. It is thereby demonstrated that approximately quasi-axisymmetric solutions can be directly constructed, i.e. without using numerical search algorithms.
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.
Recently, two novel techniques for the extraction of the phase-shift map (Tomassini {it et.~al.}, Applied Optics {bf 40} 35 (2001)) and the electronic density map estimation (Tomassini P. and Giulietti A., Optics Communication {bf 199}, pp 143-148 (2001)) have been proposed. In this paper we apply both methods to a sample laser-plasma interferogram obtained with femtoseconds probe pulse, in an experimental setup devoted to laser particle acceleration studies.
The basic idea behind Rayleighs criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision for the locations of the sources, dubbed Rayleighs curse. We generalize the concept of Rayleighs curse to the abstract problems of quantum parameter estimation with incoherent sources. To manifest the effect of Rayleighs curse on quantum parameter estimation, we define the curse matrix in terms of quantum Fisher information and introduce the global and local immunity to the curse accordingly. We further derive the expression for the curse matrix and give the necessary and sufficient condition on the immunity to Rayleighs curse. For estimating the one-dimensional location parameters with a common initial state, we demonstrate that the global immunity to the curse on quantum Fisher information is impossible for more than two sources.
In a toroidal plasma confined by a purely toroidal magnetic field the plasma transport is governed by electrostatic turbulence driven by the flute interchange instability on the low-field side of the torus cross section. In this paper we revisit experimental data obtained from the Blaamann torus at the University of Tromso. On time-scales shorter than the poloidal rotation time, the time series of potential and electron density fluctuations measured on stationary Langmuir probes essentially reflect the spatial poloidal structure of the turbulent field (Taylor hypothesis). On these time scales the signals reveals an intermittent character exposed via analysis of probability density functions and computation of multifractal dimension spectra in different regimes of time scales. This intermittency is associated with the shape and distribution of pronounced spikes in the signal. On time scales much longer than the rotation period there are strong global fluctuations in the plasma potential which are shown to to be the result of low-dimensional chaotic dynamics.
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