A formalism for treating the stability of force-free magnetic fields (VXB=a;B) based on the energy principle of Bernstein et al. is derived. An example is given to shown that force-free fields with constant a may be unstable, though previous papers give arguments in favor of the stability of such fields. It is found that the cylindrically symmetric force-free field given by Lundquist is unstable if and only if aro (where r 0 is the radius of the cylinder) exceeds the critical value 3.176. The unstable displacements have small growth rates. They are of the screw or kink type, their wavelengths along the axis having a minimum of about seven times the critical cylinder radius.The results are applied to the arms of spiral galaxies, correcting Trehan's statement that some force-free fields with constant a have a stabilizing effect on gravitational instability.
Magnetic field diagnostics in tokamaks using the motional Stark effect in fast neutral beams have been based on two kinds of polarimetry which we call ‘‘static’’ and ‘‘dynamic.’’ A detailed analysis shows that static polarimetry presents a number of advantages over dynamic polarimetry, provided it is made complete in the sense that a sufficient number of polarization analyzers are installed and different parts of the spectrum are explored to yield full information on the set of unknowns inherent in the problem. A detailed scheme of complete static polarimetry is proposed, including the case where an in-vessel mirror with changing characteristics (coating by impurities) is placed in front of the optical detection system. The main merit of this scheme relies on the fact that it is self-calibrating with respect to both the characteristics of the mirror and the transmission of the different polarization channels, the latter item implying that it is uniquely based on relative measurements of spectra. Further advantages are a greater flexibility with regard to different kinds of diagnostics and the circumstance that the technical equipment is less involved. The above scheme is based on a detection system of moderate etendue exploiting a large spectral domain, which is the regime where static polarimetry usually operates. It is also possible, however, to work with large etendue and a small spectral domain, such as commonly adopted in dynamic polarimetry. Using such a regime, static polarimetry loses the advantages mentioned above but gains, as a new advantage, the benefit of a comparatively lower level of photon noise.
Stark broadening of spectral lines is considered as a semi-classical many-body problem. Starting from a Liouville equation for a distribution function depending on the atomic Hilbert space vector and the coordinates and velocities of the classical plasma particles, BBGKY hierarchy techniques are used to derive a complete line profile for the electron contribution. The line shape formula is expressed in terms of the atomic time evolution operator for a collision with a single plasma electron. This operator is approximated by a strictly unitary exponential expression, yielding more accuracy than second order perturbation theory and being valid also in the quasi-static limit. The resulting line shape expression covers the whole frequency domain from the impact regime to the quasi-static regime. The results of the impact and quasi-static approximations are recovered as special cases for small and large distances from the line center. A numerical application to Lyman - α shows very good agreement with an experiment of Boldt and Cooper.
An improved treatment of electron correlations is presented within the framework of a previously developed unified model for Stark broadening by plasma electrons. This treatment employs the method of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in connection with a closure relation corresponding essentially to the exclusion of simultaneous strong collisions. A line-shape expression is derived for the case that the perturbing electron gas is in thermal equilibrium.This expression depends on the dynamic dielectric constant and on the two-electron correlation function. If the latter is approximated by the linearized Debye-Huckel expression {low-density case), and if the result is simplified for the vicinity of the line center by using second-order perturbation theory for the atom-perturber interaction, the results of earlier treatments of electron correlations are recovered.
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