Effect of Finite Length of Plasma Column on Electromagnetic Drift Instabilities

2009 ◽  
Vol 55 (2T) ◽  
pp. 162-167 ◽  
Author(s):  
Alexei Yu. Chirkov ◽  
Vladimir I. Khvesyuk
Keyword(s):  
Finite Length ◽  
Plasma Column

Finite length thermal equilibria of a pure electron plasma column

1979 ◽  
Vol 22 (2) ◽  
pp. 278 ◽  
Author(s):  
S. A. Prasad ◽  
T. M. O’Neil
Keyword(s):  
Finite Length ◽  
Plasma Column ◽  
Electron Plasma

Time and Space-Resolved Electron Densities in a Theta Pinch at Various Distances along the Discharge Axis

1965 ◽  
Vol 20 (10) ◽  
pp. 1268-1273
Author(s):  
A. Eberhagen ◽  
H. Glaser
Keyword(s):  
Magnetic Field ◽  
Finite Length ◽  
Plasma Column ◽  
Independent Method ◽  
Discharge Axis ◽  
Density Profiles ◽  
Theta Pinch ◽  
Trapped Magnetic Field ◽  
Electron Density Profiles ◽  
Contraction Wave

The influence of the finite length of the discharge coil on the axial behaviour of a theta pinch plasma column is investigated by measuring electron density profiles at various distances from the midplane of the coil along the discharge axis. The resulting line densities were then checked by an independent method. For a parallel trapped magnetic field it was possible in this way to measure end losses and also the collection rate of the contraction wave in the case of an antiparallel trapped magnetic field.

On mappings with finite length distortion on Riemann surfaces

2019 ◽  
Vol 33 ◽  
Author(s):  
Serhii Volkov ◽  
Vladimir Ryazanov
Keyword(s):  
Finite Length ◽  
Riemann Surfaces ◽  
Boundary Behavior ◽  
Main Tool ◽  
Natural Generalization ◽  
Finite Distortion ◽  
Lipschitz Mappings ◽  
Geometric Function ◽  
Mappings With Finite Distortion ◽  
Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

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