Asymptotic Self-Similar Solutions of Z-Pinches in Vacuum

Yuri Shtemler, Michael Mond

Research output: Contribution to conferenceAbstractpeer-review


The dynamics of axially symmetric magnetized Z-pinches is studied. Radiation is neglected, while ohmic-heating and thermal-conductivity of the plasma are taken into account. The self-similar problem is treated analytically by asymptotic expansions in the limit of high but finite thermal conductivity. An asymptotic solution is obtained with the aid of the principle of minimum singularity. Explicit expressions for radial profiles characterizing Z-pinches carrying power law in time total currents (I=I_0t^S ) are found that depend on the line density, the total current amplitude I_0, and exponent S. A non-equilibrium solution is obtained for S=-1/5 in addition to the conventional self-similar solutions for either exact (for S=± 1/3, Coppins M., Culverwell I.D. and Haines M.G., Phys. Fluids, 31(9), 2688, 1988) or long-time asymptotic equilibrium of Z-pinches (Bud'ko A.B., Kravchenko Yu., Uby L., Plasma Phys. Control. Fusion, 36, 833, 1994) . It is shown that the latter is possible only for S>-1/5. The multiplicity of the self-similar solutions is analyzed.
Original languageEnglish GB
StatePublished - 1 Oct 2003
Externally publishedYes
Event American Physical Society, 45th Annual Meeting of the Division of Plasma Physics - Albuquerque, New Mexico, Mexico
Duration: 27 Oct 200331 Oct 2003


Conference American Physical Society, 45th Annual Meeting of the Division of Plasma Physics
CityAlbuquerque, New Mexico


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