Plenary Lecture

Variational Principles and Topological Constants of Motion for Barotropic and non Barotropic Magnetohydrodynamics

Professor Asher Yahalom
Chairman of the Israeli Plasma Science & Technology Association (IPSTA)
Department of Electrical & Electronic Engineering
Faculty of Engineering
Ariel University

Abstract: Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this talk we introduce simpler Eulerian variational principles which is appropriate for some magnetic field topologies from which all the relevant equations of barotropic and non-barotropic MHD can be derived. The variational principles are given in terms of five independent functions for non-stationary non-barotropic flows and four functions for barotropic flows. This is less than the eight variables which appear in the standard equations of non barotropic MHD which are the magnetic field B ⃗ the velocity field V ⃗, the entropy s and the density ρ. For the barotropic case the entropy s has to be omitted. The functions which are needed in addition to the entropy and density are two co-moving surfaces χ and η (Euler potentials) and a multiple valued Bernoulli type function ν. We will show that the discontinuity of ν is a conserved quantity and contains information about the cross helicity per unit of magnetic flux.

Brief Biography of the Speaker: Asher Yahalom is a Full Professor in the Faculty of Engineering at Ariel University and the Academic director of the free electron laser user center which is located within the University Center campus. He was born in Israel on November 15, 1968, received the B.Sc., M.Sc. and Ph.D. degrees in mathematics and physics from the Hebrew University in Jerusalem, Israel in 1990, 1991 and 1996 respectively. From 1994 to 1998 Asher Yahalom worked with Direx Medical System on the development of a novel MRI machine as a head of the magneto-static team. Afterwards he consulted the company in various mathematical and algorithmic issues related to the development of the "gamma knife" - a radiation based head surgery system. In the years 1998-1999 Asher Yahalom joined the Israeli Free Electron Laser Group both as postdoctoral fellow and as a project manager, he is a member of the group ever since. In 1999 he joined the College of Judea & Samaria which became at 2007 Ariel University Center. During 2005-2006 on his first sabbatical he was a senior academic visitor at the institute of astronomy in Cambridge. During his second sabbatical in the years 2012-2013 he was a visiting fellow of the Isaac Newton Institute for Mathematical Sciences also in Cambridge UK. Since 2013 Asher Yahalom is a full professor and since 2014 he is the head of the department of electronic & electrical engineering. Asher Yahalom works in a wide range of scientific & technological subjects ranging from the foundations of quantum mechanics to molecular dynamic, fluid dynamics, magnetohydrodynamics, electromagnetism and communications.

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