I= STUDY OF HIGH β RELAXED STATE OF PLASMA
Pakistan Research Repository Home
 

Title of Thesis
STUDY OF HIGH β RELAXED STATE OF PLASMA

Author(s)
MUHAMMAD IQBAL
Institute/University/Department Details
Department of Physics/ Quaid-i-Azam University, Islamabad
Session
2001
Subject
Physics
Number of Pages
97
Keywords (Extracted from title, table of contents and abstract of thesis)
high β relaxed state, plasma, beltrami fields, mhd plasma, eruptive events, solar corona, helicities

Abstract
Beltrami fields, eigen functions of the curl operator, represent the static force-free relaxed state of a single-fluid MHD plasma and correspond to the alignment of magnetic field and current density. The double Beltrami fields which are the superposition of two different Beltrami fields, express a more general relaxed state of a two-fluid MHD plasma. The new relaxed states, despite its simple mathematical structure, encompass a wide class of steady states in mathematical Physics and explain interesting phenomena. Plasma configurations are investigated employing the double Beltrami fields. Our numerical results reveal that relaxed states of plasma exhibiting ultrahigh β associated with minimum values of field-aligned current and flow can be created which are suitable for the advanced fusion concept.

Furthermore, a set of algebraic equations is derived which relates the parameters of double Beltrami field (amplitudes and eigenvalues) and the ideal invariants (energy and helicities) of the system. These equations can be used to study the existence of solutions and catastrophic change of structures in relaxed equilibria in different plasma configurations. For a given set of energy and helicities, the catastrophic loss of equilibrium is observed when flux loops are compressed by varying the control parameter. This study could be very helpful to understand the eruptive events in solar corona.

Download Full Thesis
3258.91 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
348.88 KB
2 1 Introduction 3
344.08 KB
  1.1 Motivation 3
  1.2 Layout of thesis 9
3 2 Beltrami Fields 10
771.61 KB
  2.1 Self-organization in MHD System . 10
  2.2 Woltjer's Theorem 14
  2.3 Beltrami Fields 19
  2.4 Solar Coronal Loops 22
4 3 Double Beltrami Fields 25
1318.99 KB
  3.1 Steinhauer -Ishida Model 26
  3.2 Local and Global Invariance of Helicities 30
  3.3 Relaxed State 32
  3.4 Mahajan - Yoshida Model 34
  3.5 Invariance of Helicities of Double Curl Beltrami System 40
  3.6 Vaxiational Principle for Double Curl Beltrami System 43
  3.7 Double Curl Beltrami and Self-helicities 45
5 4 Analytical Solutions in Cylindrical Geometry 47
424.53 KB
  4.1 Cylindrical Plasma System 48
  4.2 Radial Profiles 52
  4.3 Internal Conductor Plasma System 59
6 5 Catastrophic Change of Relaxed Equilibria 73
276.38 KB
  5.1 Double Beltrami Fields 74
  5.2 Conservation Laws for Double Beltrami Fields 76
  5.3 Analysis of Relaxed Equilibria 83
  5.4 Application to Solar Corona 86
  5.5 Summary and Conclusions 88