[...]... algorithms presently in use by the plasma physics community, and hope that this and the references can point the way to more advanced study for those interested in pursuing such endeavors The title of the book starts with Computational Methods , not All Computational Methods Perhaps it should be Some Computational Methods because it admittedly does not cover all computational methods being used in the field... What is computational physics? Here, we take it to mean techniques for simulating continuous physical systems on computers Since mathematical physics expresses these systems as partial differential equations, an equivalent statement is that computational physics involves solving systems of partial differential equations on a computer This book is meant to provide an introduction to computational physics. .. Choosing the Jacobian determines both the (a) ψ and the (b) θ coordinate ∂f The vector ∂ψ is proportional to the projection of f in the direction orthogonal to the other remaining coordinates, and not in the ψ direction In the inverse representation we consider the cylindrical coordinates R and Z to be functions of ψ and θ Points on a constant... xix xx Computational Methods in Plasma Physics The author has taught a semester class with the title of this book to graduate students at Princeton University for over 20 years The students are mostly from the Plasma Physics, Physics, Astrophysics, and Mechanical and Aerospace Engineering departments There are no prerequisites, and most students have very little prior exposure to numerical methods, ... been shown by several authors that in certain problems involving two-fluid magnetic reconnection, an electron viscosity term known as hyper-resistivity is required to avoid singularities from developing in the solution [6, 7] It is also useful for modeling the effect of fundamentally three-dimensional reconnection physics in a two-dimensional simulation [8, 9] Introducing the coefficient λH , we can take... e xxi xxii S γ s ˆ xi Computational Methods in Plasma Physics magnetic Lundquist number adiabatic index entropy density unit vector associated with Cartesian coordinate xi Bi cS VA ith Cartesian component of the magnetic field sound speed Alfv´n velocity e Chapter 1 Introduction to Magnetohydrodynamic Equations 1.1 Introduction A high-temperature magnetized plasma such as exists in modern magnetic fusion... electron-ion plasma, Q∆e + Q∆i = Re · J ne (1.22) 4 1.2 Computational Methods in Plasma Physics Magnetohydrodynamic (MHD) Equations The fluid equations given in the last section are very general; however, they are incomplete and still contain too wide a range of time and space scales to be useful for many purposes To proceed, we make a number of simplifying approximations that allow the omission of the terms in. .. configuration for confining a high-temperature plasma There is not a clear dividing line between computational and theoretical plasma physics It is not possible to perform meaningful numerical simulations if one does not start from the right form of the equations for the questions being asked, and it is not possible to develop new advanced algorithms unless one has some understanding of the underlying mathematical... in that globally conserved quantities can be exactly maintained in a computational solution However, in computational magnetohydrodynamics of highly magnetized plasmas, the conservative formulation is not normally the preferred starting point for the following reasons: While the mass and magnetic flux conservation equations, Eqs (1.65) and (1.66) (in some form) offer clear advantages, the conservation... without introducing hanging nodes Triangular elements can be locally refined, but require unstructured mesh data structures in programming 11.9 Each arbitrary quadrilateral element in the Cartesian space (x, y) is mapped into the unit square in the logical space for that element, (ξ, η) 11.10 Relation between global numbering and local numbering in one dimension . or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system,. and Doron Rotem COMPUTATIONAL METHODS IN PLASMA PHYSICS Stephen Jardin SERIES EDITOR Horst Simon Associate Laboratory Director, Computing Sciences Lawrence