Field Precision finite-element programs

Field Precision finite-element programs covers a broad spectrum of physics and engineering applications, including charged particle accelerators and X-ray imaging. The core underlying most of our software packages is the calculation of electric and magnetic fields over threedimensional volumes. To use our electric and magnetic fields software effectively, researchers should have a background in electromagnetism and should be able to make informed decisions about solution strategies. First-time users of finite-element software may feel intimidated by these requirements. My motivation in writing this book is to share my experience in field calculations. I hope to build users knowledge and experience in steps so they can apply finiteelement programs confidently. In the end, readers will be able to solve real-world problems with the following programs: • EStat (2D electrostatics) • HiPhi (3D electrostatics) • PerMag (2D magnetostatics) • Magnum (3D magnetostatics) To begin, its important to recognize the difference between 2D and 3D programs. All finiteelement programs solve fields in three-dimensions, but often systems have geometric symmetries that can be utilized to reduce the amount of work. The term 2D applies to the following cases: • Cylindrical systems with variations in r and z but no variation in θ (azimuth). • Planar systems with variations in x and y and a long length in z. Which brings us to the first directive of finite-element calculations: never use a 3D code for a calculation that could be handled by a 2D code. The 3D calculation would increase the complexity and run time with no payback in accuracy. We need to clarify the meaning of static in electrostatics and magnetostatics. The implication is that the fields are constant or vary slowly in time. The criterion of a slow variation is that the systems do not emit electromagnetic radiation. Examples of electrostatic applications are power lines, insulator design, paint coating, ink-jet printing and biological sorting. Magnetostatic applications include MRI magnets, particle separation and permanent magnet devices. A following coarse will cover simulations of electromagnetic radiation (e.g., microwave devices). Secondly, its important to have a clear understanding of the purpose of computer calculations of electric and magnetic fields. Numerical methods should be used when it is not possible to generate accurate results with analytic methods. Numerical solutions are necessary in the following circumstances: 4 Figure 1: Screenshot of the MagView postprocessor for 3D magnetostatics. • The system has a complex asymmetric geometry. • The solution volume contains many objects with different material properties. • Materials have complex properties (e.g., saturation of iron in magnetic circuits) In an ideal case, a user makes analytic estimates of field values and then applies numerical methods to improve the accuracy. The initial analysis gives an understanding of the physics involved and the anticipated scales of quantities – essential information for effective solution setups. The worst case is when a user treats a program as an omniscient black box. No matter what software manufacturers may claim, using a field program without understanding fields is at best a gamble. Sometimes you may get lucky, but most of the time considerable effort is wasted generating meaningless results. In summary, I would like to help you become an informed software user. I suggest you start by downloading a free textbook that will help you brush up on electric and magnetic field theory. The book also gives a detailed description of the FEM techniques I will discuss: S. Humphries, Finite-element Methods for Electromagnetics (CRC Press, Boca Raton, 1997) (available for free download at http://www.fieldp.com/femethods.html). The following chapter describes how to download and to set up field-solution software packages.