Visual and Computational Plasma Physics

The following sections are included:

• Preface
• Contents

Among the physics disciplines, plasma physics is younger than relativity and quantum mechanics. Since the 1950s, evidence of solar energy being derived from nuclear fusion attracted great talents to explore plasma physics in search for an inexhaustible energy source. Thus far, plasma physics has achieved certain maturity. But challenges are great and many, and will remain so for a long time to come. Yet, the fruits of labor can be sweet and rewarding, since the advancement in plasma physics will have great impact on important areas such as controlled fusion, astrophysics, space and earth physics, nanobio and industrial applications, and not the least, the computational physics…

A theoretical investigation may get initiated by following the hints from the experimental observations, physical considerations or both. To arrive at a conclusion and to ensure its correctness, however, a theoretical undertaking nowadays may require both numerical and analytical computations. The compact analytical formulae have the advantages of clarity, insight, and convenience, while the numerical analysis provides the ultimate solution and the vivid graphical visualization. MATLAB offers the symbolic computation and reduces the overhead in programming and consequently, the time to get the answer, and the effort to visualize the result. This is useful at the beginning of a scientific endeavor when the problem may not be well defined, and quick answers on a few conjectures are desired. After the problem gets mathematically formulated and well defined, and an efficient code is geared toward production phase or even commercial application, C++ or its variants of internet ready programming languages such as Java, PhP, or Python is the recommended choice. Here, we start by introducing MATLAB for use in computer programming.

A good starting point to explore a complex plasma phenomenon is often the single particle behavior, which can be the significant first step to gain insight into the relevant plasma physics. While the collective plasma phenomena and the nonlinear many-body physics can deviate from the overly simplified single particle picture, and wave, fluid, or kinetic and statistical descriptions are indispensable, physical effects, as a rule, have to originate from the single particle motions in a consistent way. Moreover, treating all the particles self-consistently, as, in particle simulation, unmistakably reveals the underlying physics. This Chapter will introduce the single particle physics and the related numerical algorithms.

The single particle picture, while providing the first glance at the truth, is insufficient to describe the collective phenomena of many-body plasma physics. Generalizing it to keep track of all particles would be highly desirable. However, since plasma physics often involves a great number of particles, to follow their dynamics at least 6N variables for N particles in phase space are needed, not to mention the electric field, the magnetic field, and many other quantities in the configuration space. Thus, it is often too complicated to follow the kinematics of all particles analytically or numerically.On the other hand, the smoothed and averaged properties of wave, transport, and fluid, may be revealed by a few local variables in the configuration space such as density, momentum, energy, and current, to understand the governing principles by simplification with clarification. Many effects from the particle discreteness such as correlation, velocity anisotropy, runaway, kinetic effects, among others, may be neglected as a start. Therefore, resorting to a fluid model is naturally the next step in our exploration of plasma physics.

Confined plasma, as a rule, has plenty of free energy due to its spatial inhomogeneity, external heating, or fusion reactions. This makes plasma rich in wave phenomena whether in the controlled fusion device or otherwise such as in the solar flare. The long-range nonlinear many-body interactions allow waves of various wavelengths and frequencies to occur. Moreover, the plasma fluid model of MHD is a superset of hydrodynamics. As such, it exhibits wave physics of hydrodynamics and beyond. Therefore, plasma has many kinds of waves and instabilities. Knowing wave physics is an indispensable discipline for plasma physicists…

Plasma parameters are very wide ranged. The electron density can be as low as 10⁻⁵/cc in the interstellar, and as high as 10²⁵/cc in the center of the sun. The temperature could be as low as 10⁻² eV, and as high as 10⁵ eV. Moreover, the mass disparity in the electron-to-ion ratiomakes the characteristic frequencies and lengths vary by many orders of magnitude. Plasma physics thus offers great challenges in the uncompromising time and length scales for analysis or simulation…

Algorithm is the procedure for solving a mathematical problem in a finite number of steps. It is a deterministic automation, particularly suitable to program a computer to find the analytical or numerical solutions. Algorithm is central to all areas of scientific computing. It is the recipe that makes computer perform according to the knowledge, concept or expertise. It is capable of transferring the know-how to the novice for efficient and best-known procedures in problem solving. Algorithm is the spirit of computing. It can be said that where there is the algorithm, there is the solution. In truth, it is the solubility condition in computational science. If you love algorithm you may be amazed to find that algorithm does find love for some, by matching the personality traits and more…

In the N-body phase space description, the distribution function can be written as

The importance of transport goes beyond the magnetic and inertia confinement in fusion application. The solar flare, for example, involves drastic activities of magnetic fields, energetic particles, and vortex flows to result in solar wind, solar prominence, sun spots, sun quake, and coronal mass ejection. Its impact on earth has been termed the space weather capable of affecting communication satellites and sensitive electronic devices, or even crippling the power grid. Its magnificent showing of aurora is often a northern delight…

The kinetic equations can often be too complicated to solve. On the other hand, the wave, transport, and fluid effects, may be understood by a few smoothed and averaged local variables in the configuration space to reveal the governing principles by simplification with clarification. Resorting to the MHD model thus has many advantages. By neglecting some detailed structures, the large-scale phenomena may be explored from the macroscopic quantities to establish the global understanding of (fusion) plasma, allow fundamentally new design concept, give better intuition for the experimental observables, and study major instabilities that severely limit the achievable plasma parameters.

While linear physics may provide a quick glimpse at the plasma topics of interest, more often than not, it is insufficient to explain away the natural phenomena. Nonlinear physics will ultimately reflect the truth since any deviation from the linear relationship would naturally be nonlinear. The complication arises as many competing terms might contribute. A consistent ordering is the rule of thumb to make sure the dominant effects are properly taken into consideration. Dimensionless variables will value themselves on an equal footing to their importance in the underlying principles even if they are of different physical entities, as discussed in the first Chapter. Beyond the inclusion of important terms, the well posed nonlinear equations can be tricky to solve. Arguments as supported by numerical, experimental, analytical and physical interpretations will be helpful to lead to the correct answers…

The following sections are included:

• Bibliography
• Program Index
• Index