Numerical Mhd

This book is devoted to mathematical modeling of tokamak plasma. Since the appearance in 1982 of the first edition (in Russian), a considerable amount of experimental and theoretical material on tokamak research has been accumu­ lated. The new-generation devices, viz. , TFTR, JET and JT-60 were put into operation. The first experiments on these units have confirmed the correctness of the basic physical concepts underlying their construction. Experiments on plasma heating with the help of neutral beams and high-frequency (HF) waves on previous generation devices made it possible to obtain high-P plasmas. The number of "medium-size" tokamaks in operation has increased. New experi­ mental results and advances in the theory have led to more complicated and perfected models of high-temperature plasma. Rapid progress in computer hardware and software has played an important role in the further development of mathematical modeling. While preparing the English edition of the book, we have revised the text considerably. Several new models which have undergone significant advance­ ment in recent years are described. A section devoted to models of RF (radio frequency) current drive has been added to Chap. 2. The reduced magneto­ hydrodynamic (MHD) equations for high-P plasma are now considered in detail in Chap. 3. Chapter 4 contains the latest results on anomalous thermal conductivity, diffusion coefficient and pinching. Two new sections are added to Chap. 5.

This book contains eight topical review papers on Magnetohydrodynamics (MHD). For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration.

This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows.