This book is a study of plasma waves which are observed in the earth's
magnetosphere. The emphasis is on a thorough, but concise, treatment of
the necessary theory and the use of this theory to understand the
manifold varieties of waves which are observed by ground-based
instruments and by satellites. We restrict our treatment to waves with
wavelengths short compared with the spatial scales of the background
plasma in the mag- netosphere. By so doing we exclude large scale
magnetohydrodynamic phenomena such as ULF pulsations in the Pc2-5
ranges. The field is an active one and we cannot hope to discuss every
wave phenomenon ever observed in the magnetosphere! We try instead to
give a good treatment of phenomena which are well understood, and which
illustrate as many different parts of the theory as possible. It is thus
hoped to put the reader in a position to understand the current
literature. The treatment is aimed at a beginning graduate student in
the field but it is hoped that it will also be of use as a reference to
established workers. A knowledge of electromagnetic theory and some
elementary plasma physics is assumed. The mathematical background
required in- cludes a knowledge of vector calculus, linear algebra, and
Fourier trans- form theory encountered in standard undergraduate physics
curricula. A reasonable acquaintance with the theory of functions of a
complex vari- able including contour integration and the residue theorem
is assumed.