Dispersion characteristics for decaying or amplifying waves: 1. An observational approach

One‐dimensional wave packets propagating through an infinite homogeneous medium may be characterized by three properties: group velocity, phase velocity, and growth or decay rate. Analysis of such wave packets excited by a periodic source maintained indefinitely, or by a transient source, e.g., a tone burst, establishes a local velocity computed in a manner similar to Brillouin's signal velocity as anenergy velocity. The expression for this depends on the types of source considered, and whether the plane wave components maintain their energy, decay, or amplify. In this paper, observational properties are deduced for wave packets which demonstrate that periodic and transient sources excite decaying and amplifying waves, with identical frequencies but with different local velocities, phase velocities, and growth or decay rates. An analysis of the amplifying waves in a beam‐plasma system is presented which exemplifies these source‐dependent properties.