Properties of possible electrostatic and electromagnetic wave propagation in hot space plasmas can be described by plasma dispersion relation. This can be obtained using plasma kinetic theory and Maxwell's equations.
Analytical solutions exist for some special cases, however general solution needs use of numerical methods, with the input including velocity distribution function. Non- Maxwellian electron velocity distribution functions can lead to wave generation and amplication.
Examples of such instabilities leading to various types of waves are described.