Firstly, the development of radio broadcasting led to the discovery of the Earth's ionosphere, a layer of partially ionized gas in the upper atmosphere which reflects radio waves, and is responsible for the fact that radio signals can be received when the transmitter is over the horizon. Unfortunately, the ionosphere also occasionally absorbs and distorts radio waves. For instance, the Earth's magnetic field causes waves with different polarizations (relative to the orientation of the magnetic field) to propagate at different velocities, an effect which can give rise to ``ghost signals'' (i.e., signals which arrive a little before, or a little after, the main signal). In order to understand, and possibly correct, some of the deficiencies in radio communication, various scientists, such as E.V. Appleton and K.G. Budden, systematically developed the theory of electromagnetic wave propagation through non-uniform magnetized plasmas.
Secondly, astrophysicists quickly recognized that much of the Universe consists of plasma, and, thus, that a better understanding of astrophysical phenomena requires a better grasp of plasma physics. The pioneer in this field was Hannes Alfvén, who around 1940 developed the theory of magnetohydrodyamics, or MHD, in which plasma is treated essentially as a conducting fluid. This theory has been both widely and successfully employed to investigate sunspots, solar flares, the solar wind, star formation, and a host of other topics in astrophysics. Two topics of particular interest in MHD theory are magnetic reconnection and dynamo theory. Magnetic reconnection is a process by which magnetic field-lines suddenly change their topology: it can give rise to the sudden conversion of a great deal of magnetic energy into thermal energy, as well as the acceleration of some charged particles to extremely high energies, and is generally thought to be the basic mechanism behind solar flares. Dynamo theory studies how the motion of an MHD fluid can give rise to the generation of a macroscopic magnetic field. This process is important because both the terrestrial and solar magnetic fields would decay away comparatively rapidly (in astrophysical terms) were they not maintained by dynamo action. The Earth's magnetic field is maintained by the motion of its molten core, which can be treated as an MHD fluid to a reasonable approximation.
Thirdly, the creation of the hydrogen bomb in 1952 generated a great deal of interest in controlled thermonuclear fusion as a possible power source for the future. At first, this research was carried out secretly, and independently, by the United States, the Soviet Union, and Great Britain. However, in 1958 thermonuclear fusion research was declassified, leading to the publication of a number of immensely important and influential papers in the late 1950's and the early 1960's. Broadly speaking, theoretical plasma physics first emerged as a mathematically rigorous discipline in these years. Not surprisingly, Fusion physicists are mostly concerned with understanding how a thermonuclear plasma can be trapped--in most cases by a magnetic field--and investigating the many plasma instabilities which may allow it to escape.
Fourthly, James A. Van Allen's discovery in 1958 of the Van Allen radiation belts surrounding the Earth, using data transmitted by the U.S. Explorer satellite, marked the start of the systematic exploration of the Earth's magnetosphere via satellite, and opened up the field of space plasma physics. Space scientists borrowed the theory of plasma trapping by a magnetic field from fusion research, the theory of plasma waves from ionospheric physics, and the notion of magnetic reconnection as a mechanism for energy release and particle acceleration from astrophysics.
Finally, the development of high powered lasers in the 1960's opened up the field of laser plasma physics. When a high powered laser beam strikes a solid target, material is immediately ablated, and a plasma forms at the boundary between the beam and the target. Laser plasmas tend to have fairly extreme properties (e.g., densities characteristic of solids) not found in more conventional plasmas. A major application of laser plasma physics is the approach to fusion energy known as inertial confinement fusion. In this approach, tightly focused laser beams are used to implode a small solid target until the densities and temperatures characteristic of nuclear fusion (i.e., the centre of a hydrogen bomb) are achieved. Another interesting application of laser plasma physics is the use of the extremely strong electric fields generated when a high intensity laser pulse passes through a plasma to accelerate particles. High-energy physicists hope to use plasma acceleration techniques to dramatically reduce the size and cost of particle accelerators.