Complete course notes part 2

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Plasma waves Absolutely quiescent plasmas do not exist. On the contrary, electric and magnetic fluctuations can be expected in a plasma, even in its stationary state. These disturbances can propagate along the plasma if their amplitudes are higher than the level of the thermal fluctuations always present in a plasma. In this case we speak of plasma waves. There are several different waves which represent a response of the plasma to external disturbances. Waves are important, since we can obtain information on the structure of the plasma by investigating how waves move in it. We will give an account only of the simplest waves, which are also useful for spatial applications. We will assume that the thermal noise level is much smaller than the wave amplitude: this implies that our plasma is cold. On the other hand, the wave amplitudes will be supposed to be small enough to allow any disturbance to be represented as a superposition of plane waves. This means that we will not deal with nonlinear effects. As a consequence of the previous assumptions, we can represent any wave disturbance, A(x, t), in the plasma by plane waves, i.e., by its Fourier components. If the disturbance itself is a plane wave, it consists only of one Fourier component where the amplitude, A(k, ω), is a function of the wave vector, k, and the frequency, ω. This representation allows to define the phase and the group velocity of the wave The phase velocity is always parallel to the wave vector, k, and shows the direction of wave propagation. The group velocity may deviate from this direction and describes the speed and direction of the energy flow in the wave. Langmuir waves We have previously seen that in an un-magnetized plasma with fixed ions, electrons may oscillate with a (plasma) frequency:…