Cyclotron Maser Radiation from an Inhomogeneous Plasma

Cyclotron maser radiation is important in both laboratory devices such as gyrotrons and in space physics applications to phenomena such as auroral kilometric radiation. To understand the behavior, especially in the latter case where there is generally a localized region of instability, requires an understanding of how such instabilities behave in an inhomogeneous plasma. Here we consider, for simplicity, a simple ring distribution of electrons in either a step function variation of magnetic field or a continuous gradient. In each case we show that there can exist localized regions of instability from which waves, growing in time, can be radiated outwards.

Figure 1

The dispersion relation for parallel propagation for a ring distribution with $\gamma =1.02$ and $\frac{{\omega }_{ce}}{\gamma {\omega }_{pe}}=10$.

Figure 2

(a) Solutions of Eq. (4) “$\times$” real part, “$+$” imaginary part; (b) Real part of $\omega$ as a function of wave number; (c) Corresponding imaginary part.

Figure 3

(a) Wave number as a function of $x$ with $\omega =10$; (b) Wave number as a function of $x$ with $\omega =10+0.13.i$. In (b) the full and dotted lines show the real part, both positive and negative roots being plotted to illustrate the confluence of the roots. The dashed line is the imaginary part corresponding to the positive root.

Figure 4

Wave amplitude as a function of $x$.

Figure 5

Real (a) and imaginary (b) parts of $\omega$ for a horseshoe distribution.