Technical notes

Helicons are low frequency (typ. 1-100 MHz) electromagnetic waves that can propagate in the plasma in presence of a static magnetic field. In other words helicons are electromagnetic normal modes of magnetised plasmas. The term “helicon” should be applied only to cylindrical plasmas because it comes from the helical structure of the wave field in the cylindrical geometry. In a conventional (r,θ,z) coordinate system with a static magnetic field aligned with z, the electromagnetic wave field  of helicon modes have the following form:

where ω is the wave pulsation, k_z is the axial mode number and m is the azimuthal mode number. This means that helicon modes are circularly polarised fields propagating along z. The r dependence of the fields is imposed by the boundaries conditions, the intensity of the static magnetic field, the plasma density, and several other parameters.

To give an illustration of the helicons structure we have represented the corresponding evolution with z of an arbitrary transverse magnetic field B(r=0,z) at a given time t₀ (Fig. 1). With time this whole pattern would turn around the z axis at frequency ω.

Figure 1: Helical nature of helicon fields

The leading idea in designing an antenna for helicons excitation is that it should generate a radiofrequency (RF) field that matches as well as possible the helicons field structure. At first, to match the azimuthal dependence of helicons, the azimuthal current distribution in the antenna should be sinusoidal and with the same periodicity 2π/m than the desired helicon mode. To go further in the fields matching, this sinusoidal azimuthal current distribution should be twisted around the z axis with a pitch corresponding to the desired helicon axial wavelength (2π/k_z), and with a pitch turning sense corresponding to the sign of m. Finally, this twisted sinusoidal current distribution should rotate with time around the z axis at the frequency ω.