Generalized theory of helicon waves. I. Normal modes

Abstract

The theory of helicon waves is extended to include finite electron mass. This introduces an additional branch to the dispersion relation that is essentially an electron cyclotron or Trivelpiece–Gould (TG) wave with a short radial wavelength. The effect of the TG wave is expected to be important only for low dc magnetic fields and long parallel wavelengths. The normal modes at low fields are mixtures of the TG wave and the usual helicon wave and depend on the nature of the boundaries. Computations show, however, that since the TG waves are damped near the surface of the plasma, the helicon wave at high fields is almost exactly the same as is found when the electron mass is neglected.

Wave mode conversion and mode transition in very high radio frequency helicon plasma

“…Contrary to the understanding that the helicon mode launches when the abrupt jump of plasma density occurs, the helicon mode already exists only if Ͻ ce / 2 is satisfied as estimated by Chen. 9 In the plasma periphery satisfying the condition of k Ќ− 2 = k Ќ+ 2 , the mode conversion from the helicon mode to the TG mode occurs. The converted TG mode plays a main role in the plasma heating before the transition.…”

“…This indicates the limitation of helicon wave propagation at Ͻ ce /2. 9 Above 70 G ͑ Ͻ ce /2͒, however, strong surface ionization was occurred as shown in Fig. 3͑c͒.…”

“…[5][6][7][8] Although many researchers have been trying to explain the mechanisms of efficient power absorption, it has not been clearly examined yet due to difficulties in its detection. 5,9 As the TG mode tends to be localized in a thin surface layer, the direct measurement is too difficult. Due to the difficulty of measurement, almost no experimental evidence for the heating by the TG mode has been reported.…”

Plane-polarized helicon waves

“…These values would give rise to a beat pattern as the combined wave propagates along B 0 . Fortunately, a recent study [9] has shown that, at high magnetic fields, the eigenvalues of k for an insulating boundary are so closely spaced that the spectrum of possible k's is almost continuous. This is because the amplitude of the external wave in vacuum can adjust itself to satisfy the boundary condition.…”

“…Here ω c and ω p are the electron cyclotron and plasma frequencies, and we have adopted the notation of a more recent paper [9]. For a uniform plasma, the components of B can be written compactly in terms of Bessel functions:…”