Doppler-Shifted Cyclotron Resonance with Helicon Waves

The properties of helicon waves have been studied under the condition that the electron mean free path is larger than the helicon wavelength; this is often called the nonlocal limit. The free-electron theory shows that under this condition there is a threshold magnetic field. Above this threshold, undamped helicon waves can propagate in the metal. Below it, the wave is heavily damped by cylotron resonance of the electrons. This threshold field has been called the Kjeldaas absorption edge or Doppler-shifted cyclotron resonance. At fields just above the edge, the dispersion relation is modified from the simple form appropriate for the locallimit. At the edge there is a singularity in the surface impedance of the metalsample. The theory of these effects has been tested by measurements on polycrystalline sodium and potassium, using two experimental techniques. First, the dispersion relation was studied using helicon waves propagating through a metal slab. Second, the surface impedance was studied at radio frequencies. Excellent agreement between theory and experiment was obtained. The values for the radius of the Fermi surface were (0.92±0.01)×${10}^{+8\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ for sodium and (0.74±0.01)×${10}^{+8\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ for potassium. These are to be compared with the free-electron values of 0.923×${10}^{+8\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and 0.746×${10}^{+8\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. The sharpness of the edge as a function of the electron mean free path was also studied. It was found that the fractional width was essentially inversely proportional to ${\omega }_c\tau$. The edge has also been studied with polycrystalline indium.