Cyclotron Mode Frequency Shifts in Multi-Species Ion Plasmas

Plasmas exhibit a variety of cyclotron modes, which are used in a broad range of devices to manipulate and diagnose charged particles. Here we discuss cyclotron modes in trapped plasmas with a single sign of charge. Collective effects and electric fields shift these cyclotron mode frequencies away from the ``bare'' cyclotron frequencies $ \Omega_s \equiv qB/m_s c$ for each species $s$. These electric fields may arise from applied trap potentials, from space charge including collective effects, and from image charge in the trap walls. \textbullet We will describe a new laser-thermal cyclotron spectroscopy technique, applied to well-diagnosed pure ion plasmas. This technique enables detailed observations of $\cos (m \theta$) surface cyclotron modes with $m = 0$, 1, and 2 in near rigid-rotor multi-species ion plasmas. For each species $s$, we observe cyclotron mode frequency shifts which are dependent on the plasma density through the $E \times B$ rotation frequency, and on the charge concentration of species $s$, in close agreement with recent theory.\footnote{D.H.E. Dubin, Phys. Plasmas 20, 042120 (2013).} This includes the novel $m = 0$ radial ``breathing'' mode, which generates no external electric field except at the plasma ends. These cyclotron frequencies can be used to determine the plasma $E \times B$ rotation frequency and the species charge concentrations, in close agreement with our laser diagnostics. Here, this plasma characterization permits a determination of the ``bare'' cyclotron frequencies to an accuracy of 2 parts in $10^4$. \textbullet These new results\footnote{M. Affolter et al., Phys. Lett. A 378, 2406 (2014).} give a physical basis for the ``space charge'' and ``amplitude'' calibration equations of cyclotron mass spectroscopy, widely used in molecular chemistry and biology. Also, at high temperatures there is preliminary evidence that radially-standing electrostatic Bernstein waves couple to the surface cyclotron modes, producing new resonant frequencies.