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In this paper, we propose an efficient diagnostic technique for determining spatially resolved measurements of the ion density ratio in a magnetized two-ion species plasma. Shear Alfvén waves were injected into a mixed helium–neon plasma using a magnetic loop antenna, for frequencies spanning the ion cyclotron regime. Two distinct propagation bands are observed, bounded by 
$\omega < \varOmega _\textrm {Ne}$ and 
$\omega _{ii} < \omega < \varOmega _\textrm {He}$, where 
$\omega _{ii}$ is the ion–ion hybrid cutoff frequency and 
$\varOmega _\textrm {He}$ and 
$\varOmega _\textrm {Ne}$ are the helium and neon cyclotron frequencies, respectively. A theoretical analysis of the cutoff frequency was performed and shows it to be largely unaffected by kinetic electron effects and collisionality, although it can deviate significantly from 
$\omega _{{ii}}$ in the presence of warm ions due to ion finite Larmor radius effects. A new diagnostic technique and accompanying algorithm was developed in which the measured parallel wavenumber 
$k_\parallel$ is numerically fit to the predicted inertial Alfvén wave dispersion in order to resolve the local ion density ratio. A major advantage of this algorithm is that it only requires a measurement of 
$k_\parallel$ and the background magnetic field in order to be employed. This diagnostic was tested on the Large Plasma Device at UCLA and was successful in yielding radially localized measurements of the ion density ratio.
In this semi-analytic study we develop a mathematical model for determining the electromagnetic field due to a current-driven antenna immersed in a cold, magnetized plasma, valid for frequencies below the electron plasma frequency. At each point in the plasma, it is shown that the vacuum electric field of the antenna couples to the plasma conductivity tensor and acts as an infinitesimal source term to drive plasma currents – the total field is then found from the aggregate sum of these point sources, expressed as an integral across the vacuum field. A general solution is provided for both azimuthally symmetric cylindrical coordinates as well as a fully generalized Cartesian solution. As an example of how this general solution may be applied, we solve for the field due to an electric dipole antenna of length
$\ell$
, aligned along the background field, at frequencies below the ion cyclotron frequency. It is found that the near field decays exponentially with increasing
$k_{\bot }z$
, whereas the far field exhibits wave-like behaviour. The radiation zone exhibits propagation cones emanating from either end of the dipole, with a propagation angle that is consistent with past analytic studies of inertial Alfvén waves. The mathematical model presented here may be advantageous over other numerical methods, as it allows the user to solve parts of the problems analytically, thereby cutting down significantly on computation time, as well as offering physical insight into the system that may not be evident with other numerical solvers.
