Design and use of an Els\"{a}sser probe for analysis of Alfv\'{e}n wave fields in a laboratory plasma

We have designed an electric and magnetic field probe which can simultaneously measure both quantities in the directions perpendicular to the applied magnetic field. This new probe allows for the projection of measured wave fields onto modified Els\"{a}sser variables: $z^{\pm }$\textbf{=} $C_{cf }$(\textbf{\textit{E}}\textit{ $\times $ B}$_{0})$/$\vert B_{0}\vert ^{2}\pm \quad \delta B/(\mu _{0}$\textit{$\rho $}$_{0})^{0.5}$. Here the time averaged background field, $B_{0}$, and plasma mass density, \textit{$\rho $}$_{0}$, are measured separately and the correction factor was determined from cold plasma theory to be $1/C_{cf }=\pm $[(1+{\{}$k_{\bot }$\textit{$\delta $}$_{e}${\}}$^{2})$(1-\textit{$\omega $}$^{2}$\textit{/$\Omega $}$^{2})$]$^{0.5}$. Experiments were conducted in singly ionized He plasma at 1810 G in the Large Plasma Device at UCLA. The new probe monitored the propagation of Alfv\'{e}n waves in the $x--z$ plane. Collisionless dispersion of the waves, corresponding to Eq. (1) of Kletzing \textit{et al}. [1], was observed in the field measurements. Simulations of the data confirm these results. Further analysis showed that we are able to measure the Alfv\'{e}n speed ($V_{A} = E/ B)$ from the probe data within 1.5{\%} of that from the time of flight data. Results will be discussed further at confeence.\\[4pt] [1] C. A. Kletzing, D. J. Thuecks, F. Skiff, S. R. Bounds, and S. Vincena, Phys. Rev. Lett. \textbf{104}, 095001(4) (2010).