Reynolds number measurement from correlation function analysis on the SSX MHD wind tunnel

Plasma turbulence and magnetic reconnection are studied at the Swarthmore Spheromak Experiment through high velocity counter-helicity spheromak merging and single-plume relaxation experiments (typical values $n\geq10^{20}~m^{-3}, T \geq 20~eV, B\cong 0.1~T$). Fluctuations in magnetic field, velocity field, density, and soft x-ray light are measured in the SSX MHD wind tunnel configuration ($L \cong 1~m$, $r \cong 10~cm$). Magnetic structure and fluctuations in SSX plasmas are measured with a 16 channel high-resolution probe array ($4~mm$ spatial resolution, $30~MHz$ bandwidth), inserted radially at the midplane of the flux conserver. The magnetic Reynolds number of the turbulence can be estimated directly from the radial correlation function between probe channels. The correlation function $R({\bf r}) = \langle {\bf b(x) b(x+r)} \rangle \cong 1 - r^2/2 \lambda_T^2$ yields an estimate for the Taylor microscale $\lambda_T$, the scale at which dissipation commences.\footnote{Matthaeus \textit{et al.}, PRL 2005} The correlation scale $\lambda_C$ is the size of the largest magnetic eddies. The effective magnetic Reynolds number is then $R_M = (\lambda_C/\lambda_T)^2$. Preliminary estimates of $R_M$ measured this way show $R_M \sim 10$.