Plasma turbulence

Plasma turbulence is irregular, interacting multiscale motion of plasma particles and electromagnetic fields. At large scales a magnetohydrodynamics model can describe coupled velocity and magnetic fluctuations; near ion and electron scales their separate kinetic responses become important. A broadband spectrum alone is insufficient to establish how energy moves between scales.

A useful measurement combines spacecraft magnetometer data with plasma velocity and density measurements. Mixed third-order statistics of velocity and magnetic-field increments can test an energy-cascade relation. Ulysses observations found the predicted approximately linear scale dependence over an inertial range, providing evidence of transfer between scales rather than merely a noisy signal.^[ref]

For an idealized constant-density model, write the Elsässer fields $z^{\pm }=u\pm B/\sqrt{{\mu }_0\rho }$. Their nonlinear coupling shows why magnetic and velocity fluctuations should be measured together. Interpreting a spacecraft time lag as a spatial separation additionally requires a flow-advection approximation. At small scales, explaining plasma heating requires identifying how fluctuating field energy reaches particle distributions, beyond observing a spectral slope.