Bounds on Plasma Fluctuations and Anomalous Diffusion

Upper limits on the intensity and growth rate of plasma fluctuations are calculated from purely thermodynamic considerations. From these limits, an upper bound on diffusion across a magnetic field by microinstabilities is estimated. Experimental results do not violate the bound. At low β, the dominant contribution to the bound is thermal energy which feeds fluctuations through a mechanism akin to expansion cooling of a gas, possible only in finite plasmas. A rapid decrease in anomalous diffusion in discharge afterglows when the radius R exceeds a critical value R₀ ∼ 10–20 ion gyroradii can be explained if the instability radial wavelength, a parameter in the theory, is restricted to ${\mathrm{\lesssim R}}_0$ . Then the bound on the stochastic diffusion coefficient decreases like R⁻³ if R > R₀. With this restriction on wavelength, the bound used as a scaling law predicts adequately long thermonuclear confinement ($\text{≳0.1}\sec$ ) in a torus of 100 cm minor radius if the torus is stabilized against frequencies below the ion cyclotron frequency, now perhaps feasible. Otherwise, low‐frequency resonant diffusion may limit containment. This result holds at least up to β of a few percent. Bounds on velocity diffusion are obtained, also. Both spatial and velocity diffusion are slow if electrons are cold compared to ions, which may account for observations in plasmas created by energetic ion injection.