Astrophysical plasmas are typically magnetized , with the Larmor radii of the charged particles many orders of magnitude smaller than their collisional mean free paths .
The fundamental properties of such plasmas , e.g. , conduction and viscosity , may depend on the instabilities driven by the anisotropy of the particle distribution functions and operating at scales comparable to the Larmor scales .
We discuss a possibility that the pressure anisotropy of thermal electrons could produce polarization of thermal bremsstrahlung emission .
In particular , we consider coherent large-scale motions in galaxy clusters to estimate the level of anisotropy driven by stretching of the magnetic-field lines by plasma flow and by heat fluxes associated with thermal gradients .
Our estimate of the degree of polarization is \sim 0.1 \% at energies \gtrsim kT .
While this value is too low for the forthcoming generation of X-ray polarimeters , it is potentially an important proxy for the processes taking place at extremely small scales , which are impossible to resolve spatially .
The absence of the effect at the predicted level may set a lower limit on the electron collisionality in the ICM .
At the same time , the small value of the effect implies that it does not preclude the use of clusters as ( unpolarized ) calibration sources for X-ray polarimeters at this level of accuracy .