Beyond the Oberbeck–Boussinesq and long wavelength approximation
Markus Held, M. Wiesenberger
Abstract
Abstract We present the first simulations of a reduced magnetized plasma model that incorporates both arbitrary wavelength polarization and non-Oberbeck–Boussinesq effects. Significant influence of these two effects on the density, electric potential and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="bold-italic">E</mml:mi> <mml:mo>×</mml:mo> <mml:mi mathvariant="bold-italic">B</mml:mi> </mml:math> vorticity and non-linear dynamics of interchange blobs are reported. Arbitrary wavelength polarization implicates so-called gyro-amplification that compared to a long wavelength approximation leads to highly amplified small-scale <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="bold-italic">E</mml:mi> <mml:mo>×</mml:mo> <mml:mi mathvariant="bold-italic">B</mml:mi> </mml:math> vorticity fluctuations. These strongly increase the coherence and lifetime of blobs and alter the motion of the blobs through a slower blob-disintegration. Non-Oberbeck–Boussinesq effects incorporate plasma inertia, which substantially decreases the growth rate and linear acceleration of high amplitude blobs, while the maximum blob velocity is not affected. Finally, we generalize and numerically verify unified scaling laws for blob velocity, acceleration and growth rate that include both ion temperature and arbitrary blob amplitude dependence.