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Determining the origin of turbulence in galaxy clusters, and quantifying itstransport of heat, is an outstanding problem, with implications for ourunderstanding of their thermodynamic history and structure. As the diluteplasma of the intracluster medium (ICM) is magnetized, heat and momentum travelpreferentially along magnetic field lines. This anisotropy triggers a class ofbuoyancy instabilities that destabilize the ICM, and whose turbulent motionscan augment or impede heat transport. We focus on the magneto-thermalinstability (MTI), which may be active in the periphery of galaxy clusters. Weaim to take a fresh look at the problem and construct a general theory thatexplains the MTI saturation mechanism and provides scalings and estimates forthe turbulent kinetic energy, magnetic energy, and heat flux. We simulate MTIturbulence with a Boussinesq code, SNOOPY, which, in contrast to previous work,allows us to perform an extensive sampling of the parameter space. In twodimensions the saturation mechanism involves an inverse cascade carryingkinetic energy from the short MTI injection scales to larger scales, where itis arrested by the stable entropy stratification; at a characteristic "buoyancyscale", the energy is dumped into large-scale g-modes, which subsequentlydissipate. Consequently, the entropy stratification sets an upper limit on thesize and strength of turbulent eddies. Meanwhile, the MTI conveys a substantialfraction of heat, despite the tangled geometry of the magnetic field. In acompanion paper, these results are extended to three-dimensional flows, andcompared to real cluster observations.

Magneto-Thermal Instability In Galaxy Clusters I: Theory and Two-Dimensional Simulations