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Intra Cluster Media (ICMs) located at galaxy clusters is in the state of hot,tenuous, magnetized, and highly ionized X-ray emitting plasmas. This overallcollisionless, viscous, and conductive magnetohydrodynamic (MHD) turbulence inICM is simulated using hyper and physical magnetic diffusivity. The resultsshow that fluctuating random plasma motion amplifies the magnetic field, whichcascades toward the diffusivity scale passing through the viscous scale. Thekinetic eddies in the subviscous scale are driven and constrained by themagnetic tension which finally gets balanced with the highly damping effect ofthe kinetic eddies. However, the saturated kinetic energy spectrum is deeperthan that of the incompressible or compressible hydrodynamics fluid. To explainthis unusual field profile we set up two simultaneous differential equationsfor the kinetic and magnetic energy spectrum using an Eddy Damped Quasi NormalMarkovianized (EDQNM) approximation. The analytic solution tells us that themagnetic energy in addition to the viscous damping effect constrains the plasmamotion leading to the power spectra: kinetic energy spectrum $E_V^k\sim k^{-3}$and corresponding representative magnetic energy spectrum $E_M^k\sim k^{-1/2}$.Also the comparison of simulation results with different resolutions andmagnetic diffusivities implies the role of small scale magnetic energy indynamo.

Evolution of Kinetic and Magnetic Energy in Intra Cluster Media