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Abstract

Recently, a kinetic field theory for ensembles of point-like classical particles in or out of equilibrium has been applied to cosmic structure formation. This theory encodes the dynamics of a classical particle ensemble by a generating functional which is com- pletely specified by the initial probability distribution of particles in phase space and their equations of motion. In this work, we apply kinetic field theory to planetesimal formation. The initial probability distribution of dust particles in phase space is obtained by Gaussianizing the density and momentum fields of a three-dimensional local streaming- instability shearing box simulation. The particle trajectories are calculated by considering their interaction by friction with the constant background gas field and the self gravitational interaction with each other. We calculate the non-linearly evolved density and momentum-density power spectra of dust particles and find that their power spectra develop a universal k−3 tail at small scales independent of the form of the initial spectrum, suggesting scale-invariant structure formation and particle kinetic energy accumulation below a characteristic and time-dependent length scale in the protoplanetary disk. Furthermore, the analysis of the amplitude for the small-scale k−3 tails shows a critical particle size τs ≈ 3.03 which corresponds to the strongest structure formation and the maximal kinetic energy accumulation at small scales of a system when considering only the friction be- tween dust particles and the constant background gas field. Finally, we discuss the ”meter-size barrier” problem. And for particles as small as Stokes number τs ≈ 10−5, we provide evidence that accumulated self-gravitational interaction among the dust particles over a long evolution time is strong enough for them to successfully ”jump the barrier” and lead to a final gravitational collapse.