Role of energy in ballistic agglomeration

Area of Science:

• Physical Chemistry
• Astrophysics
• Materials Science

Background:

• Ballistic agglomeration is a fundamental process in various scientific fields.
• Understanding cluster dynamics requires solving complex rate equations.
• The reaction-controlled limit simplifies these dynamics but requires accounting for particle energy.

Purpose of the Study:

• To develop a simplified model for ballistic agglomeration in the reaction-controlled limit.
• To reduce the infinite set of Smoluchowski rate equations to a manageable form.
• To apply the developed formalism to the specific case of dark matter agglomeration.

Main Methods:

• Studied the reaction-controlled limit of ballistic agglomeration.
• Analyzed Smoluchowski rate equations with energy-dependent rates.
• Expressed average particle energy via total cluster density.
• Reduced governing equations to standard Smoluchowski equations.
• Derived asymptotic behaviors and performed numerical verification.

Main Results:

• The average particle energy is constant across all cluster species in the reaction-controlled limit.
• The governing equations were successfully reduced to standard Smoluchowski equations.
• Key asymptotic behaviors were derived and numerically validated.
• The formalism was demonstrated to be applicable to dark matter agglomeration.

Conclusions:

• The proposed method simplifies the study of ballistic agglomeration under reaction-controlled conditions.
• The derived model provides a tractable framework for analyzing complex cluster dynamics.
• This approach offers new insights into the agglomeration processes relevant to dark matter formation.