Effectiveness of mixing in violent relaxation

Area of Science:

• Physics
• Plasma Physics
• Astrophysics

Background:

• Collisionless dynamics in systems with long-range interactions, such as self-gravitating systems and non-neutral plasmas, exhibit peculiar relaxation processes.
• These systems are often described by the Vlasov equation and can reach quasistationary states (QSS) after a phase of violent relaxation.

Purpose of the Study:

• To investigate the underlying relaxation mechanism in collisionless dynamics that leads to quasistationary states.
• To provide a plausible explanation for the transition from initial conditions to QSS in Vlasov systems.

Main Methods:

• Numerical simulations of the Vlasov equation were performed.
• The study analyzed stretching and folding behavior in phase space.
• Area-preserving discrete-time maps with mean-field coupling were used for comparison.

Main Results:

• Stretching and folding behavior was observed in numerical simulations of the Vlasov equation.
• This stretching and folding mechanism provides a plausible route to the QSS regime.
• Similar phase space behavior was found in discrete-time maps modeling mean-field interactions.

Conclusions:

• Stretching and folding dynamics offer a potential explanation for relaxation in collisionless systems described by the Vlasov equation.
• This mechanism facilitates the transition to quasistationary states.
• Analogous behavior in simplified map models supports the generality of the findings.