One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

Area of Science:

• Classical Mechanics
• Nonlinear Dynamics
• Statistical Physics

Background:

• The Fermi accelerator model describes particle acceleration through repeated collisions with moving walls.
• Understanding energy gain mechanisms in classical systems is crucial for various physics fields.

Purpose of the Study:

• To investigate a modified one-dimensional Fermi accelerator model with a nonlinear van der Pol oscillator as a moving wall.
• To analyze the impact of particle-wall mass ratio on particle acceleration and energy gain.

Main Methods:

• Utilized a two-dimensional nonlinear mapping to model the dynamics of a classical particle between two walls.
• Considered two cases: negligible particle mass and significant particle mass compared to the wall.

Main Results:

• In the negligible mass case, observed velocity diffusion and Fermi acceleration for large nonlinearity parameters (χ).
• In the significant mass case, the van der Pol oscillator's limit cycle behavior suppressed unlimited energy gain.
• Identified complex phase space organization with attractors of varying periods.

Conclusions:

• The particle-wall mass ratio critically determines the presence or absence of Fermi acceleration.
• Nonlinear oscillator dynamics can effectively suppress unlimited energy gain in such systems.