Fermi acceleration in the randomized driven Lorentz gas and the Fermi-Ulam model

Area of Science:

• Statistical mechanics
• Nonlinear dynamics
• Particle acceleration

Background:

• The Fermi-Ulam model (FUM) and Lorentz gas describe particle dynamics in confined systems.
• Static wall approximations underestimate particle energy gain due to ignored scatterer displacement.
• Understanding particle acceleration mechanisms is crucial for applied physics.

Purpose of the Study:

• To clarify the mechanism behind increased particle acceleration in stochastic wall systems.
• To generalize the hopping wall approximation for driven systems.
• To investigate the impact of driving function symmetry on acceleration.

Main Methods:

• Investigated Fermi acceleration in stochastic two-moving wall FUM and phase randomized harmonically driven periodic Lorentz gas.
• Generalized the hopping wall approximation for application in randomized driven Lorentz gas.
• Derived asymptotic probability distribution function of particle velocity using the hopping approximation.

Main Results:

• Scatterer displacement upon collision significantly increases mean energy gain per collision.
• Harmonic driving leads to a consistent increase in acceleration for both driven Lorentz gas and FUM.
• Asymmetric sawtooth driving in FUM results in acceleration distinct from symmetric driving, offering design possibilities.

Conclusions:

• Scatterer displacement is a key factor in enhancing Fermi acceleration.
• The hopping wall approximation provides accurate velocity distribution for driven systems.
• Tailoring driving function symmetry allows for controlled particle acceleration in designed devices.