Related Experiment Video
Updated: May 26, 2026
12:11
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Kullback-Leibler entropy in the electron distribution shape relaxation for electron-atom thermalization
Reinel Sospedra-Alfonso1, Bernie D Shizgal
1Institute of Applied Mathematics, Vancouver, British Columbia, Canada, V6T 1Z2.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
Energetic electrons in neon and argon do not form a local Maxwellian distribution. A single average relaxation time characterizes electron thermalization, even with a Ramsauer-Townsend minimum.
Area of Science:
- Atomic and Molecular Physics
- Plasma Physics
- Computational Physics
Background:
- Energetic electrons in atomic gases are crucial for understanding plasma behavior and radiation processes.
- Electron thermalization describes how electrons lose energy and approach equilibrium with their environment.
- The presence of an external electric field can significantly alter electron dynamics.
Purpose of the Study:
- To investigate the thermalization of energetic electrons in inert gas moderators (neon and argon).
- To analyze the electron distribution function's relaxation towards steady-state, with and without an electric field.
- To understand the influence of the Ramsauer-Townsend minimum on electron relaxation processes.
Main Methods:
- Utilized Kullback-Leibler entropy to quantify the deviation of the electron distribution function from steady-state.
- Employed a functional analogous to Kullback-Leibler entropy to assess departure from a local Maxwellian distribution.
- Solved the time-dependent Lorentz-Fokker-Planck equation using a finite difference method.
- Applied a pseudospectral method to examine the spectral properties of the Fokker-Planck operator.
Main Results:
- No evidence for the formation of a local Maxwellian distribution followed by slower relaxation was observed in neon or argon.
- The momentum-transfer cross section for electron-neon collisions is nearly energy-independent.
- Electron-argon collisions exhibit a Ramsauer-Townsend minimum, leading to strong energy dependence in momentum transfer.
- A single average relaxation time can characterize the electron speed distribution's approach to equilibrium, despite multi-exponential time dependence.
Conclusions:
- The Ramsauer-Townsend minimum in electron-argon interactions significantly impacts electron thermalization dynamics.
- Electron thermalization in these systems does not follow a simple two-stage process involving a local Maxwellian.
- A single relaxation time is a valid metric for describing the overall approach to equilibrium for electron speed distributions.
Related Concept Videos
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:18Entropy
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
02:38Third Law of Thermodynamics
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...