Energy exchange calculations in a simple mechanical system to investigate the origin of friction

The microscopic origin of friction is an important topic in science and technology. To date, noteworthy aspects of it remain unsolved. In an effort to shed some light on the possible mechanisms that could give rise to the macroscopic emergence of friction, a very simple 1D system of two particles is considered, one of them is free but moving with an initial velocity, and the other confined by a harmonic potential. The two particles interact via a repulsive Gaussian potential. While it represents in a straightforward manner a tip substrate system in the real world, no analytic solutions can be found for its motion. Because of the interaction, the free particle (tip) may overcome the bound particle (substrate) losing part of its kinetic energy. We solve Newton’s equations of the two particles numerically and calculate the net exchange of energy in the asymptotic state in terms of the relevant parameters of the problem. The effective dissipation that emerges from this simple, classical model with no ad hoc terms shows, surprisingly, a range of rich, nontrivial, behavior. We give theoretical reasoning which provides a satisfactory qualitative description. The essential ingredient of that reasoning is that the transfer of energy from the incoming particle to the confined one can be regarded as the source of the emergent dissipation force the friction experienced by the incoming particle.

Charge asymmetry in electron/positron energy loss in nuclear Bremsstrahlung

We calculate the leading Coulomb correction to the Bremsstrahlung energy loss in the electron-nucleus collisions for arbitrary energy of the incoming particle. This correction determines the charge asymmetry, i.e., the difference of electron and positron energy loss. The result is presented in terms of the classical polylogarithms Li2 and Li3. We use modern multiloop methods based on the IBP reduction and on the differential equations for master integrals. We provide both the threshold and the high-energy asymptotics of the found asymmetry and compare them with the available results.

Particle trajectories in Weibel filaments: influence of external field obliquity and chaos

When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field $\unicode[STIX]{x1D63D}_{0}$ can prevent the filaments blocking the flow if it is aligned with them. Denoting by $B_{f}$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\unicode[STIX]{x1D6FC}=B_{0}/B_{f}>1/2$ . Here, this result is extended to the case of an oblique external field $B_{0}$ making an angle $\unicode[STIX]{x1D703}$ with the flow. The result, numerically found, is simply $\unicode[STIX]{x1D6FC}>\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})/\cos \unicode[STIX]{x1D703}$ , where $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories.

INTERRELATION BETWEEN CHARGE EXCHANGE AND ENERGY LOSS OF PARTICLES INTERACTING WITH SURFACES: A BRIEF REVIEW AND RECENT RESULTS

In the interaction of particles approaching a surface energy dissipation to the surface and charge exchange processes between the incoming ion or atom and the surface are two features which have found continuous interest over decades. Only few workers tried to resolve the interrelation of the change of the charge state of the incoming particle and the energy lost during the interaction. Here a brief review of earlier work in this field is given and some recently obtained new experimental and theoretical results are presented concerning the interaction of slow (2–5 keV) incoming He ions with a Ni(110) surface.

Electron capture in fast collisions I. Capture by fast protons in atomic hydrogen

Formal perturbation theory is employed to obtain the matrix element for electron capture by fast particles of mass M B and charge Z B from atoms of mass M A and charge Z A , allowing for the internuclear potential and distortion by the incoming particle. Explicit formulae are presented for the Is— Is transition. Detailed calculations were carried out for protons in atomic hydrogen. For this case distortion significantly reduces the cross-section at proton energies below 100 keV, but at higher energies its effects and those of the internuclear potential largely cancel each other.