Free electron model

About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.

Velocity dependence of the energy loss of very slow proton and deuteron beams in Cu and Ag

Abstract: We present energy loss measurements of protons and deuterons down to velocities of 0.1 a.u. in very thin polycrystalline Cu and Ag foils, using the transmission technique. As in previous experiments in Au, a transition between two energy loss regimes is observed, i.e., from a stopping due to the excitation of only the free conduction band electrons at the lowest velocities, to a slowing down with the participation of both the free electrons and the loosely bound $d$ electrons. This transition causes a change of the slope in the energy loss versus ion velocity curve at a characteristic threshold velocity related to the binding energy of the $d$ electrons. As shown by model calculations these threshold velocities for Cu and Ag are shifted according to their density of states distributions.

Velocity Distribution of Electrons in Field Emission. Resolution in the Projection Microscope

Abstract: The velocity distribution of electrons in field emission has been calculated on the basis of a simple free electron or one‐band model. It is found that the component of velocity transverse to the direction of emission varies approximately as the square root of the applied field. This leads to the result that resolution in the field emission microscope is practically independent of applied voltage, since transit times vary as V−½; resolution turns out to be of the order of 30A. Image formation in the case of molecules and the resolution obtainable with the proton microscope are briefly discussed.

The Formation of Gas Bubbles by Processing of Liquid n-Heptane in the Microwave Discharge

Abstract: Numerical modeling of the process of formation of gas bubbles during initiation of the microwave discharge in liquid n-heptane at atmospheric pressure has been performed. The developed model has an axial symmetry. The model is based on joint solution of the Maxwell equations, Navier–Stokes equation, heat equation, continuity equations for electrons (written in the ambipolar diffusion approximation) and the n-heptane concentration (including its thermal decomposition and dissociation by electron impact) and the Boltzmann equation for free electrons of the plasma. The calculations allowed to describe the dynamics of the formation of gas bubbles in the liquid, to evaluate the role of electron impact in the decomposition of n-heptane, and to estimate the characteristic times of various processes in the system. The results of new experiments are compared with the simulation results. On the basis of this comparison one could explain the presence in the spectra of the discharge only bands of C2.

Ion-acoustic double layers in a magnetized plasma

Abstract: Solutions for double layers (DL), propagating obliquely to the magnetic field with a speed near the slow ion‐acoustic velocity are presented. Using fluid equations for the ions and an arbitrary equation of state for the electrons, it is shown that in such a system, DL solutions exist for the two‐electron Boltzmann model. No DL exists when the electrons are isothermal, and when the free and reflected electrons are described by Maxwell distributions.