Effective Electron Radius in a Lorentz-Like Gas as a Function of Particle Density and Temperature

From the regular collision time, τcee, due to multiple Coulomb collisions between electrons an effective electron radius is proposed using the kinetic theory in plasma physics and considering we deal with what we will call a Lorentz-like gas. The effective or equivalent electron radius is deduced by corresponding the total cross section with a collision radius that can be related with the length of the electron and depends on the temperature and density a=a(n;T). This is quite unusual, but ultimately it is a measure that describes an effective radius of the electron based on supposing collision of rigid spheres corresponding to the electrons in a Lorentz-like gas with temperature and density. Unlike other electron size proposals where fixed parameters are taken, the electron radius is deduced from a many-particle system. τcee is compared with the electron-electron relaxation time, τee, obtained calculating the cross section for the momentum transfer. Taking into account typical fusion conditions (TOKAMAK), the equivalent electron radius aT as well as the corresponding electron-electron collision and relaxation times are calculated. Assuming that electron describes a diffusion equation based on Stokes law of viscosity, the friction coefficient α is calculated using the relaxation time and the dynamic viscosity η is deduced from the first order approximation of the Chapmann-Enskog theory for hard-sphere electrons.