Plasma collisions and conductivity

Transcription

1 e ion conductivity Plasma collisions and conductivity Collisions in weakly and fully ionized plasmas Electric conductivity in non-magnetized and magnetized plasmas Collision frequencies In weakly ionized plasmas the (charged) plasma particles collide mostly with neutral atoms and molecules. Let d 0 be the effective radius of the neutral particle. The cross-section for the collision is typically of the order of From this we get the collision frequency: neutrals Another important quantity is the mean free path: Collisions can be elastic or inelastic. colliding charged particle In inelastic collisions a part of the energy of the colliding particle may lead to an excitation of the atom or molecule to a higher energy level. For example, the auroral emission at nm: electron collides with an oxygen atom: e + O e + O* O* O + h 1

2 Particularly interesting inelastic collisions are the charge-exchange collisions: energetic neutral atom These are also important in (almost) fully ionized plasma. For example, the ring current around the Earth is a drift current carried mainly by westward drifting ions in the energy range 20 kev 200 kev (see Space applications of plasma physics on period II). RC is enhanced during magnetic storms. It decays by charge-exchange as the fast protons give their charge to slow H atoms of the exosphere (non-collisional atmosphere above 500 km), i.e., the new current carriers are slower and thus carry less current (drift-speed depends on velocity). At Mars, Venus and comets, the solar wind protons exchange charge with ions in the planetary (or comets ) atmospheres. These newly born (heavy) ions are accelerated by the solar wind induced electric field E = V B; they are said to be picked-up by the solar wind. In fully-ionized plasmas interparticle effects are due to the Coulomb force. Each particle interacts with all particles within its Debye sphere. almost all Coulomb interactions with distant particles only small effects on orbits from individual collisions, small-angle scattering Electron-ion collision frequency: The calculation of the Coulomb cross-section C is non-trivial. Here we present a heuristic derivation only. Coulomb Force Effective interaction time during which the momentum change For a large angle Impact parameter is this is of the same order of magnitude as Thus we can approximate the impact parameter by ion e and 2

3 Replace the average electron velocity with average thermal energy ; : Collision frequency is proprtional to electron density and inversely proprtional to T e to the power 3/2 Note that this is a very rough estimate. It does not take into account that the actual collisions are small-angle collisions, but they are many! A more rigorous calculation gives from which we get for the mean free path In fully ionized plasmas ln is the mean free path is much much larger than the Debye length Assuming that T e T i : Collision frequencies in the Earth s magnetosphere 3

4 Plasma conductivity Consider the effect of collisions as friction in the equation of motion: 1. Electron motion in unmagnetized plasma B = 0 : u is the velocity of the collision targets Assume cold electrons (v e the same for all) and non-moving targets u = 0 Assume that the force and friction are in balance (dv/dt = 0, i.e. steady state) The electron current is And we have found the classical conductivity 2. Let the plasma move across magnetic field with velocity V (one form of) generalized Ohm s law In collisionless plasma 0 (ideal MHD) In magnetized plasmas the conductivity is generally not a scalar! Start from the steady state exerc. To solve this for the current, select coordinates where Introducing the electron gyrofrequency write Thus Ohm s law is a matrix equation where components of the conductivity tensor 4

5 P is the Pedersen conductivity ( B & E) H is the Hall conductivity ( B & E) is the parallel conductivity ( B) The corresponding components of the current are called Pedersen, Hall, and field-aligned currents Currents that have a component parallel to the magnetic field are very important in plasma physics! conductivity is the most complicated regime is the most anisotropic regime, as particles are tightly bound B but free to move along B 5