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# Ambipolar diffusion

Ambipolar diffusion is diffusion of positive and negative particles in a plasma at the same rate due to their interaction via the electric field. It is closely related to the concept of quasineutrality.

### Additional recommended knowledge

In most plasmas, the forces acting on the ions are different from those acting on the electrons, so naively one would expect one species to be transported faster than the other, whether by diffusion or convection or some other process. If such differential transport has a divergence, then it will result in a change of the charge density, which will in return create an electric field that will alter the transport of one or both species in such a way that they become equal.

The simplest example is a plasma localized in an unmagnetized vacuum. (See Inertial confinement fusion.) Both electrons and ions will stream outward with their respective thermal speed. If the ions are relatively cold, their thermal speed will be small. The thermal speed of the electrons will be fast due to their high temperature and low mass: $v_e \approx \sqrt{k_BT_e/m_e}$. As the electrons leave the initial volume, they will leave behind a positive charge density of ions, which will result in an outwardly-directed electric field. This field will act on the electrons to slow them down and on the ions to speed them up. The net result is that both ions and electrons stream outward at the sound speed, $c_s = \sqrt{k_BT_e/m_i}$, which is much larger than the ion thermal speed but much smaller than the electron thermal speed.

In astrophysics, "ambipolar diffusion" refers specifically to the decoupling of neutral particles from plasma in the initial stage of star formation. The neutral particles in this case are mostly hydrogen molecules in a cloud that would undergo gravitational collapse if it were not collisionally coupled to the plasma. The plasma is composed of ions (mostly protons) and electrons, which are tied to the interstellar magnetic field and therefore resist collapse. In a molecular cloud where the fractional ionization is very low (one part per million or less), neutral particles only rarely encounter charged particles, and so are not hindered in their collapse into a star.

For a mathematical analysis, see Ambipolar Diffusion.