Ambipolar diffusion
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Ambipolar diffusion (ambipolar: relating to or consisting of both electrons and positive ions moving in opposite directions) is
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...
of positive and negative species with opposite electrical charge due to their interaction via an electric field. In the case of ionic crystals, the fluxes of the diffusing species are coupled, while in a plasma the various species diffuse at the same rate.


Diffusion in plasmas

In
plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...
, ambipolar diffusion is closely related to the concept of quasineutrality. In most plasmas, the forces acting on the
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s are different from those acting on the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s, so naively one would expect one species to be transported faster than the other, whether by
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...
or
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conve ...
or some other process. If such differential transport has a
divergence In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of t ...
, then it results in a change of the
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in ...
. The latter will in turn create an electric field that can 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 A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...
. (See
Inertial confinement fusion Inertial confinement fusion (ICF) is a fusion energy process that initiates nuclear fusion reactions by compressing and heating targets filled with thermonuclear fuel. In modern machines, the targets are small spherical pellets about the size of ...
.) Both electrons and ions will stream outward with their respective thermal velocity. If the ions are relatively cold, their thermal velocity will be small. The thermal velocity of the electrons will be fast due to their high temperature and low mass: v_e \approx \sqrt. 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 speed of sound, c_s \approx \sqrt, which is much smaller than the electron thermal velocity, but usually much larger than the ion thermal velocity. In astrophysics, "ambipolar diffusion" refers specifically to the decoupling of neutral particles from plasma, for example in the initial stage of star formation. The neutral particles in this case are mostly
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
molecules in a cloud that would undergo gravitational collapse if they were not collisionally coupled to the plasma. The plasma is composed of ions (mostly
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
) and electrons, which are tied to the interstellar magnetic field and therefore resist collapse. In a
molecular cloud A molecular cloud, sometimes called a stellar nursery (if star formation is occurring within), is a type of interstellar cloud, the density and size of which permit absorption nebulae, the formation of molecules (most commonly molecular hydroge ...
where the fractional ionization is very low (one part per million or less), neutral particles only rarely encounter charged particles, and so are not entirely hindered in their collapse (note that now is dynamical collapse, not free fall) into a star.


References

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Further reading


Mathematical analysis of ambipolar diffusion
- dead link Plasma physics