Illustrated Physics
physics, drawn
Concept

Quasineutrality — where it appears

The near-exact cancellation of positive and negative charge densities in a plasma over any scale larger than a Debye length. It fails inside a sheath, where a real space charge holds a potential of several electron temperatures, and that failure is the only place Poisson's equation must be solved.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The charge a plasma hides. The potential around a charge in a plasma, as a fraction of the bare Coulomb potential at the same distance, against distance measured in screening lengths. The electrons crowd toward the charge and the ions move away until the rearrangement cancels the field, and what is left falls as exp(−r/λ_D) on top of the ordinary 1/r. At one screening length the potential is already down to 37 per cent of the bare value, at three to 5 per cent, and at ten to 4 × 10⁻⁵ — so a charge in a plasma is invisible beyond a few λ_D, and the long range of the Coulomb force, which is what makes electrostatics awkward everywhere else, is simply gone. The screening length at 10¹¹ m⁻³ is 3.8 mm at 300 K, 6.9 mm at 1000 K, 21.8 mm at 10000 K, rising as the square root of the temperature because a hotter electron is harder to hold in place. Drawn this way the three curves coincide exactly: the shape is universal and the only thing a plasma's density and temperature decide is the length written on the axis.

The long-range force that does not reach

The Coulomb force falls off as slowly as gravity does, which is what makes electrostatics awkward — every charge is in principle in contact with every other. Put the same charge into a plasma and it becomes invisible beyond a few millimetres, because the mobile charges around it rearrange until its field is cancelled. What is left is a screened potential with a definite range, and that range is what makes a plasma a plasma.

astrophysics · Plasma oscillation The one place in a plasma where the charges do not balance. The potential and the two densities through a sheath, in Debye lengths from the sheath edge, for a plasma of hydrogen ions. The potential is measured downward in units of the electron temperature and reaches 2.84 at the wall — the value at which the two fluxes balance. The layer is 15.1 Debye lengths thick — for 3 eV electrons at 1e+16 per cubic metre, a Debye length of 129 µm and a sheath of 1.9 mm. Inside it the electron density falls as the Boltzmann factor while the ion density falls only as the ions speed up, so the two separate: at the wall the ion density exceeds the electron density by 85 per cent of itself. That is the whole of the difference between a sheath and the plasma it borders — quasineutrality is not an assumption that can be made here, and Poisson's equation has to be solved instead of replaced.

The wall a plasma builds against itself

A plasma is quasineutral everywhere except where it touches something. Electrons are faster than ions by the square root of the mass ratio, so any surface is struck by far more of them, charges negative, and goes on charging until the two arrivals balance — leaving a layer a few Debye lengths thick in which the charges do not cancel at all.

astrophysics · Plasma oscillation

Named alongside it

The objects these essays reach for when they reach for this one.

Debye lengthPlasmaBohm criterionThe Boltzmann factorCollective behaviourCoulomb forceFloating potentialFlux balanceIon sound speedLangmuir probePlasma parameterPoisson equation

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