Debye length
(Debye radius or Debye–Hückel screening length), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists.
Debye length is an important parameter in plasma physics, electrolytes, and colloids (DLVO theory).
The Debye length for a plasma consisting of particles with density
They are of interest in describing the behaviour of electrons in metals at room temperature and warm dense matter.
The Debye length arises naturally in the description of a substance with mobile charges, such as a plasma, electrolyte solution, or semiconductor.
The distribution of charged particles within this medium gives rise to an electric potential
may be considered, under the assumptions of mean field theory, to tend toward the Boltzmann distribution,
Solutions to this nonlinear equation are known for some simple systems.
Solutions for more general systems may be obtained in the high-temperature (weak coupling) limit,
which also is known as the Debye–Hückel equation:[2][3][4][5][6] The second term on the right-hand side vanishes for systems that are electrically neutral.
Substituting this length scale into the Debye–Hückel equation and neglecting the second and third terms on the right side yields the much simplified form
sets the scale for variations in the potential and in the concentrations of charged species.
To illustrate Debye screening, one can consider the example of a point charge placed in a plasma.
The bare Coulomb potential is exponentially screened by the medium, over a distance of the Debye length: this is called Debye screening or shielding.
Therefore, according to Gauss theorem, the apparent charge of the first electron is smaller than in the absence of repulsion.
Since the global deflection of particles includes the contributions of many other ones, the density of the electrons does not change, at variance with the shielding at work next to a Langmuir probe (Debye sheath).
Ions bring a similar contribution to shielding, because of the attractive Coulombian deflection of charges with opposite signs.
This intuitive picture leads to an effective calculation of Debye shielding (see section II.A.2 of [7]).
The calculation also avoids approximating weakly collisional plasmas as continuous media.
An N-body calculation reveals that the bare Coulomb acceleration of a particle by another one is modified by a contribution mediated by all other particles, a signature of Debye shielding (see section 8 of [8]).
When starting from random particle positions, the typical time-scale for shielding to set in is the time for a thermal particle to cross a Debye length, i.e. the inverse of the plasma frequency.
Therefore in a weakly collisional plasma, collisions play an essential role by bringing a cooperative self-organization process: Debye shielding.
In a non-isothermic plasma, the temperatures for electrons and heavy species may differ while the background medium may be treated as the vacuum (
although this is only valid when the mobility of ions is negligible compared to the process's timescale.
In space plasmas where the electron density is relatively low, the Debye length may reach macroscopic values, such as in the magnetosphere, solar wind, interstellar medium and intergalactic medium.
is the Bjerrum length of the medium in nm, and the factor
For deionized water at room temperature, at pH=7, λB ≈ 1μm.
where There is a method of estimating an approximate value of the Debye length in liquids using conductivity, which is described in ISO Standard,[12] and the book.
[13] The Debye length has become increasingly significant in the modeling of solid state devices as improvements in lithographic technologies have enabled smaller geometries.
where When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants.
