Month of Equations: What Does Debye Length in a Plasma Really Mean?

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Meaning of the Equation:

Debye Length, which is defined as the shielding length of a charged particle in plasma, is directly proportional to the square-root of the thermal energy of the electrons and inversely proportional to the  number density of electrons in plasma.

Debye length is defined as the radius of the sphere around a single charged particle that is formed by the crowding of oppositely charged particles around that charged particle. It is a fundamental phenomenon in plasma that further leads to quasi-neutrality of the plasma. The equation for Debye length represents its dependence on the thermal energy and number density of charged species in plasma.

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First of all, we need to understand the concept of Debye length. An isolated ion in a plasma will tend to introduce an electrostatic potential such that the electrons, because of their large kinetic energy, crowd up and surround the isolated ion in the plasma. A significant number of electrons will symmetrically surround the positively charged ion in order to neutralize the effect of ion charge in its vicinity. This phenomenon is called Debye shielding. The length of this sphere of electrons around the positively charged ions is called the Debye sphere and the radius of this sphere is called Debye length. We may also understand this concept by the following example:

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Imagine putting two conducting balls in plasma connected to a battery such that one ball is positively charged and another is negatively charged. The introduction of these external charges and hence electrostatic potential in plasma would lead to bunching of the positively charged ions around the negatively charged sphere and the electrons will surround the positively charged sphere. The radius of these spheres of oppositely charged particles around the charged balls are called their respective Debye lengths.

Today’s equation suggests the dependence of Debye length on various physical parameters such that :

  1. The Debye length is directly proportional to the thermal energy of electrons. This means that if thermal energy of the electrons , i.e, electron’s random motion is necessary for sustaining the cloud of oppositely charged particles in a Debye sphere and prevents the Debye sphere from collapsing with the charged particle it is surrounding. More is the thermal energy, more is the radius of this Debye sphere.
  2. The radius of Debye sphere. i.e, the Debye length is inversely proportional to the number density of charged species in plasma. This represents that a plasma with higher number densities of charged particles will have smaller Debye spheres because of the fact that the due to higher number of charged particles, more particles will be contained in the layers of Debye sphere leading to the assertion of charge neutrality within smaller Debye lengths.

This amazing phenomenon of Debye shielding also leads to another fundamental principle in plasma, which is that of quasi-neutrality.

Quasi-neutrality : A bulk plasma is considered to be neutral as a whole if we are observing it from distances greater than Debye lengths, however, if a process is investigated at the characteristic lengths less than the radius of Debye sphere, the plasma does not appear to be neutral. In other words, a plasma is neutral as it comprises equal number of positive and negative ions but not so neutral such that the interesting electromagnetic forces may vanish.

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