What is the Debye Shielding Problem?

In summary, the conversation discusses the use of the Boltzmann distribution to explain the distribution of electrons around a positive point charge in plasma. The equilibrium density of electrons is reached where the potential energy is 0, and the conversation prompts the reader to consider the potential of charged particles in a polarized medium.
  • #1
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Homework Statement



Consider a positive point charge +q, immersed in plasma. Show that the net charge in the Debye shielding cloud exactly cancels the test charge. Assume the ions are fixed and that e*phi <<< kTe.

Homework Equations



f(u) = A exp [-(1/2*m*u^2 + q*phi)/k_b*T_e]
u is the x component of velocity

The Attempt at a Solution



Really lost on this one. I think I could make a hand waivey argument with Gauss's Law but I don't see where to go on this one.
 
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  • #2
You should use the Boltzmann distribution:
[tex]
n(\mathbf{x}) = n_{0} \, \exp\left(-\frac{U(\mathbf{x})}{k_{B} T_{e}}\right)
[/tex]
to give the distribution of electrons. Here, [itex]n(\mathbf{x})[/itex] is the number density of electrons around a point given by the position vector [itex]\mathbf{x}[/itex], [itex]n_{0}[/itex] is their equilibrium density, [itex]U(\mathbf{x})[/itex] is the potential energy of the electrons (the equilibrium density is reached at the part of space where [itex]U = 0[/itex] according to the above formula).

Think about what is the potential of charged particles in a polarized medium where electric fields might exist. After you answer this question, we can proceed further.
 

Related to What is the Debye Shielding Problem?

1. What is the Debye Shielding Problem?

The Debye Shielding Problem is a concept in physics that describes the behavior of charged particles in a plasma. It refers to the phenomenon where a charged particle is shielded from other particles due to the presence of other charged particles around it.

2. What is the significance of the Debye Shielding Problem?

The Debye Shielding Problem is important because it helps us understand the behavior of charged particles in plasmas, which are found in many natural and man-made environments such as stars, lightning, and fusion reactors. It also has applications in fields such as space science, materials science, and nuclear engineering.

3. How is the Debye Shielding Problem solved?

The Debye Shielding Problem is solved using the Debye length, also known as the screening length. This is a characteristic length scale that describes the distance at which the electric potential of a charged particle is significantly reduced due to the presence of other charged particles. It is calculated using the Debye-Hückel equation.

4. What factors affect the Debye length?

The Debye length is affected by several factors such as temperature, plasma density, and the type of particles present in the plasma. Higher temperatures and densities result in shorter Debye lengths, while the presence of more charged particles increases the Debye length.

5. What are some real-world examples of the Debye Shielding Problem?

The Debye Shielding Problem can be observed in various natural and man-made environments. Some examples include the ionosphere, where the Earth's magnetic field creates a plasma that shields the Earth from harmful solar radiation, and in plasma processing for the production of electronic devices. It is also relevant in understanding the behavior of charged particles in fusion reactors, which aim to replicate the energy-producing process of the sun.

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