This document discusses plasma oscillations in a highly ionized gas. It describes how an initial uniform distribution of electrons and ions can become perturbed and accumulate, changing their densities. This accumulation can cause the electrons and ions to oscillate around their equilibrium positions. The document derives an equation showing the evolution of this density perturbation with time, which takes the form of a harmonic oscillator with the plasma frequency wp. Plasma oscillations at frequencies below wp will be reflected, while above wp waves can propagate freely through the plasma.

1. HIGH FREQUENCY PLASMA
OSCILLATION
SUBMITTED TO: Prof. K.R PATEL
SUBMITTED BY: VISHAL KUMAR JANGID,
M.Sc (Final) 2016-17
JNVU (Department of Physics)

2.  A highly ionized gas in which
no. of free electron = no. of positive ions
4th State of Matter

3. plasma Electron
Ions
Neutral atom
PLASMA OSCILLATION

4.  Uniform distribution
 All are moving with uniform
velocity
 EQUAL
Equilibrium state
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e
e e e e
e e e
e e
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ELECTRON DENSITY ION DENSITY

5.  Now they are accumulate, so their density changes
 Now density equation becomes
 Ne=n0+n1
ACCUMULATION
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e
e
e e e e
e e e
e e
eee
e

6. Plasma oscillation
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e e e
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e e e e
e e e
e e
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+
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7.  W.K.T ………..𝐸 = −𝛻𝜑
 Using Poisson eq. ……..𝛻𝜑2
=
𝑒𝑛1
𝜀0
 Using force on electric charge……… 𝐹 = 𝑞𝐸
 Then we get…………..
𝜕𝑣
𝜕𝑡
=
𝑒
𝑚
𝛻𝜑
 Now using eq. of continuity ……

𝜕𝑛 𝑒
𝜕𝑡
+ 𝛻. 𝑛 𝑒. 𝑣 = 0

𝜕𝑛1
𝜕𝑡
+ 𝛻. 𝑛0. 𝑣 = 0
𝐻𝑜𝑤 𝑁1 𝑒𝑣𝑜𝑙𝑣𝑒 𝑤𝑖𝑡ℎ 𝑡𝑖𝑚𝑒

8. 
𝜕2 𝑛1
𝜕𝑡2 +
𝑛0 𝑒2
𝑚𝜀0
𝑛1 = 0
 𝑤 𝑝 =
𝑛0 𝑒2
𝑚𝜀0
………plasma oscillation
 𝑤 𝑝 ≈ 50 𝑛0

9. n=1-w2
p/w2
w>wp
*[wave propagate freely]
w<wp
[reflected from surface]
Uses :refractive index

11.  Reference : nptel lecture
:Wikipedia
Thank you