Q.1 Derive an expression for plasma oscillation frequency for ions.
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![Solve the following problems
Q.1 Derive an expression for plasma oscillation frequency for ions.
Q.2 For a simple plasma oscillation with fixed ions and a space-time behavior
expli(kx – wt)], calculate the phase ô for Ø1, E1, and v, if the phase of n, is
zero.
Illustrate the relative phases by drawing sine waves representing n1, Ø1, E1 and
v, (a) as a function of x at t = 0, (b) as a function of t at x = 0 for w/k > 0,
and (c) as a function of I at x = 0 for w/k < 0. Note that the time patterns can
be obtained by translating the x patterns in the proper direction, as if the wave
were passing by a fixed observer.
Q.3. By writing the linearized Poisson's equation used in the derivation of simple
plasma oscillations in the form
V . (E E) = 0
derive an expression for the dielectric constant E applicable to high frequency
longitudinal motions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5250138-eb05-4ef6-bca7-9f3567fc039a%2F0f570dd3-a2aa-4cf0-a1f4-fccdd27b6c06%2Fqybvdsc_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the following problems
Q.1 Derive an expression for plasma oscillation frequency for ions.
Q.2 For a simple plasma oscillation with fixed ions and a space-time behavior
expli(kx – wt)], calculate the phase ô for Ø1, E1, and v, if the phase of n, is
zero.
Illustrate the relative phases by drawing sine waves representing n1, Ø1, E1 and
v, (a) as a function of x at t = 0, (b) as a function of t at x = 0 for w/k > 0,
and (c) as a function of I at x = 0 for w/k < 0. Note that the time patterns can
be obtained by translating the x patterns in the proper direction, as if the wave
were passing by a fixed observer.
Q.3. By writing the linearized Poisson's equation used in the derivation of simple
plasma oscillations in the form
V . (E E) = 0
derive an expression for the dielectric constant E applicable to high frequency
longitudinal motions.
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