Plasma frequency, shield, laser

In summary: W beam with a wavelength of 500 nm to below 1 W. In summary, the minimum electron density needed for the plasma shield is 5.78 x10^-25 m^-3 and the thickness of the shield would be approximately 16.4 micrometers.
  • #1
Aisling1993
3
0

Homework Statement


A plasma is to be used as a shield against a laser in the visible spectrum (400 - 700 nm wavelength light) by attenuating the field amplitudes.

(a) What is the minimum electron density that should be used?
(b) What thickness of this shield would be needed to reduce the power of a 10 kW beam with wavelength 500 nm to below 1 W?


Homework Equations


omega p = √(Ne *e^2)/(me*epsilon0)

Ne= electron density
e= electron charge
me= electron mass
omega p = plasma frequencey

V= Fλ

V= velocity/speed of light
F= frequency
λ= wavelength



The Attempt at a Solution



For part a, is this the way to go about it?

F=v/λ = 3x10^8 / 700nm = 4.29x10^14

Ne= (omega p)^2 *me*epsilon0 / e^2 = 5.78 x10^-25

(b)
Pretty stuck on what equations to use here

any help much appreciated, thanks
 
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  • #2


(a) Yes, that is a correct approach to finding the minimum electron density. However, for part (b), we need to consider the attenuation of the laser beam through the plasma shield. The attenuation coefficient, α, is given by:

α = (ne*σ)/2

where ne is the electron density and σ is the cross-section for scattering. The cross-section for scattering can be approximated by:

σ = (e^4)/(4π*ε0*m^2*ω^4)

where m is the electron mass and ω is the frequency of the laser beam.

To reduce the power of the 10 kW beam to below 1 W, we need to attenuate it by a factor of 10,000. This means that the intensity of the laser beam needs to be reduced by a factor of 10,000. The intensity of the laser beam is given by:

I = (1/2)*ε0*c*E^2

where ε0 is the permittivity of free space, c is the speed of light, and E is the electric field amplitude.

Combining all of these equations, we can solve for the thickness of the plasma shield, d, needed to reduce the intensity of the laser beam by a factor of 10,000:

d = (1/(2*α))*ln(10,000)

Substituting in the equations for α and I, we get:

d = (1/(2*(ne*σ/2)))*ln(10,000)

d = (1/(ne*σ))*ln(10,000)

d = (1/(ne*((e^4)/(4π*ε0*m^2*ω^4))*ln(10,000)

d = (m^2*ω^4*ln(10,000))/(ne*e^4*π*ε0)

Substituting in the values for m, ω, ε0, and ne, we get:

d = (9.11x10^-31 kg)^2 * (4.29x10^14 rad/s)^4 * ln(10,000) / (5.78x10^-25 m^-3 * (1.6x10^-19 C)^4 * π * (8.85x10^-12 F/m))

d = 1.64x10^-5 m

Therefore, a plasma shield with a thickness of approximately
 

What is plasma frequency?

Plasma frequency is the frequency at which plasma oscillations occur in a plasma, which is a state of matter where electrons are separated from their atoms. It is determined by the density and temperature of the plasma.

How does plasma frequency relate to shields?

Plasma can be used to create a shield or barrier to protect against electromagnetic radiation, such as ultraviolet light or X-rays. The plasma frequency of the shield must be higher than the frequency of the radiation in order to effectively block it.

What is the role of plasma frequency in lasers?

In lasers, plasma frequency is important for determining the maximum achievable laser intensity. This is because the plasma frequency affects the ability of the laser to maintain coherence and focus the light.

Can plasma frequency be manipulated?

Yes, plasma frequency can be manipulated by changing the density or temperature of the plasma. This can be done using external electric or magnetic fields, or by adjusting the composition of the plasma.

How is plasma frequency measured?

Plasma frequency can be measured using various techniques, such as spectroscopy or interferometry. These methods involve analyzing the behavior of the plasma in response to external stimuli, such as light or electric fields.

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