Question

High-power lasers are used to compress a plasma (a gas of charged particles) by radiation pressure. A laser generating radiation pulses with peak power $\mathbf{1}\mathbf{.5}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{\text{MW}}$is focused onto 1.00 mm² of high-electron-density plasma. Find the pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths.

Short answer

Pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths is$1\times {10}^{7}Pa$

Step-by-step solution

Listing the given quantities

Power of radiation $P=1.5\times {10}^{3}MW$

Area A=1.00 mm²

Understanding the concepts of radiation pressure formula

Substituting the given values of power, area, and speed of light in the radiation pressure formula, we can find the pressure exerted on the plasma due to the light beams.

Thrust applied on plasma is given as-

$\mathbf{F}\mathbf{=}\frac{\mathbf{2}\mathbf{IA}}{\mathbf{c}}$

Here, I is the intensity of radiation, A is the cross-sectional area and c is the speed of light in vacuum.

Calculations of the pressure exerted on the plasma

The force acting on the plasma, due to radiation, is-

$F=\frac{2IA}{c}$

The radiation pressure P_ris given as-

$\begin{array}{c}{p}_r=\frac{F}{A}\\ =\frac{2IA}{cA}\\ =\frac{2I}{c}\end{array}$

The intensity is $I=\frac{P}{A}$

P is power; A is the total area intercepted by the radiation.

$\begin{array}{c}{p}_r=\frac{2P}{Ac}\\ =\frac{2(1.5\times {10}^{9}W)}{(1\times {10}^{-6}{m}^2)(3\times {10}^8\text{\hspace{0.17em}m}/\text{s})}\\ =1\times {10}^{7}Pa\end{array}$

Pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths is$1\times {10}^{7}Pa$