# Question about Energy intensity, scale length for energy absorption

I am a Yr 12 high school student and I am writing a report about space-based particle-beam weapon for my open project assessment.

I found a paper published in Nature. When talking about energy must be provided by particle acceleration, the author wrote this: E=εlA

My question is that what the name of this formula is. Also, I could find little information about "scale length for energy absorption". I will appreciate if anyone can help.

Thanks.

• Do you need the name to search for more about the topic. Also, the line the distance over which the beam particles are degraded in energy to ... Of their original value means that the damage inflicted is not linear, if you plotted damage against energy used you would get a graph of a curve that starts high on the y axis but never touches the x axis, maybe you know this already though. – user163104 Jul 20 '17 at 13:28

I don't believe this formula will have a universal name, but I can give some insight about the parameters.

## $l$ is very close to Radiation length, $X_0$.

$$l = E\frac{dz}{dE}$$

For beams of electrons or photons, the relevant material characteristic is called Radiation Length. In Chapter 33 (Passage of Particles Through Matter) of The Review of Particle Physics by the Particle Data Group they define Radiation length as

High-energy electrons predominantly lose energy in matter by bremsstrahlung, and high-energy photons by $e^+ e^−$ pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length $X_0$, usually measured in g cm${}^{-2}$. It is both (a) the mean distance over which a high-energy electron loses all but $1/e$ of its energy by bremsstrahlung, and (b) $\frac{7}{9}$ of the mean free path for pair production by a high-energy photon. It is also the appropriate scale length for describing high-energy electromagnetic cascades.

So their description of $X_0$ is very close to the text's descripton of $l$ A common quantity used in physics is $\frac{dE}{dx}$, which is simply, the rate at which energy is deposited in the material ($dE$, amount of energy, $dx$ small distance). This is a property of the material that you are hitting but depends on the type and energy of the particle beam.

As shown in the below image, they describe $$\frac{1}{l} = \frac{1}{E}\frac{dE}{dx}$$ as the fractional energy loss per radiation length As for the equation, I believe is simply the volume multiplied by an energy density of the beam. $E = \epsilon V= \epsilon lA$