Collider Luminosity Calculation

[renegade05]

Homework Statement

A collider has an average electron current of 10 milliAmps and an average positron current of
5 milliAmps.If the ring radius is 100 m and there is one electron bunch and one positron bunch
with uniform density, radius 1 µ and length 2 mm, what is the average luminosity in cm–2s–1 ?

Homework Equations

L=N_1 N_2/A * f
density = N/(AT)

The Attempt at a Solution

Ok so I know the target thickness (T) is 2mm with and Area (A) of pi * (1µ)^2
The density I am having a problem with.
I don't know how to incorporate the current given or the ring radius.

Just having a hard time with this question in general. Not sure where to start or where to plug everything in. Please help - thanks!

 

[mfb]

You don't need a density.

How frequent do the electrons pass your collision point? You can assume that they are high-energetic and move with roughly the speed of light.
Which current does a specific amount of charge give, using the information calculated above?

 

[renegade05]

Ok so Current = Charge/ Time. So I can solve for the time?! Still a very confused on how to solve this. sorry :(

 

[mfb]

Yes you can find the revolution time. You know the speed of the electrons/positrons and the collider geometry (ring with 100m radius).

 

[renegade05]

Ok so for the electrons I get a time of... Time = 1.602X10^-19 / 0.01 = 1.6x10^-17 seconds ?
and Distance traveled will be R=2pi*100 = 200pi
NOW WHAT?!

 

[mfb]

Ok so for the electrons I get a time of... Time = 1.602X10^-19 / 0.01 = 1.6x10^-17 seconds ?

What did you calculate here? What are the units?

and Distance traveled will be R=2pi*100 = 200pi

Don't forget the units.
You know distance and speed, that allows to calculate how long the electrons need for one round in the ring.

 

[renegade05]

Ya I have the units for the first one. They are seconds. I am not sure what that time is referring to though or how to use it.

The distance traveled will be 200pi Meters, I don't know the speed though...

 

[mfb]

Ya I have the units for the first one. They are seconds.

No they are not. The first value seems to be the elementary charge, which has units of a charge (Coulomb), and I have no idea what the 0.01 is supposed to represent. It is hard to help if you throw in completely unexplained calculations.

The distance traveled will be 200pi Meters, I don't know the speed though...

See post 2.

 

[renegade05]

Current = Charge/ Time
The current given for the electron beam is 0.01 Amps
The charge of an electron is 1.602X10^-19
Thus Charge/Current = Time
right?

 

[mfb]

Ah... okay, that is the average time between electrons then.