Protons delivered per second in a proton beam

In summary, the conversation discusses a 5.0 mm-diameter proton beam with a total current of 1.5mA. The current density in the beam is given by j=j(edge)(r/R), where R is the radius of the beam and j(edge) is the current density at the edge. The conversation then goes on to discuss how many protons per second are delivered by the beam and how to determine j(edge).
  • #1
mjolnir80
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0

Homework Statement


a 5.0 mm-diameter proton beam carries a total current of 1.5mA. the current density in the proton beam, which increases with distance from the center, is given by j=j(edge)(r/R), where R is the radius of the beam and j(edge) is the current density at the edge.
a) how many protons per second are delivered by this proton beam?
b)determine j(edge)


Homework Equations





The Attempt at a Solution


a) we know that J=I/A(area) and also that in this particular case J=[tex]\int[/tex](from 0 to R) J(edge)(r/R)dr which turns out to be J(edge)R/2
now we know that I=AJ(edge)R/2 and I=Q/t so we find Q and divide it by e to get the number of protons per second
im just not really sure if this is right or not cause the end result still has J(edge) in it which we don't know. can someone help me out here please.
 
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  • #2
mjolnir80 said:

The Attempt at a Solution


a) we know that J=I/A(area) and also that in this particular case J=[tex]\int[/tex](from 0 to R) J(edge)(r/R)dr which turns out to be J(edge)R/2
now we know that I=AJ(edge)R/2 and I=Q/t so we find Q and divide it by e to get the number of protons per second
im just not really sure if this is right or not cause the end result still has J(edge) in it which we don't know. can someone help me out here please.

(a)A good way to think about it is:
  • We know I, the charge per second
  • We know the charge per proton
From that we can figure out protons per second

(b)
Actually, the current is given by

I = Jedge (r/R) dA

I.e., it is an area-integral.
 
  • #3


I would like to point out that the provided information is not sufficient to accurately calculate the number of protons delivered per second in the proton beam. We need to know the velocity of the protons and the total charge of each proton in order to accurately determine the current density and the number of protons delivered per second. Additionally, the current density formula provided is only valid for a uniform beam, which may not be the case in this scenario. Therefore, more information is needed to accurately calculate the number of protons delivered per second in this proton beam.
 

1. How are protons delivered per second in a proton beam measured?

Protons delivered per second in a proton beam are typically measured using a device called a beam current monitor. This device measures the number of protons passing through a certain point in the beam per unit time, usually in units of microamps.

2. What factors affect the number of protons delivered per second in a proton beam?

The number of protons delivered per second in a proton beam can be affected by several factors, including the strength of the particle accelerator, the energy of the protons, and the focusing capabilities of the beamline. Any fluctuations in these factors can result in variations in the number of protons delivered per second.

3. How does the number of protons delivered per second in a proton beam impact experiments?

The number of protons delivered per second in a proton beam is an important factor in determining the intensity of the beam, which directly affects the rate of collisions between protons and other particles in an experiment. A higher number of protons delivered per second can lead to more precise and accurate data in experiments.

4. Can the number of protons delivered per second in a proton beam be controlled?

Yes, the number of protons delivered per second in a proton beam can be controlled by adjusting the parameters of the particle accelerator, such as the strength of the magnetic fields and the energy of the protons. This allows scientists to fine-tune the beam for specific experiments and minimize any fluctuations in the beam intensity.

5. What is considered a high number of protons delivered per second in a proton beam?

The number of protons delivered per second in a proton beam can vary depending on the capabilities of the particle accelerator. However, in general, a high number of protons delivered per second would be in the range of millions to billions of protons per second, which is necessary for high-energy physics experiments and medical treatments using proton therapy.

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