Beam current of positrons and electrons

In summary: I really appreciate it.In summary, the conversation discusses finding the energy, wavelength, speed, p.d, and current in the annihilation process. The first step involves finding the energy using the formula ##E=2mc^2##, where m is the mass of the electron. The remaining steps involve finding the wavelength of the photon, speed of the positron, p.d using conservation of energy, and current using the formula P = V.I. There is confusion in step 3 as the wavelength of the positron is being calculated using the wavelength of the photon. In part b, the same formula P = V.I is applied to find V, which is the same as what was found in part a
  • #1
songoku
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Homework Statement
a. If a positron beam were to be used as an annihilation cutting tool, calculate the beam current that would deliver 100 kW.

b. What voltage would be needed to accelerate beam of electrons so that, at the same beam current, it could deliver the same power from mechanical collisions with the target?
Relevant Equations
##E=mc^2##

##E=hf##

##\lambda = \frac h p##

##\frac{1}{2} mv^2 = q.V##

P = V.I
a) My idea is:
1. Find the energy created by annihilation process, which is ##E=2mc^2## where m is the mass of electron
2. Find the wavelength of photon by using formula E = hf
3. Find the speed of positron by using the formula of de broglie wavelength
4. Find the p.d by using conservation of energy: ##\frac{1}{2} mv^2 = q.V##
5. Find current by using P = V.I

I am not sure at step (3) because I use the wavelength of photon as wavelength of positron. Can I do this?

b) I just use P = V.I to find V, which is the same as what I found in part (a) step (4)

Am I correct? Thanks
 
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  • #2
Step 1 looks good. None of the rest made much sense to me. A positron is not a photon. And what voltage do you think you are finding?

After step 1, how many positrons/sec are needed?
 
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  • #3
haruspex said:
Step 1 looks good. None of the rest made much sense to me. A positron is not a photon. And what voltage do you think you are finding?
I am thinking about accelerating voltage to accelerate the positron

haruspex said:
After step 1, how many positrons/sec are needed?
Number of positrons per second needed = ##\frac{P}{E}## where P is the power given by the question and E is the energy calculated in step 1

Next I multiply the result by charge of positron to get the beam current. Is this correct?

For b), is it correct to just apply P = V.I ?

Thanks
 
  • #4
songoku said:
Number of positrons per second needed = ##\frac{P}{E}## where P is the power given by the question and E is the energy calculated in step 1
Wait, should I multiply ##\frac{P}{E}## by 2? I imagine for the annihilation process, the positron and electron will move towards each other then collide so both of them will contribute to the beam current

Thanks
 
  • #5
songoku said:
Wait, should I multiply ##\frac{P}{E}## by 2? I imagine for the annihilation process, the positron and electron will move towards each other then collide so both of them will contribute to the beam current

Thanks
The electrons are in the target, not leaping out if it. Besides, you are asked for the beam current of the positrons.
 
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  • #6
Thank you very much haruspex
 

Related to Beam current of positrons and electrons

1. What is the difference between beam current of positrons and electrons?

The beam current of positrons and electrons refers to the amount of particles (positrons or electrons) that are passing through a specific point in a beam of particles per unit time. The main difference between the two is their charge - positrons have a positive charge while electrons have a negative charge.

2. How is beam current of positrons and electrons measured?

The beam current of positrons and electrons is typically measured using a device called a Faraday cup. This device collects and measures the total charge of the particles passing through it, giving an accurate measurement of the beam current.

3. What factors affect the beam current of positrons and electrons?

The beam current of positrons and electrons can be affected by several factors, including the strength of the magnetic field used to steer the particles, the voltage applied to accelerate the particles, and the density of the particles in the beam. Other factors such as beam size and shape can also impact the beam current.

4. Why is the beam current of positrons and electrons important in particle accelerators?

The beam current of positrons and electrons is an important parameter in particle accelerators because it determines the intensity of the particle beam, which is crucial for many experiments and applications. Higher beam currents allow for more particles to be delivered to a target, increasing the chances of successful collisions and data collection.

5. How is the beam current of positrons and electrons controlled?

The beam current of positrons and electrons can be controlled through various methods, including adjusting the voltage and magnetic fields, as well as using beam collimators to shape and focus the beam. Additionally, feedback systems can be used to monitor and adjust the beam current in real-time, ensuring stable and consistent beam delivery.

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