Beam current of positrons and electrons

[songoku]

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

 

[haruspex]

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?

 

[songoku]

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

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

 

[songoku]

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

 

[haruspex]

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.

 

[songoku]

Thank you very much haruspex