Particle Acceleration: Is Fission a Viable Option?

[barryn56]

In particle accelerators, is all energy for the particle provided from external sources to get them up to relativistic speeds. If a system used unstable (radioactive) particles (maybe they have?) and a fission occurred that propelled, for example, an alpha particle in the opposite direction to travel, would the very high relativistic mass of the emitted fragment provide a massive boost of velocity to the remaining atom?

I've always wondered about the argument that it requires more and more energy to accelerate a more and more massive object as you approach light speed - it seems to ignore the possibility that any on-board "fuel" mass is increasing in proportion...

 

[ZapperZ]

In particle accelerators, is all energy for the particle provided from external sources to get them up to relativistic speeds. If a system used unstable (radioactive) particles (maybe they have?) and a fission occurred that propelled, for example, an alpha particle in the opposite direction to travel, would the very high relativistic mass of the emitted fragment provide a massive boost of velocity to the remaining atom?

I've always wondered about the argument that it requires more and more energy to accelerate a more and more massive object as you approach light speed - it seems to ignore the possibility that any on-board "fuel" mass is increasing in proportion...

Have you been to a particle accelerator before to see if this actually happens? Considering that these accelerators are design so tightly that we must know exactly the beam dynamics, you'd think that if they have this wrong, the design would be quite off if the physics doesn't agree with reality. Do you seriously think this has happened?

Accelerator physics is a well-known branch of physics. It isn't simply an after thought where people simply don't know what they're doing.

Zz.

 

[Bill_K]

I've always wondered about the argument that it requires more and more energy to accelerate a more and more massive object as you approach light speed

But it doesn't! It takes just the same amount of energy to accelerate a particle from 1000 GeV to 1001 GeV as it does from 1 GeV to 2 GeV. Namely 1 GeV. (I should have been keeping a count of how many erroneous conclusions have been drawn from this idea of "relativistic mass." It's just a formal device, and an unfortunate one at that.)

Anyway, as ZapperZ points out, when it comes to running a particle collider, getting the particles to accelerate is the easy part. You need to design a thousand or so magnets that will precisely bend and focus the beam. As the particles accelerate, current in the magnets has to be ramped up in unison. And then once a stable orbit is attained, you have to maintain the particles in that orbit for hours at a time.

 

[ParticleGrl]

But it doesn't! It takes just the same amount of energy to accelerate a particle from 1000 GeV to 1001 GeV as it does from 1 GeV to 2 GeV. Namely 1 GeV. (I should have been keeping a count of how many erroneous conclusions have been drawn from this idea of "relativistic mass." It's just a formal device, and an unfortunate one at that

But going from 1 GeV to 2 GeV moves your proton from stationary to about 0.85c.

Going from 1000 GeV to 1001 GeV moves your proton from 0.9999995c to 0.999999501c.

For the way non-physicist think about acceleration, the idea that its takes more energy for diminishing returns in acceleration makes perfect sense.

 

[barryn56]

Thanks for the responses - I'm somewhat surprized that this question was construed as some sort of slight on accelerator design! ParticleGrl is correct in understanding that the thrust was the common argument as to why something (e.g. a rocket) cannot go faster than light is that the effectiveness of the energy supplied is lower due to the relativistic mass increase of the rocket. But if the source of the fuel is already on board, then it's energy supply should increase in proportion. The thought experiment was - what happens if an unstable element decays with emission of a particle at near light speeds - i.e. how much energy is imparted to the original particle. From the replies I take it this is not practically feasible (even LHC uses lead or protons only, from what I've read), but I expect there must be a theoretical answer, and I dare say it is probably the same energy as if the two particles were traveling in opposite directions and collided at the sum of the speeds.

 

[Drakkith]

I just wanted to add that Kinetic energy of an object increases something like twice as quick as the velocity.

KE=(1/2M)V^2

If you double your velocity you get FOUR TIMES as much kinetic energy. So each doubling gives you exponentially more energy.

Also, let's say M=10 kg and initial V = 10 m/s.

KE=(1/2x10) 10^2

That's KE=500

Lets increase V by 1. So, V=11 m/s.

KE=(1/2x10)11^2

KE=605. So 1 m/s increase equals an extra 105 joules. (I think it's joules)

Now, let's go to 12.

KE=(1/2x10)12^2

KE=720. 720-605=115. Increasing by another 1 m/s gives us 115 joules instead of 105.

 

[The_Duck]

Thanks for the responses - I'm somewhat surprized that this question was construed as some sort of slight on accelerator design! ParticleGrl is correct in understanding that the thrust was the common argument as to why something (e.g. a rocket) cannot go faster than light is that the effectiveness of the energy supplied is lower due to the relativistic mass increase of the rocket. But if the source of the fuel is already on board, then it's energy supply should increase in proportion. The thought experiment was - what happens if an unstable element decays with emission of a particle at near light speeds - i.e. how much energy is imparted to the original particle. From the replies I take it this is not practically feasible (even LHC uses lead or protons only, from what I've read), but I expect there must be a theoretical answer, and I dare say it is probably the same energy as if the two particles were traveling in opposite directions and collided at the sum of the speeds.

You can calculate the final speed of the decayed nucleus using the http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity". Say we have the unstable nucleus at rest, and we observe that when such a nucleus decays it emits an alpha particle and recoils in the opposite direction with some velocity $$v_r$$. Now we create a beam of these unstable particles that travels with some velocity $$v_b$$ which we might make close to c. When a nucleus in the beam happens to decay such that it emits the alpha particle directly backwards, it now attains a new, slightly higher velocity

$$\frac{v_b + v_r}{1 + v_b v_r / c^2}$$

You can convince yourself that this formula shows the same diminishing returns as other methods of acceleration--the speed boost from the decay recoil (the difference between the above velocity and the original velocity $$v_b$$) gets smaller and smaller as $$v_b$$ approaches c.

 

[daschaich]

The thought experiment was - what happens if an unstable element decays with emission of a particle at near light speeds - i.e. how much energy is imparted to the original particle.

I want to reiterate one of Bill_K's points: The effects of an unstable element decaying at near light speed must be the same (up to choice of inertial reference frame) as if the unstable element decayed at rest -- because from the particle's own "point of view", it is at rest!

The confusion here is coming from thinking of energy and velocity as though they were frame-independent quantities, and mass as though it were a frame-dependent quantity, when really the situation is exactly the opposite: energy and velocity are frame-dependent and mass is frame-independent.

ParticleGrl is correct that this is how non-physicists tend to think about acceleration, but I don't think we're doing non-physicists any favors by refraining from explaining why this way of thinking can lead to confusion. I'm with Bill_K: "relativistic mass" needs to be killed with fire.

For more, I recommend this old Physics Today article by Lev Okun, which is too large for me to attach to this post.