Acceleration of a Charged Particle

[jmatejka]

For sake of argument consider magnetically accelerating a Proton to greater than .1 "C".

In an accelerator the proton is contained and accelerated by a magnetic field. Relativistic mass issues vs. available energy is the velocity limitation. Correct?

As relativistic mass becomes an issue, is the velocity of the Proton unstable? That is, do you constantly need to keep pushing the proton, because it "wants" to slow down to non-relativistic speeds?

If you were pushing the Proton in space with a magnetic field, would you continually have to keep pushing, or could you get it to "settle" and coast at a relativistic velocity?

Thanks any insight would be helpful.

 

[CompuChip]

For sake of argument consider magnetically accelerating a Proton to greater than .1 "C".

Note that it is actually electronically (or electromagnetically, if you want) accelerating the proton. The magnetic field itself does not do work.

In an accelerator the proton is contained and accelerated by a magnetic field. Relativistic mass issues vs. available energy is the velocity limitation. Correct?

The limitation is actually a fundamental one, but yes: in practice you notice this because more and more energy you pump into the particle will go into the "relativistic mass" instead of the velocity.

As relativistic mass becomes an issue, is the velocity of the Proton unstable? That is, do you constantly need to keep pushing the proton, because it "wants" to slow down to non-relativistic speeds?

If you were pushing the Proton in space with a magnetic field, would you continually have to keep pushing, or could you get it to "settle" and coast at a relativistic velocity?

Thanks any insight would be helpful.

Well, first of all, there is no hard boundary between relativistic and non-relativistic speeds. Even if such an effect existed, it would not be like the proton kept slowing down until it reached 0.9c, or 0.5c, or 0.1c and then suddenly became "stable".
Since the basic relation F = dp/dt (and F ∝ v) still holds in the relativistic regime, a change of momentum would need to be caused by a force. So if you stop pushing, the momentum (and hence the velocity, although it is not simply p/m anymore) will stabilise.

In practice, there will always be friction - even in the most perfect vacuum we can create here on Earth there will still be atoms floating about. So in any realistic experiment the proton would bump into these (or they would bump into the proton, or they would bump into each other ;)) and dissipate energy, thereby slowing down.
In any "realistic" experiment, you would have to have it go around a circle anyway, since we cannot build infinitely long linear accelerators, which means you have to keep pushing it around anyway (just like a ball going around a circle on a string is constantly accelerated, although - again - the relativistic formulas are slightly different).

 

[jmatejka]

Thanks your input and insight is much appreciated!

 

[kloptok]

I guess you would also have to take into account that the proton loses energy due to its acceleration (an accelerating charged particle radiates), an especially profound effect in circular accelerators. This slows the proton down and you have to add energy in order for the proton to maintain its speed.