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.

 

[sardar]

I can provide some insights into the acceleration of a charged particle, specifically a proton, to relativistic speeds through the use of a magnetic field. Firstly, it is important to understand that the acceleration of a charged particle is dependent on the strength of the magnetic field it is placed in. The stronger the magnetic field, the greater the acceleration of the particle. Therefore, in order to accelerate a proton to a velocity greater than 0.1C, a very strong magnetic field would be required.

Secondly, as the proton approaches relativistic speeds, its relativistic mass increases, which means that more energy is required to maintain its acceleration. This can become a limiting factor in the velocity of the proton, as the available energy may not be enough to overcome the increase in relativistic mass. This is known as the velocity limitation.

In terms of stability, as the proton reaches relativistic speeds, it becomes increasingly difficult to maintain its velocity. This is because as the proton's velocity increases, its mass also increases, making it more resistant to acceleration. This does not mean that the proton will constantly slow down, but rather that it will require a constant force to maintain its velocity.

In a space environment, where there is no air resistance or other external factors, a proton can theoretically settle and coast at a relativistic velocity. However, this would require a constant and powerful magnetic field to counteract the proton's increasing mass and maintain its velocity. It is important to note that this is a theoretical scenario and in practical applications, such as particle accelerators, the proton would require constant acceleration to maintain its relativistic velocity.

In conclusion, the acceleration of a charged particle, such as a proton, to relativistic speeds through the use of a magnetic field is possible but comes with certain limitations and challenges. These include the strength of the magnetic field, the velocity limitation due to increasing relativistic mass, and the need for a constant force to maintain the particle's velocity. Further research and advancements in technology may provide more insights and solutions to these challenges in the future.