Re: Question about the Abraham-Lorentz force

Dono wrote:
The AL force is opposite to the particle speed (http://
en.wikipedia.org/wiki/Abraham-Lorentz_force). How do synchrotrons keep
particles on trajectory? How do they counter the AL force?

First, that wikipedia page says explicitly that this is a non-relativistic, non-quantum formula. In a modern synchrotron, the electrons are highly relativistic (gamma 1000-200,000 or so), and quantum effects are very important.

A typical synchrotron today, say in the class of the Diamond light source at RAL or the Advanced Photon Source at Argonne, has a radius of a hundred meters or so, with dipole bending magnets arranged around its circumference to keep the particles on a piecewise-straight path around the nominal circle (straight between magnets, of course). There are also quadrupole magnets interspersed with them to focus the beam transversely. And there are RF cavities to accelerate the beam and to replenish the energy lost to synchrotron radiation (basically what you are asking about). The diameter of the beam pipe is big enough so the particles can go from RF cavity to RF cavity around the ring and not hit the aperture (due to energy loss by radiation); the RF cavities participate in a feedback loop to keep their energy gain matched to the radiation energy loss so the beam stays in the center of the apertures.

Someone asked about accelerating along a circular path. In a synchrotron that is not done, because the RF cavities that provide the acceleration are not inside bending magnets (they wouldn't work in there), so the path is straight inside the RF cavities. Of course the paths of individual particles deviate in position, momentum, and angle from the nominal path, but the machine is designed to accommodate that.

A cyclotron does accelerate along a circular path. But the
region of acceleration is very short and the curvature is
not important.

For RF cavities to accelerate the beam, the beam must be bunched so that particles arrive inside the cavity at the correct phase of the RF E field to be accelerated. It turns out this essentially happens naturally (as long as they start out "close enough"). That is, there is focusing transversely from the quadrupoles that focus the beam, and there is also focusing longitudinally (in both momentum and time relative to the desired RF phase) from the RF cavities. Such focusing is essential to keep the acceptance of the machine large enough to maintain a beam.

This is indeed accelerator physics. But I don't have a short, elementary reference.


Tom Roberts
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