Re: Question about the Abraham-Lorentz force

On Feb 21, 3:37 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
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


Thank you, Tom

.

Relevant Pages

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