From: draper@sscvx1.ssc.gov
Newsgroups: sci.physics
Subject: terminal particle energy for accelerators
Date: 15 Apr 92 17:47:16 GMT
Article-I.D.: sscvx1.1992Apr15.114716.1
Distribution: world,local
Organization: Superconducting Super Collider Laboratory

In article <1992Apr14.213121.17723@lmpsbbs.mot.com>, capurka@ssd.comm.mot.com (Tom Capurka) writes:
> Hello,
> I have a question about particle accelerators:  Why does there seem to be
> a terminal particle energy for a given particle, accelerator, related to
> the radius of the acclerator?  Is this because the radiation caused by
> the fact that the article is not in an inertial frame gets too large and
> approaches equilibrium state with the energy input?
> Whatever the reason, is there any possibility that there exists
> a yet undiscovered trick around this so that one could have an SSC type
> acclerator (as far as particle energies are concerned) in a 1 meter box?
> Or is this impossible in principle, given the state of physics today.
> 
> Sorry if this is too basic but a good library is far away and this may turn
> out to be more fun.
> 

I saw an answer posted about bremsstrahlung, which does pertain but isn't
exactly to the point. For circular accelerators, the bulk of the ring is not
devoted to accelerating elements (RF cavities), but to steering and focussing
magnets that keep the particles travelling around in a circle so that they can
return to the RF cavity for another kick in the butt. The analogy is that
schoolyard game tetherball, where a ball is tied to a pole by a rope, and
players slap the ball every time it comes around to get it really going. For
the Tevatron, for example, the protons circulate about a million times through
the RF cavity before they make it up to 900GeV.

The limitation, then, is the magnetic strength of the bending magnets. The
expression for this is
		p = q*B*r       (Elementary Physics II)
where p is the momentum of the particle, q its charge, B the magnetic field,
and r is the radius of curvature. For a synchrotron, B increases as p
increases, up to the limit the magnets can provide.

The research into "table-top" accelerators takes the approach of doing all the
acceleration in one linear shot, with some kick-ass accelerating fields, as
opposed to the circular technique, which uses the same modest accelerating
field over and over and over again.

The comment about bremsstrahlung does have some bearing on the radius in the
sense that at high enough momentum (or, more accurately, high enough Lorentz
factor gamma), trying to squeeze down the size of the circle by using stronger
magnets just doesn't pay off, because a smaller circle also means more energy
loss by radiation, to the point where the accelerating cavity produces no net
gain in energy. Case in point is HERA, which uses the same tunnel for
accelerating 820GeV protons and 30GeV electrons. The magnets for the protons
are high-field superconducting magnets, the magnets for the electrons are
lower-field conventional magnets. Why not use superconducting magnets for the
electrons to get a higher electron energy? Because bremsstrahlung for electrons
is so much worse than for protons. It doesn't pay to do it.

Paul Draper
University of Texas at Arlington
Draper@sscvx1.ssc.gov