The Touschek effect describes the scattering and loss of charged particles in a
storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of th ...
. It was discovered by
Bruno Touschek
Bruno Touschek (3 February 1921 – 25 May 1978) was an Austrian physicist, a survivor of the Holocaust, and initiator of research on electron-positron colliders.
Biography
Touschek was born and attended school in Vienna. In 1937, he was not ...
.
It is determined by the average of the scattering rate around the ring
:
In fact, since the momentum acceptance for scattering with energy gain may be different from that for scattering with energy loss, the lifetime must be computed by taking into account the positive and negative momentum acceptances, i.e.
:
A formula for the local scattering rate, given by Bruck, is
:
Here,
is the
classical particle radius, ''c'' is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, ''N'' is the number of particles,
is the
relativistic gamma factor,
is the momentum acceptance,
are the RMS horizontal, vertical, and bunch sizes, respectively.
:
where the function ''F'' is given by
:
A more accurate formula, valid in a wider range of conditions is derived by Piwinski.
Momentum acceptance calculation
The standard procedure for computing the momentum acceptance via a tracking code was defined in the paper by Belgroune et al. from the
SOLEIL
SOLEIL ("Sun" in French) is a synchrotron facility near Paris, France. It performed its first acceleration of electrons on May 14, 2006. The name ''SOLEIL'' is a backronym for ''Source optimisée de lumière d’énergie intermédiaire du LURE ...
synchrotron.
Calculation in beam dynamics codes
In order to compute the Touschek lifetime for a real storage ring, one needs a beam dynamics code. The Piwinski formula may be used together with the Elegant
code for example.
References
{{Reflist
Accelerator physics