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Submitted to the Proceedings of the 2007 Fall FFAG Workshop in KURRI, Osaka, Japan. Nov. 4-10, 2007
Generalization of the ERIT Principle and Method
Alessandro G. Ruggiero
Brookhaven National Laboratory, PO Box 5000, Upton, Long Island, NY 11973, USA
Abstract. The paper describes the generalization of the method to produce secondary particles with a low-energy and
low-intensity primary beam circulating in a Storage Ring with the Emittance-Recovery by Internal-Target (ERIT).
Keywords: Storage Ring; Ionization Cooling: Production of Secondary Beams; FFAG; ERIT.
A BEAM OF IONS CIRCULATING IN A STORAGE RING
A beam of ions completely stripped of their electrons circulates in a Storage Ring of circumference C. The
central beam kinetic energy is E and the spread (rms value) GE. There is no net acceleration though the beam is
bunched by a constant frequency RF cavity system in the several MHz range. There is only one bunch so that the
revolution frequency ft = c / C equals the RF frequency fRF. We denote with $ and y the usual velocity and energy
relativistic factors, and with c the speed of light. Also p is the beam central momentum, and Bp the corresponding
value of the magnetic rigidity. The mass number of the ion is A, and the charge state equals the atomic number Z.
There are N ions circulating at any time. Denoting with e the elementary electric charge, the average particle -current
is
I = Nefo (1)
There is a thin Foil inserted at one location of the ring that is traversed by the beam of ions periodically, every
turn. The foil is made of stationary, solid material made of atoms of mass number AF and atomic number F. Of
course the atoms are neutral and are surrounded by a corresponding number (ZF) of electrons. Let us denote with S
the mass density of the Foil (in g/cm3) and with p the atom density (in cm3)
P = S/AFmp (2)
where mp = 1.67 x 10-24 g is the proton mass at rest. The Foil (Target) has a thickness g and a transverse extension
wide enough to intercept the whole beam at every traversal.
When an ion of the circulating beam traverses the Foil, one of the following events will occur:
1. The ion trajectory widens transversally by Multiple Coulomb Scattering (MCS);
2. There is a net Energy Loss (EL) of the same value to all ions;
3. There is a widening of the energy spread (Energy Straggling (ES));
4. The ion scatters with a nucleus triggering a nuclear reaction;
5. Single Coulomb Scattering (SCS) at large angle and large energy that in one event removes the particle from
the aperture of the Storage Ring.
Events 1, 2, and 3 cause a continuous, stochastic increase of the beam dimensions and spreads, but not beam loss,
unless the growth after many turns is unchecked, and the edge of the beam reaches the available aperture of the
Storage Ring. These events together are described by a total cross-section c'r that is very large, ranging in the
hundred of barns (one barn = 10-24 cm-2). On the other side, Event 4 causes immediately the loss of the particle, but
it is also the useful event, as the resulting nuclear reaction is the one sought by the set-up. Typically the cross-section
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Ruggiero, A. Generalization of the ERIT Principle and Method, report, February 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc895155/m1/2/: accessed March 29, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.