Ky Fan inequality
RIBO stands for the Radioactive Ion Beam Optimization, a concept closely linked to the extraction of rare isotopes from targets.
Overview
Indeed, rare and radioactive here are synonyms. These are nuclei with an excess or deficit of neutrons or protons with respect to the normal isotopes observed in nature. In nuclear physics the ratio N/Z (number of Neutrons to number of Protons) is close to one for light elements and then it grows to about 1.5 because protons are less favourable in terms of stability due to the Coulomb repulsion. Rare isotopes can be produced artificially in research facilities like ISOLDE (at CERN, the European Center for Nuclear Research, in Geneva) or TRIUMF (Canada) by irradiating determined targets with energetic beams (typically protons or deuterons). The isotopes thereafter created tend to have short lifetimes (that is why you don't normally 'see' them in nature) so that any experiment or measurement done with them has to be carried out very quickly. The facilities ought to be optimised for a major production of the wished isotope while keeping the quickest extraction from the target to the experimental area.
The Extraction Process
The extraction involves the diffusion of the nuclei through the target material, and the effusion through the vacuum system up to the so-called ion source. Indeed atoms need to be ionized so that electromagnetic fields can then stir, accelerate and focus them to the experimental station. Only a fraction of the radioactive atoms can be ionized before decay or extraction. All this involves a certain release efficiency.
As for the mentioned release efficiency, this key factor encompasses several processes involved in the production of radioactive ion beams with the ISOL technique. Once the isotope has been generated in the target bulk, it diffuses across solid matter up to a free surface and it then effuses through vacuum, following a random walk of collisions with the system walls, eventually sticking on them for some time. Finally, after flowing through a (eventually chemically selective temperature controlled) transfer line, the isotope reaches the ion source and, in the aimed cases it can be ionized before it finds the outlet orifice, enabling downstream electromagnetic guidance and acceleration. These processes consume a certain amount of time (t) during which radioactive decay may occur, hereby lowering the number of extracted isotopes N(t):
Where is the half-life of the isotope.
In view of gaining diffusion rapidity, the target material choice may have to be revised if an alternative projectile-target pair with similar production cross sections shows better diffusion properties. Moreover, the target structure may be redistributed, split in smaller divisions like thinner foils, finer grains ... However, by so proceeding the free effusion flight path is enlarged and the number of collisions to the walls increases. As a consequence, effusion and desorption become slower, specially for isotopes that are chemically affine to the surface walls. Next, effusion to and in the ion source can be improved with new designs of the transfer lines and ion source, but this tends to inhibit the chemical separation and to shorten the confinement in the plasma chamber, ultimately lowering the ionization efficiency.
On top of this complicated scheme, more variables may deserve consideration, such as the variation of the running temperature of the target, or the impact of homomorphic variations of the system dimensions, both addressed at an enhancement of diffusion and effusion. However, this may again have some side effects like the deterioration of the target properties (melting for a serious temperature rise) or the decrease of absolute isotope production due to the shrinkage of the amount of target.
All this justifies the development of a project that can comprehensively cope with all the coupled variables, with the capability to isolate the composing effects and to ease their individual study. M. Santana PhD Thesis 2005
Further information
Major European projects aiming at the production of extremely exotic isotopes (which should reveal new features of physics) need extraction design optimization tools that can compensate the extreme brief life of the sought nuclei. RIBO is a transport code specifically written to address the design of such projects because it includes the major phenomena involved in the transport of radioisotopes: diffusion, effusion, ionization and ion transport.