Scientists at the European Organization for Nuclear Research (CERN) in Geneva, Switzerland, recently created a new state of matter called “quark-gluon plasma,” which they believe will lead to further insight into the early evolution of the universe. According to theory, this state of matter–in which quarks, the tiniest components from which much of matter is made, and gluons, the particles associated to the interquark forces, are unbound and free to roam–existed for about 10 microseconds after the Big Bang. As the universe expanded and cooled, the plasma condensed into the composite nuclear particles that we recognize today (e.g., protons and neutrons).

In 1994, researchers at CERN set out to verify this theory, hoping to re-create the conditions that existed immediately after the Big Bang in an attempt to “unglue” the quarks and then observe their transition into complex particles as the system cooled. The experiments involved bombarding targets with a tightly focused beam of high-energy lead ions. The ions were first accelerated from rest to intermediate energy in the CERN Proton Synchrotron (PS) particle accelerator complex, and then further accelerated in the Super Proton Synchrotron (SPS) to their final energy before ejection towards the targets inside seven different experimental detectors. The collisions created temperatures over one hundred thousand times as hot as the center of the sun and energy densities twenty times that of ordinary nuclear matter.

According to Mats Lindroos, the ABS project leader at CERN, Mathematica was heavily used in the experiments, both for the analytical part of accelerator control and online as part of the Automated Beam Steering and Shaping (ABS) software. The ABS designation includes all forms of algorithms, software packages, and systems that are used as intelligent tools by operators in the accelerator control rooms for correction of trajectories, orbits, working points, and other specifications.

In the first stage of the acceleration, the beam trajectories are controlled online with the ABS system. The ABS system uses precomputed correction matrices determined with BeamOptics, an application of Mathematica that contains all the classical functions of the theory of charged particle optics. “The Mathematica package BeamOptics, which was developed here at CERN, has been the workhorse of the ABS project since the start of the ABS activities in the PS division,” says Lindroos.

The ABS system also calls an optimizer that minimizes the errors of trajectories using an algorithm called MICADO, which is also coded in Mathematica. Given a correction matrix and function, MICADO computes values for the correctors that will minimize the error in the function, with the output graphically displaying how useful each of the correctors is in minimizing the error. The graphics user-interface communicates with the algorithm via MathLink.

For more detailed information on the “Little Bang” and CERN’s Heavy Ion program, visit the CERN web site at http://public.web.cern.ch/Public/Welcome.html.