Particle accelerator magnets

Particle accelerators are needed for the investigation of two very fundamental research topics, which are nowadays strictly correlated. The first is related to particle physics, and is aimed to give an answer to basic questions like “what is matter?”, “what are its basic constituents?” and “what kind of interactions exist between particles?”. The second is related to astronomy, and is aimed to recreate with high energy collisions the same conditions existing in the initial instants of the origin of universe, immediately after the “Big Bang”. The questions are the following: “how was matter at that time?”, “how did the fundamental particles coalesce to make the atoms, the stars and the galaxies we observe today?”.

Particle accelerator at CERN (LHC)

Two kinds of accelerators exist, linear and circular. All particle beams start their acceleration in linear accelerators, but the need to reach very high energies would require linear accelerators of unacceptable lengths, so that the preferred solution is to counter-rotate particle beams in circular accelerators (called storage rings) until the desired energy is reached. The length of the circumference of the LHC (Large Hadron Collider) in construction at CERN (Geneva, Switzerland) is of about 27 Km .

In any kind of accelerator there is exactly one curve - the design orbit- on which ideally all particles should move. If this design orbit is curved, as in circular accelerators, bending forces are needed. In reality, most particles of the beam will deviate slightly from the design orbit. In order to keep these deviations small on the whole way (which might be as long as 10^11 km in a storage ring), focusing forces are required. In modern accelerators the bending forces are provided by dipole magnets, while the focusing forces are provided by quadrupole magnets.

Lorentz Force acting on charged particles

Both bending and focusing forces can be accomplished with electromagnetic fields. The bending force in particular is obtained exploiting the Lorentz force due to a magnetic field orthogonal to the the particle beam.

Superconducting magnet for LHC

As the particle velocity is extremely high, the Lorentz forces required are also high, so that very intense magnetic fields are needed. These fields can only be provided in a convenient way by superconducting magnets, that strongly reduce the consumption of electrical power with respect to conventional copper magnets.

During the particle accelerator operation, the particles velocity increases, so that to maintain the particles close to the design orbit, the magnetic field has to be increased. For this reason the typical operation of particle accelerator magnets is dynamic.

The electrodynamics of accelerator magnets is studied at the Applies Superconductivity Laboratory of the University of Bologna in collaboration with LHC division of CERN (Geneva, Switzerland) and Fermilab (Chicago, USA). The calcuation codes for the study of superconducting magnets have been developed in collaboration with Cryosoft.

In particular numerical codes and analytical formulae have been developed for the calculation of ac losses and current distribution in Rutherford cables used to wind accelerator magnets.

Degree thesis about the electrodynamics of accelerator magnets are available at the Applied Superconductivity Laboratory of the University of Bologna, with the possibility to spend part of the thesis preparation period at the LHC Division, CERN.

References

L. Bottura, M. Breschi, M. Schneider, “Measurements of magnetic field pattern in a short LHC dipole model”, LHC-MTA Internal Note, November 30, 1999

M. Breschi, L. Bottura, “Fast measurement of field harmonics through a set of Hall probes”, LHC-MTA Internal Note, January 24, 2000

L. Bottura, C. Rosso, M. Breschi, “A General Model for Thermal, Hydraulic and Electric Analysis of Superconducting Cables”, Cryogenics 40 (2000), pp.617-626

A. Akhmetov, L. Bottura, M. Breschi, “A Continuum Model for Current Distribution in Rutherford Cables”, IEEE Transactions on Applied Superconductivity, (11), 2001, pp. 2138-2141.

M. Breschi, “Current Distribution in Multistrand Superconducting Cables”, Ph.D. Thesis, University of Bologna, March 2001

L. Bottura, M. Breschi, M. Fabbri, “Analytical Solution for the Current Distribution in Multistrand Superconducting Cables”, Journal of Applied Physics, Vol. 92, 12, pp. 7571-7580, December 2002.

A. Akhmetov, L. Bottura, M. Breschi, P. L. Ribani, “A theoretical analysis of current imbalance in flat two layer superconducting cables”, Cryogenics 40 (2000), pp. 627-635.