Energy Extraction Resistors for the Main Dipole and Quadrupole Circuits of the LHC

When the LHC will be operating at its maximum beam energy, its superconducting dipole chains store a total magnetic energy of more than 11 GJ. At the same time, the QF and QD quadrupole circuits store a total energy of 400 MJ. Even with the sectorisation of each of the three principal power circuits into eight individually powered segments, the stored energy of a single circuit is considerable. During normal operation the energy in the dipole circuits is safely returned to the mains grid, using the thyristor-based, 'booster' unit of the power converters, operating in inversion. For the quadrupole chains, where the converter is of a mono-polar topology, the stored energy is dissipated into the resistive part of the warm d.c. power lines (busbars and cables) in a slow, controlled run-down. When a magnet quenches, however, such a slow energy transfer, taking 20 minutes from the rated LHC current, will not be possible. The 'cold' diode, taking over the magnet current in case of a quench, will not survive this slow current decay. For this reason, energy extraction facilities will be inserted into the power circuits. These systems are being designed to absorb the total circuit energy and de-excite the chains with a current decay time constant of 104 s for the dipoles and 40 s for the quadrupoles. The resulting maximum decay rates (-125 A/s and -325 A/s respectively) are comfortably below the levels where quench-back will occur. The energy extraction systems are based on an array of special, mechanical d.c. circuit breakers and absorber resistors, which are switched into the circuit by opening of the breakers. The design and construction of these large power resistors of a unique concept are the topics of this paper. The project is being realised as collaboration between, IHEP-Protvino, CERN and European Industry

Energy Extraction in the CERN Large Hadron Collider: a Project Overview

In case of a resistive transition (quench), fast and reliable extraction of the magnetic energy, stored in the superconducting coils of the electromagnets of a particle collider, represents an important part of its magnet protection system. In general, the quench detectors, the quench heaters and the cold by-pass diodes across each magnet, together with the energy extraction facilities provide the required protection of the quenching superconductors against damage due to local energy dissipation. In CERN's LHC machine the energy stored in each of its eight superconducting dipole chains exceeds 1300 MJ. Following an opening of the extraction switches this energy will be absorbed in large extraction resistors located in the underground collider tunnel or adjacent galleries, during the exponential current decay. Also the sixteen, 13 kA quadrupole chains (QF, QD) and more than one hundred and fifty, 600 A circuits of the corrector magnets will be equipped with extraction systems. The extraction switch-gear is based on specially designed, mechanical high-speed DC breakers, in certain cases combined with capacitive snubber circuits for arc suppression. This paper is an overview of the complete project with emphasis on the arguments and motivation for the choice of equipment and methods. It presents the basic properties of the principal components, the operational aspects and the present state of advancement. Finally, it highlights the implications of the extraction process on other systems of the LHC collider

The structure of Green functions in quantum field theory with a general state

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.Comment: 13 pages, 6 figure

Degenerate Landau-Zener model: Exact analytical solution

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1

On Nonperturbative Calculations in Quantum Electrodynamics

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $\alpha$.Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion and refs. are adde

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of "uniqueness" (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless $\phi^3$ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of Lipatov integrable chain model.Comment: 16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006

Critical exponents of the Gross-Neveu model from the effective average action

The phase transition of the Gross-Neveu model with N fermions is investigated by means of a non-perturbative evolution equation for the scale dependence of the effective average action. The critical exponents and scaling amplitudes are calculated for various values of N in d=3. It is also explicitely verified that the Neveu-Yukawa model belongs to the same universality class as the Gross-Neveu model.Comment: RevTeX, 4 pages, 2 figures, 1 table. Typos corrected in equation

Performance of GEM detectors in high intensity particle beams

We describe extensive tests of Double GEM and Triple GEM detectors, including full size prototypes for the COMPASS experiment, exposed to high intensity muon, proton and pion beams at the Paul~Scherrer Institute and at CERN. The measurements aim at detecting problems possible under these operation conditions, the main concern being the occurrence of discharges induced by beam particles. Results on the dependence of the probability for induced discharges on the experimental environment are presented and discussed. Implications for the application of GEM~detectors in experiments at high luminosity colliders are illustrated