Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics

On the Metric Dimension of Cartesian Products of Graphs

A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G*H. We prove that the metric dimension of G*G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G. Using bounds on the order of doubly resolving sets, we establish bounds on G*H for many examples of G and H. One of our main results is a family of graphs G with bounded metric dimension for which the metric dimension of G*G is unbounded

First analysis of anisotropic flow with Lee--Yang zeroes

We report on the first analysis of directed and elliptic flow with the new method of Lee--Yang zeroes. Experimental data are presented for Ru+Ru reactions at 1.69 AGeV measured with the FOPI detector at SIS/GSI. The results obtained with several methods, based on the event-plane reconstruction, on Lee--Yang zeroes, and on multi-particle cumulants (up to 5th order) applied for the first time at SIS energies, are compared. They show conclusive evidence that azimuthal correlations between nucleons and composite particles at this energy are largely dominated by anisotropic flow.Comment: 5 pages, 3 figures, submitted to Phys. Rev. C Rapid Co

Isospin dependence of relative yields of K+K^+ and K0K^0 mesons at 1.528 AGeV

Results on $K^+$ and $K^0$ meson production in $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions at a beam kinetic energy of 1.528$A$ GeV, measured with the FOPI detector at GSI-Darmstadt, are investigated as a possible probe of isospin effects in high density nuclear matter. The measured double ratio ($K^+/K^0$)$_{Ru}$/($K^+/K^0$)$_{Zr}$ is compared to the predictions of a thermal model and a Relativistic Mean Field transport model using two different collision scenarios and under different assumptions on the stiffness of the symmetry energy. We find a good agreement with the thermal model prediction and the assumption of a soft symmetry energy for infinite nuclear matter while more realistic transport simulations of the collisions show a similar agreement with the data but also exhibit a reduced sensitivity to the symmetry term.Comment: 5 pages, 3 figures. accepted for publication in Phys. Rev.

Two-proton small-angle correlations in central heavy-ion collisions: a beam-energy and system-size dependent study

Small-angle correlations of pairs of protons emitted in central collisions of Ca + Ca, Ru + Ru and Au + Au at beam energies from 400 to 1500 MeV per nucleon are investigated with the FOPI detector system at SIS/GSI Darmstadt. Dependences on system size and beam energy are presented which extend the experimental data basis of pp correlations in the SIS energy range substantially. The size of the proton-emitting source is estimated by comparing the experimental data with the output of a final-state interaction model which utilizes either static Gaussian sources or the one-body phase-space distribution of protons provided by the BUU transport approach. The trends in the experimental data, i.e. system-size and beam energy dependences, are well reproduced by this hybrid model. However, the pp correlation function is found rather insensitive to the stiffness of the equation of state entering the transport model calculations.Comment: 9 pages, 8 figures, accepted at Eur. Phys. Journ.

Direct comparison of phase-space distributions of K- and K+ mesons in heavy-ion collisions at SIS energies - evidence for in-medium modifications of kaons ?

The ratio of K- to K+ meson yields has been measured in the systems RuRu at 1.69 A GeV, Ru+Zr at 1.69 A GeV, and Ni+Ni at 1.93 A GeV incident beam kinetic energy. The yield ratio is observed to vary across the measured phase space. Relativistic transport-model calculations indicate that the data are best understood if in-medium modifications of the kaons are taken into account.Comment: 14 pages including 3 figure

Charged pion production in 4496^{96}_{44}Ru+4496^{96}_{44}Ru collisions at 400A and 1528A MeV

We present transverse momentum and rapidity spectra of charged pions in central Ru + Ru collisions at 400$A$ and 1528$A$ MeV. The data exhibit enhanced production at low transverse momenta compared to the expectations from the thermal model that includes the decay of $\Delta(1232)$-resonances and thermal pions. Modification of the $\Delta$-spectral function and the Coulomb interaction are necessary to describe the detailed shape of the transverse momentum spectra. Within the framework of the thermal model, the freeze-out radii of pions are similar at both beam energies. The IQMD model reproduces the shapes of the transverse momentum and rapidity spectra of pions, but the predicted absolute yields are larger than in the measurements, especially at lower beam energy.Comment: 12 pages, 11 figure

Strange meson production in Al+Al collisions at 1.9A GeV

The production of K$^+$, K$^-$ and $\varphi$(1020) mesons is studied in Al+Al collisions at a beam energy of 1.9A GeV which is close or below the production threshold in NN reactions. Inverse slopes, anisotropy parameters, and total emission yields of K$^{\pm}$ mesons are obtained. A comparison of the ratio of kinetic energy distributions of K$^-$ and K$^+$ mesons to the HSD transport model calculations suggests that the inclusion of the in-medium modifications of kaon properties is necessary to reproduce the ratio. The inverse slope and total yield of $\phi$ mesons are deduced. The contribution to K$^-$ production from $\phi$ meson decays is found to be [17 $\pm$ 3 (stat) $^{+2}_{-7}$ (syst)] %. The results are in line with previous K$^{\pm}$ and $\phi$ data obtained for different colliding systems at similar incident beam energies.Comment: 16 pages, 11 figure