A wavelet-based method to measure the toroidal mode number of ELMs

The high confinement mode regime (H-mode) in tokamaks is accompanied by the occurrence of burst of MHD activity at the plasma edge, so-called edge localized modes (ELMs). Because of the short time scales involved in the ELM crash (on JET typically 0.2 ms), standard Fourier analysis can hardly be used to extract their toroidal mode number. On the other hand, the assessment of linear stability of ELMs with the ion drift effects included, makes the identification of their toroidal mode numbers an important issue, while an accurate comparison with the theory of nonlinear evolution of ELMs requires the knowledge of the nonlinear spectrum. Compared to Fourier analysis, wavelets are suitable to study transient events on time scales comparable to the wave period. Spectral analysis based on sinusoidal wavelet functions has been applied to study the spectral properties of magnetic perturbations associated with ELMs and with their precursors, in JET plasmas with toroidal rotation driven by unbalanced NBI. It is shown that, combining wavelet analysis with statistical two-point correlation techniques, it is possible to get information on the toroidal mode number structure of magnetic perturbations during the phases that immediately precede the ELM and during the ELM crash itself

Resonant Excitation of Shear Alfv\'en Perturbations by Trapped Energetic Ions in a Tokamak

A new analytic expression is derived for the resonant drive of high n Alfvenic modes by particles accelerated to high energy by Ion Cyclotron Resonance Heating. This derivation includes finite orbit effects, and the formalism is completely non-perturbative. The high-n limit is used to calculate the complex particle response integrals along the orbits explicitly. This new theory is applied to downward sweeping Alfven Cascade quasimodes completing the theory of these modes, and making testable predictions. These predictions are found to be consistent with experiments carried out on the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)].Comment: 31 pages, 6 figure

Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $\sigma_0$ at large energies.Comment: 22 pages, 19 figures, submitted to PR

Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties

The quantum magnetic oscillations of electrical (Shubnikov de Haas effect) and thermal conductivities are studied for graphene which represents a distinctive example of planar systems with a linear, Dirac-like spectrum of quasiparticle excitations. We show that if a utmost care was taken to separate electron and phonon contributions in the thermal conductivity, the oscillations of electron thermal conductivity, $\kappa(B)$ and the Lorenz number, $L(B)$ would be observable in the low field (less than a few Teslas) regime.Comment: 11 pages, RevTeX4, 6 EPS figures; 2 references, 1 figure and one more section are added; final version published in PR

Superfluid density and competing orders in d-wave superconductors

We derive expressions for the superfluid density $\rho_s$ in the low-temperature limit $T \to 0$ in d-wave superconductors, taking into account the presence of competing orders such as spin-density waves, $i d_{xy}$-pairing, etc. Recent experimental data for the thermal conductivity and for elastic neutron scattering in La$_{2-x}$Sr$_x$CuO$_4$ suggest there are magnetic field induced anomalies that can be interpreted in terms of competing orders. We consider the implications of these results for the superfluid density and show in the case of competing spin-density wave order that the usual Volovik-like $\sqrt{H}$ depletion of $\rho_s(H)$ is replaced by a slower dependence on applied magnetic field. We find that it is crucial to include the competing order parameter in the self-consistent equation for the impurity scattering rate.Comment: 17 pages, RevTeX4, 6 EPS figures; final version published in PR

Study of the spectral properties of ELM precursors by means of wavelets

The high confinement regime (H-mode) in tokamaks is accompanied by the occurrence of bursts of MHD activity at the plasma edge, so-called edge localized modes (ELMs), lasting less than 1 ms. These modes are often preceded by coherent oscillations in the magnetic field, the ELM precursors, whose mode numbers along the toroidal and the poloidal directions can be measured from the phase shift between Mirnov pickup coils. When the ELM precursors have a lifetime shorter than a few milliseconds, their toroidal mode number and their nonlinear evolution before the ELM crash cannot be studied reliably with standard techniques based on Fourier analysis, since averaging in time is implicit in the computation of the Fourier coefficients. This work demonstrates significant advantages in studying spectral features of the short-lived ELM precursors by using Morlet wavelets. It is shown that the wavelet analysis is suitable for the identification of the toroidal mode numbers of ELM precursors with the shortest lifetime, as well as for studying their nonlinear evolution with a time resolution comparable to the acquisition rate of the Mirnov coils

Magneto-optical and optical probes of gapped ground states of bilayer graphene

We study the influence of different kinds of gaps in a quasiparticle spectrum on longitudinal and transverse optical conductivities of bilayer graphene. An exact analytical expression for magneto-optical conductivity is derived using a low-energy two-band Hamiltonian. We consider how the layer asymmetry gap caused by a bias electric field and a time-reversal symmetry breaking gap affect the absorption lines. The limit of zero magnetic field is then analyzed for an arbitrary carrier density in the two-band model. For a neutral bilayer graphene, the optical Hall and longitudinal conductivities are calculated exactly in the four-band model with four different gaps and zero magnetic field. It is shown that two different time-reversal symmetry breaking states can be distinguished by analyzing the dependence of the optical Hall conductivity on the energy of photon. These time-reversal symmetry breaking states are expected to be observed experimentally via optical polarization rotation either in the Faraday or Kerr effects. We analyze a possibility of such an experiment for a free-standing graphene, graphene on a thick substrate, and graphene on a double-layer substrate.Comment: 16 pages, 7 figures; final version published in PR