A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems

We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large $\epsilon$, $P(\epsilon)\sim 1/\epsilon^{1+\alpha}$ with $\alpha\in(0,2)$. Our model serves as a generalization of 1D Lloyd's model, which corresponds to $\alpha=1$. First, we verify that the ensemble average $\left\langle -\ln G\right\rangle$ is proportional to the length of the wire $L$ for all values of $\alpha$, providing the localization length $\xi$ from $\left\langle-\ln G\right\rangle=2L/\xi$. Then, we show that the probability distribution function $P(G)$ is fully determined by the exponent $\alpha$ and $\left\langle-\ln G\right\rangle$. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at $G=0$ and $1$. In addition, we show that $P(\ln G)$ is proportional to $G^\beta$, for $G\to 0$, with $\beta\le\alpha/2$, in agreement to previous studies.Comment: 5 pages, 5 figure

Wakefield-Induced Ionization injection in beam-driven plasma accelerators

We present a detailed analysis of the features and capabilities of Wakefield-Induced Ionization (WII) injection in the blowout regime of beam driven plasma accelerators. This mechanism exploits the electric wakefields to ionize electrons from a dopant gas and trap them in a well-defined region of the accelerating and focusing wake phase, leading to the formation of high-quality witness-bunches [Martinez de la Ossa et al., Phys. Rev. Lett. 111, 245003 (2013)]. The electron-beam drivers must feature high-peak currents ($I_b^0\gtrsim 8.5~\mathrm{kA}$) and a duration comparable to the plasma wavelength to excite plasma waves in the blowout regime and enable WII injection. In this regime, the disparity of the magnitude of the electric field in the driver region and the electric field in the rear of the ion cavity allows for the selective ionization and subsequent trapping from a narrow phase interval. The witness bunches generated in this manner feature a short duration and small values of the normalized transverse emittance ($k_p\sigma_z \sim k_p\epsilon_n \sim 0.1$). In addition, we show that the amount of injected charge can be adjusted by tuning the concentration of the dopant gas species, which allows for controlled beam loading and leads to a reduction of the total energy spread of the witness beams. Electron bunches, produced in this way, fulfil the requirements to drive blowout regime plasma wakes at a higher density and to trigger WII injection in a second stage. This suggests a promising new concept of self-similar staging of WII injection in steps with increasing plasma density, giving rise to the potential of producing electron beams with unprecedented energy and brilliance from plasma-wakefield accelerators

A near-IR line of Mn I as a diagnostic tool of the average magnetic energy in the solar photosphere

We report on spectropolarimetric observations of a near-IR line of Mn I located at 15262.702 A whose intensity and polarization profiles are very sensitive to the presence of hyperfine structure. A theoretical investigation of the magnetic sensitivity of this line to the magnetic field uncovers several interesting properties. The most important one is that the presence of strong Paschen-Back perturbations due to the hyperfine structure produces an intensity line profile whose shape changes according to the absolute value of the magnetic field strength. A line ratio technique is developed from the intrinsic variations of the line profile. This line ratio technique is applied to spectropolarimetric observations of the quiet solar photosphere in order to explore the probability distribution function of the magnetic field strength. Particular attention is given to the quietest area of the observed field of view, which was encircled by an enhanced network region. A detailed theoretical investigation shows that the inferred distribution yields information on the average magnetic field strength and the spatial scale at which the magnetic field is organized. A first estimation gives ~250 G for the mean field strength and a tentative value of ~0.45" for the spatial scale at which the observed magnetic field is horizontally organized.Comment: 42 pages, 17 figures, accepted for publication in the Astrophysical Journal. Figures 1 and 9 are in JPG forma