Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level

The single mode approximation has proved useful for the excitation spectrum at $\nu=1/3$. We apply it to general fractions and find that it predicts $n$ magneto-roton minima in the dispersion of the Girvin-MacDonald-Platzman collective mode for the fractional quantum Hall states at $\nu=n/(2n+1)$, and one magneto-roton minimum for both the composite Fermi sea and the paired composite fermion state. Experimental relevance of the results will be considered.Comment: 5 pages, 6 figure

Linear Phase Second Order Recursive Digital Integrators and Differentiators

In this paper, design of linear phase second order recursive digital integrators and differentiators is discussed. New second order integrators have been designed by using Genetic Algorithm (GA) optimization method. Thereafter, by modifying the transfer function of these integrators appropriately, new digital differentiators have been obtained. The proposed digital integrators and differentiators accurately approximate the ideal ones and have linear phase response over almost entire Nyquist frequency range. The proposed operators also outperform the existing operators in terms of both magnitude and phase response

Evolution of ultra-relativistic hollow-electron-beam wakefield drivers during their propagation in plasmas

Ultra-relativistic hollow electron beams can drive plasma wakefields ($\sim$ GV/m) suitable for positron acceleration. Stable propagation of hollow electron beams for long distances in plasmas is required to accelerate positrons to high energies by these plasma wakefields. In this work, we show by quasi-static kinetic simulations using the code WAKE that an ultra-relativistic azimuthally-symmetric hollow electron beam propagates in a plasma by developing fish-bone like structure and shifting its bulk, differentially along its length (rear part fastest), towards its axis due to the decrease in the betatron time period of beam electrons from the beam-front to beam-rear. Hollow electron beams with small radius collapse into their axis due to the pull by the secondary wakefields generated by some of the beam electrons reaching the axis. Hollow beams with sufficiently large radius, however, can propagate stably in plasmas for several meters and be used for positron acceleration.Comment: 8 figure