A model of electron acceleration by an electron Bernstein mode in a parabolic density profile is developed. The mode has a Gaussian profile. It could be excited via the mode conversion of an electromagnetic wave or by an electron beam. As it attains a large amplitude, it axially traps electrons moving close to its parallel phase velocity, where parallel refers to the direction of static magnetic field. As the electrons are accelerated and tend to get out of phase with the wave, the transverse field of the mode enhances its energy and relativistic mass, increasing the dephasing length. The scheme can produce electron energies up to a few MeV.
The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D = 1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.
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