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Employing a magnetized plasma medium in the interaction region of a free-electron laser (FEL) offers the possibility of generating short wavelengths using moderate energy beams. Plasma in the presence of static magnetic field supports right and left circularly polarized electromagnetic modes. By superposition of these two modes, a linearly polarized electromagnetic mode is generated which can be employed as a plasma undulator in a FEL. This configuration has a higher tunability by controlling the plasma density on top of the γ-tubability of the conventional FELs. The roles of the axial magnetic field and plasma on the laser gain and the electron trajectories of an e-beam propagating through the plasma medium have been studied and new orbits of group (I, II, and III) have been found. Moreover, the stability of these orbits for different values of plasma frequencies has been investigated. It is shown that by increasing the axial guide magnetic field strength, the gain for orbits of group I trivially increase, while a decrease in gain has been obtained for orbits of group II and group III. In addition, it is found that with increasing the plasma frequency (or plasma density) the gain for orbits of group I and group II trivially decreases and shift to the lower cyclotron frequencies, while an increase in gain has been obtained for orbits of group III.

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We consider isotropic spin-1/2 two-leg ladders with dominant spatially-modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and the entanglement entropy between legs. Numerical experiment shows that the gapless LL phases are fundamentally different. In the first LL phase, only spins on rungs are entangled, but in the second LL phase the spins on legs are long-distance entangled. Therefore, the concurrence between spins on legs can be considered as a function to distinguish the LL phases.