نوع مقاله : مقاله پژوهشی
نویسنده
دانشکده فیزیک، دانشگاه تبریز، تبریز
چکیده
The space charge waves in a long coasting charged particle beam is investigated in the context of water-bag distribution for the longitudinal distribution function. The nonlinear propagation of modulated space charge wave packets is studied, by employing a fluid beam model. It is revealed that dispersion curve obtained in linear approximation consists of two forward (0≤k<√2⁄2) and backward (√2⁄2<k≤1) segments so as they are connected at a frequency cutoff point where the group velocity becomes zero. k denotes normalized wavenumber. Considering small yet weakly nonlinear deviations from equilibrium, and using multiple-scale method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE) for the slowly varying linear charge perturbation amplitude. It is remarked that the dispersion coefficient in NLSE doesn’t depend on σ, and it is negative in 0<k<1 range which means negative group velocity dispersion. σ denotes a dimensionless parameter which depends on the beam equilibrium pressure and linear charge density, electric charge of beam particle and geometric parameterg_0 Finally, the analysis reveals that both of stable dark and instable bright excitations associated with space charge waves can propagate not only in normal dispersion (forward waves) region but also in anomalous dispersion (backward waves) region.
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