Theoretical modeling of an A6 relativistic magnetron

The analytical modeling of the initialization stage of a relativistic magnetron of the A6 cylindrical design is presented, where only two dominant modes are used: a direct current (dc) background mode and a radio frequency (rf) pump mode. These two modes interaction nonlinearly, with the dc background being driven by the dc electromagnetic forces and the ponderomotive forces of the rf mode, while the rf mode is the most unstable linear eigenmode on this dc background. In cylindrical geometry, the diocotron resonance is found to occur over a broader region than in planar models. In fact, in certain parameter regimes, the resonance can appear twice, once near the Brillouin edge, and second, just below the anode. In these parameter regimes, the oscillating electrons can be accelerated twice. Numerical results for the initiation stage agree quite well with the known experimental results on the A6. Results for 350 kV are emphasized, and similar results have also been obtained for voltages between 300 and 500 kV. Numerical data are presented that indicate a possible source for a nonlinear instability, which could give rise to pulse shortening, in the later operating stage, where the device should be smoothly delivering power

Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Solitons created by chirped initial profiles in coherent pulse propagation

"Solitons created by chirped initial profiles in coherent pulse propagation", L.V.Hmurcik and D.J.Kaup, Journal of the Optical Society of America, vol 69, p 597 (1979).If an incident pulse is chirped, the critical parameters for self-induced transparency to occur in coherent pulse propagation can no longer be obtained from the well-known McCall-Hahn area theorem. We have been able to obtain these parameters by solving the Zakharov-Shabat eigenvalue equation for the bound-state eigenvalues. We find that critical (threshold) areas will be increased for a chirped incident pulse in almost all cases, except for a box profile or for a pulse that is approximately box-like in shape. In these latter cases, the chirped critical areas will instead decrease for the second and all higher branches. The first branch’s critical area is always increased due to chirping

Renormalization Group Theory for a Perturbed KdV Equation

We show that renormalization group(RG) theory can be used to give an analytic description of the evolution of a perturbed KdV equation. The equations describing the deformation of its shape as the effect of perturbation are RG equations. The RG approach may be simpler than inverse scattering theory(IST) and another approaches, because it dose not rely on any knowledge of IST and it is very concise and easy to understand. To the best of our knowledge, this is the first time that RG has been used in this way for the perturbed soliton dynamics.Comment: 4 pages, no figure, revte

Shape coexistence in neutron-deficient Kr isotopes: Constraints on the single-particle spectrum of self-consistent mean-field models from collective excitations

We discuss shape coexistence in the neutron-deficient Kr72-Kr78 isotopes in the framework of configuration mixing calculations of particle-number and angular-momentum projected axial mean-field states obtained from self-consistent calculations with the Skyrme interaction SLy6 and a density-dependent pairing interaction. While our calculation reproduces qualitatively and quantitatively many of the global features of these nuclei, such as coexistence of prolate and oblate shapes, their strong mixing at low angular momentum, and the deformation of collective bands, the ordering of our calculated low-lying levels is at variance with experiment. We analyse the role of the single-particle spectrum of the underlying mean-field for the spectrum of collective excitations.Comment: accepted for publication in Phys. Rev.