29 citations · 95 across the 34 of their papers we have counts for
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The Hamilton-Jacobi Equation and its Application to Nonlinear Beam Dynamics: Comparison of Approaches
Stephan I. Tzenov
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact soluti…
Frobenius-Perron Operator Approach to the Beam-Beam Interaction in Circular Colliders
Stephan I. Tzenov
Unlike most publications devoted to the application of the self-consistent method of the nonlinear Vlasov-Poisson system to the study of beam-beam interaction, in this article an a…
The Method of Formal Series: Applications to Nonlinear Beam Dynamics and Invariants of Motion
Stephan I. Tzenov
A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilt…
Linear Coupling of Transverse Betatron Oscillations. Dynamic Stability and Invariants of Motion
Stephan I. Tzenov, Zhichu Chen, Hailong Wu
Based on the technique of the discrete one-turn transfer maps, the problem of linear coupling between horizontal and vertical betatron oscillations in an accelerator has been treat…
Hydrodynamic Approach to the Free Electron Laser Instability
Stephan I. Tzenov, Kiril B. Marinov
Starting from the Vlasov-Maxwell system, an exact relativistic hydrodynamic closure for a special type water bag distributions satisfying the Vlasov equation has been derived. It h…
Dynamics of Particles in Non Scaling FFAG Accelerators
James K. Jones, Bruno D. Muratori, Susan L. Smith +1
Non scaling Fixed-Field Alternating Gradient (FFAG) accelerators have an unprecedented potential for muon acceleration, as well as for medical purposes based on carbon and proton h…
Generation and Propagation of Nonlinear Waves in Travelling Wave Tubes
Stephan I. Tzenov
The generation and evolution of nonlinear waves in microwave amplifiers such as travelling wave tubes, free electron lasers and klystrons have been studied. The analysis is based o…
Solitary Waves in an Intense Beam Propagating Through a Smooth Focusing Field
Stephan I. Tzenov, Ronald C. Davidson
Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a…
Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Applications to Periodic Focusing Systems and the Coherent Beam-Beam Interaction
Stephan I. Tzenov, Ronald C. Davidson
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the origi…
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
Stephan I. Tzenov
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying pa…
Renormalization Group Approach to the Beam-Beam Interaction in Circular Colliders
Stephan I. Tzenov
Building on the Renormalization Group (RG) method the beam-beam interaction in circular colliders is studied. A regularized symplectic RG beam-beam map, that describes successfully…
Simulation of the Beam-Beam Effects in Storage Rings with a Method of Reducing the Region of Mesh
Yunhai Cai, Alex W. Chao, Stephan I. Tzenov +1
A highly accurate self-consistent particle code to simulate the beam-beam collision in storage rings has been developed. It adopts a method of solving the Poisson equation…
Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach
Stephan I. Tzenov
We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system…
Random Beam Propagation in Accelerators and Storage Rings
Stephan I. Tzenov
A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of co…
Nonlinear Longitudinal Waves in High Energy Stored Beams
Stephan I. Tzenov
We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavel…
Collision Integrals and the Generalized Kinetic Equation for Charged Particle Beams
Stephan I. Tzenov
In the present paper we study the role of particle interactions on the evolution of a high energy beam. The interparticle forces taken into account are due to space charge alone. W…
Formation of Patterns and Coherent Structures in Charged Particle Beams
Stephan I. Tzenov
In the present paper we study the long wavelength and slow time scale behavior of a coasting beam in a resonator adopting a broad-band impedance model. Based on the renormalization…
Coherent Nonlinear Phenomena in High Energy Synchrotrons: Observations and Theoretical Models
P. L. Colestock, L. K. Spentzouris, S. I. Tzenov
Nonlinear waves have been observed in synchrotrons for years but have received little attention in the literature. While pathological, these phenomena are worth studying on at leas…
Solitary Waves on a Coasting High-Energy Stored Beam
S. I. Tzenov, P. L. Colestock
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we fin…