Books by Stephan I Tzenov
This book adopts a non-traditional approach to accelerator theory. The exposition starts with the... more This book adopts a non-traditional approach to accelerator theory. The exposition starts with the synchro-betatron formalism and continues with the linear and nonlinear theories of transverse betatron motion. Various methods of studying nonlinear dynamical systems (the canonical theory of perturbations and the methods of multiple scales and formal series) are explained through examples. The renormalization group approach to studying nonlinear (continuous and discrete) dynamical systems as applied to accelerators and storage rings is used throughout the book. The statistical description of charged particle beams (the Balescu–Lenard and Landau kinetic equations as well as the Vlasov equation) is dealt with in the second part of the book. The processes of pattern formation and formation of coherent structures (solitons) are also described.
Papers by Stephan I Tzenov
Canonical Perturbation Theory
Contemporary Accelerator Physics, 2004
Effect of Impurities on the Indirect Polarization of Spins in an Anisotropic Double Ising Chain
physica status solidi (b), 1983
Special Methods in Accelerator Theory
Contemporary Accelerator Physics, 2004
The Vlasov Equation
Contemporary Accelerator Physics, 2004
The first results from commissioning EMMA - the Electron Model of Many Applications- are summaris... more The first results from commissioning EMMA - the Electron Model of Many Applications- are summarised in this paper. EMMA is a 10 to 20 MeV electron ring designed to test our understanding of beam dynamics in a relativistic linear non-scaling fixed field alternating gradient accelerator (FFAG). EMMA will be the world's first non-scaling FFAG and the paper will outline the characteristics of the beam injected in to the accelerator as well as summarising the results of the extensive EMMA systems commissioning. The paper will report on the results of simulations of this commissioning and on the progress made with beam commissioning.
In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructiv... more In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case, where the unperturbed rotation frequency of the map is far from structural resonances driven by the kick perturbation has been performed in detail. It is further shown that if the unperturbed rotation frequency is close to a resonance, the reduced RG map of the Frobenius-Perron operator (or phase-space density propagator) is equivalent to a discrete Fokker-Planck equation for the renormalized distribution function. The RG method has been also applied to study the stochastic properties of the standard Chirikov-Taylor map.
Nonlinear Waves and Turbulence in Intense Beams
Statistical Description of Charged Particle Beams
Contemporary Accelerator Physics, 2004
Physics of Particles and Nuclei, 2020
The method of formal series of Dubois-Violette as a non perturbative tool for the analysis of nonlinear beam dynamics
AIP Conference Proceedings, 1995
A new technique to compute invariant curves based on the method of formal series of Dubois-Violet... more A new technique to compute invariant curves based on the method of formal series of Dubois-Violette has been developed. The solution of the Hamilton-Jacobi equation is represented as a ratio of two series in the perturbation parameter (and the nonlinear action invariant), rather than a conventional power series proposed by canonical perturbation theory. It is well behaved even for large
Long term behavior in multi-dimensional Hamiltonian systems (Nonlinear diffusion approach)
AIP Conference Proceedings, 1995
The exact evolution equation for the angle averaged phase space density in the action‐angle space... more The exact evolution equation for the angle averaged phase space density in the action‐angle space is derived from the Fokker‐Planck equation (the usual Liouville equation in the case of vanishing external noise) using the projection operator technique. For long times the evolution equation is approximated in general with a non homogeneous diffusion equation, and an expression for the diffusion tensor is derived. An example of periodic crossing of a nonlinear resonance in one dimensional system has been considered and the diffusion coefficient has been calculated.
The concept of stochastic mechanics in particle accelerator physics
AIP Conference Proceedings, 1995
Considering the stochastic generalization of dynamical equations of motion we derive a Schrodinge... more Considering the stochastic generalization of dynamical equations of motion we derive a Schrodinger‐like equation for the transverse motion of particles in circular accelerators, in which the role of Planck’s constant is played by the transverse beam emittance. As an example we study the motion of a particle beam in a one dimensional linear lattice and cast a complete analogy with the non‐relativistic quantum mechanical harmonic oscillator.
The Schrödinger-like equation with electromagnetic potentials in the framework of stochastic quantization approach
Nonlinear beam dynamics using the method of formal series
Solitary Waves in Intense Charged Particle Beams
Statistical description of nonlinear particle motion in cyclic accelerators
Physics Letters A, 1997
The longitudinal dynamics of electrons in eB storage rings has been studied, when the radiation d... more The longitudinal dynamics of electrons in eB storage rings has been studied, when the radiation damping and quantum excitation of synchrotron radiation are taken into account. It has been shown that the electron beam propagates according to the law specified by a stochastic Schrijdinger-like equation, in which the role of Planck's constant is played by an effective longitudinal thermal beam emittance. @ 1997 Published by Elsevier Science B.V.
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Books by Stephan I Tzenov
Papers by Stephan I Tzenov