scholarly journals Nonlinear Dynamics and Phase Space Manipulations of High-Brightness Beams

2019 ◽  
Author(s):  
Philippe Piot ◽  
Bela Erdelyi
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Space ◽  
High Brightness

scholarly journals Single-shot reconstruction of core 4D phase space of high-brightness electron beams using metal grids

2018 ◽  
Vol 21 (10) ◽  
Author(s):  
D. Marx ◽  
J. Giner Navarro ◽  
D. Cesar ◽  
J. Maxson ◽  
B. Marchetti ◽  
...  
Keyword(s):  
Phase Space ◽  
Electron Beams ◽  
Single Shot ◽  
High Brightness

Stochasticity in the Josephson map

1996 ◽  
Vol 56 (3) ◽  
pp. 493-506 ◽  
Author(s):  
Y. Nomura ◽  
Y. H. Ichikawa ◽  
A. T. Filipov
Keyword(s):  
Nonlinear Dynamics ◽  
Diffusion Coefficient ◽  
Phase Space ◽  
Characteristic Function ◽  
Numerical Investigation ◽  
Stochastic Diffusion ◽  
Standard Map ◽  
External Bias ◽  
Stochastic Parameter ◽  
Phase Space Portrait

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

scholarly journals Chaotic Saddles in a Generalized Lorenz Model of Magnetoconvection

2020 ◽  
Vol 30 (12) ◽  
pp. 2030034
Author(s):  
Francis F. Franco ◽  
Erico L. Rempel
Keyword(s):  
Nonlinear Dynamics ◽  
Fractal Dimension ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Lorenz Model ◽  
Fractal Basin Boundaries ◽  
Chaotic Transients ◽  
Basin Boundaries

The nonlinear dynamics of a recently derived generalized Lorenz model [ Macek & Strumik, 2010 ] of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where attractors and nonattracting chaotic sets coexist inside a periodic window. The nonattracting chaotic sets, also called chaotic saddles, are responsible for fractal basin boundaries with a fractal dimension near the dimension of the phase space, which causes the presence of very long chaotic transients. It is shown that the chaotic saddles can be used to infer properties of chaotic attractors outside the periodic window, such as their maximum Lyapunov exponent.

CLASSICAL DYNAMICS OF RYDBERG ELECTRONS IN CROSSED FIELDS: THE STRUCTURE OF PHASE SPACE AND CHAOS-ORDER ALTERNATIONS

1994 ◽  
Vol 04 (04) ◽  
pp. 905-920 ◽  
Author(s):  
JAN VON MILCZEWSKI ◽  
G.H.F. DIERCKSEN ◽  
T. UZER
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Space ◽  
Magnetic Fields ◽  
Chaotic Systems ◽  
Rydberg Atoms ◽  
Excited Electron ◽  
Atomic Scale ◽  
Classical Dynamics ◽  
Electric And Magnetic Fields ◽  
Great Complexity

Highly excited Rydberg atoms are atomic-scale laboratories where the quantum mechanics of chaotic systems can be tested. The symmetry breaking introduced into the Coulomb potential by crossed electric and magnetic fields leads to very interesting nonlinear dynamics, but is also a source of great complexity. In this article, we analyse the phase space and dynamics of a highly excited electron in the combined Coulomb, electric, and magnetic fields by bringing out the classical structures that support the complexity of the motion.

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