摘要:

The JIFT workshop on ‘‘Nonlinear dynamics and acceleration mechanisms’’ covered the following subjects:i) Stochastic properties of low dimensional nonlinear dynamical systems,ii) Nonlinear plasma phenomena and nonlinear dynamical system:  a) Motion of charged particles in the tail of the geomagnetic sphere and magnetic field reconnection,  b) Magnetic dynamo and chaos,  c) Particle acceleration by coherent electromagnetic wave, and  d) Chaos in free electron laser;iii) Chaos in chemical reactions, andiv) Stability of particle orbits in accelerators and toroidal magnetic fields in fusion devices.The plasma confinement by magnetic fields is also discussed. (AIP)

ISSN:0094-243X    

DOI:10.1063/1.40769

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Chaotic scattering can be characterized by the infinite multi‐valuedness of cross section. Various characteristic quantities of chaotic collision are numerically pursued; distribution of conjugation points for Jacobi field, Gauss‐Riemannian curvature, Lyapounov exponent, and collision‐time distribution. New mechanism leading to chaotic collision is discussed, i.e., topological weak instability induced by the stagnant layer effect around KAM tori. The distribution of collision time obeys a inverse power law, and the universality is briefly discussed.

ISSN:0094-243X    

DOI:10.1063/1.40782

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Diffusive motion of the particle positionX, generated by the chaotic motion under the external excitation, obeyingX¨=−&ggr;X˙−sin(2&pgr;X) +A ⋅ cos(&OHgr;t), is studied. For adequate parameter values the system undergoes the type I intermittency transition.The long‐lived temporal correlation due to the intermittency causes thedrift‐like chaotic motion of the particle, which leads to the anomalous enhancement of diffusivity. Furthermore long‐time overall statistical properties associated with both the drift‐like motion and its intermission are clarified from a new statistical‐mechanical viewpoint.

ISSN:0094-243X    

DOI:10.1063/1.40760

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The power‐law energy distributions are observed in space and fusion plasmas. The power law decay of the two‐time velocity correlation function and the corresponding frequency spectrum of the correlation function are shown to be related to the power law distribution of the time interval of acceleration, which produces a power‐law energy distribution. In particular, the two time correlation function, the distribution of acceleration duration, namely the distribution of the trapping time of the quasi‐trapped orbits in the vicinity of the magnetic null such as the geomagnetic tail configurations are shown to produce a power law energy distribution function. The statistical property is applicable under conditions given here to the energy spectra of cosmic rays, electrons in laser‐plasma interaction and the radio‐frequency heated confined plasmas.

ISSN:0094-243X    

DOI:10.1063/1.40775

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Functional difference equations characterize the invariant surfaces of the Poincare´ return map of a general Hamiltonian system. Two different functional equations are derived. The first is analogous to the Hamilton‐Jacobi equation and the second is a generalization of Moser’s equation. Some properties of the equations, and schemes for solving them numerically, are discussed.

ISSN:0094-243X    

DOI:10.1063/1.40777

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Approximate invariant tori in phase space are found using a non‐perturbative, numerical solution of the Hamilton‐Jacobi equation for a nonlinear, time‐periodic Hamiltonian. The Hamiltonian is written in the action‐angle variables of its solvable part. The solution of the Hamilton‐Jacobi equation is represented as a Fourier series in the angle variables but not in the ‘time’ variable. The Fourier coefficients of the solution are regarded as the fixed point of a nonlinear map. The fixed point is found using a simple iteration or a Newton‐Broyden iteration. The Newton‐Broyden method is slower than the simple iteration, but it yields solutions at amplitudes that are significant compared to the ‘dynamic aperture.’ Invariant tori are found for the dynamics of a charged particle in a storage ring with sextupole magnets.

ISSN:0094-243X    

DOI:10.1063/1.40778

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

In this paper, we review the theory of explicit symplectic integration. We present a non‐trivial application going beyond Ruth’s original paper. Finally, we contrast the explicit and the implicit methods by deriving a hybrid integrator for a special one dimensional Hamiltonian.

ISSN:0094-243X    

DOI:10.1063/1.40779

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Spatially and temporally varying adiabatic accelerating structures have significantly different dynamics. The adiabatic invariants are different. The phase‐space area occupied by an adiabatically trapped beam differs in the two cases. In addition, in the spatially varying case ponderomotive effects can prevent trapping of certain particles no matter how large the trapping potential becomes.

ISSN:0094-243X    

DOI:10.1063/1.40780

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Equation of magnetic field line can be written in the form of Hamiltonian equation. An explicit form for the Hamiltonian applicable to the first order of &rgr;/Ris obtained, where &rgr; andRare minor and major radii.

ISSN:0094-243X    

DOI:10.1063/1.40781

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Analysis of the relativistic standard map is one of the important problems to understand nonlinear interaction between waves and charged particles in the relativistic dynamics. In the relativistic standard map, in general, chaotic motion is strongly suppressed and regular motion such as periodic points is predicted by use of symmetry lines of the map. Local stability of periodic points is investigated by introducing the residue of the orbit which characterizes the eigenvalue of the area‐preserving map. It is found that the exchange of stable and unstable points takes place at some value of the relativistic parameter. Special behavior of the residue of the Poincare‐Birkhoff period‐4 points are also examined and related bifurcations are clarified.

ISSN:0094-243X    

DOI:10.1063/1.40783

出版商:AIP    

年代:1991

数据来源: AIP