Dokument:
Transport scaling in incompletely
chaotic Hamiltonian systems
| Titel: | Transport scaling in incompletely chaotic Hamiltonian systems | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=2194 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20020523-000194-1 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | Lesnik, Dmitry [Autor] | |||||||
| Dateien: |
| |||||||
| Beitragende: | Prof. Dr. Spatschek, Karl-Heinz [Gutachter] Prof. Dr. Pukhov, Alexander [Gutachter] | |||||||
| Stichwörter: | Tokamak, dynamical system, Hamiltonian system,symplectic mapping, transport barrier, diffusion | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 530 Physik | |||||||
| Beschreibung: | Some aspects of the diffusion of phase trajectories in systems, which exhibit partially and completely chaotic behavior, are considered on the example of a nonperiodic Chirikov-Taylor (standard) map. The topic is related to the problem of transport of charged particles in hot plasma, embedded in strong magnetic field, like that in Tokamak or Stellarator. The standard map gives a good local description of the magnetic field lines behavior in the vicinity of resonances and therewith is simple enough to be treated numerically or analytically. In the first part the subcritical nondiffusive regime of weakly chaotic dynamics was explored. In this regime, KAM barriers prevent the global \'action\' transport, and therefore allow a stationary action distribution function $\\psi_p$. The function $\\psi_p$ was estimated by means of the continuous-time-random-walk model. In the framework of this model it is supposed that the chaotic portion of the phase space is subdivided into a finite number of regions, named basins. A chaotic trajectory is then reduced to the sequence of sojourns in different basins, followed by transitions to other basins. The only statistical parameters of a trajectory are sojourn-time distribution and transition probabilities. Although being a serious simplification of the exact motion, this model allows one to obtain a good estimate of the stationary distribution function. In the second part we have investigated the angular transport in a standard map both for weak and strong chaotic regimes. An angular diffusion coefficient was estimated analytically using the Frobenius-Perron evolution operator formalism. We have observed superdiffusive behavior for small stochasticity parameter $K$ ($K\\to 0$) with a transport exponent $\\mu_\\theta=2$. The transport properties for large values of $K$ depend on the boundary conditions for the action variable $p$. For a periodic boundary condition in $p$, the angular transport becomes diffusive ($\\mu_\\theta=1$), and the corresponding diffusion coefficient has been derived. On the other hand, for an unrestricted $p$ motion, the transport is found to be superdiffusive with the transport exponent $\\mu_\\theta=3$. It has been shown that the action and angle diffusion coefficients are related as $D_\\theta \\simeq \ u^2 D_p$, where $\ u$ plays a role of time. In both cases of periodical and unrestricted boundary conditions, characteristic oscillations in the transport coefficients occur. All analytical predictions reveal excellent agreement with numerical simulations. | |||||||
| Lizenz: |  Urheberrechtsschutz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Physik | |||||||
| Dokument erstellt am: | 23.05.2002 | |||||||
| Dateien geändert am: | 12.02.2007 | |||||||
| Promotionsantrag am: | 23.05.2002 | |||||||
| Datum der Promotion: | 23.05.2002 |
