Non-diffusive transport: Difference between revisions
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In recent years, it has been suggested that the plasma may contain phenomena that invalidate this picture. | In recent years, it has been suggested that the plasma may contain phenomena that invalidate this picture. | ||
There may ''turbulent eddies'' in which particles become trapped for some time, and there certainly are ''transport barriers'', associated with rational magnetic surfaces, and ''stochastic regions'' of the magnetic field. This could cause the waiting time distribution to become non-exponential. Likewise, the phenomenon of ''streamers'', appearing in many models of plasma turbulence, could carry particles across long distances in the radial direction, and the distribution of particle steps could then also be deformed and develop ''long tails''. Nobody knows exactly how important these phenomena are in the global transport picture. | There may ''turbulent eddies'' in which particles become trapped for some time, and there certainly are ''transport barriers'', associated with rational magnetic surfaces, and ''stochastic regions'' of the magnetic field. This could cause the waiting time distribution to become non-exponential; therefore motion being non Markovian. Likewise, the phenomenon of ''streamers'', appearing in many models of plasma turbulence, could carry particles across long distances in the radial direction, and the distribution of particle steps could then also be deformed and develop ''long tails''. Consequently, the transport is said to be non local, as long range events probability is not negligible. Nobody knows exactly how important these phenomena are in the global transport picture. | ||
Whatever the case, a well-established methodology exists to describe this deviation from standard diffusive transport (with characteristic scales): the Continuous Time Random Walk (CTRW) model. | Whatever the case, a well-established methodology exists to describe this deviation from standard diffusive transport (with characteristic scales): the Continuous Time Random Walk (CTRW) model. | ||
<ref>[http://books.google.es/books?id=Yaupom_qdKIC&lpg=PP1&ots=WmaABP3l92&dq=%22Balescu%22%20%22Aspects%20of%20anomalous%20transport%20in%20plasmas%22%20&lr=&pg=PP1 R. Balescu, Aspects of anomalous transport in plasmas, IOP Publishing (2005)]</ref> | <ref>[http://books.google.es/books?id=Yaupom_qdKIC&lpg=PP1&ots=WmaABP3l92&dq=%22Balescu%22%20%22Aspects%20of%20anomalous%20transport%20in%20plasmas%22%20&lr=&pg=PP1 R. Balescu, Aspects of anomalous transport in plasmas, IOP Publishing (2005)]</ref> | ||
The CTRW model provides a mathematical framework for handling non-diffusive transport, but it does not explain why such non-diffusive transport should arise: answering the latter requires detailed computer simulations of turbulence and experimental observations. | The CTRW model provides a mathematical framework for handling non-diffusive transport (arising as as generalisation of the diffusive transport when eliminating the stated characteristic scales), but it does not explain why such non-diffusive transport should arise: answering the latter requires detailed computer simulations of turbulence and experimental observations. | ||
However, even without fully understanding the origin of the non-diffusive behaviour, it is possible to construct models based on these ideas, and see whether these models fare better in predicting the global transport properties of plasmas than the standard diffusive models. | However, even without fully understanding the origin of the non-diffusive behaviour, it is possible to construct models based on these ideas, and see whether these models fare better in predicting the global transport properties of plasmas than the standard diffusive models. | ||
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<ref>[http://link.aip.org/link/?PHPAEN/11/3787/1 B.Ph. van Milligen, B.A. Carreras, and R. Sánchez, Phys. Plasmas '''11''', 3787 (2004)]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/11/3787/1 B.Ph. van Milligen, B.A. Carreras, and R. Sánchez, Phys. Plasmas '''11''', 3787 (2004)]</ref> | ||
Another approach is to test whether non-diffusive transport phenomena actually occur in simulations and experiment. To do so, ''tracer particles'' are injected into the plasma fluid, and their evolution is followed in time. The application of this method has yielded clear indications that plasma turbulence induces non-diffusive transport in simulations. | Another approach is to test whether non-diffusive transport phenomena actually occur in simulations and experiment. To do so, ''tracer particles'' are injected into the plasma fluid, and their evolution is followed in time. Since the ''tracers'' are expected to catch the essential underlying physics, their trajectories provide information about the motion. These trajectories can be studied by means of several analysis techniques, calculating for instance the relevant probability distributions related to the transport, or detecting correlations in the velocity. The application of this method has yielded clear indications that plasma turbulence induces non-diffusive transport in simulations. | ||
<ref>[http://link.aip.org/link/?PHPAEN/8/5096/1 B. Carreras, V. Lynch, and G. Zaslavsky, Phys. Plasmas '''8''', 5096 (2001)] </ref> | <ref>[http://link.aip.org/link/?PHPAEN/8/5096/1 B. Carreras, V. Lynch, and G. Zaslavsky, Phys. Plasmas '''8''', 5096 (2001)] </ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/13/022310/1 L. García and B. Carreras, Phys. Plasmas '''13''', 022310 (2006)]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/13/022310/1 L. García and B. Carreras, Phys. Plasmas '''13''', 022310 (2006)]</ref> | ||