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; 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.
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; and thus the motion would be 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 would then be non-local. 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.
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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. 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.  
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 tracer trajectories can be analyzed by means of several analysis techniques, e.g. by calculating the particle distribution probability function, or by detecting velocity correlations along trajectories.  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>