4,378
edits
Non-diffusive transport: Difference between revisions
no edit summary
No edit summary |
|||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 5: | Line 5: | ||
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. | 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. | ||
<ref>[ | <ref>J.H. Misguich at el., [[doi:10.1088/0741-3335/44/7/101|Plasma Phys. Controlled Fusion, '''44''', L29 (2002)]]</ref> | ||
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. | 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. | ||
<ref>R. Balescu, ''Aspects of Anomalous Transport in Plasmas'', Institute of Physics Pub., Bristol and Philadelphia, 2005, ISBN 9780750310307</ref> | <ref>R. Balescu, ''Aspects of Anomalous Transport in Plasmas'', Institute of Physics Pub., Bristol and Philadelphia, 2005, {{ISBN|9780750310307}}</ref> | ||
The CTRW model provides a mathematical framework for handling non-diffusive transport (arising as | The CTRW model provides a mathematical framework for handling non-diffusive transport (arising as a 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. | ||
<ref> | <ref>B.Ph. van Milligen, R. Sánchez, and B.A. Carreras, [[doi:10.1063/1.1701893|Phys. Plasmas '''11''', 2272 (2004)]]</ref> | ||
<ref> | <ref>B.Ph. van Milligen, B.A. Carreras, and R. Sánchez, [[doi:10.1063/1.1763915|Phys. Plasmas '''11''', 3787 (2004)]]</ref> | ||
Note that there is another ingredient that may be essential to explain deviations from the standard transport model: [[Self-Organised_Criticality|self-organisation]]; we will not discuss this here. | Note that there is another ingredient that may be essential to explain deviations from the standard transport model: [[Self-Organised_Criticality|self-organisation]]; we will not discuss this here. | ||
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. | 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 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> | <ref>B. Carreras, V. Lynch, and G. Zaslavsky, [[doi:10.1063/1.1416180|Phys. Plasmas '''8''', 5096 (2001)]]</ref> | ||
<ref> | <ref>L. García and B. Carreras, [[doi:10.1063/1.2172177|Phys. Plasmas '''13''', 022310 (2006)]]</ref> | ||
<ref> | <ref>D. del Castillo-Negrete, B. Carreras, and V. Lynch, [[doi:10.1063/1.1767097|Phys. Plasmas '''11''', 3854 (2004)]]</ref> | ||
<ref> | <ref>J. Mier, R. Sánchez, L. García, D. Newman, and B. Carreras, [[doi:10.1063/1.3006088|Phys. Plasmas '''15''', 112301 (2008)]]</ref> | ||
<ref> | <ref>G. Sánchez Burillo, B.Ph. van Milligen, A. Thyagaraja, [[doi:10.1063/1.3118589|Phys. Plasmas '''16''', 042319 (2009)]]</ref> | ||
No significant data are as yet available from actual experiments, due to the considerable experimental difficulty of | No significant data are as yet available from actual experiments, due to the considerable experimental difficulty of injecting and following tracer particles, although some experiments in this sense are planned. | ||
==References== | ==References== | ||
<references /> | <references /> | ||