Selforganisation in plasma physics: Special Issue Dedicated to Professor Lennart Stenflo on the Occasion of His 65th Birthday
2004 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, ISSN 0281-1847, Vol. T113, 51-55 p.Article in journal (Refereed) Published
The bottom line of modern plasma physics addressing a many body problem is the lack of thermodynamic potentials for the system in which fluxes are no longer linear functions of forces or gradients. Indeed far from the classical equilibrium, a system can still converge to a stationary state, yet not defined by the proper thermodynamic potential in contrast to the entropy production principle valid only for a linear or weakly nonlinear system. In this case, we confront an important issue of stability of a strongly nonequilibrium system occurring and lacking the thermodynamic potential. In a linear system the equilibrium is defined by the minimum of the potential and therefore the stability of the resulting steady - state is easily found. Of course, any fluctuation causes a deviation from the equilibrium. Yet, linear or weakly nonlinear system will return to this steady state due to the second law of thermodynamics. Hence, the existence of the thermodynamic potential makes the equilibrium very robust. Given the potential, any evolution of a weakly nonlinear system will result in a static stationary state. In contrast, a strongly nonlinear system may loose a steady state very easily due to instability perturbed by fluctuations. If this is the case the fluctuation will be amplified until a very different steady state not described by a minimum of the thermodynamic potential emerges. In more detail, instability in a strongly nonlinear situation has always to exceed a given threshold in order to yield a different equilibrium far from an original static steady state. In fluids and plasmas it is well-known that any laminar motion can transform into a turbulent motion once a given fluid velocity is exceeded. It may appear that this transition yields a chaotic strongly fluctuating equilibrium. Indeed although at the macroscopic level this novel equilibrium may appear to be a complete disorder and chaos, it is found experimentally that at the microscopic level the new equilibrium is characterised by a highly ordered vortices  resulting due to the inherent selforganization of this system. Here, it is important to keep in mind that fluid equations describing this phenomenon are highly nonlinear. Multiple scales emerge both in space and in time, thereby pointing to the scale free nature of the fractal geometry. The convection emerging due to multiscale vortices is organised to enhance the thermal conductivity in contrast to the second law of thermodynamics. The reason for this is that a fluctuation bound to dissipate within the framework of the weakly nonlinear approach is significantly amplified and ultimately governs the system. The entropy is of course provided by an external source in the environment and there is no contradiction to the second law. Hence, a novel highly organised equilibrium emerges which may also be time dependent. To this end, turbulent vortices differ very much from equilibrium structures like crystals because here thermal fluxes provide the order in contrast to the dissipation only in linear systems. Novel dissipative structures arise from a chaotic particle motion on all possible time and space scales.
Place, publisher, year, edition, pages
2004. Vol. T113, 51-55 p.
Computational geometry, Nonlinear equations, Nonlinear systems, Perturbation techniques, Thermal conductivity, Thermodynamics, Classical equilibrium, Linear functions, Plasma physics, Thermodynamic potential, High energy physics
Fusion, Plasma and Space Physics
IdentifiersURN: urn:nbn:se:kth:diva-26185DOI: 10.1238/Physica.Topical.113a00051ISI: 000204271900015ScopusID: 2-s2.0-39549090384OAI: oai:DiVA.org:kth-26185DiVA: diva2:371624
QC 201011222010-11-222010-11-192014-03-31Bibliographically approved