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Anomalous transport: Difference between revisions
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The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport|Neoclassical]] theory. | The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport|Neoclassical]] theory. | ||
However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]). | However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]). | ||
<ref>[http://dx.doi.org/10.1063/1.859358 A.J.Wootton et al, ''Fluctuations and anomalous transport in tokamaks'', Phys. Fluids B ''2'' (1990) 2879]</ref> | |||
The difference between actual transport and the Neoclassical expectation is called | The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly|anomalous]]" transport. | ||
It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities. | It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities. | ||
<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref> | |||
== How important is turbulence? == | == How important is turbulence? == | ||
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In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present. | In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present. | ||
And in part, because no complete theory for anomalous transport is available. | And in part, because no complete theory for anomalous transport is available. | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref> | |||
=== Arguments for === | === Arguments for === | ||
An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law|scaling]] of transport with heating power and machine size. | An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law|scaling]] of transport with heating power and machine size. | ||
<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, ''Progress in anomalous transport research in toroidal magnetic confinement devices'', IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref> | |||
The phenomenon of [[Scaling law|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation. | The phenomenon of [[Scaling law|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation. | ||
Following Freidberg, | Following Freidberg, | ||
<ref name="Freidberg" /> | |||
the cited [[Scaling law|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence). | the cited [[Scaling law|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence). | ||
Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''τ | Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''&tau;<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with [[Collisionality|collisionality]]). | ||
However, the experimental scalings give a ''decrease'' with ''T'' | However, the experimental scalings give a ''decrease'' with ''T'' | ||
(namely: ''τ | (namely: ''&tau;<sub>E</sub>'' &prop; ''T<sup>&alpha;</sup>'' with '' &alpha;'' &lt; -1). | ||
This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''. | This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''. | ||
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It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation. | It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation. | ||
<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255</ref> | |||
However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality. | However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality. | ||
As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]). | As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]). | ||
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The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients. | The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients. | ||
The most likely candidates involved in generating the observed anomalous transport are: | The most likely candidates involved in generating the observed anomalous transport are: | ||
<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref> | |||
* Ion Temperature Gradient (ITG) instabilities | * Ion Temperature Gradient (ITG) instabilities | ||
* Electron Temperature Gradient (ETG) instabilities | * Electron Temperature Gradient (ETG) instabilities | ||
* Collisionless Trapped Electron Modes (TEM) | * Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]</ref> <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref> | ||
* Dissipative Trapped Electron Modes (DTEM) | * Dissipative Trapped Electron Modes (DTEM) | ||
''(to be completed; references needed)'' | ''(to be completed; references needed)'' | ||
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There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation|simulations]] are possible. | There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation|simulations]] are possible. | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.77.71 A.M. Dimits et al, ''Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks'', Phys. Rev. Lett. '''77''' (1996) 71 - 74]</ref> | |||
However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge. | However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge. | ||
An alternative approach is to model the net effect of turbulence without simulating the fine detail. | An alternative approach is to model the net effect of turbulence without simulating the fine detail. | ||
In doing so, it is not sufficient to introduce a simple additional | In doing so, it is not sufficient to introduce a simple additional "turbulent diffusivity", as this cannot possibly reproduce the observed global transport scaling behaviour. | ||
It is probably necessary to use a [[Non-diffusive transport|non-diffusive]] description, | It is probably necessary to use a [[Non-diffusive transport|non-diffusive]] description, | ||
<ref>[http://dx.doi.org/10.1016/S0370-1573(02)00331-9 G. M. Zaslavsky, ''Chaos, fractional kinetics, and anomalous transport'', Physics Reports '''371''', Issue 6 (2002) 461-580]</ref> | |||
and include non-linear phenomena such as [[Self-Organised Criticality|critical gradients]]. | and include non-linear phenomena such as [[Self-Organised Criticality|critical gradients]]. | ||
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Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels. | Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels. | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/50/5/053001 M. Hirsch et al, ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''' (2008) 053001]</ref> | |||
== References == | == References == | ||
<references /> | |||