Profile consistency: Difference between revisions

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<ref>[http://link.aip.org/link/?PHPAEN/8/4096/1 F. Jenko et al, ''Critical gradient formula for toroidal electron temperature gradient modes'', Phys. Plasmas '''8''' (2001) 4096]</ref>
<ref>[http://link.aip.org/link/?PHPAEN/8/4096/1 F. Jenko et al, ''Critical gradient formula for toroidal electron temperature gradient modes'', Phys. Plasmas '''8''' (2001) 4096]</ref>


== Observations (tokamaks) ==
== Observations ([[Tokamak|tokamaks]]) ==


* TFTR <ref>[http://dx.doi.org/10.1088/0029-5515/26/7/002 E.D. Fredrickson, J.D. Callen, et al., ''Heat pulse propagation studies in TFTR'',  Nucl. Fusion '''26''' (1986) 849]</ref>
* TFTR <ref>[http://dx.doi.org/10.1088/0029-5515/26/7/002 E.D. Fredrickson, J.D. Callen, et al., ''Heat pulse propagation studies in TFTR'',  Nucl. Fusion '''26''' (1986) 849]</ref>
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* Various devices <ref>[http://dx.doi.org/10.1088/0741-3335/35/10/002 F. Wagner and U. Stroth, ''Transport in toroidal devices-the experimentalist's view'', Plasma Phys. Control. Fusion '''35''' (1993) 1321]</ref><ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter, C. Angioni, et al., ''Experimental studies of electron transport'', Plasma Phys. Control. Fusion '''43''' (2001) A323]</ref>
* Various devices <ref>[http://dx.doi.org/10.1088/0741-3335/35/10/002 F. Wagner and U. Stroth, ''Transport in toroidal devices-the experimentalist's view'', Plasma Phys. Control. Fusion '''35''' (1993) 1321]</ref><ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter, C. Angioni, et al., ''Experimental studies of electron transport'', Plasma Phys. Control. Fusion '''43''' (2001) A323]</ref>


== Observations (stellarators) ==
== Observations ([[Stellarator|stellarators]]) ==


* W7-AS <ref>[http://dx.doi.org/10.1088/0741-3335/40/1/002 U. Stroth, ''A comparative study of transport in stellarators and tokamaks'', Plasma Phys. Control. Fusion '''40''' (1998) 9]</ref>
* W7-AS <ref>[http://dx.doi.org/10.1088/0741-3335/40/1/002 U. Stroth, ''A comparative study of transport in stellarators and tokamaks'', Plasma Phys. Control. Fusion '''40''' (1998) 9]</ref>
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== Quantification methods ==
== Quantification methods ==


It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify 'criticality' somehow.
It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify 'criticality' somehow:
<ref>[http://dx.doi.org/10.1088/0741-3335/43/11/306 F. Imbeaux, F. Ryter, and X. Garbet, ''Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model'', Plasma Phys. Control. Fusion '''43''' (2001) 1503]</ref>
<ref>[http://dx.doi.org/10.1088/0741-3335/43/11/306 F. Imbeaux, F. Ryter, and X. Garbet, ''Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model'', Plasma Phys. Control. Fusion '''43''' (2001) 1503]</ref>
<ref>[http://dx.doi.org/10.1088/0741-3335/46/9/002 X. Garbet, P. Mantica, F. Ryter, et al., ''Profile stiffness and global confinement'', Plasma Phys. Control. Fusion '''46''' (2004) 1351]</ref>
<ref>[http://dx.doi.org/10.1088/0741-3335/46/9/002 X. Garbet, P. Mantica, F. Ryter, et al., ''Profile stiffness and global confinement'', Plasma Phys. Control. Fusion '''46''' (2004) 1351]</ref>
:<math>\chi = \chi_0 + \chi_1 \xi \left ( \frac{R}{L_T}-\frac{R}{L_{T,crit}}\right )^\alpha H_c</math>
Here, ''H<sub>c</sub>'' is a step function (to activate supercritical transport), ''L<sub>T</sub>'' is the temperature gradient scale length, and &chi; is the heat transport coefficient.
However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model.<ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, ''Quantifying profile stiffness'', Plasma and Fusion Research, '''3''' (2008) S1070]</ref>
However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model.<ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, ''Quantifying profile stiffness'', Plasma and Fusion Research, '''3''' (2008) S1070]</ref>


== References ==
== References ==
<references />
<references />

Revision as of 13:58, 18 March 2011

Profile consistency (or profile resilience) is the observation that profiles (of temperature, density, and pressure) often tend to adopt roughly the same shape (in tokamaks), regardless of the applied heating and fueling profiles. [1] [2] The resulting (stiff) profiles are known as canonical profiles. [3] This phenomenology is due to plasma self-organisation, [4] i.e., the feedback mechanism regulating the profiles (by turbulence) is often dominant over the various source terms. [5]

Observations (tokamaks)

Observations (stellarators)

Quantification methods

It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify 'criticality' somehow: [12] [13]

Here, Hc is a step function (to activate supercritical transport), LT is the temperature gradient scale length, and χ is the heat transport coefficient.

However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model.[14]

References

  1. ↑ B. Coppi, Nonclassical Transport and the "Principle of Profile Consistency", Comments Plasma Phys. Cont. Fusion 5, 6 (1980) 261-270
  2. ↑ Yu.N. Dnestrovsky et al, Sov. J. Plasma Phys. 16 (1990) 120
  3. ↑ Yu.N. Dnestrovsky et al, Canonical profiles in tokamak plasmas with an arbitrary cross section, Plasma Physics Reports 28, 11 (2002) 887-899
  4. ↑ Yu.N. Dnestrovsky et al, Self-organization of plasma in tokamaks, Plasma Physics Reports 31, 7 (2005) 529-553
  5. ↑ F. Jenko et al, Critical gradient formula for toroidal electron temperature gradient modes, Phys. Plasmas 8 (2001) 4096
  6. ↑ E.D. Fredrickson, J.D. Callen, et al., Heat pulse propagation studies in TFTR, Nucl. Fusion 26 (1986) 849
  7. ↑ G. Becker, Electron temperature profile invariance in OH, L- and H-mode plasmas and consequences for the anomalous transport, Nucl. Fusion 32 (1986) 81
  8. ↑ F. Wagner and U. Stroth, Transport in toroidal devices-the experimentalist's view, Plasma Phys. Control. Fusion 35 (1993) 1321
  9. ↑ F. Ryter, C. Angioni, et al., Experimental studies of electron transport, Plasma Phys. Control. Fusion 43 (2001) A323
  10. ↑ U. Stroth, A comparative study of transport in stellarators and tokamaks, Plasma Phys. Control. Fusion 40 (1998) 9
  11. ↑ Yu.N. Dnestrovsky et al, IAEA Fusion Energy Conference, Geneva (2008) TH/P8-24
  12. ↑ F. Imbeaux, F. Ryter, and X. Garbet, Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model, Plasma Phys. Control. Fusion 43 (2001) 1503
  13. ↑ X. Garbet, P. Mantica, F. Ryter, et al., Profile stiffness and global confinement, Plasma Phys. Control. Fusion 46 (2004) 1351
  14. ↑ B.Ph. van Milligen et al, Quantifying profile stiffness, Plasma and Fusion Research, 3 (2008) S1070
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