Tokamak Plasma’s Heat Conductivity as constructed from

Experimental Measurements and Observations

Speaker : Chung Hsieh 谢中立Nov. 11, 2009 @ Hefei

The path traveled to search for the thermal diffusivity

Google Search : “ kadomtsev on hsieh's thermal conductivity for tokamak plasma ”

• Plasma transport in tokamaks•  - 2 visits - Nov 8 Kadomtsev, combined with the constraint that the

plasma magnetic ... formulation the thermal conductivity depends on the space derivatives of the ...www.iop.org/EJ/article/0741-3335/35/12/002/pp931202.pdf - Similar -by E Minardi

• [PS] Non-linear phenomena in tokamak plasmas• File Format: Adobe PostScript

p( ) profile are the plasma particle diffusion and thermal conductivity. ..... simple Kadomtsev model. But in large tokamaks sawtooth oscillations are much ..... A third model was developed recently by Hsieh et al (1993) on the data ...www.iop.org/EJ/article/0034-4885/59/2/001/r602r1.ps.gz - Similar -by BB Kadomtsev - 1996 - Cited by 8 - Related articles - All 6 versions Show more results from www.iop.org

A third model was developed recently by Hsieh et al (1993) on the data base of the DIIID tokamak. The corresponding semi-empirical expression for the electron thermal diffusivity is given by the relation

The last factor in this expression was chosen to get the best fit of the experimental Te profile. All other factors were fitted to reproduce the major parametric dependencies observed for global energy confinement time in L- and H-mode plasmas,

where Ip is the plasma current and P is the heating power. The expression (24) gives a good fit for the electron temperature profile in the outer half of the plasma, r > 0:5a. The simulated profile shapes also remain insensitive to profile variation in the input power deposition, the plasma density and the current density (profile consistency). But some more delicate effects (for instance thermal pinch) in the internal part of the plasma are not described by the crude model of expression (24).

Non-linear phenomena in tokamak plasmas B B Kadomtsev 1996 Rep. Prog. Phys. 59 91-130

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r > 0.2 a

PLasma Phys. Control. Fusion 35 (1993) 1669-1684. Printed in the UK

Plasma transport in tokamaksE MinardiIstituto di Fisica del Plasma, Associazione EUR-ENEA-CNQVia Bassini 15, Milano. Italy

Received 16 November 1992, in final form 30 March 1993Abstract. The mechanism of high-power island pumping recently proposed by Kadomtsev, combined with the constraint that the plasma magnetic configuration of the tokamak is associated, under ohmic relaxation, with a stationary magnetic entropy (isoentropic state), allows the derivation of the iTER89-P scaling of the confinement time with considerable precision, particularly with respect to power. density and current. An equation for the thermal transport consistent with the requirements above is formulated and solved for a simple example of inhomogeneous heat deposition. In this formulation the thermal conductivity depends on the space derivatives of the temperature. The profile resiliency of the temperature follows from a certain idealized condition discussed in the paper (uniform magnetic braiding). which when combined with ohmic relaxation is characteristic of the isoentropic states. The formalism also implies a relation between the density profile and the space derivatives of the temperature. The implications of the Kadomtsev scaling of the diffusivity on the dependence of the bifurcation thresholds between the isoentropic state and H-mode, with respect to power, density and magnetic field, are also discussed.Print publication: Issue 12 (December 1993)

Impression on Minardi’s abstract and other thoughts

• It appears interesting that Minardi has used all the right key words even though I do not understand some of them – The derivation of ITER89P confinement scaling; the thermal diffusivity that contains the temperature spatial gradient; the profile resilience followed from the uniform magnetic braiding in combination with ohmic relaxation; Kadomtsev’s island pumping mechanism; diffusivity scaling on the bifurcation between L and H mode plasmas. It ought to be an interesting effort to know what is in the Minardi’s paper.

• Going beyond the words, I believe that it is essential to find whatever can be tested experimentally. For instance, can the uniform magnetic braiding (in term of magnetic fluctuation?) be measured? Can the features of Kadomtsev’s island pumping model be tested in an experiment? To an experimentalist, a model without tests is at best an empty model.

• Based on the energy confinement data, we have shown the heat conduction process of H mode plasma is essentially the same as that of L mode. What has changed is the boundary condition that make the H plasma as the internal part of a larger L plasma. We don’t know what decides the boundary condition and how the H mode boundary comes into being, so the boundary is the subject of interest, especially after one gets tired to see the same core Thomson measurements over and over because of the profile resilience.

• This leads to the need to have Thomson measurements for the plasma boundary region.

• DIII-D Thomson measurement covers the boundary region with a minimum of 3 spatial channels and it has been considered inadequate by some for the boundary study. The on-going Thomson upgrade will try to improve both the spatial and temporal resolutions.

• It is a rather difficult task for East Thomson to find a path through the machine for the Boundary Thomson Setup because of mechanical limitations. The matter may need some attention and decision.