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Langmuir probes, which protrude over the tile surface.

The temperature distribution caused by the static operation of the DED is in- homogeneous, contrary to the theoretical expectations from the early stage of in- vestigations of ergodic divertors [12]. The immanent feature of the DED heat flux density pattern are the stripe-like structures parallel to the DED coils. One can see four strike zones formed by the incoming heat fluxes. The regular patterns of heat deposition, which are formed by the laminar zone, have been identified since very first experiments with ergodic divertors (see e.g. [15] and [37]). The temperature distribution qualitatively resembles the basin structure of the field lines on the di- vertor wall. As it can be expected from the symmetry of the magnetic footprints, the heat fluxes form pattern with the four-fold symmetry.

One of the power flux stripes is marked in figure 4.8 with a yellow dashed line. In order to perform more detailed analysis of the temperature distribution and to evaluate the heat fluxes reaching the divertor wall one transforms the image of the tiles to a plane spanned by toroidal and poloidal coordinates. The image imperfec- tions due to the oblique view of the camera are corrected. This is performed with the LEOPOLD routines [10]. The result of processing the image from figure4.8with these routines is shown in figure4.9. The ordinate represents the distance along the tiles measured in millimeters, the abscissa the toroidal angle in degrees. The extent of the infrared view is about 50◦ _{in toroidal direction, which is slightly more than}

a half-period of the perturbation field for 12/4 mode. The target plates, which are closest to the left-hand side of the picture, are resolved with the lowest accuracy. This is caused by the small angle between the line of sight and the tiles.

4.5

Heat flux analysis

The heat flux density reaching the DED target plates consists mainly of the parallel heat flux density. The parallel heat flux density in the plasma edge is a sum of the ion heat flux density Qi and the electron heat flux density Qe and it is equal to:

90 CHAPTER 4. THERMOGRAPHIC MEASUREMENTS

region chosen for power flux evaluation

j[deg]

s[mm]

#92456

one of the four

helical power flux stripes

Figure 4.9: The infrared image produced by the camera processed with the LEOPOLD code. The image is deformed in such a way, that all the tiles lie in one plane (s-ϕ), where s is the poloidal coordinate along the tiles and ϕ the toroidal angle.

Q||≡Qi+Qe=γkTeΓ||, (4.1)

where γ is the sheath heat transmission coefficient, Te the electron temperature

at the plasma edge and Γ|| the particle flux density to the wall [55]. The heat

transmission factor is solved in the sheath problem and is connected to the theory of the Langmuir probes. For Ti =Te it has a value of about γ ≈7. The deposited

heat flux density on the divertor target plates Q is a function of the parallel heat flux density and the cosine of the angle between the surface normal and the field line along which the heat reaches the wall: Q=Q||cosα. The typical angles of incident

4.5. HEAT FLUX ANALYSIS 91 0 100 200 300 400 500 30 35 40 45 poloidal coordinate s [mm] temperature T [°] 0 100 200 300 400 500 0 5 10 15x 10 4 poloidal coordinate s [mm] heat flux Q [W/m 2 ] #92456 @ t = 1.5 s #92456 @ t = 1.5 s a) b)

Figure 4.10: a) The temperature profile measured on the divertor target plates taken from the region marked with the yellow rectangle in figure 4.9; b) the power flux profile evaluated with the THEODOR code for the same time as in a).

deposited heat flux density is a very small fraction of the parallel heat flux density (Q . 0.02Q||). However, it must be added that the sheath theory breaks down at

angles of incidence ofα <5◦_{. The results have to be taken therefore with some care.}

To evaluate the structure of the power fluxes reaching the target plates the area marked with the yellow rectangle in figure 4.9 was chosen. The main advantage of this choice is that here the tiles are free of overheated regions. However some reduction of the incoming heat fluxes due to shadowing takes place, as shown in figure4.13. The region covers about one degree in toroidal direction atϕ= 187◦_{. For}

92 CHAPTER 4. THERMOGRAPHIC MEASUREMENTS

the heat flux density calculations the temperature profile averaged over the toroidal extent is used. The heat flux density is derived with the “THEODOR” code [44], which is the 2D heat flux density calculation (see appendix B). The temperature profile taken from the yellow rectangle and calculated with the THEODOR a power flux profile is shown in figure 4.10. Both profiles are plotted against the poloidal coordinate. The temperature is modulated in the range from 30 ◦_{C in between}

the power flux stripes to about 40 ◦_{C in the warmest place, which corresponds to}

the maximum of the heat flux density in figure 4.10b). The perturbation field is relatively low IDED = 5 kA, therefore the level of ergodization is rather small. One

can see that the stripes are not split up. The heat flux density reaches its maximum at s= 157 mm, which isQmax ≈1.4·105 Wm−2. The heat flux density in between

the stripes is of the order ofQ= 3.5·104 _Wm−2_{. The width of the two inner power}

flux stripes is about 90 mm. The two outer ones have a width of about 80 mm. The central two strike zones carry more heat flux density than the outer ones. The main reason results from the inward shift of the plasma. Thus, the poloidal curvature of the plasma is smaller than that of the target plates. When neglecting the field deflections due to the DED, the equatorial midplane at the HFS would form the tangent point to the plasma, where the highest heat load would be located. It is impossible to make an power balance, while the non-uniformity of the heat load on the target plates, caused by the misalignment is too strong. The other reason is that other limiters had contact with the plasma bulk.

4.6

Comparison of predicted magnetic structures

and measured heat fluxes

During most experiments with the DED, the plasma position was shifted to 1.70 m6

R0 6 1.72 m. The magnetic equilibrium model [4] used in the Atlas is written

for the standard “position” of R0 = 1.75 m and does not take into account the

different curvatures of the plasma and the target surface. Therefore the model is valid for plasmas with major radius of about 1.74, 1.75 m, which are the typical

4.6. MODELLED STRUCTURES AND THE MEASUREMENTS 93