Plasma conditions JET for which bifurcation occurs

Finally the effects of ion temperature, ion density and magnetic field on the heat flux and for JET will be investigated. Only the upper boundaries will be discussed analogue to MAST and TEXTOR.

The procedures in order to determine the effect of the ion temperature, the ion density and the magnetic field are also similar to MAST.

3.5.1 Effect of ion temperature on the transition region

Figure 31: JET - Effect of the ion temperature on the upper boundaries of the transition region.

The ion temperature T_i is variable and takes the values in the interval [1,6 10^-16 J; 8,0 10^-16 J] (or [1 10³ eV ; 5 10³ eV]). with step size or increment 3,2 10^-17 J (or 200 eV). In the figure above, both the upper boundary of the total heat flux and the upper boundary of the ratio are plotted in function of the ion temperature (Fig. 31). There can be observed that increasing the ion temperature

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increases the upper boundary of both the total heat flux and . At 5,8 10^-16 J (or 3,6 10³ eV), a turning point appears where the upper boundary of both total heat flux and increases rapidly.

Before the turning point ( ) it appears the upper boundary on evolves to a constant value ( ). At and beyond this turning point however, rapidly increases proportional to .

3.5.2 Effect of ion density on the transition region

For , decreases with increasing ion density ni imposing that the range of values of in the interval diminishes for a ion density (Fig.

32). However, the upper boundary of the heat flux QM increases quadratic for ni in the interval [5 10¹⁸ ; 5 10¹⁹ ]. At and beyond , the slope of the curve ( ) increases in comparison to the slope of the curve before (keeping in mind the slope is negative due to decreasing trend of the curve ( )).

Figure 32: JET - Effect of the ion density on the upper boundaries of the transition region.

3.5.3 Effect of magnetic field on the transition region

As discussed previously for MAST and TEXTOR, the effect of the toroidal magnetic field in JET on the transition region of JET does not deviate from the behavior established in MAST and

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TEXTOR. The upper boundary and by extension the range of values are not influenced by the alternating magnetic field (Fig. 33). Only the upper boundary of the heat flux exponentially decreases with increasing magnitude of the magnetic field. The data points (B , Q_M) can be fitted with a two term exponential model (Fig. 34), i.e.

( )

Figure 33: JET - Effect of the magnetic field on the upper boundaries of the transition region.

Figure 34: JET - Exponential fitting of the data points.

2 2.5 3 3.5 4 4.5 5 5.5 6

0 1 2 3 4 5 6x 10⁴

Magnetic field B (T) Upper boundary heat flux Q M (J/m²s)

JET: Exponential fitting of the effect of magnetic field on the transition region

QM(B)

Two term exponential

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3.5.4 Combined effect of varying plasma parameters on the transition region

As for MAST and TEXTOR, the combined effects of various plasma and tokamak parameters on the upper boundaries QM and will be plotted by means of contour-plots. As opposed to the previous tokamaks, the upper boundary and by extension the interval is not significantly dependent on changes in ion temperature and ion density (Fig. 35). For the upper boundary increases slightly with increasing ion temperature evolving to 0,152 for high ion temperature ( 5,5 .10^-16 J) and low ion density ( ). The boundary has only evolved between the values . Compared to MAST and TEXTOR, the effect of ion temperature and ion density on the upper boundary of JET is insignificantly.

Figure 35: JET - Combined effect of varying the ion temperature and ion density on the upper boundary of for a constant magnetic field (4,0 T).

Also the calculated ENBI (16) will be plotted against the ion temperature Ti and the ion density ni

(Fig. 36). The point A represent the upper boundary of the transition region of JET at

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the corresponding typical values of ion temperature (Ti = 4,8 .10^-16 J), ion density (ni = 5 .10¹⁹ ) and magnetic field (B = 4,0 T) discussed in section 3.2.3. It also indicates the corresponding lower boundary of E_NBI, i.e. . There should be noticed the required for a bifurcation to occur, is minimal where T_i < 4,8 .10^-16 J. The minimal value of is not strongly depended on n_i. That is, the required is minimal for .

Figure 36: JET - The lower boundary of ENBI (in keV) at specific ion temperatures and densities for a constant magnetic field (4,0 T).

Finally the combined effect of varying the ion temperature, the ion density and the magnetic field is investigated with regard to the upper boundary of the heat flux Q_M (Fig. 37). On the next page, the contour-plots of Q_M(T_i ; n_i) at certain values of magnetic field B are given. It is clear as the magnetic field B increase the upper boundary Q_M decreases. Overall the upper boundary of the heat flux reaches its minimum values for J and .

Also the corresponding required input beam power P_NBI can be calculated using (16b) The results can be found in Appendix E. The minimal required P_NBI for which a bifurcation can occur is 1 MW.

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Figure 37: JET - Combined effect of varying plasma parameters on the upper boundary of the total heat flux (in J/m²s) for different values of the magnetic field (3,5 T ; 4,0 T ; 4,5 T).

JET: Combined effect of varying ion temperature and ion density on the upper boundary of the heat flux (in J/m²s) for a constant magnetic field (4,50 T)

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4. Conclusion

A suppression of the turbulent transport of heat is essential in improving the confinement of energy.

There exist an interval of flow shear values where turbulence is suppressed. Suppression of turbulence results into a bifurcation which leads to a reduced transport state. Based on typical plasma and tokamak parameters of MAST, TEXTOR and JET (Appendix B), their transition regions can be constructed. It is referred to as a transition region because when a bifurcation is manifest for each value of within [ , ], a transition in and κ is observed for each value of Q within [Q_m , Q_M].

In general, increases with increasing ion temperature and decreasing ion density whereas the input heat flux and neutral beam particle energy ENBI decreases with increasing ion temperature and decreasing ion density. Also the magnitude of the magnetic field can be varied. The input heat decreases exponentially with the increasing magnitude of the magnetic field. A behavior which has been observed for every tokamak. However, the ratio does not change when varying the magnetic field.

Finally, the plasma conditions can be determined for which a bifurcation can easily occur (Table 1).

That is when the required (lower boundary) neutral beam particle energy for which a

Together with the given plasma parameter regions (Table 1), a bifurcation could occur requiring a minimal input of neutral beam particle energy and input beam power. These results however are based on the theoretical model of [1]. Several assumptions were made: The simulation volume has been confined to a flux tube and the deposition of the neutral beam particle energy ENBI and momentum is assumed to be uniform across the torus. Furthermore, only the region of zero magnetic shear has been discussed since a bifurcation is less probable to occur in a region of non-zero magnetic shear. Further investigation on this topic is necessary.

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5. Appendices