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Topics 1 Progress on codes and results on stabilization of resistive wall modes including fast flowing liquid metals 2 Sputtering limitations on a hot scrape off layer with Lithium 3 Progress on exhausting the plasma outside the TF coils 4 A new ultimate upper limit on energy confinement has been found which appears reachable with this concept 5 Engineering possibilities for solid walls when exhausting the plasma outside the TF coils More Realistic Model to Examine Resistive Wall Kink Mode Stability Recall kink modes set the beta limit on tokamaks the relevant kinks are mainly driven by pressure Acceptable E must stabilize resistive wall kinks Up till now analysis code results for fast liquid metal LM stabilization has used simplified models with current driven kink modes Results are only qualitatively valid at best New model have modified ideal MHD GA code examine flowing LM stabilization of pressure driven kinks Presently still some simplifications 1 circular geometry 2 only high toroidal mode numbers 3 simplified pressure profiles Work is well on track to remove limitations 1 and 2 Despite simplifications new model is much better Realistic features of present Unrealistic feature of Model current driven model Pressure driving term with toroidal curvature and poloidal mode coupling No curvature No poloidal mode coupling High n modes become up down anti symmetric All modes are up down symmetric Kink ballooning resistive wall instabilities for n 5 10 like ARIES RS ARIES AT Instabilities for all n Ideal wall distance for stabilization constant for high n Widely varying wall stabilization distances with n some 0 Results New trends found which are not present in the current driven model Low intermediate n modes can be destabilized by high enough flow Different behavior for 1 flow from top to bottom standard CLIFF 2 flow from inboard to outbord L Zakharov For standard CLIFF High n modes are practically impossible to stabilize There is no velocity to stabilize high n modes without destabilizing low n modes Inboard to Outboard Flow Inboard to Outboard flow Growth rate of n 3 5 and 7 resistive wall kink mode vs flow magnetic Reynolds number 2 W wall n n 3 n 5 1 n 7 0 0 0 5 1 1 5 2 1 2 Flow Magnetic Reynolds Number The n 3 mode is not strongly stabilized The n 3 mode is destabilized by large LM flow Recall Flow R 1 Flow R 1 7 m s for Li 14 m s for Sn Up to Down Flow 2 5 Up to Down flow Growth rate of n 3 5 and 7 resistive wall kink mode vs rotation magnetic Reynolds number 2 Growth rate W wall n n 3 n 5 1 n 7 0 0 1 2 3 4 5 6 1 2 Flow Magnetic Reynolds Number The n 3 mode is again destabilized by large flow velocities Stabilization of the n 5 and n 7 modes requires impractical flows No flow simultaneously stabilizes n 3 and n 5 Future Work Within the next 3 months modify the code to Remove the restriction to high n modes Allow non circular geometry Examine other resistive wall kink mode stabilization schemes Stabilization by plasma rotation Include novel walls described Aug2001 to reduce the plasma rotation velocity needed for stabilization Stabilizing effect of a hot scrape off layer Ultimately the code can be interfaced with WALLCODE to examine feedback stabilization Sputtering Limitations on the Use of Flowing Liquid Lithium Plasma Facing Surfaces It is known that liquid Li can have a sputtering coeficient greater than 1 which would probably lead to a Li runaway However the self sputtering coeficient of Li saturated with D 50 Li 50 D is 3 4 times lower than pure Li Recent analysis have assumed Li is saturated with D and find that sputtering is not a major issue Brooks et al J Nucl Mater 290 293 2001 185 190 However for parameters of interest to APEX I find that the Li probably will not be in the highly D saturated state This could have a serious impact on the viability of Li as a PFC and previous analysis probably need to be revisited Why is the Li Not Saturated There is a time limit on the exposure to a high D flux as in a divertor or limiter due to surface heating This limits the total D fluence per exposure Dispersal processes such as molecular diffusion in a liquid are probably adequate to prevent a high D concentration Numerical Example The maximum allowable temperature rise is probably 150 degrees Tmelt 150 deg 100 deg margin for heat exchanger maximum temperature 400 deg Exposure of Li to 1 6 MW for 3 sec gives a surface temperature rise of 91 degrees Moir Nucl Fus 37 pg 563 10 MW m2 exposure time limit of 21 msec Following Brooks we use a plasma temperature of 180 eV With a sheath of 3 T the energy per ion is Ti 3 Te plus 1 Te for each electron 2 18 2 10 MW m thus 6 9 x 10 D cm sec 17 2 Exposure time 021 sec 1 4 x 10 D cm What depth does this accumulate in Smallest possible distance D stopping distance 5 I estimate the stopping distance is roughly 2 x 10 cm Angle of incidence in the sheath is 70 degrees 6 peneteration depth 7 x 10 cm D density 2 x 10 22 D cm Liquid Li density 4 5 x 10 22 3 D cm 2 D Li 1 2 at the end of exposure and time averaged D Li 1 4 NOT 1 1 However this neglects any D dispersal mechanisms in the Liquid Li Molecular Diffusion Typical molecular diffusion coefficients in liquids are in 4 6 2 the range 10 to 10 cm sec I do not know the value for D in Li but I use the lowest of these numbers to estimate molecular dispersal 4 Over 21 msec the diffusion distance is 1 4 x 10 cm so D density 1 0 x 10 21 D cm 3 Surface Ratio D Li 1 45 or 2 D 98 Li NOT 50 D 50 Li Of course even slight fluid turbulence could disperse the D much more than molecular diffusion Nonetheless I conclude that one should use the sputtering coefficient of Li not LiD Consequences I have written an elementary orbit code and for what I think are reasonable sheath parameters and a low angle of inclination between B and the surface I find the average angle of incidence is 70 degrees The self sputtering coeficient SLi at 70 degree incidence and 500 eV is 1 35 and for 720 eV it is probably in the range 2 I understand that about 1 3 to 1 2 of the Li sputters are charged and so will not result in self sputtering Nonetheless the self sputtering coeficient of just the neutral Li appears close to 1 Note that the net sputtering from D SD is increased by a factor of 1 1 SLi due to the self sputtering of all the Li daughters of the original Li SD 2 …


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