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Lithium Walls: The Ultimate Technology for Fusion

Lithium Walls: The Ultimate Technology for Fusion. D.N. Ruzic, M. A. Jaworski 1 , T.K. Gray 1 , V. Surla, W. Xu, S. Jung, P. Raman 1 current address: Princeton Plasma Physics Laboratory. Outline. Introduction Why Lithium is so Good – but you all know that already !

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Lithium Walls: The Ultimate Technology for Fusion

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  1. Lithium Walls: The Ultimate Technology for Fusion D.N. Ruzic, M. A. Jaworski1, T.K. Gray1, V. Surla, W. Xu, S. Jung, P. Raman 1current address: Princeton Plasma Physics Laboratory

  2. Outline • Introduction • Why Lithium is so Good – but you all know that already ! • Solid/Liquid Lithium Divertor Experiment (SLiDE) • Experimental Facility • Results • Theory • Lithium Molybdenum Infused Trenches (LiMIT) • - How this could work for HT-7 and future devices • Lithium in Divertor Erosion Vapor Shielding Exp. (DEVeX) • Lithium in the Ion-Interaction Experiment (IIAX) • Conclusions

  3. What Very-Low Recycling Does for Fusion No cold hydrogen returns from wall: Plasma stays hot Standard Case Lithium Case Courtesy: PPPL

  4. Consequences of Lithium • Increased Confinement Time – seen across the world • Higher Temperatures • Suppression of ELMS (for tokamaks) • Control of Density is possible, even with NBI • Lower Z-effective • Less Fuel Dilution (seen on NSTX) • Negative Consequences? • Helium pumping? We have shown this! M. Nieto, D.N. Ruzic, W. Olczak, R. Stubbers, “Measurement of Implanted Helium Particle Transport by a Flowing Liquid Lithium Film”, J. Nucl. Mater., 350 (2006) 101-112. • Power handling? See the rest of this talk!

  5. First Evidence? TFTR Supershots(1984) Courtesy: PPPL

  6. What Can Go Wrong with a Lithium Divertor? • Lithium melts at 180 C and evaporates very quickly above 400 C So, it will have to be used ultimately as a flowing liquid • It is a liquid conductive metal and therefore subject to MHD effects. After all, fusion devices have large circulating currents and high magnetic fields. So, careful planning is needed. Maybe it’s MHD effects can be utilized? • It has an extremely low density (half of water) and high surface tension (4 times water) and therefore difficult to deal with. It is also highly corrosive to some materials, such as copper. So, careful engineering is needed and new materials (for fusion) need to be developed

  7. Outline • Introduction • Why Lithium is so Good – but you all know that already ! • Solid/Liquid Lithium Divertor Experiment (SLiDE) • Experimental Facility • Results • Theory • Lithium Molybdenum Infused Trenches (LiMIT) • - How this could work for HT-7 and future devices • Lithium in Divertor Erosion Vapor Shielding Exp. (DEVeX) • Lithium in the Ion-Interaction Experiment (IIAX) • Conclusions

  8. CDX-U Results - The Unexpected Happened Surface tension drives flow Qinput Centerstack Lithium in tray Visible image R. Majeski et al., “Final results from the CDX-U lithium program,” Presentation at 47th Annual Meeting of the Division of Plasma Physics (APS-DPP), Denver, Colorado, October, 2005. • Trying to melt lithium in CDX-U: • - 50 MW/m2heat flux redistributed from spot heat • - No evaporation despite lithium's tendency to do so (and purpose of e-beam run!)‏ • Why did the lithium melt the entire tray and not evaporate? • - First explanation was thermocapillary phenomena • - Temperature dependent surface tension resulted in flow and strong convection away from hot spot • - If true, will this work in a divertor without over heating the Li ?

  9. A Typical Fusion Heat Flux J.N. Brooks, et al. J. Nucl. Matl.337-339 (2005) 1053-1057. • Magnetic configuration concentrates power in “diverted” plasma • -Peak heat flux, steady-state typically 5-20 MW/m2 • -Radiant heat flux at solar surface is ~63 MW/m2 • -Transients can push the peak higher • Thermally driven phenomena depend on heat flux gradients, not just peak values

  10. SLiDE at Illinois - Overview E-beam source 10cm 25cm Current density profile 10cm 10cm Tray • Solid/Liquid Lithium Divertor Experiment (SLiDE)‏ • - Produces temperature gradients with an electron beam • - Creates magnetic field with external magnet system (these tests at normal incidence)‏ • - Measures temperature distribution in tray containing lithium • - Active cooling for steady-state operation • Camera system monitors surface velocity • Designed, constructed and operated for this work

  11. Machine Layout • A sheet electron beam hits an instrumented tray filled with lithium in a magnetic field. • Future versions will allow the tray to tilt so the angle between the heat flux and the field will be like in a tokamak – almost parallel.

  12. Electron Beam Drawings and Simulations There are four filaments, each 10cm long, parallel to eachother 7 keV, 2 A, 16 G 20 keV, 0.75 A, 1 kG

  13. Electron Beam • Designed to mimic divertor heat flux • - Actual run parameters shown in table • - Operated at 300W in this set of experiments – capable of 15kW, which is 35 MW/m2 ! • - Typical q0 in NSTX is ~10MW/m2 • - Typical dq/dx in NSTX is ~100 MW/m2-m . We matched this number. • Line source with gaussian profile

  14. Tray System Overview • Coolant supplied from building sources • - Water at 35 psi • - Compressed air at 80 psi • - Steady-state cooling with liquid lithium temperatures and input power range of 50W – 1500W (with stainless steel tray)‏ • 28 thermocouples within tray • - 14 positions for heat flux modeling • - 4 external TCs for coolant calorimetry

  15. Data Acquisition and Control • Thermocouple data acquired via computer system • - LABJACK USB data modules and amplifiers digitize analog signals. LabVIEW VI monitors temperatures in real time • - Control of magnets and eBeam voltage via computer system (filaments on manual)‏ • Post-run analysis handled semi-autonomously • - Analysis program written to reference and analyze data sets • - Output summarizes and formats for easy plotting and further analysis

  16. Camera System • Mirror used to view lithium surface • - Electron beam occludes direct view • - Mirror requires periodic cleaning from lithium evaporation • Two cameras used • - Low quality webcam for simple monitoring • - High quality, high-definition camera used for velocity measurement movies • - Both utilize mirror illumination provided by electron beam filaments

  17. Thermocapillary Flow, Basics Thermocapillary - “Thermo” meaning temperature - “Capillary” meaning related to surface tension - Temperature gradient on surface of a liquid creates surface tension gradients - Surface tension gradients result in flow generation Long history of study from mid-19th century Surface tension drives flow Qinput • Other surface tension driven flows • - “Tears” or “legs” in wine glass (concentration gradients from alcohol evaporation)‏ • - Soap boats with detergent droplet (concentration gradient)‏

  18. Thermoelectric MHD, Basics • Thermoelectric effect • - Causes thermocouple junction voltages • - Thermoelectric power present in most materials • - Electromotive force generated by temperature gradients • - Requires different material (or TE power) to provide current return path and generate current • Replace one material with a liquid in magnetic field • - TE current and B-field generate Lorentz foce

  19. Theory: TCMHD and TEMHD Thermocapillary and TEMHD produce different flow patterns TC forces act parallel to surface gradients in surface tension – force vectors radiate away from heat stripe (induce poloidal flow) TEMHD forces are produced in the bulk lithium due to gradients at the lithium-steel interface TE current the same process as produces voltages in thermocouple junctions Cross-product of JTEMHD and B results in azimuthal flow Beam generated forces (JxB) also result in an azimuthal flow (current converges into impact point) – sense of rotation is opposite of TEMHD Increased field damps both flows TCMHD is damped byB-2 TEMHD is damped as B-1 at high fields (due to thermoelectric propulsive force) Thermocapillary force vectors. TEMHD current diagram.

  20. Is it really TEMHD? Qualitative Tests • Magnetic field reversal • - Flow direction reverses upon reversal of field • - Flow is consistent and steady in swirl • Flow direction consistent with TEMHD source • - Mirror system reverses apparent sense of rotation • - Magnets measured to determine direction • - E-beam and TE have opposite rotation senses • Addition of insulator halts any swirling flow • - Quartz slides added between tray and lithium • - No flow observed at all in these cases

  21. Another test: “Spin Down” Test based on the time required for the lithium to come to a stop Viscous damping brings fluid to a rest without additional forces to maintain flow (seconds) Magnetic fields enhance the destruction of kinetic energy and spin down faster (confirmed with a mercury test) If thermoelectric currents exist, these will decay at the thermal time constant of the lithium-tray system (minutes) Maintaining the magnetic field will sustain the flow, as opposed to damping it Turning magnetic field back on after a viscous spin-down should induce motion once more Test procedure: • Obtain steady thermal conditions and lithium flow • Shut off beam and magnetic field and measure spin-down time • Return system to steady thermal conditions and lithium flow • Shut off beam but maintain magnetic field – measure spin-down time • Repeat step 2, but turn magnetic field back on after flow comes to rest and look for spin startup Movie of spin-down test “spinDown.mov”

  22. Quantitative Analysis: Velocity • Purpose: Bring together thermal and velocity measurements • Velocity measurements based on video analysis • - Particles measured on a frame-by-frame basis • - Multiple measurements made over course of particle visibility • - Radial distance also measured • Velocity and radius used to determine most likely velocity at r = 1cm • - u(r) ~ r0.5 based on Davidson swirling flow theory • - Consistent with SLiDE data

  23. Heat Flux Calculation • Time series data reduced • - Mean taken • - Standard error calculated by standard formulas • Fourier model applied to calculate heat flux • - Scaling factor applied to account for tray warping • - Radially symmetric pattern observed • - Most obvious in “off-center” sensor sets • - Radially symmetric pattern observed in all cases run • - Some TC pairs eliminated due to tray damage directly underneath beam strike

  24. Quantitative Prediction: TEMHD Moderate Hartmann number regime – TEMHD and MHD braking in equilibrium Dependent on thermoelectric power of the metal pair, P Temperature gradient along the interface determines flow velocity (for Ha > 1) Mean current density due to TE currents depends on geometry and conductivities (C variable) Velocity prediction can be converted to Reynolds number using depth as the characteristic length scale 1D current driven flow in a semi-infinite domain.

  25. TEMHD Solution 1: Semi-Infinite Domain • Solution for free surface • Identical to Shercliff, 1979 channel flow • Lithium-Iron example: P = 20e-6[V/K], h=5[mm], dT/dy = 1000[K/m] • Pre-factor = 8.4[m/s] • Solution depends on several factors • Hartmann again present • “C” is ratio of liquid/wall impedances • “Pre-factor” and velocity function {...}

  26. Bödewadt-Hartmann Flow • Bödewadt flow • - Rotating fluid over stationary disk • - Variation of Karman flow (rotating disk)‏ • - Use Karman similarity variables to analyze • Bödewadt-Hartmann flow • - Rotating flow with a magnetic field • - Non-dimensionalized system of equations results • Elsässer No. - Balance of MHD to Coriolis force

  27. Approximate Solutions for Velocity Profile • Make use of Davidson, 2002 approximate solutions • Linearized equations about core flow solution • Compares well with direct numerical integration • Aids further analysis Distance from wall

  28. Quantitative Assessment --- Consistent with Data • Theory of TEMHD driven swirling flow predicts radial velocities -- agrees with data ! No free parameters • Range of Hartmann number covers peaking area of swirling flow theory • Range of Elsässer number covers MHD and Coriolis dominated flows • Torque balance method works ! TEMHD fits observables.

  29. Spin Down Time Constant – Also Consistent • Spin down time requires thermal gradients to sustain currents • Thermal time constant of the system can be estimated • - Simple thermal resistance model applied • - Measurements from the system used to make calculation • - 78 seconds is theoretical thermal time constant • Observed spin down time is equivalent to 2-3 thermal time constants – and that is what is observed.

  30. Quantitative Prediction: Thermocapillary MHD • Consider a semi-infinite domain • - Free-surface at y=h • - Magnetic field B • - Surface subject to constant temperature gradient b • Two cases • - No return flow (dP/dx = 0)‏ • - Return flow (dP/dx related to height of the fluid)‏ • Surface tension boundary condition • - Surface tension gradient results in viscous shear at surface

  31. Which one does theory say is dominant?Ratio of Semi-Infinite Solutions • Ratio of TEMHD to TCMHD velocity: • - Ratio = 1 indicates equal effectiveness • - Ratio > 1 indicates TEMHD dominance • - Ratio depends on material parameters capture by dimensionless number, ς, the “Jaworski” number. • - Also depends on container geometry captured in F(Ha) function • In Lithium-steel system, TEMHD dominates for Ha > 1

  32. Ratio of TEMHD to TC in SLiDE • All quantitative data cases show evidence of swirling flow. • - TEMHD indirectly shown for Ha>1.4 by temperature • - TEMHD directly shown for Ha>17 • However, TC was capable of being seen in an oscillatory flow behavior. • TEMHD flow distributes heat and smooths out the gradient along the Li – steel interface • With no gradient there, only the surface temperature gradient exists, therefore TCMHD until interface gradient builds up again Jaworski Number was always greater than 1 !

  33. Can you see TCMHD in the lulls? • If conditions are right, when the TEMHD flow stops, TCMHD “Maragoni-effect” flow can be seen (motion on surface away from heated stripe due to surface temperature gradient causing a surface tension gradient) If conditions are right, when the TEMHD flow stops, TCMHD “Maragoni-effect” flow can be seen (motion on surface away from heated stripe due to surface temperature gradient causing a surface tension gradient) TCflowExample.mov

  34. Outline • Introduction • Why Lithium is so Good – but you all know that already ! • Solid/Liquid Lithium Divertor Experiment (SLiDE) • Experimental Facility • Results • Theory • Lithium Molybdenum Infused Trenches (LiMIT) • - How this could work for HT-7 and future devices • Lithium in Divertor Erosion Vapor Shielding Exp. (DEVeX) • Lithium in the Ion-Interaction Experiment (IIAX) • Conclusions

  35. 39 How Powerful is the ThermoElectric Effect? Apparatus for Seebeck Coefficient Apparatus for Seebeck Coefficient Measurement DV T + DT T Lithium Extrusion HEATER

  36. Big! Use it with what holds the Lithium There is a large difference in S between Li and most other metals and it increases with temperature.[3] • Like a thermocouple, a voltage is created at a junction of two metals dependent on the temperature.[1] • A current will flow based on that voltage difference: where σ is the conductivity, and ΔS is the difference in Seebeck coefficients.[2] Seebeck Coefficient of Li Black: our measurementsLithium Lithium j Molybdenum j

  37. Does it work? Yes! SLiDE Results • As I showed previously, TEMHD is real and moves Lithium at significant velocities. Theoretical vs experimental velocities : [4] M.A. Jaworski, et al. Phys. Rev. Lett. 104, 094503 (2010)

  38. The Idea: “LiMIT” Design HT-7 Cross-section: • Left is a cross-section of HT-7 showing the toroidal limiter. • Right is the LiMIT concept: molybdenum tiles with radial trenches containing lithium. The trenches run in the radial (polodial) direction such that they lie primarily perpendicular to the torroidal magnetic field. Plasma primary heat-flux location

  39. Lithium Flow in the Trenches is Self-Pumping Heat flux Hot Li flow Cooling channels Outlet Inlet Passive Li replenishment The top surface of the Li is hotter than the surface that is deeper. Therefore there is a VERTICAL temperature gradient • Concept for heat removal using TEMHD. The Li flows in the slots of the Mo plate powered by the vertical temperature gradient. This vertical temperature gradient generates vertical current, which when “crossed” by the torroidal magnetic field, will create a radial force on the Li driving it along the slot. This flow will transfer the heat from the strike point to other portions of the torroidal limiter. The bulk of the Mo plate could be actively cooled for a long-pulsed device or passively cooled for something like NSTX. Under the plate the Li flows back naturally. J F B

  40. Thermoelectric Driven Flow Calculation Heat flux: divertor strike point width, 1cm Z direction t w Flow h Grad T TE current B L • Look just at one channel. All channels are equivalent • The width of Li (w) is 1mm and the width of the Mo (t) trench is 1mm. The depth of Li (h) is 5mm. The length of the Li (L) is 100mm. The magnetic field is 2T. The heat flux on top surface is The unit for heat flux is MW/m2 and the unit for x is m. (based on the formal HT-7 heat flux data) This represents the divertor heat flux maximum value for the calculations here, but the concept should work for even higher values..

  41. Heat flux on the limiter (along radius direction) The heat flux figure is from F. Gao et al. Fusion Engineering and Design 83 (2008) 1–5 6 MW/m2 on our geometrical segment is 960 W

  42. Heat load on LiMIT: What Velocity is Needed? • The assumed heat flux means the 1mm Li slot needs to handle 960W heat load. • To put this in the proper perspective, the temperature rise over the 5 second shot of an uncooled one-half inch thick (1.2cm) Mo plate the same size as our imagined Li/Mo trench/finger can be calculated using as follows: E = 960W*5s = 4800 J. V = (0.2cm)(1.2cm)(10cm) = 2.4 cm3Cv=2.57 J cm-3 K-1 for Mo. Therefore the temperature rise for a passive plate is 778K. • To see if a flowing surface can remove that much power with a lower temperature rise, we can use the following equation [5] : • Here the first term is the heat conduction term and the second is the heat convection which transfers the heat along the trench. ΔT+ is the temperature difference across the depth of Li and ΔTll is the temperature difference between the inlet and outlet of the Li trench. When using the HT-7 heat flux data, and both temperature differences are assumed to be 200K, the velocity needed is u=35.2cm/s.With this flow the temperature rise would only be 200K.

  43. What Velocity is Generated by TEMHD ? • The Seebeck coefficient for Mo is about 13μV/K (at 400C). The value for Li reported in the literature and measured ourselves is 43μV/K (at 400Cfor a difference of 30μV/K • The current and velocity can be calculated with these two equations [1] [1] • Here P is the difference of Seebeck coefficient (thermoelectric power) between two material. Ha is the Hartmann number . C is a parameter coming from the conservation of current: • The velocity with a higher thermoelectric power is 59.6 cm/s. This is large enough to carry away the heat and prevent the Li from getting more than 200C hotter than when it came in.

  44. Further Analysis: 3D – FLUENT Calculation Mo plate Li channel 6MW/m2 heat flux Back flow of Li • What will really happen to the temperature of the Li when the strike point heat flux hits LiMIT? Is the 200K gradient assumption reasonable? A simple 3D heat transfer model is run with FLUENT. • FLUENT has convection flow and 3D heat transfer included. • Boundary Conditions: The Li flows through the slot between two Mo plate and flow back below the Li slot. The inlet velocity is set to be 60 cm/s. The initial temperature is 470K. The top heat flux is that on HT-7. The bottom temperature is set to be 470K as a constant. Will we remain under 670K as the one-D calculation indicated?

  45. Answer: Yes !!!! • Left figure is the temperature distribution of the top surface of Li slot and right figure is the temperature change along the center line of the top surface. • The temperature difference between the inlet and the outlet is about 200K– great! The highest temperature is 691K (418C). There will be evaporation there – which gives additional cooling not included in the model. Some evaporation (radiative cooling) is acceptable and even desired.

  46. Does the Radial Temp. Gradient Cause Ejection? Lorentz Force Heat flux B Li Grad T TE current Mo • One concern about using free surface Li is the ejection problem. The temperature gradient along the Li flowing direction will generate a thermoelectric current along the same direction and the Lorentz force may could eject the Li into the plasma. Fortunately the primary gradient pushes the Li downward. • On the inboard side, the force is upward. Similar to the capillary porous system (CPS) [6] which effectively has very narrow channels, LiMIT’s trench design has very narrow slots (1 mm) to utilize the capillary force to hold the Li in place. J J F F

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