1. Assessment and comparison of pulsed and steady-state tokamak power plants Farrokh Najmabadi UC San Diego 21 st International Toki Conference, 28 Novemeber-1 December 2011 Toki, Japan

2. Choice between steady-state and pulsed operation is purely an economic consideration  A widely-held belief is that steady-state operation of a tokamak needs a high bootstrap fraction (e.g., > 85%). It requires operation in reverse-shear mode with high  N and a high degree of control of plasma profiles. Thus, steady-state operation requires a major extrapolation from present data base.  However, the first steady-state power plant proposals (ARIES-I and SSTR) operated in the 1 st stability regime (monotonic q profile)  Both designs had bootstrap fraction ~60-70%  Required current-drive powers of 70 MW (SSTR) to 100-150 MW (ARIES-I & ARIES-I’ versions).  In fact, ARIES-I plasma profiles are very similar to “Hybrid” mode (sans pedestal) and a high-degree of profile control is NOT required.  Thus, the trade-off is between the cost of additional current- drive power vs issues associated with pulsed operation.  A widely-held belief is that steady-state operation of a tokamak needs a high bootstrap fraction (e.g., > 85%). It requires operation in reverse-shear mode with high  N and a high degree of control of plasma profiles. Thus, steady-state operation requires a major extrapolation from present data base.  However, the first steady-state power plant proposals (ARIES-I and SSTR) operated in the 1 st stability regime (monotonic q profile)  Both designs had bootstrap fraction ~60-70%  Required current-drive powers of 70 MW (SSTR) to 100-150 MW (ARIES-I & ARIES-I’ versions).  In fact, ARIES-I plasma profiles are very similar to “Hybrid” mode (sans pedestal) and a high-degree of profile control is NOT required.  Thus, the trade-off is between the cost of additional current- drive power vs issues associated with pulsed operation.

3. Outline I.System-level issues which are generic to any pulsed power plant (e.g., thermal energy storage). II.Tokamak-specific issues: operating points and magnets. III.Engineering design of power components  Recent work on high-heat flux components I.System-level issues which are generic to any pulsed power plant (e.g., thermal energy storage). II.Tokamak-specific issues: operating points and magnets. III.Engineering design of power components  Recent work on high-heat flux components

4. System Level Issues – Thermal Energy Storage

5. A pulsed-power plant requires thermal energy storage  Connecting a power plant to the grid is NOT a trivial issue:  Utilities require a minimum electric power for a plant to stay on the grid.  Load balancing requires a slow rate of change in introducing electric power into the grid.  Overall, it is extremely expensive to attach an intermittent electric power source to the grid, a steady electric power is required.  Large thermal power equipments such as pumps and heat exchangers cannot operate in a pulse mode. For example, the rate of change of temperature in a steam-generator is < 2 o C/min in order to avoid induced stress and boiling instabilities.  Overall, a thermal energy storage is needed to ensure a constant thermal power flow to the “balance of the plant”.  Connecting a power plant to the grid is NOT a trivial issue:  Utilities require a minimum electric power for a plant to stay on the grid.  Load balancing requires a slow rate of change in introducing electric power into the grid.  Overall, it is extremely expensive to attach an intermittent electric power source to the grid, a steady electric power is required.  Large thermal power equipments such as pumps and heat exchangers cannot operate in a pulse mode. For example, the rate of change of temperature in a steam-generator is < 2 o C/min in order to avoid induced stress and boiling instabilities.  Overall, a thermal energy storage is needed to ensure a constant thermal power flow to the “balance of the plant”.

6. The thermal energy storage system is quite massive.  During the “dwell” time (no fusion power), thermal energy storage should supply thermal energy to the power cycle.  Stored energy = M c p  T charge -T discharge )  Rate of change of storage temperature,  T/  t, is set by the power cycle.  Small  T/  t leads to a large mass for the storage system with a complicated design to ensure a relatively uniform storage temperature.  During the dwell time, fusion core temperature will follow the storage temperature. At the start of the burn phase, fusion core components see a large temperature change from T discharge to operating temperature (> T charge ) which could result in large strains.  There is substantial benefit in minimizing  T charge -T discharge ) or the dwell time.  Other critical issues include tritium extraction and permeation to energy storage system, power needed for plasma start-up, …  During the “dwell” time (no fusion power), thermal energy storage should supply thermal energy to the power cycle.  Stored energy = M c p  T charge -T discharge )  Rate of change of storage temperature,  T/  t, is set by the power cycle.  Small  T/  t leads to a large mass for the storage system with a complicated design to ensure a relatively uniform storage temperature.  During the dwell time, fusion core temperature will follow the storage temperature. At the start of the burn phase, fusion core components see a large temperature change from T discharge to operating temperature (> T charge ) which could result in large strains.  There is substantial benefit in minimizing  T charge -T discharge ) or the dwell time.  Other critical issues include tritium extraction and permeation to energy storage system, power needed for plasma start-up, …

7. Pulsar thermal energy storage system Energy accumulated in the outer shield D=during the burn phase Thermal power is extracted from shield and is regulated by mass-flow-rate control during dwell phase  Limited storage capability (limited by shield mass and temperature limit) means limited dwell time (< 200 s).  This approach requires precise mass flow rate controlled and assumes good coolant mixing and temperature uniformity.  Judged by industrial people to be beyond current capabilities.  Extension to modern blanket design (such as DCLL)?  Limited storage capability (limited by shield mass and temperature limit) means limited dwell time (< 200 s).  This approach requires precise mass flow rate controlled and assumes good coolant mixing and temperature uniformity.  Judged by industrial people to be beyond current capabilities.  Extension to modern blanket design (such as DCLL)?

8. Thermal energy storage dictates design choices.  Thermal energy storage dictates many aspects of the design (including thermal conversion efficiency). In principle, it would be best to produce a credible storage design/power cycle before optimizing the tokamak.  Cost of thermal energy storage scales linearly with the dwell time.  Minimizing dwell time is important.  Thermal energy storage dictates many aspects of the design (including thermal conversion efficiency). In principle, it would be best to produce a credible storage design/power cycle before optimizing the tokamak.  Cost of thermal energy storage scales linearly with the dwell time.  Minimizing dwell time is important.  Efforts to increase pulse length beyond ~20 X dwell time have little benefits.  Average plant power already close to burn value,  Impact of reducing number of cycle by a factor of two on fatigue issues are small.  Efforts to increase pulse length beyond ~20 X dwell time have little benefits.  Average plant power already close to burn value,  Impact of reducing number of cycle by a factor of two on fatigue issues are small. Allowable stress for 316LN

9. Tokamak-specific Issues

10. Pulsed and steady-state devices optimize in different regimes  Steady-state, 1 st stability tokamaks (monotonic q profiles)  Require minimization of current drive power  Operate at high aspect ratio (to reduce I), maximize bootstrap fraction (  p  1) and raise on-axis q  Can achieve 60%-70% bootstrap fraction with  N  3-3.2  Current-drive power ~70-150 MW.  Typically optimizes at A ~ 4-6.  Pulsed plasma  Pressure (density/temperature) profile sets the achievable plasma  (no control of current profile).  Can achieve 30%-40% bootstrap fraction with  N  2.7-2.9.  Optimizes at larger plasma current, “medium” aspect ratio, and higher   Steady-state, 1 st stability tokamaks (monotonic q profiles)  Require minimization of current drive power  Operate at high aspect ratio (to reduce I), maximize bootstrap fraction (  p  1) and raise on-axis q  Can achieve 60%-70% bootstrap fraction with  N  3-3.2  Current-drive power ~70-150 MW.  Typically optimizes at A ~ 4-6.  Pulsed plasma  Pressure (density/temperature) profile sets the achievable plasma  (no control of current profile).  Can achieve 30%-40% bootstrap fraction with  N  2.7-2.9.  Optimizes at larger plasma current, “medium” aspect ratio, and higher 

11. Magnet systems for steady-state devices can be quite simpler  For steady-state devices (assuming a “long” start-up with current-drive assist), TF system can be substantially simpler  Typical ARIES magnets consists of TF coils bucked against a bucking cylinder. The overturning forces are reacted against each other through structural caps on the top and bottom of TF coils.  Pulsed plasma  Lower allowable stress on the structure and lower current-density in the conductor.  Torridly continuous structures are avoided as much as possible in order to minimize large eddy currents during start-up o Large Joule losses in cryogenic structures o Reduced coupling of PF coils to the plasma o Impact on plasma equilibrium and position.  For the same magnet technology, we found that the field in the coil is lower and magnet cost are substantially higher.  For steady-state devices (assuming a “long” start-up with current-drive assist), TF system can be substantially simpler  Typical ARIES magnets consists of TF coils bucked against a bucking cylinder. The overturning forces are reacted against each other through structural caps on the top and bottom of TF coils.  Pulsed plasma  Lower allowable stress on the structure and lower current-density in the conductor.  Torridly continuous structures are avoided as much as possible in order to minimize large eddy currents during start-up o Large Joule losses in cryogenic structures o Reduced coupling of PF coils to the plasma o Impact on plasma equilibrium and position.  For the same magnet technology, we found that the field in the coil is lower and magnet cost are substantially higher.

12. Even with shield-storage, we found the steady-state system to be superior. Major Parameters of ARIES and PULSAR Power Plants PULSAR ARIES-I Aspect ratio 4.0 4.5 4.5 Plasma major radius (m) 9.2 6.75 7.9 Plasma minor radius (m) 2.3 1.5 1.75 Toroidal field on axis (T) 6.7 11.3 9 Toroidal field on the coil (T) 12 21 16 Plasma beta 2.8% 1.9% 1.9% Plasma current (MA) 14 10 10 Bootstrap fraction 0.37 0.68 0.68 Neutron wall loading (MW/m2) 1.1 2.5 2.0 Cost of electricity (mills/kWh) 105 ∗ 83 ∗ Assuming the same plant availability and unit cost for components.

13. Engineering Design of Power Components

14. Engineering design of components in fusion is mostly based on elastic analysis.  Conservative design rules allow elastic analysis to be used, e.g. no ratcheting requires P L +P B <3S m where S m =min(1/3 S u, 2/3 S y ).  There are many design rules accounting for primary & secondary stress, fracture, fatigue, …  Design rules for high-temperature operation are incomplete (e.g., interaction of different failure mechanism such as creep & fatigue).  Conservative design rules allow elastic analysis to be used, e.g. no ratcheting requires P L +P B <3S m where S m =min(1/3 S u, 2/3 S y ).  There are many design rules accounting for primary & secondary stress, fracture, fatigue, …  Design rules for high-temperature operation are incomplete (e.g., interaction of different failure mechanism such as creep & fatigue).

15. “Plastic” analysis may yield a significantly larger design window for “steady-state”  For plasma-facing components (first wall, divertors) relaxation from local plasticity can significantly expand the design window, enabling operation at a higher heat flux.  Pulsed operation reduces the benefit significantly.  High temperature creep and creep-fatigue interaction will restrict the operating space even further. More analysis (and data) is needed.  Pulsed operation reduces the benefit significantly.  High temperature creep and creep-fatigue interaction will restrict the operating space even further. More analysis (and data) is needed.

16. We have performed “plasto-elastic” analysis of several components.  Three components were considered:  Finger-type divertor  Joint between W and Steel for the divertor  First wall (high heat flux and transients due to convective SOL).  3D elastic-plastic analysis with thermal stress relaxation (yield)  Application of accumulated strain limit (0.5 e ue ) instead of 3S m  Birth-to-death modeling (Fabrication steps, operating scenarios, off-normal events)  Plans to analyze high temperature creep and creep-fatigue interaction (which will restrict the operating space further).  Three components were considered:  Finger-type divertor  Joint between W and Steel for the divertor  First wall (high heat flux and transients due to convective SOL).  3D elastic-plastic analysis with thermal stress relaxation (yield)  Application of accumulated strain limit (0.5 e ue ) instead of 3S m  Birth-to-death modeling (Fabrication steps, operating scenarios, off-normal events)  Plans to analyze high temperature creep and creep-fatigue interaction (which will restrict the operating space further).

17. Examples of “birth-to-death” thermal cycles. Fabrication Cycle FW Operating Cycle with warm shutdown Time Temperature Heat Flux (gradients) fabrication normal operation with shutdowns transients

18. He-cooled W divertor explored in the ARIES Designs Plates with jet and/or pin-fin cooling Finger/plate combinations T-tube Finger

19. Inclusion of yield extends finger divertor limits Elastic analysis,15 MW/m 2 Elasto-plastic analysis,15 MW/m 2  SF= Allowable (3S m ) / Maximum stress  SF > 1 to meet the ASME 3S m criterion  The minimum elastic safety factor is 0.3 in the armor and 0.9 in the thimble  SF= Allowable (3S m ) / Maximum stress  SF > 1 to meet the ASME 3S m criterion  The minimum elastic safety factor is 0.3 in the armor and 0.9 in the thimble  But plastic strain (one cycle) is well within the 1% strain limit (  ue /2)

20. External transition joints help alleviate one of the more challenging aspects of HHFC’s mat’lε 2d ε allowable ODS0.77%~1% Ta0.54%5-15% W~0 %~1% Cu braze W TaODS steel coolant

21. Ratcheting leads to strain (damage) accumulation  Design does not meet 3S m criterion.  Cold shutdown is the most severe condition (considering 1050 C stress-free temperature).  In our case, ratcheting saturates after ~100 cycles.  Creep, fatigue, and creep-fatigue interaction are all expected to be more severe under cyclic loading  Design does not meet 3S m criterion.  Cold shutdown is the most severe condition (considering 1050 C stress-free temperature).  In our case, ratcheting saturates after ~100 cycles.  Creep, fatigue, and creep-fatigue interaction are all expected to be more severe under cyclic loading (4 time steps per cycle) Warm shutdown Cold shutdown

22. A modified first wall concept using W pins was proposed to better resist transients  Goal of 1 MW/m 2 normal, 2 MW/m 2 transient  W pins are brazed into ODS steel plates, which are brazed to RAFS cooling channels  Pins help resist thermal transients and erosion  Similar to micro brush concept developed for the ITER divertor  Minor impact on neutronics  Goal of 1 MW/m 2 normal, 2 MW/m 2 transient  W pins are brazed into ODS steel plates, which are brazed to RAFS cooling channels  Pins help resist thermal transients and erosion  Similar to micro brush concept developed for the ITER divertor  Minor impact on neutronics

23. Inclusion of thermal stress relaxation also extends the first wall performance Maximum ODS XY shear stress at: Room temperature: 20˚C Coolant temperature: 385 ˚C Peak temperature: 582˚C 3S m ~ 600 / 550 / 400 MPa 4 1 2 3 Elastic analysis σ xy = 885 / 600 / 450 MPa Plastic analysis σ xy = 460 / 200 / 90 MPa 1 23 4

24. Highlights  The trade-off is between the cost of additional current-drive power vs issues associated with pulsed operation.  Thermal energy storage is needed. It dictates many aspects of the design. It would be best to produce a credible storage design/power cycle before optimizing the tokamak.  Efforts to increase pulse length beyond ~20 X dwell time have little benefits.  Pulsed-plasma and steady-state plants operate at different plasma operating regimes.  Substantial simplification in TF design and capabilities for “long”, non-inductive start-up  Plasto-elastic analysis of plasma-facing components indicate a larger operating window for steady-state operation.  The trade-off is between the cost of additional current-drive power vs issues associated with pulsed operation.  Thermal energy storage is needed. It dictates many aspects of the design. It would be best to produce a credible storage design/power cycle before optimizing the tokamak.  Efforts to increase pulse length beyond ~20 X dwell time have little benefits.  Pulsed-plasma and steady-state plants operate at different plasma operating regimes.  Substantial simplification in TF design and capabilities for “long”, non-inductive start-up  Plasto-elastic analysis of plasma-facing components indicate a larger operating window for steady-state operation.

25. Thank you!