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
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 β 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 currentdrive power vs issues associated with pulsed operation.
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
System Level Issues Thermal Energy Storage
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.
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,
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)?
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. 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
Tokamak-specific Issues
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 (εβ p 1) and raise on-axis q Can achieve 60%-70% bootstrap fraction with β 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 β (no control of current profile). Can achieve 30%-40% bootstrap fraction with β N 2.7-2.9. Optimizes at larger plasma current, medium aspect ratio, and higher β.
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.
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.
Engineering Design of Power Components
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).
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.
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).
Examples of birth-to-death thermal cycles. Fabrication Cycle fabrication normal operation with shutdowns transients Temperature Heat Flux (gradients) Time FW Operating Cycle with warm shutdown
He-cooled W divertor explored in the ARIES Designs T-tube Plates with jet and/or pin-fin cooling Finger Finger/plate combinations
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 But plastic strain (one cycle) is well within the 1% strain limit (ε ue /2)
External transition joints help alleviate one of the more challenging aspects of HHFC s W Ta ODS steel coolant mat l ε 2d ε allowable ODS 0.77% ~1% Ta 0.54% 5-15% W ~0 % ~1% Cu braze
Ratcheting leads to strain (damage) accumulation Cold shutdown Warm shutdown (4 time steps per cycle) 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
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
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 Elastic analysis σ xy = 885 / 600 / 450 MPa 1 4 4 2 3 2 3 1 Plastic analysis σ xy = 460 / 200 / 90 MPa
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.
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