Assessment and comparison of pulsed and steady-state tokamak power plants

Farrokh NajmabadiUC San Diego

21st International Toki Conference, 28 Novemeber-1 December 2011Toki, 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 bN 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 1st 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.

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 < 2oC/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 cp (Tcharge-Tdischarge) Rate of change of storage temperature, DT/ Dt, is set by the power cycle. Small DT/ Dt 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 Tdischarge to operating temperature (> Tcharge) which could result in large strains. There is substantial benefit in minimizing (Tcharge-Tdischarge) 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 systemEnergy accumulated in the outer shieldD=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, 1st stability tokamaks (monotonic q profiles) Require minimization of current drive power Operate at high aspect ratio (to reduce I), maximize bootstrap

fraction (ebp 1) and raise on-axis q

Can achieve 60%-70% bootstrap fraction with bN 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 b

(no control of current profile). Can achieve 30%-40% bootstrap fraction with bN 2.7-2.9. Optimizes at larger plasma current, “medium” aspect ratio, and

higher b.

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-upo Large Joule losses in cryogenic structureso Reduced coupling of PF coils to the plasmao 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 7.9Plasma 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 10Bootstrap 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 PL+PB<3Sm where Sm=min(1/3 Su, 2/3 Sy).

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 eue) instead of 3Sm

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

FW Operating Cycle with warm shutdown

Time

Tem

pera

ture

Hea

t Flu

x (g

radi

ents

)

fabricationnormal operation with shutdowns transients

He-cooled W divertor explored in the ARIES Designs

Plates with jet and/or pin-fin cooling

Finger/platecombinations

T-tube

Finger

Inclusion of yield extends finger divertor limits

Elastic analysis,15 MW/m2 Elasto-plastic analysis,15 MW/m2

SF= Allowable (3Sm) / Maximum stress

SF > 1 to meet the ASME 3Sm 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 (eue/2)

External transition joints help alleviate one of the more challenging aspects of HHFC’s

mat’l ε2d εallowable

ODS 0.77% ~1%Ta 0.54% 5-15%W ~0 % ~1%

Cu braze

WTa ODS steel

coolant

Ratcheting leads to strain (damage) accumulation

Design does not meet 3Sm 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

A modified first wall concept using W pins was proposed to better resist transients

Goal of 1 MW/m2 normal, 2 MW/m2 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˚CCoolant temperature: 385 ˚CPeak temperature: 582˚C3Sm ~ 600 / 550 / 400 MPa

4

1

2

3

Elastic analysisσ xy= 885 / 600 / 450 MPa

Plastic analysisσ xy= 460 / 200 / 90 MPa

1

2 3

4

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.

Thank you!