Transcript Slide 1

Assessment and comparison of
pulsed and steady-state tokamak
power plants
Farrokh Najmabadi
UC San Diego
21st 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 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 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 < 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 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, 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-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
Aspect ratio
4.0
Plasma major radius (m)
9.2
Plasma minor radius (m)
2.3
Toroidal field on axis (T)
6.7
Toroidal field on the coil (T)
12
Plasma beta
2.8%
Plasma current (MA)
14
Bootstrap fraction
0.37
Neutron wall loading (MW/m2)
1.1
Cost of electricity (mills/kWh)
105∗
ARIES-I
4.5
6.75
1.5
11.3
21
1.9%
10
0.68
2.5
4.5
7.9
1.75
9
16
1.9%
10
0.68
2.0
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
Time
FW Operating Cycle with
warm shutdown
transients
Heat Flux (gradients)
Temperature
fabrication
normal operation
with shutdowns
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/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
Ta
ODS steel
W
coolant
Cu braze
mat’l
ε2d
εallowable
ODS
Ta
W
0.77%
0.54%
~0 %
~1%
5-15%
~1%
Ratcheting leads to strain (damage)
accumulation
Cold shutdown
Warm shutdown
(4 time steps per cycle)
 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
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˚C
Coolant temperature: 385 ˚C
Peak temperature: 582˚C
3Sm ~ 600 / 550 / 400 MPa
Elastic analysis
σ xy= 885 / 600 / 450
MPa
1
4
2
3
4
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.
Thank you!