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"PROCESS": a systems code for fusion power plants - Part 2:Engineering

M Kovari, F. Fox, C. Harrington, R. Kembleton, P. Knight, H. Lux, J. Morris

arXiv:1601.06147v1physics.ins-detphysics.plasm-ph

TL;DR

Assessing fusion-plant engineering and economic feasibility requires whole-plant systems models. This paper describes PROCESS’s engineering models, which let users choose constraints and variables; in a pulsed-plant example, substantial changes in power requirement or coil current ratio produce comparatively small changes in major radius.

  • Problem

    Assessing whether a fusion plant is engineering- and economically feasible is an important complement to investigating plasma confinement.

    Source: §1 · p. 1

  • Method

    PROCESS uses simple plant models and user-selected constraints and iteration variables to optimize a chosen Figure of Merit, including models for energy conversion and availability.

    Source: §1 · p. 1, §7.3 · p. 14, §8 · p. 15

  • Results

    A 2.2-fold increase in output power grows major radius by only 9%; a fivefold increase in TF-coil operating-current-to-critical-current ratio reduces major radius by 12 cm (1.4%).

    Source: §9 · p. 20

  • Takeaways & Limitations

    Because users choose which constraints are enforced, evaluating PROCESS results requires checking the selected constraint list.

    Source: §10 · p. 21

    Safety, first-wall erosion, and fatigue-life algorithms are not yet included in PROCESS.

    Source: §10 · p. 21

Abstract

from arXiv · show

PROCESS is a reactor systems code - it assesses the engineering and economic viability of a hypothetical fusion power station using simple models of all parts of a reactor system. PROCESS allows the user to choose which constraints to impose and which to ignore, so when evaluating the results it is vital to study the list of constraints used. New algorithms submitted by collaborators can be incorporated - for example safety, first wall erosion, and fatigue life will be crucial and are not yet taken into account. This paper describes algorithms relating to the engineering aspects of the plant. The toroidal field (TF) coils and the central solenoid are assumed by default to be wound from niobium-tin superconductor with the same properties as the ITER conductors. The winding temperature and induced voltage during a quench provide a limit on the current density in the TF coils. Upper limits are placed on the stresses in the structural materials of the TF coil, using a simple two-layer model of the inboard leg of the coil. The thermal efficiency of the plant can be estimated using the maximum coolant temperature, and the capacity factor is derived from estimates of the planned and unplanned downtime, and the duty cycle if the reactor is pulsed. An example of a pulsed power plant is given.

1. Introduction`

Assessing a fusion plant’s engineering and economic feasibility requires reactor systems codes that model the whole plant. This paper describes PROCESS’s engineering models and its user-configurable optimization constraints.

1. Introduction`

  • Reactor systems codes collate simple models of a whole power plant, including physics, engineering, and costs, to assess engineering and economic feasibility.This paper focuses on the engineering assumptions and models.Source: §1 · p. 1
  • PROCESS adjusts user-selected iteration variables to optimize a chosen Figure of Merit while enforcing only the constraints the user specifies.The user can choose which parameters are inputs and which are outputs.Source: §1 · p. 1
  • The paper covers superconducting magnets, first wall, blanket and shield, thermal-power conversion, and availability models, then presents a pulsed DEMO model.The pulsed model is illustrated in Figure 1.Source: §1 · p. 2
  • Figure 1 shows cross-sections of the pulsed-reactor model, but omits explicit thermal shielding and diagnostic and remote-handling ports.The ports are omitted because PROCESS does not model them.Source: Figure 1 · p. 2

2. Toroidal field coil (TFC)

PROCESS models TF-coil access, current-density limits, quench protection, and structural stresses using user-selectable inputs and constraints. Its stress model uses a vault-supported coil and a simplified inboard-leg calculation.

2. Toroidal field coil (TFC)

  • The TF-coil model offers selectable constraints on case and conduit stress, operating-to-critical-current ratio, temperature margin, quench voltage, and quench temperature.The coil is represented as a homogeneous-current-density winding pack surrounded by a structural case; constraints apply only when selected by the user.Source: §2 · p. 2

2.1. Access required for neutral beams

  • Neutral-beam access is constrained by the maximum tangency radius allowed by TF-coil geometry; the model omits a possible conflict with full-height blanket modules accessed from above.Current drive is usually maximal when tangency radius equals or slightly exceeds the major radius.Source: §2.1 · pp. 2–3, Figure 2 · p. 3

2.2. TF coil current density

  • The default Nb3Sn critical-current model uses the ITER parameterization for magnetic field, temperature, and strain, with strand cross-section and copper fraction corrections.Cable geometry and helium coolant area are used to calculate conductor cross-section; the current per turn is an input and may be an iteration variable.Source: §2.2 · pp. 3–5

2.3. Quench protection of TFC

  • The maximum permissible winding temperature during a quench limits cable current density, while a user-set peak-voltage limit can further constrain the discharge.The model assumes thermal equilibrium among superconductor, copper, and helium, neglects conduit heat uptake and magnetic-field effects on copper resistivity, and assumes each dump resistor absorbs one coil’s stored energy.Source: §2.3 · pp. 5–6

2.4. Stress in the TFC

  • PROCESS assumes a vault supports the TF coils and calculates only steady-state stress in the inboard leg at midplane, excluding central-solenoid and poloidal-field coil fields.The model represents the winding pack as a homogeneous material and allows additional structural material, such as radial plates, to represent support for the cable.Source: §2.4 · pp. 6–7

2.4.1. Horizontal stress components

  • Horizontal stress is calculated with a two-layer winding-pack-and-case model, using radial displacement and force balance to derive stress across each layer.Peak tangential stress exceeds peak radial stress; the highest case and winding stresses occur at their respective innermost radii.Source: §2.4.1 · pp. 8–9

2.4.2. Vertical stress components

  • Vertical tensile stress in the inboard leg is obtained from the force on the upper coil half, with conductor stiffness neglected in the vertical direction.The model divides the tensile force by the case, conduit, and radial-plate area; the resulting extension is not a true conductor strain if the conductor is twisted.Source: §2.4.2 · p. 9

2.4.3. Stress criteria

  • The model calculates von Mises stress in the case and structural winding-pack material and constrains each peak to a user-specified permissible value.Both peak values occur at the inner radius; the winding-pack limit uses the larger value for the assumed radial and tangential webs.Source: §2.4.3 · pp. 9–10

3. Central solenoid (CS)

The central solenoid supplies voltage for plasma initiation and current ramp-up, and in pulsed reactors also helps maintain burn. Its structural steel is sized against allowable stress, but the model omits quench protection and cyclic fatigue.

3. Central solenoid (CS)

  • For pulsed reactors, the central solenoid supplies some of the voltage needed to maintain fusion burn, as well as supporting initiation and current ramp-up.Quench protection is not included.Source: §3 · p. 10
  • The model considers only steady-state stress in the central solenoid and does not account for cyclic fatigue, which may be significant in pulsed reactors.The CS contains structural steel with the same allowable stresses as the TF coils.Source: §3 · p. 10
  • Steel cross-section is sized from the hoop force and allowable stress, while superconductor current density accounts for steel and helium areas.Temperature margin is evaluated at Beginning of Flat-top and End of Pulse by comparing actual and critical current densities; the smaller margin is reported and can be constrained.Source: §3 · p. 10

4. Poloidal field (PF) coils

The PF-coil model derives turns and superconductor mass from the input conductor current and coil geometry. It sizes steel structure using permissible tensile stress and a specified share of hoop force.

4. Poloidal field (PF) coils

  • The input current per turn determines the number of turns from the coil's total current.Superconductor mass is calculated from cross-section, length, void fraction, and density.Source: §4 · p. 10
  • The PF-coil hoop force is calculated from coil radius, inner- and outer-edge fields, and peak current.The passage labels the fields BPF and BPF2, respectively.Source: §4 · p. 10
  • Steel cross-section and mass are sized using the maximum permissible tensile stress and a specified fraction of the hoop force.The required steel is not included in the dimensions output.Source: §4 · p. 10

5. First wall, blanket and shield

The first-wall neutron loading is estimated from neutron power and wall area, while component volumes are calculated using alternative geometric models. Blanket mass then follows from volume and assumed composition.

5. First wall, blanket and shield

  • Neutron wall loading is calculated by dividing neutron power by wall area.It is a nominal quantity that only loosely represents actual neutron flux, whose angular and energy spectra matter.Source: §5 · p. 10
  • Component volumes use either a D-shaped cross-section with a cylindrical inboard part or half-ellipses for both inboard and outboard parts.Blanket and shield top thicknesses are set to the mean of inboard and outboard thicknesses; vacuum-vessel thickness is constant.Source: §5 · p. 11, Figure 8 · p. 11
  • Blanket mass is determined by its volume and volumetric composition, which by default includes TiBe12, Li4SiO4, helium, and steel.Source: §5 · p. 11

6. Plant power balance

The plant power model separates useful primary heat from low-grade heat and estimates component nuclear heating using fitted functions. Neutron transport informs deposition, with a normalization assumption that all neutrons are absorbed.

6.1. Reactor power

  • Primary heat contributes to electricity production, whereas low-grade heat is rejected; the user specifies heating and current-drive wall-plug efficiency.The power-flow options are summarized in Table 2.Source: §6.1 · p. 11, Table 2 · p. 12

6.2. Power deposition

  • Nuclear power deposition in reactor components is derived from a neutron and secondary-particle transport model.First-wall and divertor photon power instead come from the radiation model described previously.Source: §6.2 · p. 12, Figure 10 · p. 12
  • Fitted functions estimate nuclear heating in each component, with deposition renormalized under the assumption that 100% of neutrons are absorbed.The fits use fusion power, component masses, and integrated line densities.Source: §6.2 · pp. 12–13

7. Heat extraction from first wall and electricity generation

PROCESS models heat extraction and electricity generation with either simplified blanket-based efficiencies or detailed coolant, first-wall, and power-cycle calculations. The detailed approach constrains first-wall temperature and stress, while the cycle model estimates efficiency from coolant outlet temperature.

7.1. Simple model

  • Primary-coolant pumping power is modeled as a user-input fraction of deposited coolant heat, with separate coolant assumptions allowed for each system.Default fractions are 0.0005 for water and 0.085 for helium.Source: §7.1 · p. 13
  • The simple model assigns blanket-specific cycle efficiencies and accounts for whether divertor heat is used or discarded.The efficiencies are fixed by blanket choice, without variation with primary coolant temperature; Table 3 defines the modeled cycle-efficiency scope.Source: §7.1 · p. 13, Table 3 · p. 13

7.2. Detailed model: first wall

  • The detailed first-wall model calculates peak temperature for specified coolant conditions and reduces wall thickness only when needed to meet material limits.It assumes parallel semicircular pipes, accounts for volumetric neutron and surface radiative heating, and returns an error if temperature and pressure-thickness requirements cannot both be met.Source: §7.2 · p. 14
  • The detailed first-wall calculation checks pipe hoop stress, applies specified erosion thinning, and separately accounts for a neutron-fluence lifetime limit.The calculated hoop stress must remain below permissible stress.Source: §7.2 · p. 14
  • First-wall and breeder-zone pumping power remains difficult to calculate because it depends on channel diameter and feeder-pipe and manifold design.The relevant algorithms are still under development.Source: §7.2 · p. 14

7.3. Detailed model: energy conversion

  • Detailed energy conversion estimates cycle efficiency from coolant outlet temperature, with user choice of steam Rankine or supercritical CO2 Brayton cycle.The cycle fits account for divertor heat, used to preheat Rankine feedwater or included in the CO2 main heat exchanger.Source: §7.3 · pp. 14–15
  • Detailed cycle fits incorporate temperature-dependent efficiencies and a correction for the lower-temperature divertor coolant.Table 4 identifies primary blanket and divertor coolant temperatures and secondary-fluid turbine-inlet temperature as fit inputs.Source: §7.3 · p. 14, Table 4 · p. 15

8. Availability

PROCESS defines availability and capacity factor separately for pulsed reactors, then estimates planned and unplanned downtime from component lifetimes, maintenance, and reliability models. Its pulsed blanket model predicts that increasing neutron flux can improve blanket availability until planned downtime dominates.

8. Availability

  • Availability is the fraction of time operating normally, while pulsed-reactor capacity factor also reflects duty cycle and is therefore lower.Dwell time between pulses counts as normal operation; the code feeds capacity factor into cost-of-electricity estimates.Source: §8 · p. 15

8.1. Planned Unavailability

  • Planned unavailability links blanket and divertor lifetimes to replacement downtime, using neutron flux for blanket life and divertor heat load for divertor life.The divertor lifetime scaling usually shortens as power into the divertor rises, but its absolute values should not be taken seriously.Source: §8.1 · pp. 15–16
  • Planned replacement downtime is estimated from repair times, including divertor-only replacement at 70% of the time required to replace blanket and divertor together.The combined repair-time fit is based on remote-handling systems working in parallel and includes preparation and dose-reduction time.Source: §8.1 · p. 16

8.2. Unplanned downtime

  • The unplanned-downtime model sums subsystem risks and increases failure risk as designs approach operational or technological limits, encouraging design margins.Heating and current-drive unavailability is assumed to be 2%, described as far below current systems.Source: §8.2 · p. 16

8.2.1. Magnets

  • Magnet unavailability is tied to maintenance time and estimated time between quenches, with quench likelihood potentially depending on TF-coil temperature margin.Figure 11 illustrates the estimated time between TF-coil quenches.Source: §8.2.1 · p. 16, Figure 11 · p. 17

8.2.2. First wall, blanket and divertor

  • For pulsed reactors, blanket reliability is modeled over cycles between planned replacements, with availability declining linearly after a reference lifetime.The divertor availability is estimated similarly.Source: §8.2.2 · pp. 17–18
  • Increasing neutron flux can improve modeled blanket availability until planned downtime dominates, assuming flux affects total blanket life but not cycle life.This counterintuitive result follows from the pulsed-reactor blanket reliability approach.Source: §8.2.2 · p. 17

8.2.3. Vacuum System

  • Vacuum-system downtime accounts for cryopump failures beyond redundant-pump capacity during operating periods between planned shutdowns.The model assumes two alternately regenerated cryopumps per duct and includes a lower unavailability limit for common-mode failures.Source: §8.2.3 · p. 18

9. Application to DEMO

The DEMO A application illustrates how selected engineering constraints shape a pulsed 500 MW net-electricity plant and how multiple constraints limit changes in optimized design. Its examples show that larger output requirements produce only modest growth in major radius.

9. Application to DEMO

  • DEMO A is a pulsed-reactor model for 500 MW net electricity, with engineering constraints listed in Table 5.Power flows are summarized in Table 6, and thermodynamic and energy parameters in Table 7.Source: §9 · p. 18, Table 5 · p. 19, Table 6 · p. 19
  • The cryostat measures 36 m in diameter by 29 m in height, and the heating system assumes 40% wall-plug efficiency versus achieved values of about 25% [14].The TF coils allow neutral-beam tangency at or beyond the plasma axis for potentially optimum current drive.Source: §9 · p. 19
  • 12 cm, or 1.4%, is the major-radius reduction despite a fivefold increase in the TF-coil operating-to-critical-current ratio.The coil cross-section decreases only a little because substantial non-superconducting area is needed for copper stabilizer, insulation, and especially structural support; stronger structural materials would also be needed to use improved superconductors effectively.Source: Figure 12 · p. 20, §9 · p. 20
  • 9% major-radius growth accompanies a 2.2-fold increase in required output power.As output rises, seeded impurity and radiation increase to maintain constant power per unit length into the divertor; injected power is fixed in this run, and current-drive electric power falls as a fraction of gross electric power.Source: §9 · p. 20, Figure 13 · p. 21

10. Discussion and Future work

Future PROCESS work includes incorporating fitted neutronics models and developing cost estimates, while sensitivity, optimizer robustness, and important engineering constraints remain areas of concern.

10. Discussion and Future work

  • 594 FATI models spanning lithium fraction, 6Li enrichment, and blanket thickness were fitted with analytical expressions for incorporation into PROCESS.The models simulated depletion of breeding and neutron-multiplying isotopes in an HCPB blanket.Source: §10 · p. 21
  • Improved parametric expressions for energy multiplication and nuclear energy deposition in coils remain future needs, while approximate tokamak construction-cost estimates are in development.The cost estimates assume outstanding issues can be resolved.Source: §10 · p. 21
  • PROCESS results depend on user-selected constraints, and safety, first-wall erosion, and fatigue-life algorithms are not yet included.Sensitivity to input variations and robustness of the optimizer in finding global solutions are also under study.Source: §10 · p. 21
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