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Confinement and Current Drive Technology for a 1500MW Tokamak

Confinement and Current Drive Technology for a 1500MW Tokamak. Professor Weston Stacey NRE 4610 – Plasma Physics and Fusion Engineering Brian Heissenbuttel , Nicholas Branch, Karem Chaudry, Raymond Chester, Peyton Maynard. Purpose and Design Objectives. Purpose

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Confinement and Current Drive Technology for a 1500MW Tokamak

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  1. Confinement and Current Drive Technology for a 1500MW Tokamak Professor Weston Stacey NRE 4610 – Plasma Physics and Fusion Engineering Brian Heissenbuttel, Nicholas Branch, Karem Chaudry, Raymond Chester, Peyton Maynard

  2. Purpose and Design Objectives Purpose Conduct a preliminary study on the ability of available plasma heating and magnetic confinement technology to support the operation of an advanced Tokamak fusion reactor capable of 1500MWth output Objectives • Determine necessary magnetic field geometry and coil design required to confine plasma • Determine appropriate coil sizing and field strength to induce the required plasma current at startup • Determine necessary current drive power to maintain plasma current during steady state operations • Verify capability of existing technology to meet heating power and current drive requirements, startup coil requirements, and confinement magnetic requirements • Verify the ability to produce the desired fusion factor Background Image Source: [16]

  3. Approach • Use governing equations to make initial estimates for current drive, heating, and plasma containment parameters required to meet the given 1500MWth DEMO reactor criteria • Reference literature for existing technology and relevant scaling laws and efficiency relations • Provide reasonable estimates for future technology capabilities • Determine optimal technology combination for future reactor design • Impose constraints on reactor design based on existing or in-development Tokamak reactors • Incorporate feedback from cross-focus parties to iterate on design parameters

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  5. Tokamak Design Overview Tokamaks are a closed, toroidal structures designed to use multiple sets of external magnets to confine the plasma • Toroidal magnets to capture charged particles along the center of the vacuum vessel torus • Poloidal magnets to prevent gradient and curvature drifts of charged particles • Central solenoids to provide inductive startup emfs to drive the plasma Existing high-strength magnets utilize cryogenic superconductors to carry high currents with minimal ohmic losses Characteristic parameters of Tokamak reactors include: • R, torus major radius • a, torus minor radius • Bφ, toroidal magnetic field strength • Ip, total plasma current

  6. Confinement Technology PRINCIPLES AND APPLICATION

  7. Toroidal Field Requirements Source: [21] Guiding and Calculated Parameters • Toroidal Field at Coils ≡ = 11.8 T • Blanket Shield Thickness ≡ = 1.0 m Current of Superconductor ≡ ≈ 68 kA [12] Number of TF Coils = TF Coil Thickness = 1.09 m TF Coil Cross-sectional Area = 1.42 ASME Code Requirements • ≤ 1.5 Physics Team Requirements •Toroidal Field at Plasma ≡ = 7.3 T •Major Radius ≡ R = 6.5 m •Minor Radius ≡ a = 1.5 m

  8. Toroidal Field Physics • Toroidal Field Coils are “D”-shaped • TF Coils main job is to provide a Toroidal Magnetic Field to stabilize plasma • Magnetic Field in the plasma changes as the major radius changes. This is dictated by Ampere’s Law such that . [1] • We can test this using the equation: • Current in TF Coils • Number of Turns

  9. Toroidal Field Design Calculations (Forces) Centering Force Tensile Force Tensile Hoop Stress Based on resource [12]:

  10. Toroidal Field Forces Source: [18] In ITER, maximum for a single coil test . [13] This compared slightly similarly to our calculated The calculated centering force, , was surprisingly much smaller at around: -49 MN ITER has recorded that the net centripetal force on each coil was 403 MN.[13]

  11. Toroidal Field Design Considerations The sum of the hoop stress and the bending stress must be less than or equal to 1.5 per ASME requirements. Using the assumption that for steel at 4 K the ultimate stress is 1400 MPa.[1] As such: - Since , for steel: Using this information and the values and we can see: ≤ 1.5 We are comfortably within ASME requirements. Superconductor material consists of that can support 68kA of current operating ideally at 4 K. [12] Sticking to “D”- Shaped magnets using Sb3Sn as the superconductor.

  12. Existing Toroidal Confinement Technology ITER ITER has very similar operating conditions to GT-DEMO, lending credibility to the above design parameters. Both possess maximum fields of 11.8 T and have the same conductor material and coil current. The stresses are however different and our TF Coils are larger and will experience more stress. This is important to note as this will negatively impact the TF Coils lifetime. ARIES The ARIES DEMO have slightly larger dimensions and a sizably larger max Toroidal Field at 16 T. While some of the design parameters were based off the ARIES DEMO, it was more based off of the ITER design.

  13. Poloidal Field Requirements Generated poloidal magnetic field at plasma surface, defined On the order of 1T; approximately 1.21T. Magnetic flux to be overcome from ohmic current effects Calculated to  228.2Wb coil average, similar to EUDEMO, ITER

  14. Poloidal Field Physics Individualized, based on tokamak geometry and requirements based upon plasma instability. Current in poloidal coil varies with distance from the coil to the plasma, scaling linearly with distance. From a modified Ampere's law relation, assuming a uniform elliptical geometry, the current in each coil is defined as follows: The current in each coil ranges from 55kA-1.3MA, depending on the number of coils included.

  15. Poloidal Field Calculations

  16. Poloidal Field Design Considerations Superconductor; NbTi (ITER), SC/Cu Alloy (EU DEMO) Arrangement of coils to create a uniform poloidal field; stack EU DEMO PF arrangement, pulse calibration, strict tolerances A) Hydraulic channel representation B) PF-1 cross section; Lorentz force considerations on stress, strain

  17. Poloidal Field Design Considerations, Cont. • Construction durability • Weight range 140-200 tons, metric • Preloading of support ties to avoid deformation • Sliding supports in conjunction with flexible plates

  18. Advancements in PF Coil Technology Uniform cross-section feasability in models post-2017 Tighter distribution of Lorentz forces Inclusion of access ports for easy maintenance

  19. Plasma Heating and Current Drive PRINCIPLES AND OPTIMIZATION

  20. Heating and Current Drive Overview • There exist several common methods of maintaining the plasma temperature and providing steady state current drive to overcome losses in Tokamak reactors • Neutral Beam Injection • Ion Cyclotron (Fast Wave) Resonance Heating and Current Drive • Electron Cyclotron (Gyrotron) Resonance Heating and Current Drive • Lower Hybrid Resonance Heating and Current Drive • Each current drive system possesses optimal regions for efficiency of power deposition that vary with the temperature and density of the plasma and localized magnetic field strength • Before the heating and current drive systems are incorporated, the plasma is first accelerated to steady state mode by inductive current drive via the central solenoids

  21. Startup Current Drive ΔTFC ΔBC ΔBS a R rv=2.37 [m] Initial startup based on central solenoid Faraday’s law-Electromotive force

  22. Central Solenoid Design ΔBOH=12.9 [T] IOH = 109 [kA] JCR = 50 [MA/m2] 10 loops of Nb3Sn cable ΔCS=0.46 [m] Jmax = 29 [MA/m2] Operating temperature of 6.25 [K] Image Source: European DEMO [8]

  23. Neutral Beam Injection Overview Source: [6]  Method of operation • Production of low temperature ions [6] • Deuterium production  • Acceleration of ions • Accelerated to high-energy by using high voltage • Results in monoenergetic beam of high energy ions • Neutralizer • Ions undergo charge exchange with the neutral particles • Results of high energy neutral particles  • Magnetic Deflector • Separates high-energy ions from neutral particles • Energy is then collected on beam dump

  24. NBI Efficiencies  Source: K-DEMO [2] Current density profile NBI is best in the range of       0.2< r/a< 0.65 The efficiency factor is cited as 0.3-0.4 in article [2] The current drive efficiency has been found to be about 0.04-0.06 in past work

  25. NBI Energy and Power Source: Fusion [1] Source: Fusion [1] Energy • Minimum NBI Energy for Class DEMO • NBI Operating Energy Range  • Positive Ion: 10-50keV • Negative Ion: 0.5- 2 MeV Power • Calculated NBI Power for Class DEMO • NBI Reasonable Powers  50-100 MW

  26. Advantages and Disadvantages of NBI • Pros • Magnetic Field Resistant •  Unaffected by magnetic field • High Neutralization Efficiency • Negative ions- 65% through energies between 100keV and 2MeV  • Positive ions- lower than 50% and under 10% at energies of 300keV • Cons • Optimum Value of Beam Energy • Beam energy too low leads to noneffective heating • Beam energy too high leads to very few interactions • Beam Energy • Experimental conditions differ from reactor • Experiments only need order of 100 keV • Reactor requires beam energies order of 1 MeV

  27. Electron Cyclotron Heating 1 • Uses the principle of electron cyclotron resonance to accelerate the electrons within the plasma (also known as gyrotron heating) • As electrons travel through a constant magnetic field, they experience a force perpendicular to their velocity known as the Lorentz Force, equal to • The Lorentz force produces a rotation of the electron around the B-field line, for which we can equate the Lorentz force with centripetal acceleration, Therefore, we can define the gyroradius and gyrofrequency as: ,

  28. Electron Cyclotron Heating 2 • By imposing a sinusoidally varying B-field on top of the confinement field, the plasma electrons are accelerated, which then collisionally heat the rest of the plasma • Typical frequencies for established reactors: • ITER – 170 GHz, 24x1MW • European Demo – 230GHz, 290 GHz • K-Demo – 190GHz to 300GHz, • DIII-D – 110GHz, 10MW (ea) (post upgrade) • CFETR – 30MW (Scen. B) • The ECR efficiency in a Tokamak is typically defined as: which is often quoted as approximately 0.2 for ITER Gif Source: By Lynnbwilsoniii - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=40080147

  29. Electron Cyclotron Heating Efficiencies • ECR is most effective in the intermediate region of the plasma Source: K-DEMO [2] Source: European Demo [3] • For K-Demo, the estimate for current to input power ratio at 210GHz is 25A/kW [2] • This ratio estimate corresponds to a γCD of 0.26-0.36 for the European Demo • K-Demo and European Demo in strong agreement

  30. Ion Cyclotron Heating Overview • Uses the same gyrofrequency acceleration principles as ECR, but instead, the frequency of the antenna is tuned emit a fast magnetosonic wave that couples to the ions present in the plasma instead of the electrons • Ion cyclotron frequency ranges from 50-110MHz [3] • Reactors: • Alcator C-Mod: 80MHz, • K-DEMO: 50-110MHz, 10MW/m2 • WEST: 55MHz, 3MW • ITER: 2x10MW • The efficiency factor is typically defined as follows, and is typically cited as 0.2-0.3 in the literature [1][3]: • lternatively, current drive efficiency is denoted as follows, and has been estimated in recent works as 0.06-0.07 [2][10]:

  31. Lower Hybrid Current Drive Overview • The lower hybrid resonance frequency results from the coupling of gyrotron and ion plasma frequencies to drive plasma electrons, mathematically expressed as follows [11]: • The wave only travels longitudinally with the static portion of the B field (poloidal direction of the Tokamak), and achieves optimal when injected against the plasma current (in the direction of electron movement) • Reactors: • K-Demo: 5GHz, 30MW (20MW/m2) • Alcator C-Mod: 4.6GHz, 1MW • Italian Demo: 5GHz, 80MW (30MW/m2) • ITER: 5GHz, 2x20MW • CFETR: ~5GHz, 31MW Image source: [7]

  32. Heating Methods Overview • The general efficiencies at their peak value are presented in the table below, which will be used for power balance and fusion factor analysis • At the cost of reducing heating capability in the 0. range, ECR heating can be increased to for a 280GHz antenna • NBI achieves higher efficiency than ECR at the cost of increased vacuum vessel complexity Source: [2][3][4][7][9][10][15]

  33. Fusion Factor Analysis • In order to reach a 1500MWth with a Q factor of 27, then the input heating and current drive power must be limited . • Given a: • Plasma current • Bootstrap fraction • Plasma density • And major radius • Then the necessary current drive efficiency per the relation is as follows: • The necessary current drive • To achieve a the necessary current drive power of 55.6MW, then the required average current drive efficiency is as follows:

  34. Fusion Factor Analysis 2 • To determine a realistic fusion factor, the following process is followed: • Extrapolate a 10% increase in best-case efficiency factors of current drive systems: • FW system with γ=0.3(110%)=0.33 • NBI system with γ=0.4(110%)=0.44 • LH system with γ=0.31(110%)=0.341 • Assume the parameters , , , as previously indicated • Approximate a constant density profile as per Cardinali et al. (SS operation indicated by green line) • Assume distinct regions of heating for each system as indicated by color blocks on chart NBI LH FW Source: Cardinali et al. [7]

  35. Fusion Factor Analysis 3 • Calculate average efficiency as: • Then the minimum input power to achieve is [1]: Source: [2][3][9][10][15]

  36. Conclusion • Inductive startup to 16 MA is feasible • Based on a review of current practices to achieve optimal heating efficiencies, three heating methods are required: • LHR heating for the outer plasma • NBI or ECR heating for the intermediate plasma • FW heating for the core • Realistic values of fusion factor are limited toQ20 • Total input power is at a minimum of 75MW to drive a current

  37. References [1] W. Stacey, “Fusion: An Introduction to the Physics and Technology of Magnetic Confinement Fusion.” Weinheim Wiley-VCH., Ed. 2. 2010. [2] K. Kim, et al., “Design Concept of K-DEMO for near-term Implementation”, Nuclear Fusion, vol 55, no. 5, 2015. [3] E. Poli, et al., “Electron-cyclotron-current-drive efficiency in DEMO plasmas”, Nuclear Fusion, vol. 53, no. 1, 2013. [4] G. Federici, et al., “DEMO design activity in Europe: Progress and Updates”, Fusion Engineering and Design, vol. 136, pt A, pp. 729-741, 2018. [5] J. Maglica, et al., "Plasma Heating with Neutral Beam Injection" Ljubljana Faculty of Math and Physics, 2005. [6] G. Ikovic, et al., "Neutral Beam Plasma Heating " Ljubljana Faculty of Math and Physics, 2014. [7] A. Cardinali., et al., “Role of the lower hybrid spectrum in the current drive modeling for DEMO scenarios”, Plasma Physics and Controlled Fusion, vol. 59, no. 7, 2017.

  38. References 2 [8] R. Wesche, “Central solenoid winding pack design for DEMO” Fusion Engineering and Design, vol. 124, pp. 82-85, 2017. [9] L. Liu et al., “Development of ramp up design workflow on CFETR Integrated Design Platform”, Fusion Engineering and Design, vol. 123, pp. 137-142, 2017. [10] J. Jacquinot et al., “Progress on the heating and current drive systems for ITER”, Fusion Engineering and Design, vol. 84, no.2, pp. 125-130, 2009. [11] T Stix. “Waves in Plasmas”. American Institute of Physics. 1992. [12] R. Albanese et al. "Optimization of the PF coil system in axisymmetric fusion devices." Fusion Engineering and Design, vol. 133, pp.163-172, 2018. [13] F. Simon et al. "Assembly of the Poloidal Field Coilsin the ITER Tokamak." EE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, vol. 26, no. 4, June 2016. [14] A. Zappatore et al. "Performance Analysis of the NbTi PF Coils for the EU DEMO Fusion Reactor." IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, vol. 28, no. 4, June 2018.

  39. References 3 [15] Y. Wan, et al., “Overview of the present progress and activities on the CFETR”, Nuclear Fusion, vol. 57, 2017. [16] "ITER -the way to new energy", ITER, 2017. [Online]. Available: https://www.iter.org. [Accessed: 03-Dec-2018]. [17] ITER. ITER EDA DOCUMENTATION SERIES No.24. IAEA, Jan. 2002. [18] Libeyre, P., et al. Mechanical Tests of the ITER Toroidal Field Model Coil. IAEA. [19] Reiersen, W., et al. The Toroidal Field Coil Design for ARIES-ST. Princeton, 2003. [20] Titus, P., et al. ARIES-RS Magnet Systems. Stone and Webster, 1997. [21] V. Duez, et al., “On the stability of Non Force-Free Equilibria in Stars”, Journal of Astrophysics, vol. 724, 2010.

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