The Field-Reversed Configuration (FRC) as a

Practical Fusion Reactor CoreEdward DeWit, Jordan Morelli

Department of Physics, Engineering Physics, and Astronomy

Queen’s University, Kingston, ON

CAP Congress

June 4, 2019

Outline

Topics to be discussed• The case for fusion• Basic fusion physics• Basic FRC description• Brief history of FRC research• Technical benefits of the FRC• Results from TAE• Edge-biasing experiment• Summary and conclusion

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FIG: Conceptual drawing of the field-reversed configuration (FRC)

The case for fusion

3

The world needs energy

Best case≈ 2 ×

Realistic scenario“Do nothing”

Worst case

4

Global energy

consumption until 2100.

IIASA–WEC Study

“Global Energy

Perspectives”

Kikuchi, M., Lackner, K., and Tran, M. Q. (2012).

Traditional sources of energy

Fossil fuels are• In limited supply• Polluting• Geographically contested• Archaic

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Traditional sources of energy (cont’d.)

Solar and wind are• Intermittent• Low density

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Traditional sources of energy (cont’d.)

Nuclear fission is dangerous• Radioactive waste• Meltdown scenarios• Proliferation of weapons

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Nuclear fusion

Benefits of nuclear fusion• Energy dense• Unlimited, low cost fuel supply• No proliferation issues• No possibility of meltdown• No long-lived radioactive waste• Thermal or direct energy

conversion options

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Basic fusion physics

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Fusion in the sun

4𝑝 → 4𝐻𝑒 + 2𝑒+ + 2𝜈𝑒

Proton-proton chain reaction

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Fusion fuel

11Kikuchi, M., Lackner, K., and Tran, M. Q. (2012).

Main approaches to fusion on Earth

Magnetic confinement fusion Inertial confinement fusion

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https://www.iter.org/ https://lasers.llnl.gov/

Maxwell-Boltzmann and nuclear potential

13

Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Alternative approaches to fusion

14Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Basic FRC description

15

FRC formation and structure

Steps of theta-pinch formation1. Pre-ionization2. Field reversal3. Radial compression and field line

connection4. Axial contraction5. Equilibrium

16Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

FIG: FRC formation in theta-pinch coils

Compact toroid

𝐴𝑠𝑝𝑒𝑐𝑡 𝑟𝑎𝑡𝑖𝑜 =𝑅

𝑎

17Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

FIG: Schematic diagram of a spheromak

Comparison to Tokamak and Stellarator

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Ongena, J., Koch, R., Wolf, R., and Zohm, H. Nature Physics 12, 398 EP – May (2016).

FIG: Artist rendering of the ITER tokamak FIG: Artist rendering of Wendelstein-7x stellarator

Brief history of FRC research

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Early FRC research eraPioneering experiments

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FIG: Early FRC schematic

Early FRC research era (cont’d.)Mitigation of the rotational instability

21FIG: Elliptical deformation of FRC due to onset of rotational instability

Modern FRC research era

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Modern FRC research era (cont’d.)

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Technical benefits of the FRC

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Simple linear geometry

Physics of FRC geometry• Axial magnetic field• Radial pressure gradient• Azimuthal plasma rotation

𝑣⊥ =𝐸 × 𝐵

𝐵2−∇𝑝 × 𝐵

𝑞𝑛𝐵2𝜃

• Diamagnetic current

𝑗𝐷 = 𝑛𝑒 𝑣𝐷𝑖 − 𝑣𝐷𝑒

25Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Simple magnetic topologyMagnetic mirrors

Grad-B drift

𝑣∇𝐵 = ±1

2𝑣⊥𝑟𝐿

𝐵 × ∇𝐵

𝐵226

Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Simple magnetic topologyCurvature drift

Curved vacuum field

𝑣𝑅 + 𝑣∇𝐵 =𝑚

𝑞𝑣∥2 +

1

2𝑣⊥2

𝑅𝑐 × 𝐵

𝑅𝑐2𝐵2

• Not present in FRCs• Causes reactor damage in

tokamaks• Complex stellarator field coils

27Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

High plasma pressure

FRC magnetic efficiency• Low magnetic field strength, ∼ 1𝑇• High beta

𝛽 =𝑛𝑘𝐵𝑇

𝐵2/2𝜇0∼ 1

• Large temperatures per unit magnetic field

• Aneutronic fusion capable!

𝑝 + 11𝐵 → 3𝛼

28Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Natural Diverter

Particle extraction and direct energy conversion

• Particles follow open magneticfield lines

• Electrodes at the diverters can collect charged fusion products

• Electricity can be generateddirectly from ionic flow in plasma

Particle extraction and direct energy conversion

29Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

Translation

Translation trapping• Translated by magnetic field

gradients• Confined by magnetic mirrors• Kinetic to thermal energy

conversion

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Gradient magnetic fields

FIG: Magnetic field gradient and mirror coils

FIG: Early translation trapping experiment

Results from TAE

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Tri Alpha EnergyC-2U confinement chamber

32Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

Operating ParametersExternal magnetic field – 1 TElectron density – 3 × 1019

Ion temperature – 600 eVElectron temperature – 150 eV 75 ft x 35 ft x 25 ft

Tri Alpha Energy (cont’d.)FRC formation by collisional merging

33Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

High performance FRCRecord FRC confinement

34Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

High performance FRCCorrelation with neutral beam power

35Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

Role of edge-biasingFluid drifts

36Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

Role of edge-biasingMitigation of rotational instability

37Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

FIG: Particle trajectory in FRC

FIG: Measurement of line-integrated density

Edge-biasing experiment

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Summer research project at Nihon UniversityFAT-CM experiment

39https://www.cst.nihon-u.ac.jp/research/facilities/lebra_a.html

Summer research project at Nihon University (cont’d.) Edge-biasing of an FRC plasma

z

-1.0 [m] -0.5 0

Mirror coil

Gas puff

rMidplane

Central coil

Objectives• Experimentally and theoretically

verify the possibility of global and microscopic stability

• Radial electric field applied by biasing from the end regions of formation chamber

• Stabilization by driven toroidal flow shear and reduced spin-up

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FIG: Conceptual drawing of coaxial layered biasing electrodes

*Learn more about this at the poster session

Summary and conclusion

• The FRC is a practical means of harnessing fusion power• Simple geometry

• Simple magnetic topology

• High-beta

• Natural divertor

• Translatable

• Recent advancements have enabled high performance FRCs• Collisional merging

• Neutral beam injection

• Edge-biasing

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Acknowledgements

Queen’s University supported this work through generous scholarships

Future work will be funded in part by Mitacs and JSPS

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References

[1] Kolb, A., Dobbie, C., and Griem, H. Physical Review Letters 3(1), 5 (1959).

[2] Armstrong, W., et al. The Physics of Fluids 24(11), 2068{2089 (1981).

[3] Tuszewski, M. Nuclear Fusion 28(11), 2033 (1988).6

[4] Steinhauer, L. C. Physics of Plasmas 18(7), 070501 (2011).

[5] Ohi, S., et al. Physical review letters 51(12), 1042 (1983).

[6] Tuszewski, et al. Physical review letters 108(25), 255008 (2012).

[7] Binderbauer, et al. Physics of Plasmas 22(5), 056110 (2015).

[8] Hirano, Y., Sekiguchi, J., Matsumoto, T., Asai, et al. Nuclear Fusion 58(1), 016004 (2017).

[9] Chen, F. F. Introduction to plasma physics and controlled fusion, volume 3. Springer, (2015).

[10] Miyamoto, K. et al. Plasma physics for controlled fusion, volume 92. Springer, (2016).

[11] Kikuchi, M., Lackner, K., and Tran, M. Q. (2012).

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