Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Direct observation of ion acceleration from a beam-driven wave in a magnetic fusion experiment


Efficiently heating a magnetically confined plasma to thermonuclear temperatures remains a central issue in fusion energy research. One well-established technique is to inject beams of neutral particles into the plasma, a process known as neutral beam injection. In the classical picture, fast ions generated from neutral beam injection predominantly heat electrons as they are slowed by friction. This electron heat is then collisionally coupled to the plasma ions, which comprise the fusion fuel. Fast ions can also drive plasma waves, which divert energy from the fuel and can degrade confinement. Here we present new observations from a field reversed configuration plasma in which a beam-driven wave in the open field line region couples directly to fuel ions, drawing a high-energy tail on subcollisional timescales that dramatically enhances the fusion rate. This mode therefore allows the beam energy to bypass the electron channel and does so without having a deleterious effect on global plasma confinement. Our results demonstrate a means of directly and non-destructively coupling energy from fast ions to plasma ions, which may pave the way for improved neutral beam injection heating efficiency or the prevention of ash accumulation with alpha channelling.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Illustration of the FRC.
Fig. 2: Basic plasma and NBI parameters, and a comparison of the measured and calculated neutron emission rates.
Fig. 3: Summary of measurements of fluctuations in the electron density and magnetic field associated with the beam-driven mode.
Fig. 4: Measurements of the energy spectra of charge exchange neutrals at the edge of the plasma reveal ion acceleration coincident with a rise in neutron emission.
Fig. 5: Simulation of the beam-plasma system reveals the three features observed in experiment: fluctuations at harmonics of the ion cyclotron frequency, a high-energy tail on the main ion species and enhanced neutron production.
Fig. 6: Controlling mode activity by reducing velocity space gradients.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Tuszewski, M. Reversed field configurations. Nucl. Fusion 28, 2033–2092 (1988).

    Article  Google Scholar 

  2. 2.

    Rosenbluth, M. N., Krall, N. A. & Rostoker, N. Finite larmor radius stabilization of ’weakly’ unstable confined plasmas. Nucl. Fusion Suppl. 1, 143–150 (1962).

    MATH  Google Scholar 

  3. 3.

    Binderbauer, M. W. et al. A high performance field-reversed configuration. Phys. Plasmas 22, 056110 (2015).

    ADS  Article  Google Scholar 

  4. 4.

    Binderbauer, M. W. et al. Dynamic formation of a hot field reversed configuration with improved confinement by supersonic merging of two colliding high beta compact toroids. Phys. Rev. Lett. 105, 045003 (2010).

    ADS  Article  Google Scholar 

  5. 5.

    Binderbauer, M. W. et al. Recent breakthroughs on C-2U: Norman’s legacy. AIP Conf. Proc. 1721, 030003 (2016).

    Article  Google Scholar 

  6. 6.

    Gota, H. et al. Achievement of field-reversed configuration plasma sustainment via 10 mW neutral-beam injection on the C-2U device. Nucl. Fusion 57, 116021 (2017).

    ADS  Article  Google Scholar 

  7. 7.

    Guo, H. Y. et al. Achieving a long-lived high-beta plasma state by energetic beam injection. Nat. Commun. 6, 6897 (2015).

    Article  Google Scholar 

  8. 8.

    Schmitz, L. et al. Suppressed ion-scale turbulence in a hot high plasma. Nat. Commun. 7, 13860 (2016).

    ADS  Article  Google Scholar 

  9. 9.

    Heidbrink, W. W. Basic physics of Alfvén instabilities driven by energetic particles in toroidally confined plasmas. Phys. Plasmas 15, 055501 (2008).

    ADS  Article  Google Scholar 

  10. 10.

    Belova, E. V. et al. Coupling of neutral-beam-driven compressional Alfvén eigenmodes to kinetic Alfvén waves in NSTX tokamak and energy channeling. Phys. Rev. Lett. 115, 015001 (2015).

    ADS  Article  Google Scholar 

  11. 11.

    Anderson, J. K. et al. Fast ion confinement and stability in a neutral beam injected reversed field pinch. Phys. Plasmas 20, 056102 (2013).

    ADS  Article  Google Scholar 

  12. 12.

    Gates, D. A., Gorelenkov, N. N. & White, R. B. Ion heating by fastparticle-induced Alfvén turbulence. Phys. Rev. Lett. 87, 205003 (2001).

    ADS  Article  Google Scholar 

  13. 13.

    Berk, H., Horton, W., Rosenbluth, M. N. & Rutherford, P. H. Microinstability theory of two-energy-component toroidal systems. Nucl. Fusion 15, 819–844 (1975).

    Article  Google Scholar 

  14. 14.

    Magee, R. M. et al. Absolute calibration of neutron detectors on the C-2U advanced beam-driven FRC. Rev. Sci. Instrum. 87, 11D815 (2016).

    Article  Google Scholar 

  15. 15.

    Roche, T. et al. Enhanced magnetic field probe array for improved excluded flux calculations on the C-2U advanced beam-driven field-reversed configuration plasma experiment. Rev. Sci. Instrum. 87, 11D409 (2016).

    Article  Google Scholar 

  16. 16.

    Beall, M., Deng, B. & Gota, H. Improved density profile measurements in the C-2U advanced beam-driven field-reversed configuration (FRC) plasmas. Rev. Sci. Instrum. 87, 11E128 (2016).

    Article  Google Scholar 

  17. 17.

    Wesson, J. Tokamaks 3rd edn 246–253 (Clarendon Press, Oxford, 2004).

  18. 18.

    Deng, B. H. et al. High sensitivity far infrared laser diagnostics for the C-2U advanced beam-driven field-reversed configuration plasmas. Rev. Sci. Instrum. 87, 11E125 (2016).

    Article  Google Scholar 

  19. 19.

    Clary, R. et al. A mass resolved, high resolution neutral particle analyzer for C-2U. Rev. Sci. Instrum. 87, 11E703 (2016).

    Article  Google Scholar 

  20. 20.

    Matsuura, H. & Nakao, Y. Distortion of bulk-ion distribution function due to nuclear elastic scattering and its effect on T(d,n)4He reaction rate coefficient in neutral-beam-injected deuterium-tritium plasmas. Phys. Plasmas 14, 054504 (2007).

    ADS  Article  Google Scholar 

  21. 21.

    Arber, T. D. et al. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Control Fusion 57, 113001 (2015).

    ADS  Article  Google Scholar 

  22. 22.

    Tajima, T. & Dawson, J. M. Laser electron accelerator. Phys. Rev. Lett. 43, 267 (1979).

    ADS  Article  Google Scholar 

  23. 23.

    Fisch, N. J. The alpha channelling effect. AIP Conf. Proc. 2015, 020001 (2015).

    Article  Google Scholar 

  24. 24.

    Goorley, T. Initial MCNP6 release overview. Nucl. Technol. 180, 298–315 (2012).

    Article  Google Scholar 

  25. 25.

    Thompson, M. C. et al. Magnetic diagnostic suite of the C-2 field-reversed configuration experiment confinement vessel. Rev. Sci. Instrum. 83, 10D709 (2012).

  26. 26.

    Bosch, H.-S. & Hale, G. M. Improved formulas for fusion cross-sections and thermal reactivities. Nucl. Fusion 32, 611–631 (1992).

    ADS  Article  Google Scholar 

  27. 27.

    Zhai, K. et al. The upgrade of the Thomson scattering system for measurement on the C-2/C-2U devices. Rev. Sci. Instrum. 87, 11D602 (2016).

    Article  Google Scholar 

  28. 28.

    Boris, J. P. Relativistic plasma simulation-optimization of a hybrid code. in Proc. 4th Conference on Numerical Simulation of Plasmas 3–67 (1970).

  29. 29.

    Esirkepov, T. Zh. Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor.Comput. Phys. Commun. 135, 144–153 (2001).

    ADS  Article  Google Scholar 

  30. 30.

    Yee, K. S. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14, 302–307 (1966).

    ADS  Article  Google Scholar 

Download references


The authors thank the investors for their support of TAE Technologies and the TAE and Budker teams for their contributions to this project. Special thanks go to E. Granstedt and E. Trask for help with the design of the experiment. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under contract no. DE-AC05-00OR22725.

Author information




R.M.M. contributed neutron measurements and neutron calculations, created all the figures and wrote the majority of the text. A.N. ran the PIC simulations, provided output data, and provided text for the ‘Simulation and theory’ section. R.C. provided NPA measurements. S.K. provided neutral beam injection. S.N. provided the analytical theory for benchmarking. T.R. and M.C.T. provided magnetic data. M.W.B. is the driving force behind the C-2U device and helped edited the text. T.T. provided theoretical interpretation of the experimental and simulation data and contributed significantly to the editing of the text.

Corresponding author

Correspondence to R. M. Magee.

Ethics declarations

Competing interests

TAE Technologies, Inc. is a private corporation owned and financially supported by its shareholders. Some or all of the authors of this manuscript may have a financial interest in the company.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Magee, R.M., Necas, A., Clary, R. et al. Direct observation of ion acceleration from a beam-driven wave in a magnetic fusion experiment. Nat. Phys. 15, 281–286 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing