Mandelbrot set

Everybody likes the Mandelbrot set, right?*

About Me

Hi there! I'm a dad, a postdoctoral researcher in plasma physics, and generally a fan of learning something new! As you're reading this, I'm probably somewhere between chasing around a toddler and writing a paper, so it's likely the website is still lacking that "polished" feel.

Broadly speaking, my work investigates energy transfer in plasmas.

During grad school, my research focused on magnetically-confined plasmas. I characterized nonlinear interactions between magnetic field instabilities and populations of energetic ions in tokamaks and stellarators. Notably, I used wavelet-based bispectral analysis to document wave-wave coupling on sub-millisecond time scales, which could enhance active feedback controls of potentially catastrophic disruptions in forthcoming fusion reactors.

Nowadays, I'm poring over mountains of spacecraft data from THEMIS and Arase to assess and model the latitudinal dependence of ultra-low frequency (ULF) wave power in the outer radiation belt. This is important because ULF waves are crucial drivers of radial diffusion in energetic electron populations, but most investigations consider only particles with nearly-perpendicular pitch angles (i.e., "trapped" at the magnetic equator).

With any luck, I'll be able to post/link/upload enough of my work so that this can function as a back-up of sorts... How does it seem like I'm doing?

Highlights

2023: I attended the Sherwood Fusion Theory Conference in Knoxville, TN, and the APS Division of Plasma Physics Conference in Denver, CO.

2024: We received a Featured Article in Physics of Plasmas and I successfully defended my dissertation!

2025: I talked at the ITPA Energetic Particle Topical Group meeting in Seville, Spain, and attended the GEM/CEDAR Workshop in Des Moines, IA. Also, the power series for an infinite exponential is
$$ \Lambda(\alpha,z) \equiv \text{\huge{$\Omega$}}_{k=0}^\infty e^{\alpha^k z} = e^{z e^{\alpha z e^{\alpha^2 z e^{{.^{.^.}}}}} } = \sum_{i=0}^\infty L_i(\alpha) z^i, $$ $$ L_{i+1}(\alpha) = \frac{1}{i+1}\sum_{n=0}^{i} (n+1) \alpha^n L_{n}(\alpha) L_{i-n}(\alpha) $$

Greg Riggs

gariggs@mix.wvu.edu

Talk pic

Dept. of Physics & Astronomy
West Virginia University

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Research

Dissertation
Talks
  1. Statistical ULF wave latitude distribution: A key to understanding off-equatorial radiation belt electron radial diffusion
    GEM/CEDAR Workshop (Jun. 25, 2025)
    G. Riggs, W. Tu, T. Sarris
  2. Instantaneous difference-frequency locking observed in coupled eigenmodes on the DIII-D tokamak
    ITPA EP Topical Group Meeting (Mar. 21, 2025)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong, Y. Ghai
  3. Time-resolved bispectral signatures of TAE mode-mode coupling observed in the DIII-D tokamak
    ITPA EP Topical Group Meeting (Oct. 2, 2024)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong, Y. Ghai
  4. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak
    KINETIC Center Workshop (Aug. 22, 2024)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong, Y. Ghai
  5. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak [video] [slides]
    Princeton Plasma Physics Laboratory Energetic Particle Seminars (Nov. 29, 2023)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong, Y. Ghai
  6. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak
    DIII-D Energetic Particle Group (Oct. 11, 2023)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
Manuscripts submitted/in preparation
  1. Statistical ULF wave latitude distribution: A key to understanding off-equatorial radiation belt electron radial diffusion
    In preparation for submission to Journal of Geophysical Research: Space Physics
    G. Riggs, W. Tu, T. Sarris
  2. Instantaneous difference-frequency locking observed in coupled eigenmodes on the DIII-D tokamak
    In preparation for submission to Physical Review Letters
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
  3. Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution (Part 2: Time evolution)
    Submitted to Nuclear Fusion (2025)
    W. Heidbrink, G. DeGrandchamp, J. Lestz, K. Thome, S. Vincena, N. Crocker, X. Du, R. Pinsker, G. Riggs, S. Tang, M. Van Zeeland
  4. Formal power series expansion for infinite exponential of analytic function
    Submitted to The American Mathematical Monthly (2025)
    G. Riggs
  5. BicAn: An integrated, open-source framework for polyspectral analysis
    Submitted to Computer Physics Communications (2025)
    G. Riggs, M. Koepke, T. Matheny
Peer-reviewed publications
  1. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled Alfven eigenmodes on the DIII-D tokamak
    Physics of Plasmas (2024)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
  2. Role of simple spatial gradient in reinforcing the accuracy of temperature determination of HED plasma via spectral line-area ratios
    Atoms (2023)
    G. Riggs, M. Koepke, T. Lane, T. Steinberger, P. Kozlowski, I. Golovkin
  3. Establishing an isoelectronic line ratio temperature diagnostic for soft X-ray absorption spectroscopy
    High Energy Density Physics (2022)
    T. Lane, M. Koepke, P. Kozlowski, G. Riggs, T. Steinberger, I. Golovkin
  4. Bispectral analysis of broadband turbulence and geodesic acoustic modes in the T-10 tokamak
    Journal of Plasma Physics (2021)
    G. Riggs, S. Nogami, M. Koepke, A. Melnikov, L. Eliseev, S. Lysenko, P. Khabanov, M. Drabinskij, N. Kharchev, A. Kozachek, M. Ufimtsev and HIBP Team
Conference presentations
  1. Statistical ULF wave latitude distribution: A key to understanding off-equatorial radiation belt electron radial diffusion
    GEM/CEDAR Workshop (June 2025)
    G. Riggs, W. Tu, T. Sarris
  2. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak
    65th Annual Meeting of the APS Division of Plasma Physics (2023)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
  3. Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak
    Sherwood Fusion Theory Conference (2023)
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
  4. Preliminary identification and characterization of nonlinear wave-wave, wave-beam, and wave-particle interactions in beam-driven tokamak plasma
    64th Annual Meeting of the APS Division of Plasma Physics (2022) [slides]
    G. Riggs, M. Koepke, W. Heidbrink, M. Van Zeeland, D. Spong
  5. TJ-II observations of nonlinear wave-wave coupling in play during Alfven-Eigenmode:Turbulence:Zonal-Flow interactions
    64th Annual Meeting of the APS Division of Plasma Physics (2022)
    M. Koepke, F. Papoušek, M. Ochando, C. Hidalgo, B. van Milligen, G. Riggs
  6. Constraining magnitudes of nonzero temperature and density gradients using absorption spectra of radiatively heated target-foil plasma
    Stewardship Science Academic Programs Symposium (2022)
    G. Riggs, T. Lane, P. Kozlowski, M. Koepke
  7. Constraining magnitudes of nonzero temperature and density gradients using absorption spectra of radiatively heated target-foil plasma
    63rd Annual Meeting of the APS Division of Plasma Physics (2021)
    G. Riggs, M. Koepke, T. Lane, P. Kozlowski
  8. Spectroscopic method to obtain n, T applied to soft x-ray absorption spectra in radiatively heated Z-pinch plasmas
    Stewardship Science Academic Programs Symposium (2021)
    G. Riggs, T. Lane, P. Kozlowski, M. Koepke
  9. Bispectral analysis of broadband and quasi-coherent oscillations (geodesic-acoustic modes) to interpret wave-wave interactions in the T-10 Tokamak
    61st Annual Meeting of the APS Division of Plasma Physics (2019)
    M. Koepke, S. Nogami, G. Riggs, A. Melnikov, L. Eliseev, S. Lysenko, P. Khabanov, M. Drabinskij, N. Kharchev, A. Kozachek, M. Ufimtsev
  10. Interpretation of bi-coherence in space and lab plasma-wave dynamics
    60th Annual Meeting of the APS Division of Plasma Physics (2018)
    G. Riggs, S. Nogami, M. Koepke, N. Crocker, G. Howes, S. Savin, V. Budaev, L. Zelenyi
  11. Alfvén Eigenmode (AE) interactions in Tokamaks: DIII-D Frontier Science Experiments connecting the physics of nonlinear waves and processes in space plasmas
    60th Annual Meeting of the APS Division of Plasma Physics (2018)
    M. Koepke, S. Nogami, G. Riggs, G. Howes, N. Crocker, T. Carter, W. Heidbrink, M. Van Zeeland
Master's Thesis
Technical Reports
Honors & Awards
    Research Trust Fund Seehra Research Award (April 2021 & April 2024)**
    Oleg D. and Valentina P. Jefimenko Physics Fellowship (April 2023)**
    Sherwood Fusion Theory Student Poster Award (May 2023)
    ITPA EP topical group expert member (March 2024)
    Featured Article in Physics of Plasmas (April 2024)

Projects

Bispectral analysis
  • BicAn
    Matlab object that makes time-resolved detection of phase-coherency a snap! See technical report (above) for more information.
  • PyBic
    Implementation of bicoherence analyzer in Python.
Simulations
  • Visualization of field-particle correlation in 1D-1V Vlasov-Poisson plasma (final project for a course in space physics; see Greg Howes' work for more context).

  • Surface waves on various membranes:

    || ... Sphere ... || ... Torus ... || ... Level 1 Menger sponge ... ||

  • Calculation of field due to different antennas (part of final project for a second course in E&M):

    || ... Linear ... || ... Ring ... || ... Tapered helix ... ||

  • Frequency modulation in driven van der Pol oscillator

  • Benchmarking non-oscillatory scheme for 2.5D ideal MHD code with the Orzag-Tang vortex (final project for a course in MHD).
Code stuff
Electronics
Music

[Canvas sprite creator]


*This is taken from my Deep Dream page, the source image can be found here.

**See here for a more complete description of department scholarships and awards.
Plain Academic