ISSI Bern > International Teams > Cross-Scale Energy Transfer in Space…

Project outputs

Summary of the project outcomes

A key challenge in understanding energy transfer across scales in turbulent space plasmas is the current lack of simultaneous in-situ cross-scale observations. The upcoming HelioSwarm (nine spacecraft) and Plasma Observatory (seven spacecraft) missions will offer unprecedented opportunities to simultaneously study plasmas at multiple scales. To prepare for studies using such multi-spacecraft constellations, our international team focused on two key areas: (1) assessing and quantifying the errors of energy transfer proxies for weakly collisional plasmas using in-situ measurements, and (2) exploiting and improving existing four-spacecraft tools (ISSI books SR-001 and SR-008).

Utilizing simultaneous in-situ measurements from four or more probes allows for the quantification of energy conversion between different forms and energy transfer across scales. Using the four-spacecraft Magnetospheric Multiscale (MMS) observations and kinetic particle-in-cell simulations, a new measure linking macroscale turbulence to kinetic plasma properties has been proposed (Yang et al. 2024). MMS measurements have been used to estimate the electric field, a key mediator of the energy exchange between electromagnetic and kinetic energy at several scales (Lewis et al. 2023). Particularly, Roberts et al. (2023) investigated the calculation error of a proxy for the energy conversion between bulk flow and internal plasma energy. Unlike single-spacecraft methods, multi-point analyses inherently minimize ambiguity in estimating three-dimensional spatial derivatives of key electromagnetic and plasma quantities. Using representative configurations of HelioSwarm, novel approaches have been developed to provide more accurate magnetic field reconstructions from in-situ data compared to the standard linear method (Broeren et al. 2024). Specifically, Shen et al. (2025) proposed a new technique for estimating quadratic spatial gradients using 7 and 9 spacecraft. Furthermore, Broeren & Klein (2024) proposed a more precise tool for extracting plasma wave properties, including wave vector and magnitude, accompanied by comprehensive uncertainty analyses (Broeren & Klein, 2023; Klein et al. 2024).

In summary, our team has advanced energy transfer study by developing innovative multi-point tools. In the coming years, we will compile review papers to further stimulate discussion on the energy transfer problem and multi-point tools in the community and to support the multi-spacecraft missions. We are very grateful to ISSI for supporting our international team.

2 highlight slides with the key result of the project ISSI_outcome_summary_v2

Publications from our team

  1. Broeren, T. & K. G. Klein (2023), “Data-driven Uncertainty Quantification of the Wave Telescope Technique: General Equations and Demonstration Using HelioSwarm”, ApJS 266 12, doi.org:10.3847/1538-4365/acc6c7.
  2. Roberts, O. W., Z. Vörös, K. Torkar, J. Stawarz, R. Bandyopadhyay, D. J. Gershman, Y. Narita, R. Kieokaew, B. Lavraud, K. Klein, Y. Yang, R. Nakamura, A. Chasapis, W. H. Matthaeus (2023), “Estimation of the error in the calculation of the pressure-strain term: application in the terrestrial magnetosphere”, JGR Space Physics, doi.org:10.1029/2023JA031565/.
  3. Lewis, H. C., J. E. Stawarz, L. Franci, L. Matteini, K. G. Klein, C. S. Salem, J. L. Burch, R. E. Ergun, B. L. Giles, C. T. Russell, P. Lindqvist (2023), “Magnetospheric Multiscale Measurements of Generalized Ohm’s Law in Earth’s Magnetosheath: How do plasma conditions influence turbulent electric fields? Physics of Plasmas, doi.org/10.1063/5.0158067.
  4. Yang, Y., W. H. Matthaeus, S. Oughton, R. Bandyopadhyay, F. Pecora, T. N. Parashar, V. Roytershteyn, A. Chasapis, M. A. Shay (2024), “Effective viscosity, resistivity, and Reynolds number in weakly collisional plasma turbulence”, MNRAS 528, 6119 – 6128, doi.org/10.1093/mnras/stae355.
  5. Broeren, T., K. G. Klein, and J. M. TenBarge (2024), “Multi‐Spacecraft Magnetic Field Reconstructions: A Cross‐Scale Comparison of Methods”, Earth and Space Science, 11, e2023EA003369, doi.org:10.1029/2023EA003369.
  6. Broeren, T. (2024), “Multi-Spacecraft Observatory Data Analysis Techniques: Uncertainty Quantification & Comparison”, Thesis, University of Arizona.
  7. Broeren, T. & K.G. Klein, (2024), “Multi-Point Gradient Estimation in Turbulence”, arXiv preprint, https://arxiv.org/abs/2405.14889.
  8. Broeren, T. & K.G. Klein, (2024), “Constrained Wave-telescope Technique”, Res. Notes AAS 8 130, doi:10.3847/2515-5172/ad498e.
  9. Pecora, F., F. Pucci, F. Malara, K. G. Klein, M. F. Marcucci, A. Retinò, and W. H. Matthaeus (2024), “Evaluation of Scale-dependent Kurtosis with HelioSwarm”, ApJL 970 L36, doi:10.3847/2041-8213/ad5fff.
  10. Klein, K. G., Broeren, T., Roberts, O., & Schulz, L. (2024). Wave-telescope analysis for multipoint observatories: Impact of timing and spatial uncertainties. Journal of Geophysical Research: Space Physics, 129, e2024JA033428. https://doi.org/10.1029/2024JA033428
  11. Lewis, H. C., Stawarz, J. E., Matteini, L., Franci, L., Klein, K. G., Wicks, R. T., et al. (2024). Turbulent energy conversion associated with kinetic microinstabilities in Earth’s magnetosheath. Geophysical Research Letters, 51, e2024GL112038. https://doi.org/10.1029/2024GL112038
  12. Roberts, O. W., K. G. Klein, Z. Vörös, R. Nakamura, X. Li, Y. Narita, D. Schmid, R. Bandyopadhyay, W. H. Matthaeus (2024). Measurement of the Taylor Microscale and the Effective Magnetic Reynolds Number in the Solar Wind With Cluster, JGR Space Physics, https://doi.org/10.1029/2024JA032968.
  13. Ren, N., C. Shen, Y. Ji, J. Park, J. Shue, Y. Zhou (2024). Applicability of Bernoulli’s theorem to upstream and downstream of the bow shock. Physics of Fluids, 36 (10): 106610. https://doi.org/10.1063/5.0223996
  14. Shen, C., G. Zeng, R. Kieokaew, Y. Zhou (2025). Quadratic Magnetic Gradients from 7- and 9-Spacecraft Constellations. Annales Geophysicae 43, 115–135, https://doi.org/10.5194/angeo-43-115-2025.

Tools/resources from our team members