open access publication

Article, 2023

4D and 5D phase-space tomography using slowing-down physics regularization

In: Nuclear Fusion, ISSN 0029-5515, 1741-4326, Volume 63, 7, 10.1088/1741-4326/acd6a6

Contributors (21)

Schmidt, Bo Simmendefeldt (0000-0001-5302-9489) (Corresponding author) [1] Salewski, Mirko (0000-0002-3699-679X) [1] Moseev, Dmitry (0000-0001-7955-8565) [2] Baquero-Ruiz, Marcelo [3] Hansen, Per Christian (0000-0002-7333-7216) [1] Eriksson, Jacob (0000-0002-0892-3358) [4] Ford, Oliver P (0000-0002-5646-4758) [2] Gorini, Giuseppe (0000-0002-4673-0901) [5] Järleblad, Henrik (0000-0003-1126-686X) [1] Kazakov, Ye O [6] Kulla, David (0000-0003-1621-7338) [2] Lazerson, Samuel Aaron (0000-0001-8002-0121) [2] Mencke, Jacob Emil (0000-0003-0889-622X) [3] Mykytchuk, Dmytry [3] Nocente, Massimo (0000-0003-0170-5275) [5] [7] Poloskei, Peter Zsolt [2] Rud, M. [1] Snicker, Antti (0000-0001-9604-9666) [8] Stagner, Luke (0000-0001-5516-3729) [9] Äkäslompolo, Simppa (0000-0002-9554-5147) [2] Team, the W7-X


  1. [1] Technical University of Denmark
  2. [NORA names: DTU Technical University of Denmark; University; Denmark; Europe, EU; Nordic; OECD]
  3. [2] Max Planck Institute for Plasma Physics
  4. [NORA names: Germany; Europe, EU; OECD]
  5. [3] École Polytechnique Fédérale de Lausanne
  6. [NORA names: Switzerland; Europe, Non-EU; OECD]
  7. [4] Uppsala University
  8. [NORA names: Sweden; Europe, EU; Nordic; OECD]
  9. [5] University of Milano-Bicocca
  10. [NORA names: Italy; Europe, EU; OECD]


We compute reconstructions of 4D and 5D fast-ion phase-space distribution functions in fusion plasmas from synthetic projections of these functions. The fast-ion phase-space distribution functions originating from neutral beam injection (NBI) at TCV and Wendelstein 7-X (W7-X) at full, half, and one-third injection energies can be distinguished and particle densities of each component inferred based on 20 synthetic spectra of projected velocities at TCV and 680 at W7-X. Further, we demonstrate that an expansion into a basis of slowing-down distribution functions is equivalent to regularization using slowing-down physics as prior information. Using this technique in a Tikhonov formulation, we infer the particle density fractions for each NBI energy for each NBI beam from synthetic measurements, resulting in six unknowns at TCV and 24 unknowns at W7-X. Additionally, we show that installing 40 LOS in each of 17 ports at W7-X, providing full beam coverage and almost full angle coverage, produces the highest quality reconstructions.


LOS, TCV, Tikhonov formulation, W7, Wendelstein 7, angle coverage, basis, beam, beam coverage, beam injection, components, coverage, density, density fractions, distribution function, energy, expansion, formulation, fraction, full angle coverage, function, fusion plasmas, half, high-quality reconstruction, information, injection, injection energy, measurements, neutral beam injection, particle density, phase space tomography, phase-space distribution function, physics, plasma, ports, prior information, projections, quality reconstruction, reconstruction, regularization, spectra, synthetic measurements, synthetic projections, synthetic spectra, technique, tomography, unknowns, velocity


  • Federal Department of Economic Affairs Education and Research
  • European Commission