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Impact of the Langdon effect on crossed-beam energy transfer


The prediction that laser plasma heating distorts the electron distribution function away from Maxwellian and towards a super-Gaussian distribution dates back four decades1. In conditions relevant to inertial confinement fusion, however, no direct evidence of this so-called ‘Langdon effect’ has previously been observed. Here we present measurements of the spatially and temporally resolved Thomson scattering spectrum that indicate the presence of super-Gaussian electron distribution functions consistent with existing theory2. In such plasmas, ion acoustic wave frequencies increase monotonically with the super-Gaussian exponent3. Our results show that the measured power transfer between crossed laser beams mediated by ion acoustic waves requires a model that accounts for the non-Maxwellian electron distribution function, whereas the standard Maxwellian calculations overpredict power transfer over a wide region of parameter space. Including this effect is expected to improve the predictive capability of crossed-beam energy transfer modelling at the National Ignition Facility in California and may restore a larger operable design space for inertial confinement fusion experiments. This is also expected to motivate further inquiry in other areas affected by non-Maxwellian electron distribution functions, such as laser absorption, heat transport and X-ray spectroscopy.

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Fig. 1: Platform for TOP9 experiments.
Fig. 2: Thomson scattering results.
Fig. 3: Effect of non-Maxwellian EDF on CBET gain.
Fig. 4: CBET results.
Fig. 5: CBET calculation for the National Ignition Facility.

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Data availability

Source Data for Fig. 2b,c are provided with the paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The computer programs that support the findings of this study are available from the corresponding author upon reasonable request.


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This material is based upon work supported by the Department of Energy National Nuclear Security Administration under award number DE-NA0003856, the University of Rochester, and the New York State Energy Research and Development Authority. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favouring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.

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Authors and Affiliations



D.T. was the Principal Investigator (PI) for the experimental campaign. A.C. was the theory and modelling PI. D.H.F. was the experimental plasma physics group leader. Other authors contributed as follows: experimental support and plasma characterization (A.M.H.); non-Maxwellian electron susceptibility calculations (A.L.M.); theory support (J.P.P.); instrument specialist (J.K.); laser specialists (C.D. and B.E.K.); motivational discussions and supporting simulations (D.J.S.).

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Correspondence to David Turnbull.

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Extended data

Extended Data Fig. 1 Tabulated Langdon effect intensity scaling plasma characterization results.

Different experiments were conducted in which the number of beams present after an initial plasma-forming period was varied from 1 to 4, each having nominally identical power and spatial smoothing. Overlapped intensity therefore scaled linearly with the number of beams. This resulted in an increase of more than threefold in the Langdon parameter (α) despite the moderating influence of the higher electron temperature. In each case, the super-Gaussian exponent, m, of the EDF measured by Thomson scattering was found to be in excellent agreement with the value expected from equation (3).

Source data

Source Data Fig. 2

EPW and IAW Thomson scattering spectra for the data and time indicated in Fig. 2, which require a non-Maxwellian EDF and cannot be fitted adequately using the typical Maxwellian assumption.

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Turnbull, D., Colaïtis, A., Hansen, A.M. et al. Impact of the Langdon effect on crossed-beam energy transfer. Nat. Phys. 16, 181–185 (2020).

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