Pith. sign in

REVIEW 4 major objections 5 minor 67 references

Hybrid Fourier Neural Operator-Plasma Fluid Model for Fast and Accurate Multiscale Simulations of High Power Microwave Breakdown

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A neural network that replaces the electromagnetic field solver reproduces microwave streamer growth and runs roughly 60 times faster than the full FDTD-plasma fluid model.

desk verdict A useful proof-of-concept for embedding an FNO surrogate in a coupled EM-plasma fluid solver, with a credible 60x speedup and good qualitative streamer agreement, but the paper overstates its closed-loop fidelity and has a normalization leakage that should be fixed. read the letter →

arxiv 2509.05799 v1 pith:247K6EBZ submitted 2025-09-06 physics.plasm-ph cs.AIcs.LGphysics.comp-ph

Kalp Pandya , Pratik Ghosh , Ajeya Mandikal , Shivam Gandha , Bhaskar Chaudhury This is my paper · ORCID
classification physics.plasm-phcs.AIcs.LGphysics.comp-ph PACS 52.65.-y52.80.Pi
keywords high-powermicrowavebreakdownstreamerplasmafluidmodelFourierneuraloperatorFDTDhybridsimulationEM–plasmainteractionmachinelearningsurrogate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

High-power microwave breakdown simulations couple Maxwell's equations to a plasma continuity equation, and the electromagnetic update consumes more than 99 percent of the runtime, making large or long simulations impractical. This paper claims that a Fourier Neural Operator can learn the mapping from plasma density plus incident wave to the time-averaged scattered electric field, and that plugging this surrogate into the coupled solver—while keeping the plasma density update physics-based—reproduces microwave streamer formation for incident field amplitudes not seen in training. The reported result is close overlap with the full FDTD-fluid model in streamer shape, growth rate, tip field, and temporal evolution, at 57–63x speedup that turns multi-day runs into sub-hour runs. The paper also shows how an existing compiled C solver can be wrapped and driven from Python to host such a surrogate. If the claim holds, multiscale HPM breakdown studies that currently require months of serial computation become feasible on ordinary hardware.

What carries the argument

The load-bearing component is a Fourier Neural Operator used as an image-to-image surrogate: the input is a two-channel image of normalized plasma density and incident electric field, and the output is the scattered RMS electric field. Four Fourier layers, each retaining 16 low-frequency modes, learn the global EM-plasma coupling in the spectral domain, while a pointwise convolution bias captures localized streamer-tip features. In the closed loop, the surrogate replaces the per-wave-cycle FDTD EM update; the C-based plasma solver advances electron density once per EM wave cycle using transport coefficients computed from the predicted RMS field.

What would settle it

Run the closed-loop hybrid and the full FDTD-fluid model on the same unseen case, say E0 = 2.75 MV/m, but continue past the paper's 80%-of-domain termination condition; if streamer length or tip field diverges from the reference after the training horizon, the no-error-accumulation assumption fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the expensive finite-difference time-domain electromagnetic solver inside a coupled EM-plasma fluid model for high-power microwave breakdown can be replaced by a Fourier Neural Operator surrogate without losing the physics of streamer formation. Trained on scattered-field snapshots from an in-house FDTD-plasma fluid solver, the surrogate maps a two-channel snapshot of plasma density and incident field to the RMS scattered electric field. When cycled against the unchanged plasma continuity solver, the hybrid reproduces streamer length, streamer growth rate, and tip electric field enhancement for unseen incident fields of 2.55, 2.65, 2.75, 2.85, and 2.95 MV/m,

Load-bearing premise

That the roughly 12 percent average error in each predicted field snapshot does not compound through the nonlinear field–plasma feedback into uncontrolled streamer growth over the hundreds of update cycles of a full simulation.

Editorial extensions

If this is right

  • A 10λ × 10λ domain that the paper estimates at roughly 500 days with the reference FDTD-fluid model would become a few days of computation at the measured speedup.
  • Parameter sweeps over incident field amplitude inside the trained 2.5–3.0 MV/m range could be run quickly, making breakdown-threshold and streamer-dynamics studies practical.
  • The hybrid retains the plasma continuity equation solver, so the acceleration comes without replacing the fluid description of plasma evolution.
  • The demonstrated Python–shared-library–C interface offers a template for retrofitting other legacy compiled EM-plasma codes with machine-learning surrogates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The 60x figure is tied to the EM update consuming more than 99 percent of runtime; a problem where other physics takes a larger share would show a smaller speedup.
  • Training and testing cover only 2.5–3.0 MV/m at 110 GHz and 760 Torr, so behavior outside that interval of field amplitude, pressure, or frequency remains an open question.
  • At a reported per-cycle average percent error near 12 percent, the long-horizon reliability of the closed loop depends on error cancellation; measuring the growth rate of streamer-length error over many cycles would make that assumption quantitative.
  • Because the surrogate predicts time-averaged RMS fields, sub-cycle electromagnetic dynamics that matter for gas heating or higher-harmonic effects are outside what this architecture captures.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a hybrid simulation framework for high-power microwave (HPM) breakdown in which a Fourier Neural Operator (FNO) replaces the FDTD-based electromagnetic solver inside an established EM-plasma fluid model. The FNO maps a two-channel input (plasma density and incident electric field) to the scattered RMS electric field; the plasma continuity solver and the Python/C coupling are retained. The FNO is trained on data generated by the same FDTD-fluid solver, and the hybrid model is tested on incident amplitudes (2.55, 2.65, 2.75, 2.85, 2.95 MV/m) not used in training. The authors report FNO stand-alone metrics (MSE 0.0394, APE 0.12, SSIM 0.9999), near-perfect overlap of streamer length, growth rate, and tip field between the hybrid and full FDTD-fluid models, and a speedup of roughly 57-63x. The manuscript also documents a modular Python-C implementation that may facilitate adoption of ML surrogates in legacy plasma codes.

Significance. If the central claims survive scrutiny, the paper demonstrates a practical and transferable strategy for accelerating multiscale EM-plasma simulations: the FNO surrogate is coupled in a closed loop with a conventional plasma-fluid solver, achieving an order-of-magnitude speedup while closely matching the reference solution. The work's strengths include the use of an established FDTD plasma-fluid model for data generation, a non-trivial closed-loop coupling, and a concrete runtime comparison (Table 2). The reported speedup is attractive for parametric studies and for extending simulations to larger domains. However, the validation is limited in important ways: the FNO is trained on and compared against the same numerical solver, the test amplitudes are interpolated within the training range, the normalization uses test-set statistics, and the closed-loop error accumulation is not quantified. These issues do not invalidate the framework but materially weaken the current evidence for 'near-perfect' fidelity and broad generalization.

major comments (4)
  1. [Section 4.1] The min-max normalization is performed using global minimum and maximum values computed over the entire training and testing sets, for both the input channels and the output Erms. This is a data-leakage issue: the test-set statistics are used during training preprocessing, which can artificially improve the reported MSE/APE/SSIM. Since the incident-field channel encodes E0 directly and the test E0 values lie between training values, the benefit may be substantial. The authors should re-normalize using training-set statistics only and report the resulting metrics.
  2. [Section 4.1 / Table 1] The five 'unseen' incident amplitudes, 2.55, 2.65, 2.75, 2.85, and 2.95 MV/m, are exactly the midpoints between the training amplitudes (2.5, 2.6, ..., 3.0 MV/m). This is an interpolation test, not a test of generalization to 'any electric field within the specified range' or to new physical regimes. Because the FNO input includes the incident field amplitude, the model can exploit the local linearity of the training sweep. The claims of generalization should be restricted to interpolation within the tested range, and the authors should include an extrapolation case (e.g., E0=3.1 MV/m) or a test with a different frequency/domain to support broader claims.
  3. [Section 5, Section 5.2] The closed-loop stability of the FNO-fluid coupling is not quantitatively established. The manuscript itself warns that 'even a small discontinuity or mismatch in prediction of E_rms could lead to uncontrolled plasma streamer growth over long durations' (Section 5). The standalone APE is about 12%, and the plasma update (Eq. 6) is nonlinear and ionization-dominated; errors in the predicted Erms can be amplified or rectified over hundreds of update cycles. The current validation overlays streamer length, growth rate, and tip-field curves but provides no per-cycle error measured along the actual hybrid trajectory, no perturbed-initial-condition experiments, and no error-growth bound. Without such an analysis, the statement that hybrid predictions show 'almost perfect overlap' is not yet supported. At minimum, the authors should report error bars or quantiles for the curves in Figures 11-12
  4. [Sections 3 and 5.1] It is ambiguous whether the FNO predicts the scattered Erms or the total Erms. The text in Section 3 says the FNO 'predict the scattered electric field (E_rms)', while Section 5.1 compares 'FNO predicted and actual FDTD generated E_rms data'. In the coupled model, the plasma solver needs the total (or effective) field to compute ionization and transport coefficients, but if the FNO outputs only the scattered field, the incident contribution must be added analytically. The paper does not clearly state which quantity is used in Eq. (6). This is essential for interpreting the reported MSE/APE and for reproducing the hybrid implementation. Please clarify the output definition and how the total Erms is assembled in the loop.
minor comments (5)
  1. [Abstract / throughout] Typos: 'sceince' in the abstract, 'suare' in Section 2.2, 'therfore' in Section 2.1. Please proofread.
  2. [Section 5.2 / Table 2 / Conclusion] The speedup numbers are inconsistent: Section 5.2 reports 57.10-62.77x, the abstract says 'of the order of 60X', and the conclusion says 'between 55x to 60x'. The Table 2 values should be cited consistently.
  3. [Section 2.2] The text refers to 'Figure 2 (a)' when discussing plasma density evolution and streamer dynamics, but the relevant panels appear to be in Figure 3. Please correct the cross-references.
  4. [Section 4.2.1] The description of the Fourier layer is inconsistent: it says only the lowest m=16 modes are retained, but Eq. (8) says 'leaving higher modes unchanged'. Please clarify whether higher modes are set to zero, retained, or processed differently.
  5. [Section 4.1] All metrics (MSE, APE, SSIM) are computed on the min-max normalized, 0-255-rescaled images. Reporting values on this scale, rather than in physical units (V/m and m^-3), makes the errors harder to interpret. Please report at least one error metric in physical units.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the FNO is a surrogate for the FDTD solver and is evaluated on held-out incident amplitudes; the closed-loop streamer agreement is an emergent, nontrivial result despite sharing the same reference solver.

full rationale

The paper's derivation chain is a supervised surrogate construction, not a first-principles derivation. Section 4.1 states 'The data required for model training and testing has been generated using the FDTD-based HPM breakdown simulation described in subsection 2.2,' and Section 5.2 validates by comparing hybrid predictions against 'the FDTD-based plasma fluid model.' At first glance this looks like validating on the training-data source, but the test protocol uses electric-field amplitudes '2.55, 2.65, 2.75, 2.85 and 2.95 MV/m' that were not used during training (Section 4.1), and the compared quantities -- streamer length, growth rate, and tip Erms in Figures 11-12 -- are not direct FNO outputs; they emerge from the closed-loop iteration of the FNO field surrogate with the unchanged plasma continuity solver (Eq. 6). Thus the near-overlap is not forced by construction: the FNO could have drifted in the nonlinear ionization-diffusion feedback loop. The physical model and transport coefficients are cited to prior work including the authors' own [9,10,11], but those are standard, externally published plasma-fluid models, not an imported uniqueness theorem that forbids alternatives; no load-bearing self-citation chain is used to justify the central claim. The absence of a quantitative closed-loop error-amplification bound (the paper itself warns in Section 5 that 'even a small discontinuity or mismatch in prediction of Erms could lead to uncontrolled plasma streamer growth over long durations') is a correctness/stability concern, not a circularity. Score 1 reflects only minor self-citations for the base physical model and scaling estimates, none of which make the result equivalent to its inputs.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the FNO weights and hyperparameters plus the data-dependent normalization bounds. The physical transport coefficients and effective-field approximation are taken from prior literature, and the core domain assumptions about quasi-neutrality, fixed temperatures, and diffusion-dominated transport are inherited from the reference models.

free parameters (3)
  • FNO neural network weights = Learned during training
    The surrogate mapping from plasma density and incident field to scattered field is fitted to FDTD-generated data. These weights are the primary free parameters determining the model output.
  • FNO hyperparameters = 4 Fourier layers, 16 modes, 32 latent channels, zero-padding 5, lr 1e-3, batch 32, 300 epochs
    These architecture and training choices are selected by hand and influence the surrogate accuracy and generalization.
  • Min-max normalization bounds = Computed from training and test sets combined
    The global min and max used for input and output scaling are derived from the data, and using test statistics is a data-dependent choice that can affect reported metrics.
assumptions (6)
  • domain assumption Plasma is quasi-neutral and ion current is negligible
    Section 2.1 states the ion contribution to the total current density is neglected, treating the plasma as quasi-neutral.
  • domain assumption Cycle-averaged plasma continuity equation with only diffusive flux
    Section 2.1 retains only the diffusion term in the flux divergence, justified by time-scale separation between the EM wave period and plasma evolution.
  • domain assumption Electron temperature is constant at 2 eV and gas temperature stays constant
    Section 2.1 fixes electron temperature at 2 eV, and Section 1 limits simulation time so gas heating is ignored. These are strong modeling assumptions inherited from [10, 11].
  • domain assumption Effective field approximation determines transport coefficients
    Equation (1) defines E_eff using the RMS field and collision frequency, and this effective field controls ionization and attachment rates. This is a standard but approximate treatment.
  • standard math Scattered-field FDTD with Mur absorbing boundary conditions is the reference solver
    Section 2.2 uses the scattered-field formulation and Mur ABCs as the numerical foundation; this is a well-established numerical method.
  • ad hoc to paper FNO can learn the mapping (ne, incident field) -> Erms and generalize over the tested range
    The entire hybrid approach assumes the trained neural operator provides accurate field predictions when embedded in the closed-loop simulation, which is only tested on interpolated values without a stability guarantee.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hybrid Fourier Neural Operator-Plasma Fluid Model for Fast and Accurate Multiscale Simulations of High Power Microwave Breakdown." pith.science (2026). https://pith.science/paper/247K6EBZ

@misc{pith2026250905799,
  author       = {Pith},
  title        = {Pith review of: Hybrid Fourier Neural Operator-Plasma Fluid Model for Fast and Accurate Multiscale Simulations of High Power Microwave Breakdown},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/247K6EBZ}},
  note         = {Machine review of arXiv:2509.05799}
}
read the original abstract

Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this work, we present a hybrid modeling approach that combines the accuracy of a differential equation-based plasma fluid solver with the computational efficiency of FNO (Fourier Neural Operator) based EM solver. Trained on data from an in-house FDTD-based plasma-fluid solver, the FNO replaces computationally expensive EM field updates, while the plasma solver governs the dynamic plasma response. The hybrid model is validated on microwave streamer formation, due to diffusion ionization mechanism, in a 2D scenario for unseen incident electric fields corresponding to entirely new plasma streamer simulations not included in model training, showing excellent agreement with FDTD based fluid simulations in terms of streamer shape, velocity, and temporal evolution. This hybrid FNO based strategy delivers significant acceleration of the order of 60X compared to traditional simulations for the specified problem size and offers an efficient alternative for computationally demanding multiscale and multiphysics simulations involved in HPM breakdown. Our work also demonstrate how such hybrid pipelines can be used to seamlessly to integrate existing C-based simulation codes with Python-based machine learning frameworks for simulations of plasma science and engineering problems.

Figures

Figures reproduced from arXiv: 2509.05799 by the authors.

Figure 1
Figure 1. The figure illustrates the FDTD-based plasma fluid model showing the iterative coupling between the EM and plasma solvers over the full physical time period (tend − tstart), with each operating at different time steps. The plasma solver is invoked after ”n” iterations of the EM solver, where ”n” corresponds to the number of EM solver iterations in one EM wave period. properties depend solely on the local effective f… view at source ↗
Figure 2
Figure 2. (a) Schematic of the computational domain for the HPM breakdown sim￾ulation. The domain spans Lx = 1λ and Ly = 0.5λ, with an initial Gaussian plasma centrally located at (Lx/2, Ly/2). Dotted lines, x-central and y-central are two lines passing through the center of the computational domain. Two identical linearly polar￾ized plane waves (110 GHz), with electric field oriented along the x-axis, are incident from the t… view at source ↗
Figure 3
Figure 3. (a) Spatiotemporal evolution of plasma density (top row) and scattered electric field (second row) at different physical times, for incident electric field of E0 = 2.5 MV/m as described in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Overview of the modular architecture of the deep learning-based hybrid simulation framework. The workflow shows Python used for high-level control and integration of performance optimized C-based components for numerical routines. Our proposed hybrid simulation framewo…
Figure 5
Figure 5. Figure 5: Pipeline for integrating the Python-based DL surrogate EM solver with the C-based plasma solver using shared library linking. Step 1 compiles selected C functions into a platform-compatible shared object (.so) file. Step 2 loads the shared object into Python for execut…
Figure 6
Figure 6. Figure 6: Temporal evolution of key plasma streamer parameters for different E0 values. (a) normalized streamer length Ls/λ, (b) streamer growth rate over time, and (c) scattered Erms at the plasma tip. All E0 values are in MV/m. Following the normalization and rescaling process…
Figure 7
Figure 7. Figure 7: Overview of the FNO model pipeline. The input consists of a two-channel image comprising the normalized plasma density and incident electric field. A lifting layer maps the input to a 32-channel latent space. This is followed by four Fourier layers that perform spectra…
Figure 8
Figure 8. Figure 8: Working of a single Fourier layer. The input tensor (plasma density and related feature maps) is padded and transformed using 2D FFT. Low-frequency modes are linearly transformed using a learnable complex-valued matrix to capture global plasma–field coupling. After app…
Figure 9
Figure 9. Figure 9: Training loop for the FNO model. Input and ground-truth output fields are normalized and rescaled. The predicted field is compared with the target using the MSE loss. Model weights are updated via backpropagation. Performance is evaluated using SSIM and APE to monitor …
Figure 10
Figure 10. Figure 10: (a) presents a qualitative comparison between FNO predicted and ac￾tual FDTD generated Erms data for different electric field and density profile inputs. The high similarity between the results obtained from two methods is evident in both the 2D maps and the 1D profil…
Figure 11
Figure 11. Figure 11: Comparison of temporal evolution of key plasma streamer parameters for different E0 values between the FNO-based hybrid model and the FDTD-based plasma fluid model. (a) normalized streamer length Ls/λ, (b) streamer growth rate over time, and (c) scattered Erms at the …
Figure 12
Figure 12. Figure 12: Comparison of plasma density and scattered Erms fields for E0 = 2.75 MV/m between the full FDTD based plasma fluid simulation and the proposed FNO-based hybrid fluid simulation. Both 2D maps and 1D x-central cuts exhibit ex￾cellent agreement between DE based conventio…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 66 canonical work pages

  1. [1]

    A. D. Macdonald.”Microwave breakdown in gases”. Wiley, New York, 1966

    work page 1966

  2. [2]

    Hamiaz, X

    A. Hamiaz, X. Ferrieres, and O. Pascal. Efficient numerical algorithm to simulate a 3D coupled Maxwell-plasma problem.Math. Comput. Simul., 174:19–31, 2020

    work page 2020

  3. [3]

    A. I. Saifutdinov, A. G. Karpenko, and V. A. Lashkov. Dynamics of focused pulsed microwave discharge in air.Plasma Phys. Rep., 45(6):602–609, jun 2019

    work page 2019

  4. [4]

    A. I. Saifutdinov and E. V. Kustova. Dynamics of plasma formation and gas heating in a focused-microwave discharge in nitrogen.J. Appl. Phys., 129(2):023301, 2021

    work page 2021

  5. [5]

    A. M. Cook, J. S. Hummelt, M. A. Shapiro, and R. J. Temkin. Mea- surements of electron avalanche formation time in W-band microwave air breakdown.Phys. Plasmas, 18(8):080707, 2011

    work page 2011

  6. [6]

    Anirudh, R

    R. Anirudh, R. Archibald, M. Asif, M. Becker, S. Benkadda, P.-T. Bremer, R. Bud´ e, C. Chang, L. Chen, R. Churchill, J. Citrin, J. Gaffney, A. Gainaru, W. Gekelman, T. Gibbs, S. Hamaguchi, C. Hill, K. Humbird, S. Jalas, and X. Zhang. 2022 review of data-driven plasma science.IEEE Transactions on Plasma Science, PP:1–89, 07 2023

    work page 2022

  7. [7]

    Arcese, F

    E. Arcese, F. Rogier, and j.-p. Boeuf. Plasma fluid modeling of microwave streamers: Approximations and accuracy.Physics of Plasmas, 24:113517, 11 2017

    work page 2017

  8. [8]

    Chaudhury, A

    B. Chaudhury, A. Gupta, H. Shah, and S. Bhadani. Accelerated simulation of microwave breakdown in gases on Xeon Phi based cluster-application to self-organized plasma pattern formation.Comput. Phys. Commun., 229:20 – 35, 2018. 24

    work page 2018

Show all 67 references
  1. [9]

    Chaudhury, J

    B. Chaudhury, J. P. Boeuf, and G. Q. Zhu. Pattern formation and propa- gation during microwave breakdown.Phys. Plasmas, 17(12):123505, 2010

    2010

  2. [10]

    Chaudhury, J

    B. Chaudhury, J. P. Boeuf, G. Q. Zhu, and O. Pascal. Physics and mod- elling of microwave streamers at atmospheric pressure.J. Appl. Phys., 110(11):113306, 2011

    2011

  3. [11]

    Chaudhury and J-P Boeuf

    B. Chaudhury and J-P Boeuf. Computational Studies of Filamentary Pat- tern Formation in a High Power Microwave Breakdown Generated Air Plasma.IEEE Transactions on Plasma Science, 38(9):2281–2288, 2010

    2010

  4. [12]

    Brovkin and P

    V. Brovkin and P. Vedenin. Study of the microwave streamer evolution using a new semi-analytical model.Journal of Applied Physics, 128:113301, 09 2020

    2020

  5. [13]

    Brunton and J

    S. Brunton and J. Kutz.Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. 06 2022

    2022

  6. [14]

    Carleo, I

    G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt, and L. Zdeborova. Machine learning and the physical sciences.Reviews of Modern Physics, 91, 12 2019

    2019

  7. [15]

    Chinesta and E

    F. Chinesta and E. Cueto. Empowering engineering with data, machine learning and artificial intelligence: a short introductive review.Advanced Modeling and Simulation in Engineering Sciences, 9:21, 10 2022

    2022

  8. [16]

    A. Cook, M. Shapiro, and R. Temkin. Pressure dependence of plasma structure in microwave gas breakdown at 110 ghz.Applied Physics Letters - APPL PHYS LETT, 97:1504–011504, 07 2010

    2010

  9. [17]

    Desai, P

    M. Desai, P. Ghosh, A. Kumar, and B. Chaudhury. Deep-learning architecture-based approach for 2-d-simulation of microwave plasma inter- action.IEEE Transactions on Microwave Theory and Techniques, PP:1–10, 12 2022

    2022

  10. [18]

    Fukunari.Experimental Studies of Microwave Discharge Induced by Gyrotron, pages 105–141

    M. Fukunari.Experimental Studies of Microwave Discharge Induced by Gyrotron, pages 105–141. 05 2024

    2024

  11. [19]

    Fukunari, S

    M. Fukunari, S. Tanaka, R. Shinbayashi, Y. Yamaguchi, Y. Tatematsu, and T. Saito. Observation of a comb-shaped filamentary plasma array under subcritical condition in 303-ghz millimetre-wave air discharge.Scientific Reports, 9:17972, 11 2019

    2019

  12. [20]

    Fuster, G

    L. Fuster, G. Hagelaar, R. Pascaud, A. Simon, P. Hoffmann, L. Liard, O. Pascal, and T. Callegari. Plasma-based microwave power limitation in a printed transmission line: a self-consistent model compared with experi- mental data.Plasma Sources Science and Technology, 31, 02 2022

    2022

  13. [21]

    G. Mur. Absorbing Boundary Conditions for the Finite-Difference Ap- proximation of the Time-Domain Electromagnetic-Field Equations.IEEE Trans. Electromagn. Compat., EMC-23(4):377–382, Nov 1981. 25

    1981

  14. [22]

    Ghosh and B

    P. Ghosh and B. Chaudhury. Efficient dynamic mesh refinement technique for simulation of hpm breakdown-induced plasma pattern formation.IEEE Transactions on Plasma Science, 51(1):66–74, 2023

    2023

  15. [23]

    Ghosh, B

    P. Ghosh, B. Chaudhury, S. Purohit, V. Joshi, A. Kothari, and D. Shetran- jiwala. Deep learning assisted microwave-plasma interaction based tech- nique for plasma density estimation.Journal of Physics D: Applied Physics, 57, 10 2023

    2023

  16. [24]

    Gopakumar, S

    V. Gopakumar, S. Pamela, L. Zanisi, Z. Li, A. Gray, D. Brennand, N. Bha- tia, G. Stathopoulos, M. Kusner, M. Deisenroth, and A. Anandkumar. Plasma surrogate modelling using fourier neural operators.Nuclear Fu- sion, 64, 04 2024

    2024

  17. [25]

    J. B. Michael, A. Dogariu, M. N. Shneider, and R. B. Miles. Subcriti- cal microwave coupling to femtosecond and picosecond laser ionization for localized, multipoint ignition of methane/air mixtures.J. Appl. Phys., 108(9):093308, 2010

    2010

  18. [26]

    J. Benford. Space Applications of High-Power Microwaves.IEEE Trans Plasma Sci, 36:569 – 581, 07 2008

    2008

  19. [27]

    J. P. Boeuf, B. Chaudhury, and G. Q. Zhu. Theory and Modeling of Self- Organization and Propagation of Filamentary Plasma Arrays in Microwave Breakdown at Atmospheric Pressure.Phys. Rev. Lett., 104:015002, Jan 2010

    2010

  20. [28]

    Kourtzanidis, J

    K. Kourtzanidis, J. P. Boeuf and F. Rogier. Three dimensional simula- tions of pattern formation during high-pressure, freely localized microwave breakdown in air.Phys. Plasmas, 21(12):123513, 2014

    2014

  21. [29]

    Kurtzanidis, F

    K. Kurtzanidis, F. Rogier, and J. P. Boeuf. Gas heating effects on the formation and propagation of a microwave streamer in air.J. Appl. Phys., 118:103301, 09 2015

    2015

  22. [30]

    K. S. Yee. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media.IEEE Trans. Antennas Propag., 14(3):302–307, 1966

    1966

  23. [31]

    K. V. Aleksandrov, L. P. Grachev, I. I. Esakov, V. V. Fedorov, and K. V. Khodataev. Domains of existence of various types of microwave discharge in quasi-optical electromagnetic beams.Tech. Phys., 51(11):1448–1456, Nov 2006

    2006

  24. [32]

    K. V. Khodataev. Microwave Discharges and Possible Applications in Aerospace Technologies.J. Propuls. Power, 24(5):962–972, 2008

    2008

  25. [33]

    Karniadakis, Y

    G. Karniadakis, Y. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang. Physics-informed machine learning.Nature Reviews Physics, pages 1–19, 05 2021. 26

    2021

  26. [34]

    Kunz and R.J

    K.S. Kunz and R.J. Luebbers.The Finite Difference Time Domain Method for Electromagnetics. Taylor & Francis, 1993

    1993

  27. [35]

    G. Li, T. Shu, C. Yuan, J. Yang, J. Yang, Z. Jin, Y. Yin, D. Wu, J. Zhu, H. Ren, and J. Yang. Coupling output of multichannel high power mi- crowaves.Physics of Plasmas, 17:123110–123110, 12 2010

    2010

  28. [36]

    Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stu- art, and A. Anandkumar. Fourier neural operator for parametric partial differential equations.arXiv preprint arXiv:2010.08895, 2020

    2010 arXiv

  29. [37]

    M. Lino, S. Fotiadis, A. Bharath, and C. Cantwell. Current and emerging deep-learning methods for the simulation of fluid dynamics.Proceedings of the Royal Society A, 479, 07 2023

    2023

  30. [38]

    Fukunari, T

    M. Fukunari, T. Yamaguchi, Y. Nakamura, K. Komurasaki, Y. Oda, K. Kajiwara, K. Takahashi, and K. Sakamoto. Thrust generation experiments on microwave rocket with a beam concentrator for long distance wireless power feeding.Acta Astronaut., 145:263–267, Apr. 2018

    2018

  31. [39]

    Takahashi and N

    M. Takahashi and N. Ohnishi. Gas propellant dependency of plasma structure and thrust performance of microwave rocket.J. Appl. Phys., 125(16):163303, 2019

    2019

  32. [40]

    Takahashi, Y

    M. Takahashi, Y. Kageyama, and N. Ohnishi. Joule-heating-supported plasma filamentation and branching during subcritical microwave irradia- tion.AIP Adv., 7(5):055206, 2017

    2017

  33. [41]

    C. Meng, S. Griesemer, D. Cao, S. Seo, and Y. Liu. When physics meets machine learning: a survey of physics-informed machine learning.Machine Learning for Computational Science and Engineering, 1, 05 2025

    2025

  34. [42]

    Bulat, I

    P. Bulat, I. Esakov, L. Grachev and K. Volkov and I. Volobuev. Experimen- tal Study of Air Breakdown Induced by Subcritical Streamer Microwave Discharge.IEEE Trans. Plasma Sci., 49(3):1041–1049, 2021

    2021

  35. [43]

    Ghosh and B

    P. Ghosh and B. Chaudhury. Mesh Refinement Based Simulation of Com- plex Plasma Dynamics during High Power Millimeter Wave Breakdown. In 2020 IEEE MTT-S Int. Conf. Numer. Electromagn. Multiphys. Modeling and Optimization (NEMO), pages 1–4, Dec 2020

    2020

  36. [44]

    Ghosh and B

    P. Ghosh and B. Chaudhury. Computational Investigation of Microwave Breakdown in HPM Switching and Protection. In2021 IEEE MTT-S In- ternational Microwave and RF Conference (IMARC), pages 1–4, 2021

    2021

  37. [45]

    Zhao , C

    P. Zhao , C. Liao, W. Lin, L. Chang, and H. Fu. Numerical studies of the high power microwave breakdown in gas using the fluid model with a mod- ified electron energy distribution function.Phys. Plasmas, 18(10):102111, 2011. 27

    2011

  38. [46]

    Zhou and Z

    Q. Zhou and Z. Dong. Modeling study on pressure dependence of plasma structure and formation in 110 GHz microwave air breakdown.Appl. Phys. Lett., 98(16):161504, 2011

    2011

  39. [47]

    S. C. Schaub, J. S. Hummelt, W. C. Guss, M. A. Shapiro and R. J. Temkin. Electron density and gas density measurements in a millimeter-wave dis- charge.Phys. Plasmas, 23(8):083512, 2016

    2016

  40. [48]

    Gold and G

    S. Gold and G. Nusinovich. Review of high-power microwave source re- search.Rev. Sci. Instrum., 68:3945–3974, 11 1997

    1997

  41. [49]

    S. K. Nam and J. P. Verboncoeur. Theory of Filamentary Plasma Array Formation in Microwave Breakdown at Near-Atmospheric Pressure.Phys. Rev. Lett., 103:055004, Jul 2009

    2009

  42. [50]

    S. Yan , A. D. Greenwood, and J. Jin. Simulation of High-Power Microwave Air Breakdown Modeled by a Coupled Maxwell Euler System With a Non- Maxwellian EEDF.IEEE Trans. Antennas Propag., 66(4):1882–1893, April 2018

    2018

  43. [51]

    S. Yan, A. D. Greenwood, and J. Jin. Modeling of Plasma Formation During High-Power Microwave Breakdown in Air Using the Discontinu- ous Galerkin Time-Domain Method.IEEE J. Multiscale and Multiphys. Comput. Techn., 1:2–13, 2016

    2016

  44. [52]

    Saifutdinov and E

    A. Saifutdinov and E. Kustova. Simulation of filamentation dynamics of microwave discharge in nitrogen.Plasma Sources Science and Technology, 32, 12 2023

    2023

  45. [53]

    Sharma, R

    A. Sharma, R. Upadhyay, A. Karpatne, V. Subramaniam, D. Breden, and L. Raja. Modeling of atmospheric gas-stream processing using a microwave excited all-dielectric resonant plasma discharge.Journal of Physics D: Ap- plied Physics, 54, 08 2021

    2021

  46. [54]

    Gedney.Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

    Stephen D. Gedney.Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics. Morgan & Claypool, 2011

    2011

  47. [55]

    Suzuki, M

    S. Suzuki, M. Matsukura, T. Yamada, Y. Masuda, M. Takahashi, K. Shi- mamura, R. Minami, and T. Kariya. Experimental demonstration of in- terferometric discharge structure identification of atmospheric millimeter- wave discharge at subcritical conditions using 28 ghz gyrotron.P...

    2025

  48. [56]

    T. Tang, C. Liao, P. Zhao, Q. Gao and Y. Wu. Breakdown characteristics of ultra-wideband high-power microwave transmission through the lower atmosphere. In2010 Int. Conf. Microw. Millim. Wave Technol., pages 805–808, 2010. 28

    2010

  49. [57]

    Tabata, A

    K. Tabata, A. Manabe, K. Komurasaki, and Y. Oda. Observation of atmospheric millimeter-wave discharges at 94 ghz and comparison with other microwave and millimeter-wave frequencies.Applied Physics Letters, 124:263903, 06 2024

    2024

  50. [58]

    Takahashi

    M. Takahashi. Discharge from a high-intensity millimeter wave beam and its application to propulsion.Advances in Physics: X, 3:1417744, 01 2018

    2018

  51. [59]

    Takahashi and Y

    M. Takahashi and Y. Nakamura.Modeling and Theoretical Studies on Beamed-Induced Plasma, pages 143–178. Springer Nature Singapore, Sin- gapore, 2024

    2024

  52. [60]

    V. E. Semenov, E. I. Rakova, M Yu Glyavin and G. S. Nusinovich. Study of a Stationary Breakdown Wave Under the Conditions of Noticeable Reflec- tion of the Incident Electromagnetic Wave from a Gas-Discharge Plasma. Radiophys. Quantum Electron., 58(5):327–338, Oct. 2015

    2015

  53. [61]

    J. M. Woo, M. Ju, and J.-B. Lee. Plasma-discharge-integrated slot structure for microwave power limiter.Scientific Reports, 13, 06 2023

    2023

  54. [62]

    Hidaka, E

    Y. Hidaka, E. M. Choi, I. Mastovsky, M. A. Shapiro, J. R. Sirigiri, and R. J.Temkin. Observation of Large Arrays of Plasma Filaments in Air Break- down by 1.5-MW 110-GHz Gyrotron Pulses.Phys. Rev. Lett., 100:035003, Jan 2008

    2008

  55. [63]

    Nakamura, K

    Y. Nakamura, K. Komurasaki, M. Fukunari and H. Koizumi. Numerical analysis of plasma structure observed in atmospheric millimeter-wave dis- charge at under-critical intensity.J. Appl. Phys., 124(3):033303, 2018

    2018

  56. [64]

    Y. Oda, K. Komurasaki, K. Takahashi, A.Kasugai, and K. Sakamoto. Plasma generation using high-power millimeter-wave beam and its appli- cation for thrust generation.J. Appl. Phys., 100(11):113307, 2006

    2006

  57. [65]

    Y. Oda, M. Takahashi, N. Ohnishi, K. Komurasaki, K. Sakamoto, and T. Imai. A study on the macroscopic self-organized structure of high- power millimeter-wave breakdown plasma.Plasma Sources Sci. Technol., 29(7):075010, jul 2020

    2020

  58. [66]

    Y.Hidaka, E. M. Choi, I.Mastovsky, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, G. F. Edmiston, A. A. Neuber, and Y. Oda. Plasma structures observed in gas breakdown using a 1.5 MW, 110 GHz pulsed gyrotron. Phys. Plasmas, 16(5):055702, 2009

    2009

  59. [67]

    Zheng, T

    X. Zheng, T. J. Peng, J. Hou, Y. Zhang, L. Chen, S. L. Qin, Y. Q. Mao, W. B. Lu, J. N. Zhang, J. W. You, and T. J. Cui. Hybrid physics-data- driven neural network for accurate modeling of scattering problems.IEEE Transactions on Antennas and Propagation, pages 1–1, 2025. 29

    2025

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.