Pith. sign in

REVIEW 4 major objections 5 minor 55 references

A novel scheme for measuring the growth of Alfven wave parametric decay instability using counter-propagating waves

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A counter-propagating seed Alfvén wave removes the threshold for parametric decay instability and makes PDI growth directly measurable.

desk verdict A useful seeded-amplification scheme for measuring Alfvén wave PDI in the lab, but the paper's treatment of seed damping is confusing and the central model is not tested against seed-damping variations. read the letter →

arxiv 2507.13590 v1 pith:3OYP2I3D submitted 2025-07-18 physics.plasm-ph physics.space-ph

Feiyu Li , Seth Dorfman , Xiangrong Fu This is my paper · ORCID
classification physics.plasm-phphysics.space-ph
keywords Alfvénwaveparametricdecayinstabilitycounter-propagatingwavesseedamplificationhybridsimulationlaboratoryplasmathreshold-freeionLandaudampingmeasurement
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

Alfvén wave parametric decay instability (PDI) has never been measured directly in the laboratory because the threshold growth rate of Eq. (1) is hard to reach in real devices. This paper proposes a way around the threshold: launch a small, continuously driven counter-propagating seed wave at the exact frequency of the daughter Alfvén wave. The seed wave then has no temporal damping, so the threshold disappears, and the pump-to-seed energy transfer shows up as a reduction in the seed's spatial damping. The paper shows in hybrid simulations that the ratio of seed amplitudes with the pump on versus off is a quantitative proxy for PDI growth, R = exp(Σ γeff δt), and that this ratio matches theory across scans of acoustic damping, plasma beta, and pump amplitude. If the scheme works as claimed, it turns an elusive instability into a controlled laboratory measurement.

What carries the argument

The load-bearing element is the seeded counter-propagating wave configuration: a continuously driven seed Alfvén wave at the backward daughter frequency, injected a few wavelengths from the pump. Because the seed is continuously driven, its temporal damping is zero, reducing the threshold condition to γeff > 0; the spatial damping that remains is offset by pump-to-seed energy transfer. The measured quantity is the amplitude ratio R(z) = δB2,on(z)/δB2,off(z), which the paper shows equals exp(Σ γeff δt) over the discretized path, and which is corrected for injection-reflection artifacts by envelope averaging.

What would settle it

Measure the seed-to-pump amplitude ratio in a laboratory plasma with independent, direct measurement of the ion acoustic wave damping (e.g., by launching a separate sound wave probe); if the ratio deviates from exp(Σγeff δt) computed with that measured damping by more than the diagnostic noise, the proxy is falsified.

Watch

Extended reading notes

Core claim

The central claim is that a small, continuously driven, counter-propagating seed Alfvén wave tuned to the PDI daughter frequency eliminates the threshold condition of Eq. (1) and turns PDI growth into an observable: the ratio of seed amplitudes with the pump on versus off, R = exp(Σ γeff δt), where γeff is the effective growth rate of Eq. (2). In 1D hybrid simulations the seed wave gains about 20% in amplitude by the time it reaches the pump, the pump loses a few percent of its energy, and the measured R follows the theoretical prediction across variations of the electron-to-ion temperature ratio, plasma beta, and pump amplitude. The authors argue that the scheme is directly implementable in current linear plasma devices, and that the same seeded-wave logic applies to other parametric instabilities.

Load-bearing premise

The agreement between simulation and theory rests on the empirical formula for ion Landau damping of the sound wave; if that formula is inaccurate in the scanned parameter range, the extracted growth rates and the claimed validation become unreliable.

Editorial extensions

If this is right

  • A direct laboratory measurement of Alfvén wave PDI becomes feasible, since the seeded scheme removes the threshold that has blocked previous single-pump experiments.
  • The measured growth rates can be compared with the textbook theory of parametric instabilities, providing a quantitative test of Eq. (2) in a controlled setting.
  • The scheme yields a spatially resolved growth profile along the device, not just a single growth rate, by scanning the seed-wave amplitude ratio as a function of position.
  • The same counter-propagating seed approach could be applied to other wave-wave parametric decays where the child mode suffers strong damping.
  • If implemented on a linear device, the scheme could distinguish genuine PDI amplification from competing nonlinear processes by checking the frequency and wavevector resonance conditions.

Reading between the lines

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

  • The authors leave unexplored the possibility that the seed ratio R(z) can also be used to map the local pump depletion along z, effectively measuring the spatial structure of the three-wave coupling rather than just its integrated growth.
  • Because the scheme is threshold-free, it may enable controlled studies of PDI saturation and turbulence generation in devices where the ideal threshold cannot be reached; this is an extension the paper does not pursue.
  • The same seeding logic could be ported to stimulated Raman or Brillouin scattering experiments, where a counter-propagating seed pulse already plays this role; the paper's ratio diagnostic might offer a sharper growth measurement there, though this is speculative.
  • A natural next step is to repeat the simulations in 2D or 3D with finite perpendicular wavevectors, since the paper's argument assumes parallel propagation and k⊥ = 0; if the perpendicular coupling changes the ratio, the proxy would need modification.
Share X Bluesky LinkedIn Reddit HN

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 proposes a laboratory scheme for measuring the growth of the Alfvén-wave parametric decay instability (PDI) by driving a large pump Alfvén wave and a small counter-propagating seed Alfvén wave whose frequency matches the PDI daughter. The seed is continuously driven at the boundary, and the ratio of seed amplitude with the pump on versus off is shown, via a convective model in Eq. (3), to isolate the pump-induced growth. The model is compared with one-dimensional hybrid (kinetic-ion) simulations across scans of the electron-to-ion temperature ratio, plasma beta, and pump amplitude, and the paper reports good agreement with theory. The authors claim that the seeded configuration removes the threshold condition of Eq. (1) and that the scheme is ready for implementation on linear devices such as the LAPD.

Significance. If the central claim holds, the paper offers a genuinely new and experimentally practical route to a direct laboratory measurement of Alfvén-wave PDI, a process that has so far been observed only indirectly. The approach is conceptually attractive: it converts an unstable-mode threshold problem into a seeded convective-amplification measurement, and the comparison with theory uses published PDI growth rates [42] and a textbook Landau-damping formula [53] with no parameters fitted to the simulation data. The derivation of Eq. (3) is explicit, and Appendix A provides a useful validation of the envelope-averaging correction for reflection artifacts. The parameter scans in Fig. 3 constitute falsifiable predictions. The main weaknesses are the ambiguous treatment of seed damping between Eq. (2) and Eq. (3), the unspecified source of the local pump amplitude used to evaluate the theoretical curves, and the absence of uncertainty estimates in the simulation-theory comparison.

major comments (4)
  1. [Section II, Eq. (2) and Section III.B, Eq. (3)] The treatment of the daughter Alfvén-wave damping appears internally inconsistent. Section II states that a continuously driven seed wave has no temporal damping and therefore sets Γ2 = 0 in Eq. (2), which is the basis for the threshold-free claim. Section III.B, however, assigns the same seed a finite temporal damping γd when modeling the pump-off baseline, writing δB2,off(zi−1) = δB2,off(zi) exp(−γdδt), and Eq. (3) then cancels this damping between the pump-on and pump-off cases. If γd is physically the same damping rate Γ2 that appears in the PDI dispersion relation, then Eq. (2) should contain Γ2 and the quantitative predictions of Eq. (3) would change; if γd is meant to be a separate spatial-damping effect that must be added to the PDI gain, this should be stated explicitly and justified. As written, the same physical process is treated as zero in Eq. (2) and nonzero in Eq. (3), and this ambiguity is load-bearing for the no-threshold claim and for the interpretation of γeff in Fig. 3. Please clarify the distinction and, ideally, test the model by varying γd (for example through collisions or beta) to confirm that the amplitude ratio R is indeed independent of γd as Eq. (3) predicts.
  2. [Section III.B and Fig. 3] The theoretical curves in Fig. 3 are computed from Eq. (3), but the paper does not state how the local pump amplitude δB1(z) entering γeff(z) is obtained. The text says that γeff varies with z because of pump spatial damping, but it does not say whether δB1(z) is taken from the simulated pump profile, from an analytic damping law, or from a seed-off reference run. If the simulated pump profile is used, the comparison is partially circular and the degree of validation is weaker than claimed. Please specify the input used to generate the dashed curves and, if possible, show how the agreement changes when an analytic or pump-on profile is used instead.
  3. [Fig. 3 and Section III.B] The quantitative support for the central claim is limited by the absence of uncertainty quantification. The amplitude ratios are extracted from single simulation runs, the reflection correction is an envelope-averaging procedure, and the reported signals are of order 20%. The 'good agreement' between the scatter points and the theoretical curves is assessed visually, with no error bars, no run-to-run variability, and no goodness-of-fit metric. Given that the empirical ion Landau damping formula [53] is used to set Γs, and the authors attribute deviations to this formula and to unmodeled nonlinear acoustic effects, the paper should provide at least an estimate of the uncertainty in the measured ratios, for example from time-window sensitivity or multiple realizations, before the claimed quantitative validation can be considered established.
  4. [Section II and Abstract] The phrase 'no threshold for PDI excitation' should be qualified. What the scheme actually demonstrates is seeded, convective amplification of an externally driven daughter wave: the amplitude ratio R = exp(Σ γeff δt) exceeds unity for any positive γeff, but this does not imply that the unseeded PDI instability has lost its threshold. The distinction between seeded amplification and self-sustained instability is important for the experimental interpretation and should be stated explicitly in Section II and in the abstract. The current wording, 'PDI can now be excited without any intrinsic threshold,' overstates what Eq. (3) measures.
minor comments (5)
  1. [Abstract] The phrase 'reduces the latter's spatial damping' is imprecise: in the convective model the seed's damping rate is unchanged, and the pump adds a growth term that offsets it. Consider rewording to 'offsets its spatial damping' or 'reduces its net damping.'
  2. [Section III.A] The sentence explaining why the counter-propagating interaction does not produce Alfvénic turbulence is useful, but the condition k⊥,1 × k⊥,2 ≠ 0 is stated without a citation or derivation; please add a reference or a brief explanation.
  3. [Appendix A] The reflection model in Appendix A uses a reflection coefficient r = 0.1, while the text describes the simulated reflections as 'few-percent-level.' Please clarify whether the larger coefficient is used as a conservative test, or whether the actual reflection level in the simulations was assessed and shown to be comparable to the model value.
  4. [Section III.B] The empirical Landau damping formula Γs/ωs = 1.1 Θ^(−7/4) exp(−Θ^(−2)) is quoted from reference [53] without stating its range of validity beyond 1 < Θ < 10. Please also note whether the scanned values of Θ (notably 4 and 5.65) lie safely within this range and whether the formula has been benchmarked against the kinetic-ion simulation response for these parameters.
  5. [Section IV] The discussion of experimental feasibility would benefit from a quantitative estimate of the expected signal size under LAPD conditions, since the simulated seed amplification is only about 20% over the interaction length and experimental noise and reflection effects may reduce the detectability of such a signal.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central theory curve uses external PDI growth-rate and Landau-damping formulas, and no parameter is fitted to the simulation data.

full rationale

The paper's derivation chain is self-contained against external benchmarks rather than circular. The predicted seed-wave amplification R in Eq. (3) is compared with hybrid simulations using an effective growth rate γeff_g from Eq. (2), which in turn is the published Nishikawa linear PDI growth formula [42] with Γ2 set to zero as an explicit modeling assumption for a continuously driven seed. The acoustic damping Γs is taken from a textbook Landau-damping estimate [53], and no free parameter is fitted to the simulation ratios. The threshold-free statement is a transparent algebraic consequence of the stated Γ2 = 0 assumption, not a hidden re-importation of the simulation result. Self-citations to the authors' earlier H3D developments [36,43,50] and prior experiments [38,39] are background and not load-bearing: the present validation is the comparison to independently specified theory. The apparent tension between setting Γ2 = 0 in Eq. (2) while modeling the pump-off seed with a finite spatial damping γd in Eq. (3) is a scientific modeling-consistency concern about the scheme's assumptions, but it is not circularity: in the ratio construction the common γd cancels, and the quantitative prediction entering the comparison is γeff_g from Eq. (2), not a quantity inferred from the measured ratio. Thus no circular step can be exhibited, and the correct finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; the scheme uses existing Alfvén and ion acoustic modes. The central theoretical comparison uses no free parameters fitted to the simulation data; all inputs are published constants, scan variables, or explicitly stated simulation setup choices.

assumptions (5)
  • domain assumption The three-wave PDI growth-rate formula Eq. (2), taken from Nishikawa [42], applies in the seeded convective regime with Γ2 = 0.
    Section II and Section III.B use Eq. (2) to define γeff and to build the convective amplification model Eq. (3). This is a published theoretical result assumed valid for the counter-propagating seed configuration.
  • domain assumption The ion Landau damping estimate Γs/ωs = 1.1 Θ^(−7/4) exp(−Θ^(−2)) from ref [53] is accurate in the scanned parameter range.
    Section III.B uses this empirical formula to compute the theoretical curves in Fig. 3(a). The authors note that deviations may stem from its approximate nature and from nonlinear acoustic effects.
  • domain assumption The convective model Eq. (3), which treats each spatial bin as independent and grows the seed by exp(γeff δt) with δt = δz/vg, captures the spatial evolution of the seed.
    Section III.B constructs the predicted amplitude ratio from Eq. (3). This neglects pump depletion and nonlinear sound-wave dynamics, which the authors acknowledge.
  • domain assumption A 1D geometry with k⊥ = 0 implies that counter-propagating Alfvén wave interactions do not produce Alfvénic turbulence, so only the parallel resonant acoustic coupling contributes.
    Section III.A argues that nonlinear interactions of counter-propagating waves require nonzero perpendicular wavevector cross products, and that with k⊥ = 0 the PDI channel dominates. Realistic 3D experiments may have finite k⊥.
  • domain assumption A continuously driven seed wave makes the temporal damping of the child Alfvén wave Γ2 = 0 in the threshold condition.
    Section II uses this to reduce the threshold condition Eq. (1) to γg > 0 and to derive Eq. (2). This is the conceptual basis for the threshold-less claim.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A novel scheme for measuring the growth of Alfven wave parametric decay instability using counter-propagating waves." pith.science (2026). https://pith.science/paper/3OYP2I3D

@misc{pith2026250713590,
  author       = {Pith},
  title        = {Pith review of: A novel scheme for measuring the growth of Alfven wave parametric decay instability using counter-propagating waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3OYP2I3D}},
  note         = {Machine review of arXiv:2507.13590}
}
read the original abstract

The parametric decay instability (PDI) of Alfven waves -- where a pump Alfven wave decays into a backward-propagating child Alfven wave and a forward ion acoustic wave -- is a fundamental nonlinear wave-wave interaction and holds significant implications for space and laboratory plasmas. However, to date there has been no direct experimental measurement of PDI. Here, we propose a novel and experimentally viable scheme to quantify the growth of Alfven wave PDI on a linear device using a large pump Alfven wave and a small counter-propagating seed Alfven wave, with the seed wave frequency tuned to match the backward Alfven wave generated by standard PDI. Using hybrid simulations, we show that energy transfer from the pump to the seed reduces the latter's spatial damping. By comparing seed wave amplitudes with and without the pump wave, this damping reduction can be used as a direct and reliable proxy for PDI growth. The method is validated in our simulations across a range of plasma and wave parameters and agrees well with theoretical predictions. Notably, the scheme exhibits no threshold for PDI excitation and is, in principle, readily implementable under current laboratory conditions. This scheme is a critical step toward solving the challenge of experimentally accessing Alfven wave PDI and provides an elegant method that may be used to validate fundamental theories of parametric instabilities in controlled laboratory settings.

Figures

Figures reproduced from arXiv: 2507.13590 by the authors.

Figure 1
Figure 1. FIG. 1. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A 1D hybrid simulation example. (a) Seed wave amplitude vs [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Comparison between measured PDI growth (scatters) and Eq. (3) (dashed curves). (a) Dependence of seed amplitude [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Seed wave amplitudes vs [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [42]

    Gekelman, P

    W. Gekelman, P. Pribyl, Z. Lucky, M. Drandell, D. Lene- man, J. Maggs, S. Vincena, B. Van Compernolle, S. Tri- pathi, G. Morales, et al., The upgraded large plasma device, a machine for studying frontier basic plasma physics, Review of Scientific Instruments 87 (2016)

    work page 2016

  2. [53]

    J. V. Hollweg, Beat, modulational, and decay instabilities of a circularly polarized alfven wave, Journal of Geophys- ical Research: Space Physics 99, 23431 (1994)

    work page 1994

  3. [1]

    Hurricane, P

    O. Hurricane, P. Patel, R. Betti, D. Froula, S. Regan, S. Slutz, M. Gomez, and M. Sweeney, Physics principles of inertial confinement fusion and us program overview, Reviews of Modern Physics 95, 025005 (2023)

    work page 2023

  4. [2]

    pump-on & no- reflection

    At the left boundary z = 0 (where the pump is injected and potential reflection may occur), the wave amplitude drops to δB2(z = 0) = 0 .3δB2(zm). The seed wave amplitudes as a function of z are repre- sented by the blue dashed curve in the figure. In the presence of PDI but without reflection, the seed wave evolves into δB ′ 2 = δB2(zm) exp[γ′ d(z − zm)] ...

    work page

  5. [3]

    D. S. Montgomery, Two decades of progress in under- standing and control of laser plasma instabilities in indi- rect drive inertial fusion, Physics of Plasmas 23 (2016)

    work page 2016

  6. [4]

    Klimo and V

    O. Klimo and V. Tikhonchuk, Laser–plasma interaction studies in the context of shock ignition: the regime dom- inated by parametric instabilities, Plasma Physics and Controlled Fusion 55, 095002 (2013)

    work page 2013

  7. [5]

    Hasegawa and L

    A. Hasegawa and L. Chen, Parametric decay of” kinetic alfv´ en wave” and its application to plasma heating, Phys- ical Review Letters 36, 1362 (1976)

    work page 1976

  8. [6]

    Sharma, S

    J. Sharma, S. C. Sharma, and A. Gahlot, Kinetic theory of effect of dust charge fluctuations on the parametric decay of lower hybrid wave instability by relativistic run- away electrons in tokamak, Physics of Plasmas28 (2021)

    work page 2021

Show all 55 references
  1. [7]

    A. Clod, M. Senstius, A. Nielsen, R. Ragona, A. Thrysøe, U. Kumar, S. Coda, S. Nielsen, and T. team, Cascades of parametric instabilities in the tokamak plasma edge during electron cyclotron resonance heating, Physical Re- view Letters 132, 135101 (2024)

    2024

  2. [8]

    A. S. Chirkin, V. V. Volkov, G. D. Laptev, and E. Y. Morozov, Consecutive three-wave interactions in nonlin- ear optics of periodically inhomogeneous media, Quan- tum Electronics 30, 847 (2000)

    2000

  3. [9]

    L. G. Wright, F. O. Wu, D. N. Christodoulides, and F. W. Wise, Physics of highly multimode nonlinear optical sys- tems, Nature Physics 18, 1018 (2022)

    2022

  4. [10]

    T. P. McKenna, H. S. Stokowski, V. Ansari, J. Mishra, M. Jankowski, C. J. Sarabalis, J. F. Herrmann, C. Lan- grock, M. M. Fejer, and A. H. Safavi-Naeini, Ultra-low- power second-order nonlinear optics on a chip, Nature Communications 13, 4532 (2022)

    2022

  5. [11]

    Ledezma, R

    L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A. Marandi, Intense optical parametric amplifica- tion in dispersion-engineered nanophotonic lithium nio- bate waveguides, Optica 9, 303 (2022)

    2022

  6. [12]

    Kadri and M

    U. Kadri and M. Stiassnie, Generation of an acoustic- gravity wave by two gravity waves, and their subsequent mutual interaction, Journal of Fluid Mechanics 735, R6 (2013)

    2013

  7. [13]

    M. Q. May and H. Qin, Nonlinear solution of classi- cal three-wave interaction via finite-dimensional quan- tum model, Journal of Plasma Physics 90, 805900302 (2024)

    2024

  8. [14]

    J. W. Belcher and L. Davis Jr, Large-amplitude alfv´ en waves in the interplanetary medium, 2, Journal of Geo- physical Research 76, 3534 (1971)

    1971

  9. [15]

    Knudsen, M

    D. Knudsen, M. Kelley, and J. Vickrey, Alfv´ en waves in the auroral ionosphere: A numerical model compared with measurements, Journal of Geophysical Research: Space Physics 97, 77 (1992)

    1992

  10. [16]

    De Pontieu, S

    B. De Pontieu, S. McIntosh, M. Carlsson, V. Hansteen, T. Tarbell, C. Schrijver, R. Shine, S. Tsuneta, Y. Kat- sukawa, K. Ichimoto, et al. , Chromospheric alfv´ enic waves strong enough to power the solar wind, Science 318, 1574 (2007)

    2007

  11. [17]

    J. C. Kasper, S. D. Bale, J. W. Belcher, M. Berthomier, A. W. Case, B. D. Chandran, D. Curtis, D. Gallagher, S. Gary, L. Golub, et al., Alfv´ enic velocity spikes and rotational flows in the near-sun solar wind, Nature 576, 228 (2019)

    2019

  12. [18]

    Lysak, Kinetic alfv´ en waves and auroral particle ac- celeration: A review, Reviews of Modern Plasma Physics 7, 6 (2023)

    R. Lysak, Kinetic alfv´ en waves and auroral particle ac- celeration: A review, Reviews of Modern Plasma Physics 7, 6 (2023)

    2023

  13. [19]

    Chen and F

    L. Chen and F. Zonca, Physics of alfv´ en waves and en- ergetic particles in burning plasmas, Reviews of Modern Physics 88, 015008 (2016). 7

    2016

  14. [20]

    Gekelman, S

    W. Gekelman, S. Vincena, B. Van Compernolle, G. Morales, J. Maggs, P. Pribyl, and T. Carter, The many faces of shear alfv´ en waves, Physics of Plasmas18 (2011)

    2011

  15. [21]

    Carter, B

    T. Carter, B. Brugman, P. Pribyl, and W. Lybarger, Lab- oratory observation of a nonlinear interaction between shear alfv´ en waves, Physical review letters 96, 155001 (2006)

    2006

  16. [22]

    Howes, D

    G. Howes, D. Drake, K. Nielson, T. Carter, C. Kletz- ing, and F. Skiff, Toward astrophysical turbulence in the laboratory, Physical review letters 109, 255001 (2012)

    2012

  17. [23]

    J. W. Schroeder, G. Howes, C. Kletzing, F. Skiff, T. Carter, S. Vincena, and S. Dorfman, Laboratory mea- surements of the physics of auroral electron acceleration by alfv´ en waves, Nature communications12, 3103 (2021)

    2021

  18. [24]

    Del Zanna, M

    L. Del Zanna, M. Velli, and P. Londrillo, Parametric decay of circularly polarized alfv´ en waves: Multidimen- sional simulations in periodic and open domains, Astron- omy & Astrophysics 367, 705 (2001)

    2001

  19. [25]

    G. G. Howes and K. D. Nielson, Alfv´ en wave collisions, the fundamental building block of plasma turbulence. i. asymptotic solution, Physics of Plasmas 20 (2013)

    2013

  20. [26]

    B. D. Chandran, Parametric instability, inverse cascade and the range of solar-wind turbulence, Journal of plasma physics 84 (2018)

    2018

  21. [27]

    Z. Qiu, L. Chen, F. Zonca, and W. Chen, Nonlinear de- cay and plasma heating by a toroidal alfv´ en eigenmode, Physical Review Letters 120, 135001 (2018)

    2018

  22. [28]

    Malara, L

    F. Malara, L. Primavera, and P. Veltri, Parametric insta- bility: an evolutive mechanism for the alfv´ enic turbulence in the solar wind, Universe 8, 391 (2022)

    2022

  23. [29]

    Shoda, T

    M. Shoda, T. Yokoyama, and T. K. Suzuki, Frequency- dependent alfv´ en-wave propagation in the solar wind: Onset and suppression of parametric decay instability, The Astrophysical Journal 860, 17 (2018)

    2018

  24. [30]

    Y. J. Rivera, S. T. Badman, M. L. Stevens, J. L. Verniero, J. E. Stawarz, C. Shi, J. M. Raines, K. W. Paulson, C. J. Owen, T. Niembro, P. Louarn, S. A. Livi, S. T. Lepri, J. C. Kasper, T. S. Horbury, J. S. Halekas, R. M. Dewey, R. D. Marco, and S. D. Bale, In situ observations...

    2024

  25. [31]

    M. Hahn, X. Fu, and D. W. Savin, Evidence for paramet- ric decay instability in the lower solar atmosphere, The Astrophysical Journal 933, 52 (2022)

    2022

  26. [32]

    T. A. Bowen, S. Badman, P. Hellinger, and S. D. Bale, Density fluctuations in the solar wind driven by alfv´ en wave parametric decay, The Astrophysical Journal Let- ters 854, L33 (2018)

    2018

  27. [33]

    Derby Jr, Modulational instability of finite-amplitude, circularly polarized alfven waves, The Astrophysical Journal 224, 1013 (1978)

    N. Derby Jr, Modulational instability of finite-amplitude, circularly polarized alfven waves, The Astrophysical Journal 224, 1013 (1978)

    1978

  28. [34]

    M. L. Goldstein, An instability of finite amplitude circu- larly polarized alfv´ en waves, The Astrophysical Journal 219, 700 (1978)

    1978

  29. [35]

    J. V. Hollweg, R. Esser, and V. Jayanti, Modulational and decay instabilities of alfv´ en waves: Effects of stream- ing he++, Journal of Geophysical Research: Space Physics 98, 3491 (1993)

    1993

  30. [36]

    X. Fu, H. Li, F. Guo, X. Li, and V. Roytershteyn, Para- metric decay instability and dissipation of low-frequency alfv´ en waves in low-beta turbulent plasmas, The Astro- physical Journal 855, 139 (2018)

    2018

  31. [37]

    F. Li, X. Fu, and S. Dorfman, Parametric decay of alfv´ enic wave packets in nonperiodic low-beta plasmas, The Astrophysical Journal 924, 33 (2022)

    2022

  32. [38]

    Nariyuki, S

    Y. Nariyuki, S. Matsukiyo, and T. Hada, Parametric in- stabilities of large-amplitude parallel propagating alfv´ en waves: 2d pic simulation, New Journal of Physics 10, 083004 (2008)

    2008

  33. [39]

    Dorfman and T

    S. Dorfman and T. Carter, Nonlinear excitation of acous- tic modes by large-amplitude alfv´ en waves in a laboratory plasma, Physical Review Letters 110, 195001 (2013)

    2013

  34. [40]

    Dorfman and T

    S. Dorfman and T. Carter, Observation of an alfv´ en wave parametric instability in a laboratory plasma, Physical Review Letters 116, 195002 (2016)

    2016

  35. [41]

    X. Zhu, L. Zeng, Z. Qiu, S. Lin, T. Zhang, J. Bao, Y. Hu, T. Tang, H. Liu, D. Kong, et al., Nonlinear mode couplings between geodesic acoustic mode and toroidal alfv´ en eigenmodes in the east tokamak, Physics of Plas- mas 29 (2022)

    2022

  36. [43]

    Nishikawa, Parametric excitation of coupled waves i

    K. Nishikawa, Parametric excitation of coupled waves i. general formulation, Journal of the Physical Society of Japan 24, 916 (1968)

    1968

  37. [44]

    F. Li, X. Fu, and S. Dorfman, Effects of wave damp- ing and finite perpendicular scale on three-dimensional alfv´ en wave parametric decay in low-beta plasmas, Physics of Plasmas 31, 082113 (2024)

    2024

  38. [45]

    R. Z. Sagdeev and A. A. Galeev, Nonlinear plasma the- ory, Nonlinear Plasma Theory (1969)

    1969

  39. [46]

    Morales and J

    G. Morales and J. Maggs, Structure of kinetic alfv´ en waves with small transverse scale length, Physics of Plas- mas 4, 4118 (1997)

    1997

  40. [47]

    Thuecks, C

    D. Thuecks, C. Kletzing, F. Skiff, S. Bounds, and S. Vin- cena, Tests of collision operators using laboratory mea- surements of shear alfv´ en wave dispersion and damping, Physics of plasmas 16, 052110 (2009)

    2009

  41. [48]

    S. Bose, T. Carter, M. Hahn, S. Tripathi, S. Vincena, and D. W. Savin, Measured reduction in alfv´ en wave en- ergy propagating through longitudinal gradients scaled to match solar coronal holes, The Astrophysical Journal 882, 183 (2019)

    2019

  42. [49]

    R. M. G. M. Trines, F. Fi´ uza, R. Bingham, R. A. Fonseca, L. O. Silva, R. A. Cairns, and P. A. Norreys, Simulations of efficient Raman amplification into the multipetawatt regime, Nature Physics 7, 87 (2011)

    2011

  43. [50]

    Karimabadi, H

    H. Karimabadi, H. Vu, D. Krauss-Varban, and Y. Omelchenko, Global hybrid simulations of the earth’s magnetosphere, in Numerical Modeling of Space Plasma Flows, Vol. 359 (2006) p. 257

    2006

  44. [51]

    F. Li, X. Fu, and S. Dorfman, Hybrid simulation of alfv´ en wave parametric decay instability in a laboratory relevant plasma, Physics of Plasmas 29, 092108 (2022)

    2022

  45. [52]

    Gigliotti, W

    A. Gigliotti, W. Gekelman, P. Pribyl, S. Vincena, A. Kar- avaev, X. Shao, A. S. Sharma, and D. Papadopoulos, Generation of polarized shear alfv´ en waves by a rotat- ing magnetic field source, Physics of Plasmas 16, 092106 (2009)

    2009

  46. [54]

    Chen, Introduction to plasma physics and controlled fusion (Springer, 2015)

    F. Chen, Introduction to plasma physics and controlled fusion (Springer, 2015)

    2015

  47. [55]

    S. Bose, J. M. TenBarge, T. Carter, M. Hahn, H. Ji, 8 J. Juno, D. W. Savin, S. Tripathi, and S. Vincena, Ex- perimental study of alfv´ en wave reflection from an alfv´ en- speed gradient relevant to the solar coronal holes, The Astrophysical Journal 971, 72 (2024)

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.