Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities

Dmitri A. Uzdensky; Gregory R. Werner; Mitchell C. Begelman; Tsun Hin Navin Tsung

REVIEW 4 major objections 8 minor 53 references

Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities

T0 review · 4 major / 8 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read At a jet-wind boundary combining velocity and magnetic shear, the Kelvin-Helmholtz and drift-kink instabilities act together to dissipate up to half the available energy and generate nonthermal particle tails.

desk verdict A clean 2D PIC study showing KH and DK instabilities interact to dissipate much more energy than either alone; the main caveat is that tearing modes are excluded by the 2D setup, so the astrophysical extrapolation is not yet closed. read the letter →

arxiv 2501.04090 v1 pith:IMSRVBW6 submitted 2025-01-07 astro-ph.HE physics.plasm-ph

Tsun Hin Navin Tsung , Gregory R. Werner , Dmitri A. Uzdensky , Mitchell C. Begelman This is my paper · ORCID

classification astro-ph.HEphysics.plasm-ph

keywords relativisticjetsKelvin-Helmholtzinstabilitydrift-kinkparticle-in-cellsimulationmagneticdissipationnonthermalparticleaccelerationpairplasmashearflow

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

Astrophysical jets are thought to have a fast spine and a slower sheath, so their boundaries combine velocity shear with magnetic-field shear. This paper uses first-principles particle-in-cell simulations of a collisionless relativistic pair plasma to ask what happens when both shears are present at once. Its central claim is that the Kelvin-Helmholtz and drift-kink instabilities do not merely add: drift-kink modes shred the vortices made by the Kelvin-Helmholtz modes, and this interplay dissipates up to about half of the initial magnetic and bulk kinetic energy, whereas pure velocity shear dissipates almost none. The same interaction produces nonthermal power-law particle tails with a spectral index near 2.5 through coherent instability-driven electric fields acting on Speiser-like orbits close to the shear layer. If correct, the result means that jet-wind boundaries are much more efficient dissipators and particle accelerators than either shear alone would suggest.

What carries the argument

The central mechanism is the nonlinear interaction between two named instabilities: the Kelvin-Helmholtz instability, the rollup of a velocity-shear interface into vortices, and the drift-kink instability, the kink of a thin current sheet with a reversing magnetic field. In the combined-shear runs, the DK plumes disrupt the KHI cat's-eye vortices on the DK timescale, which breaks the spatial periodicity that would otherwise make the time-averaged electric field along a particle's trajectory cancel out. The resulting coherent perturbed electric field, mainly $E_x$ (with additional $E_y$ contributions), accelerates particles performing Speiser-like bounces across the shear interface; the same periodicity-breaking is what turns the free energy of the sheared fields into heat and nonthermal particles. The paper tracks this quantitatively with a time- and space-averaged profile $\langle E_x(y)\rangle$, whose peak magnitude tracks the magnetic-energy dissipation across the explored range of $u_j$.

What would settle it

Run a three-dimensional particle-in-cell simulation with the same physical parameters used here ($\theta_j = 1$, $\sigma_j = 1$, $u_j = 0.3$, $B_w/B_j = -1$) and a box elongated in the $z$-direction long enough to let tearing modes grow; if the dissipated fractions $\Delta E_B/E_{B,0}$ and $\Delta E_{KE}/E_{KE,0}$ no longer reach the 2D values, or the nonthermal tail index moves far from 2.5, then the reported KH-DK enhancement is not the dominant dissipation channel in three dimensions.

Watch

Extended reading notes

Core claim

The central discovery is that the nonlinear interaction of the Kelvin-Helmholtz instability (KHI), driven by velocity shear, and the drift-kink instability (DKI), driven by magnetic-field shear, creates a turbulent shear layer and dissipates far more energy than either instability alone. In the velocity-shear-only control case the KHI produces cat's-eye vortices that persist without dissipating magnetic energy and convert less than 5% of the bulk kinetic energy, because the periodic vortices give particles an oscillating electric field that cancels along their paths. When magnetic shear is added, the DK plumes disrupt those vortices, break the periodicity, and produce a net averaged electric field near the interface; particles then gain energy in Speiser-like orbits, yielding nonthermal power-law tails with index about 2.5. The dissipated fractions of magnetic and bulk kinetic energy reach approximately half at moderate velocity shear ($0.2 < u_j < 0.6$) and are suppressed both for weak shear and for super-magnetosonic shear, showing that the synergy is sharply tuned by the flow speed.

Load-bearing premise

The load-bearing premise is that simulating only two dimensions, which also removes the tearing instability and magnetic reconnection, still captures how a real three-dimensional jet-wind boundary dissipates its energy.

Editorial extensions

If this is right

When both shears are present, up to half of the initial magnetic and bulk kinetic energy is converted into heat, whereas velocity shear alone dissipates none of the magnetic energy and less than 5% of the bulk kinetic energy.
The dissipation efficiency is sharply sensitive to the velocity shear: it peaks in the range $0.2 < u_j < 0.6$, drops for weak shear because the flow suppresses DK plumes, and drops again for super-magnetosonic shear because KHI itself is suppressed.
Nonthermal particle acceleration with a power-law index near 2.5 arises in this 2D system without any magnetic reconnection, through the alignment of instability-driven electric fields with Speiser-like particle motion.
The saturated state is a relatively stagnant, field-suppressed annihilated core wrapped in an active KH cocoon, so the thickness of the magnetic shear layer is a reliable proxy for how much magnetic energy has been dissipated.

Reading between the lines

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

The periodicity-breaking principle is likely general: any secondary instability or imposed perturbation that decorrelates the electric field along particle trajectories could convert oscillatory $E_x$ into net acceleration, so the KH-DK synergy may be one instance of a broader dissipation channel in sheared collisionless plasmas.
Because the 2D setup deliberately forbids tearing modes, the quantitative dissipation fractions in a real three-dimensional jet-wind boundary could differ; the natural extension is to run a 3D simulation with a finite $L_z$ and test whether tearing-driven reconnection replaces, augments, or overwhelms the KH-DK enhancement.
The pronounced peak at intermediate $u_j$ suggests a matching condition between the KH and DK growth rates or wavelengths; a linear-theory scan across $\sigma_j$, $B_w/B_j$, and the shear width $\Delta$ could predict where the synergy is strongest before running expensive PIC simulations.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear [Colleague],

The paper you'll want to know about: Tsung et al. run 2D PIC simulations of a relativistic pair-plasma shear layer with both velocity and magnetic shear, deliberately arranged so that only KH and DK instabilities can grow and tearing modes cannot. That setup is new as far as I know, and it pays off: they find that the combined shears dissipate up to ~50% of the initial magnetic and bulk kinetic energy, while pure velocity shear dissipates almost nothing, and the dissipation peaks at intermediate shear velocities in a way that tracks the thickened shear layer width. They also see nonthermal tails with a spectral index around 2.5, and particle tracking shows Speiser-like motion with net acceleration driven by a coherent Ex that arises when the KH vortices break the periodicity of DK plumes.

The evidence is solid for what it claims. Energy conservation holds to 0.2%. The control cases (VS only, MS only) isolate each instability, and the parameter scan over uj shows a non-monotonic response that is not trivially predictable from linear theory. The dissipation fractions and layer widths are direct simulation outputs, not fitted constants. The code and method details are transparent enough to reproduce.

The soft spots are real but not fatal. The biggest one is the 2D geometry: tearing modes are excluded by design, which is fine for isolating KH and DK, but the astrophysical punchline about jet-wind boundaries assumes that tearing would not dominate in 3D. That is exactly the standard competitor in this kind of current sheet. The paper acknowledges this and leaves 3D to future work, but it does not provide even a linear-timescale comparison with tearing, so the extrapolation is open. A second gap is that the 'vortex disruption' mechanism is qualitative. They mention the linear growth rates are not shown; showing those, even in an appendix, would help. No convergence tests are shown (resolution, box, particle number), and the particle-acceleration analysis leans on a time- and x-averaged Ex proxy, which they themselves flag as preliminary. None of these undercut the central dissipation result; they just mean the paper is a strong first step, not the last word.

Who should read it: anyone working on kinetic dissipation in shear layers, jet-wind boundaries, or the competition between instabilities in current sheets. It deserves a serious referee. My recommendation: send it to review, and ask the authors for the linear growth-rate comparison and at least a one-dimensional statement about tearing timescales in 3D. That would turn a conditional into a clear accept.

Referee Report

4 major / 8 minor

Summary. This Letter reports 2D relativistic pair-plasma PIC simulations of a double shear layer in which both velocity shear and magnetic shear are present, so that the Kelvin-Helmholtz (KH) and drift-kink (DK) instabilities can operate while tearing modes are excluded by the 2D geometry. The authors compare the combined-shear case with velocity-shear-only (VS) and magnetic-shear-only (MS) controls, and find that the KH and DK instabilities interact nonlinearly: DK plumes disrupt the KH cat's-eye vortices, producing a turbulent shear layer, an 'annihilated core', and substantial dissipation of magnetic and bulk kinetic energy (up to ~50% for moderate velocity shear). They also report nonthermal power-law tails (p ≈ 2.5) and argue that a time- and x-averaged Ex generated by the KH-DK interaction is responsible for net particle acceleration via Speiser-like motion. The central claim is that combined shear leads to a significant enhancement of dissipation and particle acceleration relative to either instability acting alone.

Significance. If the central result holds, the paper provides the first kinetic-level demonstration that simultaneous velocity and magnetic shear can produce dissipation and nonthermal particle acceleration qualitatively different from either shear alone, with direct relevance to spine-sheath jet boundaries. The study is carefully set up: it uses a self-consistent Maxwell-Jüttner initial condition with pressure balance, two independent control cases, and reports total energy conservation to 0.2%. The measured quantities (dissipation fractions, shear-layer widths, power-law indices) are direct simulation outputs rather than fitted parameters, and the authors are appropriately candid about the 2D limitation concerning tearing modes. The main weaknesses are the reliance on an untested 2D suppression of tearing modes for the astrophysical extrapolation, the use of an averaged-field proxy rather than per-particle diagnostics for the acceleration mechanism, and the absence of the linear growth-rate calculation used to support the interpretation of the non-monotonic shear-width dependence.

major comments (4)

[Abstract; Results (Fig. 4 and surrounding text)] The abstract states that the combined case produces 'a significant enhancement of dissipation over cases with only velocity shear or only magnetic shear,' but the Results show that this is not true for all parameters: the text says 'even a weak velocity shear is enough to reduce the dissipation of magnetic energy with DK plumes alone.' For uj < 0.1 the combined case evidently dissipates less magnetic energy than the MS case. The headline claim should be qualified to the moderate-shear regime (roughly 0.2 < uj < 0.6) where the enhancement is actually observed, otherwise the abstract overstates the range of validity of the synergy.
[Methods, second paragraph; Conclusions] The suppression of tearing modes is load-bearing for the astrophysical conclusion. The manuscript states explicitly that 'Since the z-direction is not simulated, no tearing modes can be excited (a full 3D study is left to future work)' and that this 'allows us to focus on the KH and DK modes and their interplay.' However, the equilibrium is a reversing current sheet, and in 3D tearing-type reconnection is a standard competitor to DKI on exactly such configurations. If a k_z-dependent tearing mode grows on a comparable or faster timescale, it could pre-empt the DK plumes, alter the 'annihilated core' morphology, and change the reported -ΔE_B/E_B,0 and -ΔE_KE/E_KE,0 values. Because the conclusions are framed in terms of real jet-wind boundaries, the paper should provide at least a quantitative linear estimate (or a single 3D run) showing that tearing growth is slow compared with the KH-DK interaction timescale. As written, the extrapolation rests on an untested assumption.
[Results, Fig. 8 and the paragraph introducing it] The particle-acceleration mechanism is inferred from a time- and x-averaged profile of Ex(y), which the authors explicitly call 'a proxy for the average Ex experienced by the particles.' But 10^5 particles are tracked, so the actual Ex experienced along each trajectory can be computed directly. Without trajectory-resolved averages, the claim that a net averaged Ex is responsible for the acceleration and its correlation with dissipation remains indirect. Please compute the mean Ex along the accelerated-particle trajectories (and, if feasible, the correlation between trajectory-averaged Ex and final Lorentz factor) to support the proposed mechanism.
[Results, Fig. 3 and the subsequent paragraph] The non-monotonic dependence of the saturated shear-layer width on uj is attributed to nonlinear interplay based on the statement that the linear growth rate 'shows no such rebound (not shown here for brevity).' Since this linear calculation is the key evidence that the rebound is nonlinear, it should be shown (or a precise reference with the same parameters should be given). Without it, the interpretation of the non-monotonic width—and the related dissipation trend—is not fully verifiable.

minor comments (8)

[Introduction, first paragraph] There is a typo: 'DK coexisits with KH' should be 'DK coexists with KH'.
[Methods, first paragraph] The sentence 'the total rest-frame densities (electron plus position)' should read 'electron plus positron'; similarly, 'tracked the trajectories of 10 5 electrons and positions' should be 'positrons' and the superscript should be formatted as 10^5.
[Fig. 6 caption] The caption uses 'tc/Lc = 27.3'; this should be 'tc/Lx = 27.3' for consistency with the rest of the paper.
[Fig. 6, right panel] The axis label 'uj = 0.3c' is confusing: uj is a 4-velocity, not a velocity, so the 'c' should be omitted (as in the text, which uses 'uj = 0.3').
[Fig. 7 caption] The word 'oranged dashed line' should be 'orange dashed line'.
[Results, Fig. 6 discussion] The power-law index p ≈ 2.5 is presented without a fit range or uncertainty; the right panel of Fig. 6 shows that p varies substantially with energy, so the paper should state the energy interval over which the index is approximately constant, or describe the tail as only 'crude' (as the text does) without implying a robust power law.
[Results, description of Fig. 2] The phrase 'the upper-top two panels' is awkward; consider 'the top two panels'.
[Appendix C, step 5] The phrase 'over all volume' should be 'over the entire volume'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: combined-shear dissipation is a direct simulation measurement, not a fitted or self-referential result.

full rationale

The central claim is an empirical result of first-principles PIC simulations: the dissipation fractions (Figs. 3 and 4), shear-layer widths, and nonthermal power-law indices are read directly from the simulated plasma evolution, not derived by construction from the input parameters. No parameter is fitted to reproduce the enhancement, and no equation defines the combined-shear dissipation in terms of the initial profiles in a self-referential way. The self-citations present in the paper (the Zeltron code paper [44], and prior reconnection studies [30,38]) are background tools and external benchmarks, not load-bearing inputs that force the KH-DK synergy conclusion. The explicit limitation in Methods, 'Since the z-direction is not simulated, no tearing modes can be excited (a full 3D study is left to future work)', is an assumption about scope rather than a circular step: the paper does not invoke a tearing-mode result as an input to derive the KH-DK interaction. Without a demonstrated reduction of an output equation to an input equation, or a fitted parameter renamed as a prediction, no circularity is present. The 2D restriction is a genuine physical caveat for astrophysical extrapolation, but it does not make the derivation circular. Therefore the circularity score is 0.

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

The central claim rests on the representativeness of the 2D PIC setup and on several chosen dimensionless parameters. No new physical entities are introduced, and no numbers are fitted to external data. The most fragile inputs are the 2D suppression of tearing modes and the unpublished linear growth-rate comparison.

free parameters (5)

shear layer half-thickness Delta = 5 de,j
Chosen initial width of the velocity and magnetic shear layers; it controls the growth rates and saturation of KH and DK modes. Not fitted, but not scanned in this study.
jet magnetization sigma_j = 1
Chosen so that the electron inertial length, Debye length, and gyroradius are comparable. Not varied, so the result may depend on this value.
jet temperature theta_j = 1
Chosen to make the plasma relativistically warm. Not varied, so the result is specific to this thermal state.
wind-to-jet magnetic field ratio B_w/B_j = -1 (main scan), 0 and +1 in controls
Sets the magnetic shear direction and magnitude. The central combined-shear result uses B_w/B_j = -1; the controls use 0 (velocity shear only) and +1 (uniform field).
jet 4-velocity scan range u_j = 0.01 to 0.9
The independent control parameter scanned to map the dissipation dependence. The claimed peak in dissipation for intermediate values (0.2-0.6) depends on this range.

assumptions (5)

domain assumption The PIC method with 1024x3072 grid and 128 particles per cell adequately resolves kinetic scales and numerical noise does not dominate dissipation.
Used in Methods; no convergence study is shown.
domain assumption The initial equilibrium in Appendix A (pressure balance, ideal-MHD Ohm's law, Maxwell-Juttner sampling) is a valid representation of a jet-wind boundary and does not seed spurious modes.
The equilibrium is self-consistent but uses equal rest-frame densities and temperatures, and no noise calibration is reported.
domain assumption The Eckart-frame decomposition in Appendix C correctly separates thermal and bulk kinetic energy for relativistic pair flows.
The decomposition assumes the zero-particle-flux frame; other frame choices can change the bulk energy estimate, and no comparison is given.
domain assumption Suppressing the z dimension forbids tearing modes, so only KH and DK instabilities act.
Methods: 'Since the z-direction is not simulated, no tearing modes can be excited (a full 3D study is left to future work).' This is the key isolation premise.
ad hoc to paper The linear growth-rate analysis (not shown) correctly supports the interpretation of the non-monotonic shear-width dependence.
Results: 'This is quite different from the uj-dependence of the linear growth rate (not shown here for brevity).' The reader cannot verify this premise from the paper.

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Cite this review

Pith. "Pith review of Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities." pith.science (2026). https://pith.science/paper/IMSRVBW6

@misc{pith2026250104090,
  author       = {Pith},
  title        = {Pith review of: Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMSRVBW6}},
  note         = {Machine review of arXiv:2501.04090}
}

read the original abstract

We present 2D particle-in-cell simulations of a magnetized, collisionless, relativistic pair plasma subjected to combined velocity and magnetic-field shear, a scenario typical for astrophysical black-hole jet-wind boundaries. We create conditions where only the Kelvin-Helmholtz (KH) and Drift-Kink (DK) instabilities can develop, while tearing modes are forbidden. We find that DKI can effectively disrupt the cats-eye vortices generated by KHI, creating a turbulent shear layer on the DK timescale. This interplay leads to a significant enhancement of dissipation over cases with only velocity shear or only magnetic shear. Moreover, we observe efficient nonthermal particle acceleration caused by the alignment of the instability-driven electric fields with Speiser-like motion of particles close to the shear interface. This study highlights the sensitivity of dissipation to multiple simultaneous instabilities, thus providing a strong motivation for further studies of their nonlinear interaction at the kinetic level.

Figures

Figures reproduced from arXiv: 2501.04090 by the authors.

**Figure 3.** FIG. 3. Left [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 2.** FIG. 2. Snapshots of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Top and bottom left: The total magnetic and bulk ki [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 6.** Figure 6: FIG. 6. Left: Particle energy distributions for the VS, MS [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: FIG. 7. Top left: Initial positions of particles (blue dots) [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

These lab-frame quanti- ties are outputted automatically in Zeltron

For each species s, calculate the number density n = P l wl/∆V , the stress tensor Πij = P l γlms,lwlvl,ivl,j/∆V , momentum den- sity Up,i = P l γlms,lwlvl,i/∆V , energy density Ue = P l γlwlms,lc2/∆V and particle flux Fi =P l wlvl,i/∆V at each grid point, where the sum is taken over all (macro)particles in the neighborhood of a cell, wl is the weight of ...

work page

[2] [2]

Note that scalar quantities such as Ue, nare rotationally in- variant

Rotate the lab-frame vector and tensor quantities Up, F, Π to the frame x′, y′, z′ such that the par- ticle flux F′ points in the x′-direction. Note that scalar quantities such as Ue, nare rotationally in- variant

work page

[3] [3]

The components of the comoving thermal pressure tensor in the rotated frame can be obtained by the following equations: P ′ x′x′ = Γ2 b Π′ x′x′ − 2vbU ′ p,x′ + (vb/c)2Ue , P ′ x′y′ = Γb Π′ x′y′ − vbU ′ p,y′ , P ′ x′z′ = Γb Π′ x′z′ − vbU ′ p,z′ , P ′ y′y′ = Π′ y′y′, P ′ y′z′ = Π′ y′z′, P ′ z′z′ = Π′ z′z′, where vb = F ′ x′/n is the bulk speed of the Eckart...

work page

[4] [4]

The bulk-flow dynamic pressure can be obtained by subtracting Pij from Πij (i.e

Inverse-rotate P ′ i′j′ to obtain the thermal pressure tensor Pij in the lab frame. The bulk-flow dynamic pressure can be obtained by subtracting Pij from Πij (i.e. Pb,ij = Π ij − Pij). These are then the thermal and dynamic pressure tensors for species s

work page

[5] [5]

The justification for the procedure is as follows

The total bulk-flow kinetic and thermal ener- gies can then be obtained by taking the trace of the respective pressure tensors over all volumeP V P i Pb,ii∆V and P V P i Pii∆V , for all species present. The justification for the procedure is as follows. First, note that thermal pressure is defined in the bulk frame of the plasma: Pij = Z d3¯ p¯f ¯γms¯vi¯v...

work page

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R. D. Blandford and J. E. Pringle, Kelvin-Helmholtz in- stability of relativistic beams., MNRAS 176, 443 (1976)

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J. M. Attridge, D. H. Roberts, and J. F. C. Wardle, Ra- dio Jet-Ambient Medium Interactions on Parsec Scales in the Blazar 1055+018, ApJ Lett. 518, L87 (1999), arXiv:astro-ph/9903330 [astro-ph]

arXiv 1999

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Radio Emission from 3D Relativistic Hydrodynamic Jets: Observational Evidence of Jet Stratification

M.-A. Aloy, J.-L. G´ omez, J.-M. Ib´ a˜ nez, J.-M. Mart ´ ı, and E. M¨ uller, Radio Emission from Three-dimensional Relativistic Hydrodynamic Jets: Observational Evi- dence of Jet Stratification, ApJ Lett. 528, L85 (2000), arXiv:astro-ph/9911153 [astro-ph]

work page Pith review arXiv 2000