How quickly can electron-seeded matter–antimatter avalanches grow in realistic intense laser fields? The authors derive a general analytical growth-rate model that includes electrons, positrons and photons escaping from the strongest-field region. Comparisons with Monte Carlo and particle-in-cell simulations support its predictions, including a focus-dependent onset threshold and a high-field regime where local production dominates escape. The model also estimates conditions for dense pair plasma and screening of the generating field. It assumes a cascade can reach a quasisteady state and seed

Strong-field physics · Theory & simulation

Powerful lasers could bring the extreme physics around neutron stars into a laboratory. First, a tiny chain reaction has to win a race.

One particle. Then a possibility.

Start with an electron, a tiny particle carrying negative electric charge. In exceptionally strong light, it can help make more particles. Follow the three steps.

What lets the next generation repeat the cycle?

Make the avalanche survive.

Two opposing lasers make a region of intense electric field. Particles multiply there, but they also leave. Raise the field until reproduction wins.

Change the conditions

a₀ is the combined peak field in the paper’s units. Double a₀ and the laser intensity becomes four times larger.

A wider spot gives particles more time to reproduce before leaving. Here, peak field and spot size are varied independently.

Particles leave faster than the chain can replace them. Increase the peak field to cross the threshold.

Calculated from the authors’ growth model, not experimental measurements. One laser cycle is about 2.7 femtoseconds; one femtosecond is a millionth of a billionth of a second. Motion is slowed for exploration.

The new insight is the escape threshold. Strong light alone is not enough: the local population grows only when the chain reaction can replace its losses. At much stronger fields, reproduction is so fast that escape has much less influence.

The paper calls an electron–positron avalanche a quantum electrodynamic cascade . Quantum electrodynamics describes how light and charged particles interact. The plotted population is the expected local population divided by its value at the start of the steady exponential phase. It is not the fate of a single, guaranteed seed particle. The plot uses a logarithmic population axis; its vertical range adapts to the selected conditions, with the top value shown.

Emission and pair-creation probability rates are calculated using the authors’ supplemental tables. The characteristic emission state comes from Equation 16; Equations 24 and 26 supply the rates used in Equation 28. The largest growth-rate solution of Equation 22 includes both charge and photon migration:

Wrad is the photon-emission rate; Wcr is the pair-creation rate. νe and νγ are the rates at which charges and photons leave. For these focused beams, the estimates per laser cycle are νeT = 1 + 2λ/w₀ and νγT = 2λ/w₀ (Section V A). a₀ = eE₀/(mcω) expresses the peak electric field using electron properties and laser frequency.

The experiment fixes wavelength at 0.8 μm and assumes circular polarization, seed electrons already at the focus, a quasisteady cascade, and a low enough density that the particles have not changed the laser field. It has no finite pulse envelope. The illustrative paths do not solve individual particle motion.

A wider spot. A bigger bill?

A wide spot lets particles stay longer. That lowers the field needed to start an avalanche. But illuminating a larger area also costs more total laser power.

Intensity per beam: 17.2 × 10²³ W/cm²

Tight focusing needs a stronger field, but it reaches the threshold with less total power.

Paper predictions, Table I, page 14. λ is one laser wavelength, here 0.8 μm. One petawatt (PW) is one million billion watts. These are peak powers for extremely short pulses.

If total laser power is your limit, which spot helps?

The race appears in the evidence.

The researchers compared their analytical model with simulations that track particles and fields. The focused-beam results show both parts of the story.

Different thresholds. A shared high-field trend.

Near the left side, the different spot sizes have distinct onset thresholds. Escape matters most here: a small change in field or focus can change whether the local population shrinks or grows.

Farther right, at stronger fields, the colored curves approach one another. Pair creation happens rapidly in the strongest region, so the local field becomes the main driver.

The paper extends this calculation to a uniform rotating electric field, a standing wave, a single tightly focused beam, and an optimized eight-beam arrangement.

The horizontal axis gives the combined peak field a₀ = eE₀/(mcω); the top axis translates it to the intensity of one beam. The vertical axis is growth per field period, ΓT. Both axes use logarithmic spacing. The colored dashed lines mark Γ = 0 thresholds; negative growth cannot appear on this logarithmic vertical axis. The inset shows where the electric field is strongest.

A path toward laboratory astrophysics.

The authors predict that arranging eight beams to reinforce the field at one focus could bring the avalanche onset within a much smaller power budget.

Table I and Section V C. The arrangements have different field geometry and polarization; this is a comparison of their predicted power requirements.

Starting an avalanche is the first step. The larger ambition is a pair plasma : a cloud of electrons and positrons dense enough to act together and influence the light that created it.

For the optimized eight-beam setup, the paper estimates about 22 PW to reach the reference plasma density within one laser cycle, given an initial electron density of 1% of that reference density. A much larger power, about 190 PW , is estimated for strong screening of the field.

These are predictions for future experiments. Making such a plasma could let researchers investigate matter and radiation processes relevant to the surroundings of neutron stars and black holes.

Table II, page 17, and discussion, pages 18–19. The reference is the electron critical density for the chosen laser frequency.

Growth Rate of Self-Sustained QED Cascades Induced by Intense Lasers

A. Mercuri-Baron, A. A. Mironov, C. Riconda, A. Grassi, and M. Grech. Physical Review X 15, 011062 (2025). DOI: 10.1103/PhysRevX.15.011062.

Article and reused figures: Creative Commons Attribution 4.0. Figure 8 is cropped and compressed. The AI-generated conceptual illustration was adapted with Figure 1 as a visual reference, preserving the colliding-beam geometry, particle cycle and escape mechanism.

Supplementary calculation material: probability-rate tables from the authors’ PairAvalanchesQED.jl package (GPL-3.0). Growth rates calculated here from the paper’s equations. The illustration and simulated particle motion are conceptual; numerical results describe the stated model.

The laser supplies energy throughout the cycle. In detail view, scroll across the illustration.