[Paper Review] Modeling of photon and pair production due to quantum electrodynamics effects in particle-in-cell simulation

Wenqi Wang, Z. M. Sheng+2 more|arXiv (Cornell University)|Aug 23, 2016

Quantum Electrodynamics and Casimir Effect3 citations

TL;DR

This paper presents KLAPS, a particle-in-cell (PIC) code enhanced with quantum electrodynamics (QED) effects to model photon generation via Compton scattering and electron-positron pair production via the Breit-Wheeler process in ultraintense laser-plasma interactions. The method employs two equivalent QED formulas for radiation rates and Monte Carlo event generators, with simulations showing excellent agreement with theoretical predictions and benchmark data from prior studies, validating its use for QED-dominant plasma simulations.

ABSTRACT

We develop the particle-in-cell (PIC) code KLAPS to include the photon generation via the Compton scattering and electron-positron creation via the Breit-Wheeler process due to quantum electrodynamics (QED) effects. We compare two sets of existing formulas for the photon generation and different Monte Carlo algorithms. Then we benchmark the PIC simulation results.

Motivation & Objective

• To develop a particle-in-cell (PIC) code capable of simulating quantum electrodynamics (QED) effects in ultraintense laser-plasma interactions.
• To implement accurate models for photon generation via Compton scattering and pair production via the Breit-Wheeler process.
• To benchmark the simulation results against theoretical formulas and established QED-PIC results from the literature.
• To validate the accuracy of different Monte Carlo algorithms for event generation under varying time steps and particle densities.
• To enable reliable simulation of QED-dominant regimes expected in next-generation 10-PW and 100-PW laser facilities.

Proposed method

• The KLAPS code incorporates QED effects using two equivalent formulas for photon emission rates: one based on Elkina and Nerush (Eq. 1), and another from Erber and Kirk (Eq. 4), both derived under weak-field and quasi-stationary approximations.
• Photon generation is modeled using a Monte Carlo event generator where the total emission rate determines the probability of photon emission per time step, with energy distribution sampled via inverse transform sampling using the cumulative distribution function.
• For pair production, the same formalism is applied using the formula for pair creation rate (Eq. 6), assuming symmetric emission behavior for electrons and positrons.
• Three distinct Monte Carlo event generation methods are implemented and compared: (I) rejection sampling with uniform random numbers, (II) cumulative probability with exponential distribution, and (III) modified cumulative condition.
• The simulation uses a 128×192 grid with one electron per cell, and time steps are adjusted adaptively to ensure $W \times Dt \leq 0.2$ for numerical stability.
• Benchmarking is performed against analytical solutions of the radiation and pair production rates, and against a published cascade simulation from Elkina et al.

Experimental results

Research questions

• RQ1 How accurately can a PIC code simulate photon emission rates via Compton scattering under high QED parameter regimes ($\chi_e \gtrsim 1$)?
• RQ2 Which of the two existing theoretical formulas for QED radiation rates (Elkina-Nerush vs. Erber-Kirk) provides better agreement with simulation results?
• RQ3 How do different Monte Carlo event generation algorithms affect the statistical convergence and accuracy of photon and pair production rates?
• RQ4 What time step resolution is required to maintain accuracy in QED-PIC simulations of high-energy processes?
• RQ5 Can the developed QED-PIC code reproduce established benchmark results for electron-positron cascade development in strong magnetic fields?

Key findings

• The two theoretical formulas for photon emission rates (Eq. 1 and Eq. 4) yield nearly identical results across different $\chi_e$ values, validating their equivalence in the simulation regime.
• The classic limit (Eq. 5) overestimates the high-energy photon emission rate, confirming the necessity of using full QED expressions in strong-field regimes.
• All three Monte Carlo event generation methods (I, II, III) produce statistically equivalent results, indicating robustness of the implementation across different sampling strategies.
• Simulation results for photon generation rates agree well with theoretical predictions across a range of $\chi_e$ values, with the best agreement achieved at $Dt = 0.2/W$.
• When the time step is increased to $Dt = 6/W$, the simulation deviates significantly from theory, highlighting the importance of small time steps for accuracy.
• The code successfully reproduces the benchmark cascade simulation from Elkina et al., with the number of pairs above 100 MeV matching published data within statistical uncertainty after 4000 runs.