# Simulations of relativistic quantum plasmas using real-time lattice scalar QED

## Abstract

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, andmore »

- Authors:

- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Univ. of Science and Technology of China, Hefei (China). School of Nuclear Science and Technology and Dept. of Modern Physics
- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China). School of Nuclear Science and Technology and Dept. of Modern Physics

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Natural Science Foundation of China (NNSFC); Japan Society for the Promotion of Science (JSPS); Chinese Scholar Council (CSC); Chinese Academy of Sciences (CAS)

- OSTI Identifier:
- 1465665

- Alternate Identifier(s):
- OSTI ID: 1436538

- Grant/Contract Number:
- [NA0002948; AC02-09CH11466; NSFC-11575185; 11575186; 11305171; NSFC-11261140328; QYZDB-SSW-SYS004; 201506340103; 2015GB111003; 2014GB124005]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- [ Journal Volume: 97; Journal Issue: 5]; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; laser-plasma interactions; lattice field theory; lattice gauge theory; nonlinear phenomena in plasmas; nonperturbative effects in field theory; particle acceleration in plasmas; radiation and particle generation in plasmas

### Citation Formats

```
Shi, Yuan, Xiao, Jianyuan, Qin, Hong, and Fisch, Nathaniel J. Simulations of relativistic quantum plasmas using real-time lattice scalar QED. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.97.053206.
```

```
Shi, Yuan, Xiao, Jianyuan, Qin, Hong, & Fisch, Nathaniel J. Simulations of relativistic quantum plasmas using real-time lattice scalar QED. United States. doi:10.1103/PhysRevE.97.053206.
```

```
Shi, Yuan, Xiao, Jianyuan, Qin, Hong, and Fisch, Nathaniel J. Wed .
"Simulations of relativistic quantum plasmas using real-time lattice scalar QED". United States. doi:10.1103/PhysRevE.97.053206. https://www.osti.gov/servlets/purl/1465665.
```

```
@article{osti_1465665,
```

title = {Simulations of relativistic quantum plasmas using real-time lattice scalar QED},

author = {Shi, Yuan and Xiao, Jianyuan and Qin, Hong and Fisch, Nathaniel J.},

abstractNote = {Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may also be computed using quantum parallelism in the future.},

doi = {10.1103/PhysRevE.97.053206},

journal = {Physical Review E},

number = [5],

volume = [97],

place = {United States},

year = {2018},

month = {5}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*txy*-submanifold of spacetime using a rectangular lattice. The discrete function

*∅*lives on the vertexes (blue squares). For example,

_{v}*∅$n\atop{i,j,k}$*

*∅ (t*lives on the vertex (

_{n}, x_{i}, y_{j}, z_{k})*n, i, j, k*). The discrete 1-form

*A*lives along edges (red circles). For example,more »

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*