The BLAST codes contain a large collection of original algorithms that were introduced by their developers. This plays to one of the strengths of LBNL in code development: a convergence of expertise in beam and plasma physics and in mathematical and computational techniques. As we develop this page, it will contain links to papers on each algorithm, as well as news articles.

## BEAMBEAM3D

- Shifted-Green-function method
- Mixed particle-field decomposition method (note: also implemented independently in Warp)

## IMPACT

- Integrated maps for rf cavity dynamics
- Spectral-finite difference multigrid solver
- 3D Poisson solver with large aspect ratio
- Integrated Green’s function
- New convolution integral with smooth kernel
- 2nd stochastic leap-frog integrator for multiplicative noise
- 3D Poisson solver in open conducting pipe
- 2nd particle emission model
- Adaptive unified differential evolution algorithm for global optimization
- Variable population with external storage parallel differential algorithm for multi-objective function optimization

## WARP/WarpX

- Damped EM and particle pushers
- Warped coordinates PIC in bends
- Improved Perfectly Matched Layer
- Adaptive Mesh Refinement (AMR)-PIC electrostatic
- AMR-PIC electromagnetic
- Hybrid Lorentz particle pusher
- Lorentz boosted frame
- Explicit Lorentz invariant particle pusher
- PIC with tunable electromagnetic solver
- Efficient digital filer for parallel PIC
- Laser launcher from moving planar antenna
- Novel domain decomposition method for electromagnetic pseudo-spectral solver (see Journal of
- Computational Physics 243 (2013), pp. 260-268; development is the subject of an LBNL Laboratory-
- Directed R&D project beginning in 2014).

## POSINST

- Detailed secondary emission of electrons

## HiPACE++ (lead: DESY)

- Quasi-static particle-in-cell
- Advanced field solver
- Multiple plasma particle pushers (Leapfrog & Adams-Bashforth)
- Laser envelope solver and particle beam pusher
- Adaptive time step and beam sub-cycling
- SALAME algorithm for ideal load balancing
- GPU-capable, with a novel parallelization pipeline
- Multi-physics (Ion motion, Binary Coulomb collisions, ADK field ionization)
- openPMD writers and readers for laser and beam profiles