---

[0][1]***********************************************.
[0][1]____O_______O__A_______A________M__________M.
[0][1]___O_O______O__A______A_A_______M_M______M_M.
[0][1]__O___O_____O_A______A___A______M_M______M_M.
[0][1]_OOOOOOO____0A______AAAAAAA_____M___M___M__M.
[0][1]_O_____0____O_A____A_______A____M_____M____M.
[0][1]O_______O___O__A__A_________A___M__________M.
[0][1]Arbitrary_Kinetic_Algorithm___________M_____.
[0][1]***********************************************.

---

AKAM

AKAM is a three-dimensional hybrid PIC–fluid code for multiphysics plasma modeling. Ions are treated kinetically, while electrons are described by a ten-moment fluid model, enabling efficient simulation of ion-scale dynamics, pressure anisotropy, and non-Maxwellian effects. Laser–plasma interaction is modeled using a laser envelope formulation that captures energy deposition, electrons ponderomotive heating, and ions collisional absorption. The framework is designed for scalable, end-to-end simulations of laser-driven and high-energy-density plasmas.

stack: C++11, MPI, HDF5, python2-3

Paper reference: [Andrey Sladkov, Hybrid PIC-fluid model for numerical simulation of laser-plasma interaction, 2026. (https://arxiv.org/abs/2601.01633)]

---

HOWTO

---

1. before 'make' need to set in makefile
   HDF5_PATH= path to hdf5 lib (last well used 1.10.5)
   MPI_PATH= path to mpi lib (last well used openmpi 9.0.0)
   PYTHON_INC= path to python include
   PYTHON_LIB= path to python lib

2. for running default example from src/input/Initializer.py
   mpirun -n 2 akam.exe

3. normally need to set input file path containing Initializer.py
   mpirun -n 2 akam.exe PATH/TO/PYTHON/INPUT/FILE

4. before running need to create output folder and set in Initializer.py

5. for visualization use python notebook in folder NOTEBOOK/

---

physics included:

---

• space and time quantities are normalized on:

  • ion inertia length d0 = c/omega_pi
  • inverse ion gyrofrequency 1/Omega_ci

• electro-magnetic fields are calculated on two staggered grid (G1 and G2)
  using predictor-corrector scheme (see EleMagManager.cpp)

  E = -[VixB] + [JxB]/n - divPe/n - eta ΔJ

  B' = -rotE

  J = rotB

• ions are described in a kinetic way,
  dynamics is solved using first order interpolation of em fields

• electrons are described in a fluid way by:

  • density (equals to ion density ne=ni=n)
  • bulk velocity Ve = Vi - J/n
  • six-component pressure tensor Pij

• six-component pressure tensor P is integrated in time
  using subcycling explicit scheme

  P' = - Ve.∇P - P∇.Ve - P.∇Ve - (P.∇Ve)^T - q/m [ PxB + (PxB)^T ]

  where Ve - electron flow velocity
  q - electron charge
  m - electron mass
  B - magnetic field

• laser–plasma interaction is done via envelope model with ponderomotive heating and inverse Bremsstrahlung absorption

• electron–ion collisions are included through a Landau–Spitzer relaxation operator, enabling temperature equilibration and pressure feedback between ions and the electron fluid

• ionisation processes are included via rate-based evolution of particle charge states driven by local electron density and temperature.

---

FEATURES

---

1. AKAM is 3D, parallel (MPI), multispecies code

2. BC type for em fields and hydro quantities: 1 - periodic, 0 - ideal (see GridManager.cpp)

3. BC type for particle properties: 2 - reflect 1 - periodic 0 - outflow (see BoundaryManager.cpp) *outflow BC - reaching border particle leaves domain forever

4. for small scale dissipation use resistivity (eta) parameter

5. for pressure tensor integration need to set:

   • electron mass
   • relaxation factor for izotropization operator (see ClosureManager.cpp)
   • smooth stride for pressure tensor smoothing

6. use 'make FLAGS=-DLOG' to set debug log level in Logger.hpp