English versionEN

The HECKLE code 

(Ce texte n'est pas disponible en français, nous nous en excusons.)

The HECKLE code has been written by Roch Smets and Nicolas Aunai.

This is a hybrid code (protons are treated as macro-particles and electrons as a fluid) with two spatial dimensions and three velocity dimensions. The code is partly parallelized using MPI. The electromagnetic fields are calculated self-consistently using a predictor-corrector scheme by Harned (1982). A detail of the algorithm is also provided in Winske & Quest (1986). The displacement current is neglected in the Maxwell-Faraday equation. Such an assumption prevents the development of high frequency modes. Ohm's law is then needed to compute the electric field, that takes into account the Hall term and the electron pressure term.

We choose an isothermal closure equation for the electron fluid, which is a priori justified when studying processes with phase velocity smaller than electron thermal velocity, with a constant value of the electron temperature .

Details on the equations, the associated normalization, the algorithms, the initialization, the grids definition, the boundary conditions and the constraints on the code are provided in this pdf file.

You can access the SOURCE CODE here as well as some IDL VISUALISATION SCRIPTS.


There are two configurations files : "hyb.txt" contains all the informations about the grid, the time step, the mass and charge of the species... and another ascii file "kh1.txt" for the kelvin-helmholtz instability) containing all the informations about the magnetic topology and the plasma parameters (beta value, anisotropy factor...). The same type of files for the reconnection simulation is "reconnection.txt". If the code has to be used in a different topology, it just needs to write in a new file the associated functions. Note that these functions have the same name (magnetic, density...) that are self-explanatory.

A few examples are provided below:

  • Magnetic reconnection in a thin current sheet

    Quadrupolar out-of plane magnetic field characteristic of collisionless magnetic reconnection


    Movies are also available : bz167small.mp4 and bz167small.mov
    dn004A.mp4 : evolution of the plasma density in typical magnetic reconnection run



  • Kelvin-Helmholtz instability

    Passive tracor dispersion (color coded) during the development of a KH instability:




  • Whistler wave dispersion relation
    Numerical and theoretical dispersion relation of the whistler wave with electron inertia (using the "whistler.c" initialization file):


Voir aussi dans la même rubrique