Adding force term for plasma streamer simulation

I am trying to solve Boltzmann equation with force term for the conditions inside an electric streamer. The set of equations couples Boltzmann equations for electrons and ions plus Maxwell equations that drive electric and magnetic fields with BGK collision term on the right hand side:
to be short, E is a constant field that drives the propagation of the streamer and acts on the whole fluid , but E’ and B’ are local fields values that are related to the small wavy plasma disturbance calculated from Maxwell equations (I hope it is not needed - I couldn’t upload the second image as a new user).

I still try to solve the equation with finite differences in velocity space and spectral methods in x space but it is hard for me to achieve convergence in longer runs.

Do you know any use cases of Palabos for such configuration?

Thank you in advance!

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I guess it could. What are the different parameters of these equations: n_e, Phi_e?

Thank you for the reply!

The rest of the equations are here:

So, yes - Great Phi_e and Phi_i are Maxwellian distribution functions that can be anisotropic. The other phi is of course the scalar potential that is being calculated from charge density rho. The other parameters are pretty self-explanatory: n-density, A is vector potential, E’ and B’ - electric and magnetic field additions of the wavy disturbance, j - current density.

The point is that in velocity space these external force part (e/m_e(E + E’ + v x B’) ) can produce huge accelerations. I don’t know if Palabos may handle it and how to implement it (in all use cases I see no external force part.