• VM15D.nb: [Mathematica notebook] checks the Jacobi identity and the Casimir invariants for the bracket Bracket[F,G] given by Eq. (6) of the article Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations by C. Chandre and B.A. Shadwick

• GrowthRates.mlx: [Matlab livescript] computes the growth rates for the linearized equations of motion near a homogeneous equilibrium. It reproduces the figures of the article Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations by C. Chandre and B.A. Shadwick

• VM15D python code

  • VM15D_dict.py: to be edited to change the parameters of the VM15D computation (see below for a dictionary of parameters)

  • VM15D.py: contains the VM15D class and main functions (not to be edited)

  • VM15D_modules.py: contains the methods to run VM15D (not to be edited)

  • Once VM15D_dict.py has been edited with the relevant parameters, run the file as

  python3 VM15D.py

  • NB: in case of error, check your version of the python modules used in the code (see modules_version.txt)

• Tf: double; duration of the integration (in units of ω_p^-1)

• alpha: double; value of the parameter α of the closure

• lam: double; value of the parameter λ of the closure

• integrator_kinetic: string ('position-Verlet'); choice of solver for the integration of the Vlasov equation

• nsteps: integer; number of steps in one period of plasma oscillations (1/ω_p) for the integration of the Vlasov equation

• integrator_fluid: string ('RK45', ‘RK23’, ‘DOP853’, ‘BDF’, ‘LSODA’); choice of solver for the integration of the fluid equation

• precision: double; numerical precision of the integrator for the fluid equations; threshold for the Fourier transforms

• n_casimirs: integer; number of Casimir invariants to be monitored

• Lz: double; the z-axis is (-Lz, Lz)

• Lvx: double; the vx-axis is (-Lvx, Lvx)

• Lvz: double; the vz-axis is (-Lvz, Lvz)

• Nz: integer; number of points in z to represent the field variables

• Nvx: integer; number of points in vx to represent the field variables

• Nvz: integer; number of points in vz to represent the field variables

• f_init: lambda function; initial distribution f(z,vx,vz,t=0)

• Kinetic: list of strings in ['Compute', 'Plot']; list of instructions for the 1.5D Vlasov-Maxwell simulation

• Fluid: list of strings in ['Compute', 'Plot']; list of instructions for the fluid simulation; if contains 'Save', the results are saved in a .mat file

• darkmode: boolean; if True, plots are done in dark mode

• tqdm_display: boolean; if True, displays a progress bar in the terminal

Reference: C. Chandre, B.A. Shadwick, Hamiltonian fluid reduction of the 1.5D Vlasov–Maxwell equationsn, Physics of Plasmas 28, 092114 (2021); arXiv:2105.03194

@article{chandre2021,
         title = {Hamiltonian fluid reduction of the 1.5D Vlasov–Maxwell equations},
         author = {Chandre, C. and Shadwick, B.A.},
         journal = {Physics of Plasmas},
         volume = {28},
         number = {9},
         pages = {092114},
         year = {2021},
         doi = {10.1063/5.0056155},
         URL = {https://doi.org/10.1063/5.0056155}
}

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