Guiding-Center (GC) dynamics in plasma physics

• nondimensionalization.mlx: Matlab Live Script for the computation of the dimensionless parameters A, ρ and η used in the code and in the analysis

• gc2d_dict.py: to be edited to change the parameters of the GC computation (see below for a dictionary of parameters)

• gc2d.py: contains the GC classes and main functions defining the GC dynamics

• gc2d_modules.py: contains the methods to integrate the GC dynamics

Once gc2d_dict.py has been edited with the relevant parameters, run the file as

python3 gc2d.py

or

nohup python3 -u gc2d.py &>gc2d.out < /dev/null &

The list of Python packages and their version are specified in requirements.txt

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Parameter dictionary

• Potential: string; 'KMdCN' or 'turbulent'
• Method: string
  • 'potentials' (only for Potential='turbulent'): plots the electrostatic potential as well as the first and second order guiding-center potentials
  • 'diffusion_fo': computes the diffusion coefficient for the full orbits
  • 'diffusion_gc': computes the diffusion coefficient for the guiding centers
  • 'poincare_fo': plots the full orbits in the plane (x, y) for every period of the potential (stroboscopic plot)
  • 'poincare_gc': plots the guiding-center trajectories in the plane (x, y) for every period of the potential (stroboscopic plot)

• FLR: tuple of 2 strings; 'all', 'pade' or 'none'; if 'all', FLR to all orders is taken into account; if 'pade', a Padé approximant is considered for the FLR effects; if 'none', no FLR effects are taken into account

• A: float or array of floats; amplitude(s) of the electrostatic potential [theory: A=ε_δ/B]
• rho: float or array of floats; value(s) of the Larmor radius; for full orbits, this value corresponds to the thermal Larmor radius
• eta: float or array of floats; value(s) of the coefficient in front of the GC order 2 potential; η>0 for positive charge, η<0 for negative charge [theory: η=1/(2Ω)]

• Ntraj: integer; number of trajectories to be integrated
• Tf: integer; number of periods for the integration of the trajectories
• threshold: float; value used to discriminate between trapped and untrapped trajectories (recommended: 4)
• TwoStepIntegration: boolean; if True, computes trajectories from 0 to 2πT_mid, removes the trapped trajectories, and continues integration from 2πT_mid to 2πT_f
• Tmid: integer; number of periods for the integration of trajectories in the first step (if TwoStepIntegration=True)
• TimeStep: float; time step used by the integrator (recommended: 5x10^-3 for guiding centers and 5x10^-4 for full orbits)
• check_energy: boolean; if True, the autonomous system is integrated, and the output (.mat file) includes the total energy (only if SaveData=True)
• init: string; 'random' or 'fixed'; method to generate initial conditions

• SaveData: boolean; if True, the results are saved in a .mat file; Poincaré sections and diffusion plots r²(t) are saved as fig_extension files; NB: the diffusion data are saved in a .txt file regardless of the value of SaveData
• PlotResults: boolean; if True, the results are plotted right after the computation
• Parallelization: tuple (boolean, int); True for parallelization, int is the number of cores to be used or int='all' to use all available cores

• modulo: boolean; if True, x and y are represented modulo 2π (only for Method='poincare' and PlotResults=True)
• grid: boolean; if True, show the grid lines on plots
• darkmode: boolean; if True, plots are done in dark mode
• fig_extension: string; e.g., '.png', '.pdf', '.svg'; format of the figures to be saved

• M: integer; number of modes (default = 5 for 'KMdCN' and 25 for 'turbulent')
• N: integer; number of points on each axis for 'turbulent' (recommended: 2¹²)

---

Reference:

• M. Stanzani, F. Arlotti, G. Ciraolo, X. Garbet, C. Chandre, Transition to super-diffusive transport in turbulent plasmas, arXiv:2309.02461

@unpublished{stanzani2023,
  title = {Transition to super-diffusive transport in turbulent plasmas},
  author = {Stanzani, M. and Arlotti, F. and Ciraolo, G. and Garbet, X. and Chandre, C.},
  year = {2023},
  URL = {https://arxiv.org/abs/2309.02461}
}

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