Notations

• \(B_0\): background magnetic field

• \(α\): pitch angle, \(w = \cos(α)\) is the pitch angle cosine

• \(ψ\): gryo phase

• θ : azimuthal angle, angle between \(B_0\) and \(B_N = B_0 \cos(θ)\)

• φ : polar angle

• β : half of in plnae rotation angle \(ω_{in}\)

Results

Scan the parameter with angle difference by 10 degree and velocity by …

Transition matrix for different particle energies

Examples of transition matrix

Updates

2024-10-30

2024-10-29

Questions

• Order of magnitude of estimation of the scattering rate.

• The validality of small \(κ\) in observations and its implications in quasi-adibatic approximation.

• The validality of approximate Hamiltonian form for off-center scattering.

• “How long does it take for an irreducible finite state Markov chain to converge to equilibrium?”

  • References: The Spectral Gap, Spectral gap of nonreversible Markov chains

TODOs

• Cite Juno observations
• Check the algorithm for energy conservation (Boris pusher)
• GPU acceleration
• The independence of the parameters from discontinuities observations

DynamicalSystems.jl - Currently, the limits can not be changed with time.

• Saving as a DataFrame is more space-efficient than saving as a vector of dictionaries