Fig. 4: Phase space portrait of the 2D Hamiltonian map in low-frequency regime. | Communications Physics

Fig. 4: Phase space portrait of the 2D Hamiltonian map in low-frequency regime.

From: Validity of gyrokinetic theory in magnetized plasmas

Fig. 4

Colors indicate distinct particles. In this case, we evolve 180 particle orbits in time according to the Hamiltonian (1) for a ω = 0.06, A = 0.9, b ω = 0.059, A = 0.9, c ω = 0.06, A = 1.01, and d ω = 0.059, A = 1.01, where initial conditions (q0, p0) are selected randomly in [ − 3, 3] × [ − 1.5, 1.5]. Then the 2D Hamiltonian map \({{{\boldsymbol{x}}}}_{n+1}={{{\mathcal{M}}}}_{T}{{{\boldsymbol{x}}}}_{n}\) is constructed such that the point xn at tn is advanced to the next crossing point xn+1 at tn+1 = tn + T, with the wave period T = 2π/ω.

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