Guiding Center 4d Deeply Passing with Gauss-Legendre VPRK Methods and Projections
The time step and number of time steps are those of this orbit, set in src/guiding-center-4d.jl; the toroidal momentum is shown alongside the energy, as the second invariant of the guiding centre dynamics.
VPRKGauss(1)
Simulation crashed after 1389 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss1pnonetoroidalmomentum_error failed: MethodError.
SymplecticGauss(1) with standard projection
Plotting vprkgauss1pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss1pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(1) with symmetric projection
Plotting vprkgauss1psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss1psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(1) with symplectic projection
Plotting vprkgauss1psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss1psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(1) with midpoint projection
Plotting vprkgauss1pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss1pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(1) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(2)
Simulation crashed after 1129 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss2pnonetoroidalmomentum_error failed: MethodError.
SymplecticGauss(2) with standard projection
Plotting vprkgauss2pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss2pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(2) with symmetric projection
Plotting vprkgauss2psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss2psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(2) with symplectic projection
Plotting vprkgauss2psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss2psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(2) with midpoint projection
Plotting vprkgauss2pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss2pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(2) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(3)
Simulation crashed after 2409 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss3pnonetoroidalmomentum_error failed: MethodError.
SymplecticGauss(3) with standard projection
Plotting vprkgauss3pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss3pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(3) with symmetric projection
Plotting vprkgauss3psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss3psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(3) with symplectic projection
Plotting vprkgauss3psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss3psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(3) with midpoint projection
Plotting vprkgauss3pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss3pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(3) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(4)
Simulation crashed after 2809 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss4pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss4pnonetoroidalmomentum_drift failed: MethodError.
SymplecticGauss(4) with standard projection
Plotting vprkgauss4pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss4pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(4) with symmetric projection
Plotting vprkgauss4psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss4psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(4) with symplectic projection
Plotting vprkgauss4psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss4psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(4) with midpoint projection
Plotting vprkgauss4pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss4pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(4) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(5)
Simulation crashed after 4202 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss5pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss5pnonetoroidalmomentum_drift failed: MethodError.
SymplecticGauss(5) with standard projection
Plotting vprkgauss5pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss5pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(5) with symmetric projection
Plotting vprkgauss5psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss5psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(5) with symplectic projection
Plotting vprkgauss5psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss5psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(5) with midpoint projection
Plotting vprkgauss5pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss5pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(5) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.
VPRKGauss(6)
Simulation crashed after 4584 of 12500 time steps: solver error – non-finite direction vector.
Plotting vprkgauss6pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss6pnonetoroidalmomentum_drift failed: MethodError.
SymplecticGauss(6) with standard projection
Plotting vprkgauss6pstandardtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss6pstandardtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(6) with symmetric projection
Plotting vprkgauss6psymmetrictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss6psymmetrictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(6) with symplectic projection
Plotting vprkgauss6psymplectictoroidalmomentum_error failed: MethodError.
Plotting vprkgauss6psymplectictoroidalmomentum_drift failed: MethodError.
SymplecticGauss(6) with midpoint projection
Plotting vprkgauss6pmidpointtoroidalmomentum_error failed: MethodError.
Plotting vprkgauss6pmidpointtoroidalmomentum_drift failed: MethodError.
SymplecticGauss(6) with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.