Guiding Center 4d Small Tokamak Barely Trapped with Gauss-Legendre VPRK Methods and Projections
The variational formulation of the same orbit as on the Gauss-Legendre Runge-Kutta page, integrated with the Gauss-Legendre variational partitioned Runge-Kutta methods and each of the projections onto the constraint submanifold. The internal stage projection has no integrator in GeometricIntegrators 0.16 and its runs fail here, as they do on every other VPRK page.
The small tokamak's particles are slow, so the time step is \Delta t = 800 against the medium tokamak's 2.5; the toroidal momentum is shown alongside the energy. Both are set in src/guiding-center-4d.jl.
VPRKGauss(1)
Plotting vprkgauss1pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss1pnonetoroidalmomentum_drift 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)
Plotting vprkgauss2pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss2pnonetoroidalmomentum_drift 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)
Plotting vprkgauss3pnonetoroidalmomentum_error failed: MethodError.
Plotting vprkgauss3pnonetoroidalmomentum_drift 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)
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)
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)
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.