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.

Guiding Center 4d Small Tokamak Barely Trapped with Gauss-Legendre VPRK Methods and Projections

VPRKGauss(1)

SymplecticGauss(1) with standard projection

SymplecticGauss(1) with symmetric projection

SymplecticGauss(1) with symplectic projection

SymplecticGauss(1) with midpoint projection

SymplecticGauss(1) with internal stage projection

VPRKGauss(2)

SymplecticGauss(2) with standard projection

SymplecticGauss(2) with symmetric projection

SymplecticGauss(2) with symplectic projection

SymplecticGauss(2) with midpoint projection

SymplecticGauss(2) with internal stage projection

VPRKGauss(3)

SymplecticGauss(3) with standard projection

SymplecticGauss(3) with symmetric projection

SymplecticGauss(3) with symplectic projection

SymplecticGauss(3) with midpoint projection

SymplecticGauss(3) with internal stage projection

VPRKGauss(4)

SymplecticGauss(4) with standard projection

SymplecticGauss(4) with symmetric projection

SymplecticGauss(4) with symplectic projection

SymplecticGauss(4) with midpoint projection

SymplecticGauss(4) with internal stage projection

VPRKGauss(5)

SymplecticGauss(5) with standard projection

SymplecticGauss(5) with symmetric projection

SymplecticGauss(5) with symplectic projection

SymplecticGauss(5) with midpoint projection

SymplecticGauss(5) with internal stage projection

VPRKGauss(6)

SymplecticGauss(6) with standard projection

SymplecticGauss(6) with symmetric projection

SymplecticGauss(6) with symplectic projection

SymplecticGauss(6) with midpoint projection

SymplecticGauss(6) with internal stage projection