Solvers

gtracr provides three integration methods for the relativistic Lorentz force equation, all implemented in C++.

Comparison

Solver	solver=	B-field evals/step	Step size	Key properties
Frozen-field RK4	"rk4"	1	Fixed	Default; O(h^4) with frozen-field O(h^2) error
Boris pusher	"boris"	1	Fixed	Symplectic; ~30% faster than RK4; 2x better momentum conservation
Adaptive RK45	"rk45"	~6 (FSAL)	Adaptive	Dormand-Prince; uses atol/rtol; ~100x fewer steps for escaping trajectories

When to use each solver

Single trajectory visualization

Use "rk4" or "boris" with bfield_type="igrf":

• Fixed time steps produce regularly spaced output points, good for plotting.
• Boris is faster and conserves energy better, but outputs Cartesian internally (converted back to spherical).
• RK4 is the safe default.

GMRC cutoff scanning

Use "rk45" with bfield_type="table":

• Adaptive stepping takes far fewer steps for escaping trajectories.
• Combined with the tabulated IGRF (~7x faster field evaluation), this gives the highest throughput (~35k trajectories/s in batch mode).
• Default tolerances (atol=1e-3, rtol=1e-6) work well for cutoff determination.

High-precision work

For position accuracy comparable to RK4 at dt=1e-5, tighten the RK45 tolerances:

traj = Trajectory(..., solver="rk45", atol=1e-6, rtol=1e-6)

Tolerance tuning (RK45)

atol	rtol	Use case
1e-3	1e-6	Default — good for GMRC cutoff determination
1e-6	1e-6	High precision — position accuracy matching RK4 at dt=1e-5
1e-8	1e-8	Reference solutions for validation

Benchmarking solvers

Run the solver comparison script to compare accuracy and performance:

python examples/eval_solver_comparison.py --n-perf 100