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PolskiStrong Focusing: Quadrupole FODO Lattice (2D)
2D beam-optics lab: a FODO lattice of focusing/defocusing quadrupole magnets on a flat beamline, with live betatron envelope curves, phase advance, tune and stability readouts.
This 2D companion drives the exact same FODO transfer-matrix optics as the 3D version, unrolled onto a flat beamline strip instead of a rotating 3D scene: focusing (QF, blue) and defocusing (QD, red) quadrupole blocks alternate along the top, and the ±betatron envelope for both the x-plane and y-plane traces out below as a ring of test particles rides the beam through the lattice, using the same linear-optics transfer matrices, phase-advance and stability formulas as real accelerator design codes.
2D beam-optics lab: a FODO lattice of focusing/defocusing quadrupole magnets on a flat beamline, with live betatron envelope curves, phase advance, tune and stability readouts.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install
It marks the beam's current position s along the lattice, in sync with the particle dots riding the x-plane and y-plane curves below.
If the quadrupole strength or drift length pushes the lattice past the stability condition (|½·trace(M)| > 1), particle amplitudes grow without bound and are marked lost once they exceed the vacuum-chamber aperture — the same failure mode a real synchrotron would see.
Same physics, same transfer matrices and readouts — the 3D version renders the lattice as an orbitable 3D ring, this 2D version unrolls it into a flat, easier-to-read strip-chart view.