implement tracking through a quadrupole

bmad-sim / BeamTracking.jl

Julia routines for tracking particle beams through accelerators

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implement tracking through a quadrupole #5

Open dtabell opened 2 months ago

dtabell commented 2 months ago

element Quadrupole

[x] without spin
[ ] with spin

dtabell commented 1 week ago

@mattsignorelli I have an initial implementation. see the branch 5-track-symplectic-quad. It needs testing, and I have plenty of questions about both type stability and performance. The former we should address ASAP. The latter we can address later.

In addition, I added two new functions to utils.jl: sincu and sinch. These also need attention from an expert in type stability.

We should also discuss spin.

dtabell commented 6 days ago

Some possible tests:

[ ] zero strength quad == drift
[ ] low-energy beam
[ ] high-energy beam
[ ] ultra-relativistic beam
[ ] $e^-$, $e^+$, $p^+$, $p^-$
[ ] symmetry checks, e.g. $\mathcal{M}_Q(-x,0,-y,0,\delta)$
[ ] $+q \text{ in } QD \equiv -q \text{ in } QF$
[ ] very-short, very-strong quad should look like a thin lens
[ ] $\mathcal{M}_Q(L) \mathcal{M}_Q(L)$ should yield very nearly the same result as $\mathcal{M}_Q(2L)$
[ ] the previous comparison should be exact if we use two slices for the latter mapping
[ ] particles with $q$ some multiple of the elementary charge $e$
[ ] others ???