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Simulating the Solar Shadow. Allen I. Mincer NYU LANL 6/2/05. The General Problem. Integrate the equations: Numerical approach:

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1. Simulating the Solar Shadow Allen I. Mincer NYU LANL 6/2/05

2. The General Problem • Integrate the equations: • Numerical approach: • Tried AIM version using kinematic equations and steps with midpoint acceleration, better than 4th order Runge Kutta, OK for Moon but not precise or fast enough for Sun.

3. Old Comparison

4. Stoermer Rule, as Modified by Henrici

5. Aim Modified Version:

6. Some More Calculation Details

7. New Method Used • Old method sent particles from Earth to Moon to find nominal shadow direction, then started at Moon and generated events to Milagro. • But D(Earth-Sun) ~ 400 D(Earth-Moon) and A(Sun) ~ 105 A(Moon). • Would need to generate ~105 times the events to get the same shadow statistics. • Instead, using Liouville’s theorem, isotropic C.R.s + B fields give isotropic C.R.s at Earth, unless absorbed. • Generate backwards going C.R.s from Milagro to Sun. Shadow if sun is hit.

8. Preliminary Run • 10 day run late March. • Pick sun position every 100 seconds. • For each position, pick energy on E-2.7 spectrum starting at 0.5 TeV. • For each position generate 10K events centered on the vertices of a 100 x 100 grid ± 5 degrees around straight line to sun : 0.1 degree steps in Θ, ΦcosΘ. • Run 4 cases: • B Earth only • Sun dipole parallel to Earth’s dipole • B Earth + Sun dipole parallel to Earth’s dipole • B Earth + Sun dipole perp. to Earth’s dipole

9. B Earth

10. Solar dipole parallel Earth’s, No B Earth

11. Solar Dipole parallel Earth’s

12. Rotating Solar Dipole perp Earth’s

13. Comparisons

14. Conclusion/conjecture: • As B field increases, major change is fewer shadowed particles, since localized B large enough to cause ~degree type shifts will prevent particles from being shadowed. • Build in realistic fields. • Improve effective area,… • Detector resolution. • Compare with Solar data shadow under different solar conditions. To Do:

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