1 / 22

Advancements in Solar Shadow Simulation: A Numerical Approach Utilizing Liouville's Theorem

This work presents an innovative numerical method for simulating solar shadow dynamics, leveraging Liouville's theorem to generate isotropic cosmic rays (C.R.s) from Milagro to the Sun. The study explores integrating the equations while contrasting older methods, such as the Stoermer Rule and modifications by Henrici, highlighting efficiency and precision for celestial body interactions. Results from preliminary simulations indicate that increasing the magnetic field can reduce the number of shadowed particles. Future work will focus on refining detection capabilities and resolving solar exposure under varying conditions.

quinta
Télécharger la présentation

Advancements in Solar Shadow Simulation: A Numerical Approach Utilizing Liouville's Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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:

More Related