Topical lectures cosmic rays Sijbrand de Jong IMAPP

Topical lectures cosmic rays Sijbrand de Jong IMAPP, Radboud Universiteit Nijmegen & Nikhef 1 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Schedule Monday 23 April 2015 10. 00 -10: 10 10. 10 -11. 00 -12. 00 -13. 00 -14. 00 -15. 15 -15. 30 -17. 00 -17. 30 2 H 331 Introduction (Sd. J) H 331 Cosmic Rays history (Sd. J) H 331 FOM courses explaned (Lydia van der Vlist) Lunch H 331 Cosmic Rays basics (Sd. J) H 331 Supernovae as accelerators (Jacco Vink) H 331 explanation of project (Sd. J) Coffee/tea SPECTRUM Working session project H 331 Presentations and discussion of proposals Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Schedule Tuesday 24 April 2015 09. 00 -10. 15 -11. 30 -12. 30 -13. 30 -14. 15 14. 30 -15. 15 -15. 30 15. 45 -16. 30 -17. 30 3 H 331 working session project / setup Coffee/tea H 331 Radio detection of Cosmic Rays (Olaf Scholten) H 331 check of setup project H 331 Cosmic Rays atmospheric interaction (Sd. J) Lunch / check of setup project H 331 Hi. SPARC (Bob van Eijk) H 331/SPECTRUM Working session project Coffee/tea H 331/SPECTRUM Working session project H 331 presentations (3’) and discussion project Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Change of Schedule Tuesday 24 April 2015 09. 00 -10. 15 -11. 30 -12. 30 -13. 30 -14. 30 -15. 00 -15. 15 -16. 30 -17. 30 4 H 331 working session project / setup Coffee/tea H 331 Radio detection of Cosmic Rays (Olaf Scholten) H 331 check of setup project H 331/SPECTRUM Working session project Lunch / check of setup project H 331 Hi. SPARC (Bob van Eijk) H 331 Cosmic Rays atmospheric interaction (Sd. J) H 331/SPECTRUM Working session project Coffee/tea / check of setup project H 331/SPECTRUM Working session project H 331 presentations (3’) and discussion project Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Schedule Wednesday 25 April 2015 09. 00 -10. 00 -11. 15 11. 30 -12. 30 -13. 30 -15. 15 -15. 30 -16. 00 -17. 00 - 5 H 331 Transport of Cosmic Rays (Jörg Hörandel) H 331 Working session project Coffee/tea H 331 The challenges of UHE Cosmic Ray research (Sd. J) Lunch / check of setup project SPECTRUM Working session project Tea break SPECTRUM Working session project H 331 presentations (5’) and discussion project Drinks ! Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic Ray atmospheric interactions & detection Drawing on: Heitler, The Quantum Theory of Radiation, third ed. , Oxford University Press, 1954, London, p. 386 (section 38); Matthews, Astroparticle Physics 22 (2005) 387– 397; Montanus, ar. Xiv: 1311. 0642 v 3. 6 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Interactions of Cosmic Rays in the atmosphere Heitler model of a shower (similar to calorimeter in particle physics) Hadronic cascade EM cascade Muon component 7 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth EM cascade: splitting length X 0 ln(2), Radiation length: X 0=36. 7 g/cm 2 N particles after 2 n splitting lengths, N=exp(x/X 0) Average particle energy E=E 0/N Shower stops at E=Eecrit=85 Me. V, thus at N=E 0/Eecrit Counting N gives E 0 Maximum # particles at Xmax=X 0 ln(E/Eecrit) Heitler model is approximation, not accounting for: • multiple photon radiation • ranging out of e± • particle loss for other reasons Scale N down by factor ~10 EGS 4 simulates this numerically from first principles more or less perfectly 8 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Hadronic cascade: nuclear interaction length l. I=120 g/cm 2 Epcrit=20 Ge. V (this large number is caused by the fact that at this energy their decay into muons becomes more probable than a next interaction. this cricital energy decreases with increasing E 0) spliting in ~15 pions (Nch=10 charged, Nn=5 neutral) (# of pions produced grows as approximately E 1/5 in pp interactions) Shower stops at: N = E 0/Epcrit , after nc = ln(E 0/Epcrit )/ln(3/2 Nch) steps 9 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Speculation exercise #5 Why does the critical energy of pions decrease with increasing energy of the incoming cosmic ray ? 10 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Total energy estimate, using all shower components: Take Np± = Nm N = 10 Ne Then: E 0 = 10 Eecrit ( Ne + (Epcrit/10 Eecrit) Nm ) ≈ 0. 85 Ge. V (Ne+24 Nm) Fit by CASA-MIA group: E 0 = 0. 8 Ge. V (Ne+25 Nm) Indepent on particle type (p or Fe) Over large range of energies Only 2/3 of energy goes to charged pions, hence muons: ln(Nm)=(ln(10)/ln(15))ln(E 0/Epcrit ) Nm= (E 0/Epcrit )0. 85 (MC studies give powers from 0. 85 -0. 92) 11 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J) M. A. K. Glasmacher, et al. (CASA-MIA), Astropart. Phys. 12 (2000) 1– 17.

Cosmic rays: down to Earth From the previous considerations: E 0= (Nm)1/0. 85 Epcrit EM fraction of energy: EEM/E 0= (E 0 -Nm. Epcrit)/E 0 = 1 - (E 0/Epcrit)0. 85 -1 = 1 - (E 0/Epcrit)-0. 15 Series expansion near E 0=105 Epcrit gives: Ne = N/10 = (1/10) EEM/Eecrit ≈ 106 (E 0/1 Pe. V)a with a≈1. 03 E 0 = (1. 5 Ge. V) Ne 0. 97 Full simulation gives: E 0 = (1. 6 Ge. V) Ne 0. 99 12 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Depth of shower: Elongation rate: L = d. Xmax/dlog(E 0) EM showers: L = 2. 3 X 0 = 85 g/cm 2 Full shower of a proton: First (hadronic) interaction at: X(0) = l. I ln(2) # charged particles produced: Nch=41. 2 (E 0/1 Pe. V)1/5 Then Nch/2 p 0 are produced giving Nch photons, each initiating an EM shower of energy E 0/3 Nch EM shower dominates henceforward Xmax= X(0)+X 0 ln(E 0/(3 Nch Eecrit)) = (470+58 log(E 0/1 Pe. V)) g/cm 2 L = d. Xmax/dlog(E 0) = 58 g/cm 2 Nucleus shower (superposition model, A showers of energy E 0/A): XAmax = Xpmax – X 0 ln(A) more EM showers with less energy NAm = Npm A 0. 15 less collision generation, EM shower part less 13 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Depth of shower: EM Heitler model Model from previous pages Full simulation Not treated: Inelasticity Leading particle taking away a large part of the energy, unavailable for the shower for a while 14 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)

Cosmic rays: down to Earth Spill over: Hadronic shower produces: photons p 0 => EM shower p± => muons electrons muons hadrons 15 Topical Lectures: Cosmic Rays, 23 -25 March 2015 (Sd. J)