10 Feb 2009PS638 T. Gaisser1 Lecture 1: Introduction Cosmic-ray spectrum and measurements

10 Feb 2009PS638 T. Gaisser2 Spectrometers (  A = 1 resolution, good E resolution) Calorimeters (less good resolution) + TRACER Primary spectrum Air showers Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly. Current questions

10 Feb 2009PS638 T. Gaisser3 Energetics of cosmic rays Total local energy density: –(4  /c) ∫ E  (E) dE ~ erg/cm 3 ~ B 2 / 8  Power needed: (4  /c) ∫ E  (E) /  esc (E) dE galactic  esc ~ 10 7 E -0.6 yrs Power ~ erg/cm 3 s Supernova power: erg per SN ~3 SN per century in disk ~ erg/cm 3 s SN model of galactic CR Power spectrum from shock acceleration, propagation Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4  /c) E  (E) = local differential CR energy density

10 Feb 2009PS638 T. Gaisser4 Solar flare shock acceleration Coronal mass ejection 09 Mar Mar 2000

10 Feb 2009PS638 T. Gaisser5 SOHO/ LASCO CME of 06-Nov 1997

10 Feb 2009PS638 T. Gaisser6 Supernova progenitor SN ejecta Shocked ISM Supernova blast wave acceleration Unshocked ISM SNR expands into ISM with velocity V~ 10 4 km/s. Drives forward shock at 4/3 V Forward shock u 1 ~ 4/3 V Particle with E 1 E 2 =  E 1 Contact discontinuity, V T SN ~ 1000 yrs before slowdown E max ~ Z x 100 TeV

10 Feb 2009PS638 T. Gaisser7 Composition

10 Feb 2009PS638 T. Gaisser8 Four ways to plot spectra 1.Particles per GeV / nucleon for propagation/fragmentation in gas 2.Particles per GV / nucleon for propagation/acceleration in magnetic fields 3.Nucleons per GeV / nucleon for production of secondaries in the atmosphere 4.Particles per GeV / nucleus for air shower experiments

10 Feb 2009PS638 T. Gaisser9 Two kinds of measurements Hodoscope: e.g. EAS Inclusive: e.g. muon flux

10 Feb 2009PS638 T. Gaisser10 Two kinds of measurement at accelerators Spectrometer measures inclusive cross section – for example, the HARP experiment 4π detector –Goal is to detect all particles produced in an interaction – for example, a collider detector like Atlas

10 Feb 2009PS638 T. Gaisser11 Definition of energy spectrum Number of particles per m 2 sr s –i.e. Rate per unit area per solid angle –Differential: dN / d ln (E) = E x dN / dE Preferable to dN / dE for power-law spectrum δE / E ~ constant, so binning of data is logarithmic –Integral: N(>E) per m 2 sr s If dN / d ln (E) ~ K (E) -   then dN / d ln (E) =  x N(>E)

10 Feb 2009PS638 T. Gaisser12 Acceptance Detector acceptance = area x solid angle Example: –2 parallel planes of area A 1, A 2 –Separation d >> sqrt (A 1 ) and d >> sqrt(A 2 ) –Approx acceptance = A 1 x A 2 / d 2 –In general A x Ω = ∫∫ dx 1 dy 1 x ∫ dφ ∫ sin(θ) dθ For each point inside A 1 constraints on the solid angle integral depend on (x 1,y 1 ) and require the vector in the (θ,φ) direction to pass inside A 2 Evaluate integral by Monte Carlo

10 Feb 2009PS638 T. Gaisser13 AΩ ~ 0.3 m 2 x 0.3 m 2 / 10 m 2 ~ 0.01 m 2 sr CAPRICE 1998 CAPRICE spectrometer

10 Feb 2009PS638 T. Gaisser14 BESS spectrometer AΩ ~ m 2 sr

10 Feb 2009PS638 T. Gaisser15 Magnetic spectrometer Momentum measurement –Gyroradius: r L = Pc / (zeB) ≡ R / B –Rigidity: R = Pc / ze (units = GV) –Measure z with dE / dX in scintillator ~ z 2 –P = A x p N ; p N = momentum / nucleon –Example: 100 GeV/c proton in B = 10 4 Gauss r L = 333 m Maximum Detectable Momentum (MDM) – δp ~ eB ┴ δt from Lorentz force equation; δt ~ L / c – δx / L ~ δp / p ~ eB ┴ L / (pc)  (pc) max ~ eB ┴ L 2 / δx min –Example: for B ┴ L 2 = 0.8 Tm 2, (pc) max ~ 240 GeV for protons in a detector with 1 mm spatial resolution

10 Feb 2009PS638 T. Gaisser16 Time of Flight (TOF) Two scintillators separated by L – β = L / (cΔt) – δβ = -(L/cΔt) x (δt/Δt) = β x (δt/Δt) – δβ / β ~ δt / Δt – Need sub-nanosecond time resolution to measure velocity of a relativistic particle over a scale of 1 m

10 Feb 2009PS638 T. Gaisser17 Cherenkov radiation Cherenkov angle: cos(θ c ) = 1 / (βn) Threshold: β > 1 / n Intensity: ~ z 2 x sin 2 (θ c ) = z 2 x [1 – 1 / (βn) 2 ] Uses: –Threshold detector, e.g. separate e + from p Use gas or other material with small n ~ –Measure energy near threshold Use plastic or clear material with n ~ 1.5

10 Feb 2009PS638 T. Gaisser18 TRACER uses transition radiation

10 Feb 2009PS638 T. Gaisser19 Compilation from RPP Note TRACER measurements in 3 energy ranges

10 Feb 2009PS638 T. Gaisser20 Balloon-borne calorimeters RUNJOB emulsion chamber Russian-Japanese collaboration Detector material interleaved with sheets of photographic emulsion Primary ID (pink) Interaction in Target (yellow) Secondaries separate (blue) Photons make cascades in calorimeter (violet) Calibrate at accelerator Important for overlap with EAS