Theore&cal evalua&on of fluorescence emission and energy deposi&on in air generated by electrons

Transcription

1 Theore&cal evalua&on of fluorescence emission and energy deposi&on in air generated by electrons Fernando Arqueros Universidad Complutense de Madrid 0

2 Introduc)on Rela)ve intensi)es Outline The role of secondary electrons MC simula)on Results Energy deposi)on Fluorescence emission Remarks on P measurements Fluorescence yield vs. E and PR Absolute Fluorescence yield Conclusions 1

3 Introduc)on Air- fluorescence induced by electrons. Spectrum: 2P and 1N systems Intensity (arbitrary units) P(2-0) 10 Pa (Rosado et al.) 1N system 2P system 2P(1-0) 2P(0-0) 2P(0-1) 2P(1-2) 2P(1-3) 2P(2-4) 2P(0-2) 1N(0-0) 2P(1-4) 2P(0-3) 1N(1-2) 1N(0-1) Wavelength (nm) 800 hpa AIRFLY 2

4 Fluorescence yield Y (# photons/unit deposit energy): parameter to convert the telescope signal in shower energy. Fluorescence is quenched by collisional de- excita)on and thus, the FY depends on atmospheric parameters (P, T, h). Y! = 0 Y! ; P! (T, h) 1+ P P! The fluorescence yield is NOT a name (e.g. Nagano, Kakimoto,..) but a set of parameters: 1) Absolute value (e.g. Y 337, Y Δλ ) 2) Wavelength spectrum 3) Pressure dependence in dry air (P λ ) 4) Humidity dependence (P w ) 5) Temperature dependence (α) Main source of uncertainty Non- negligible contribu=on Introduc)on 3

5 Rela=ve intensi=es - Common upper level v: propor)onal to Einstein coefficients I vv'! A vv' - Different upper levels: Franck- Condon coefficients q X!v P >>P I vv' I 00 = q X!vA vv' q X!0 A P / P' 0 1+ P / P' v " q X!vA vv' q X!0 A 00 P' v P' 0 independent of P Applicability of F- C principle is not expected a priori because fluorescence is induced by low- energy secondaries, nevertheless 4

6 Rela)ve intensi)es q X!v A vv' P' v 5

7 Rela)ve intensi)es (air) q X!v A vv' P' v 6

8 I vv' = q P >>P X!vA vv' 1+ P / P' 0 " q X!vA vv' P' v I 00 q X!0 A P / P' v q X!0 A 00 P' 0 Rela)ve intensi)es independent of P Applicability of F- C principle is not expected a priori, nevertheless it works for 2P(0- v ) and 2P(1- v ) bands (90% contribu)on) and also for weaker bands when taking into account experimental uncertain)es. Accurate I λ within nm from AIRFLY Beyond this interval (small contribu)ons), the above formula can be used safely. 7

9 Seconday electrons N e X Σg N2 B Σu Excita)on cross sec)on of the 2P system peaked at few evs à High energy electrons cannot produce 2P fluorescence (dominant at high pressure) N e X Σg N2 C Πu 2P fluorescence is generated by low energy electrons from ioniza)ons. Suggested by Bunner (PhD thesis 1967). First detailed calcula)on up to GeVs: F. Blanco and F. Arqueros Phys. Lep. A 345 (2005) 355 8

10 Secondary electrons Δx R R interaction volume A simple analytical model MC simulation ph/m! vv' (E) = N 1 " $! vv' (E)+! & $ vv' # (1! e!n<! inel>r )! ion (E)' 1+ P / P v ' %$! inel ($ Direct excitation Probability to escape the observation region Secondary electrons contribution ph/m 1! vv' (E) = N {! vv' (E)+! vv' (E, P, R)! ion (E) } 1+ P / P v ' Direct excitation Average #ph per secondary electron Phys. Lep. A 345 (2005) 355 9

11 Secondary electrons Phys. Lep. A 345 (2005) 355 Low P and E Nagano Kakimoto High P and E Fluorescence intensity vs pressure Fluorescence intensity vs energy The model accounts for experimental results previously not well understood 10

12 loop for each electron e- source primary electron elast. electrons step = (N σ ) -1 E > 11 ev? yes inside geometry? yes brem. excit. secondary electron no no ioniz. next e - next e - if X-ray emission * F. Arqueros et al. New J. Phys. 11 (2009) updated details in J. Rosado Ph.D. thesis (in press) MC simula=on* Elas)c scapering - Individual e - - molecule collision Excita)on - E = E - <E exc > - n 337 = σ 337 /σ exc Ioniza)on - e - ejected with E s - E = E - <E ion exc > - E s - n 391 = σ 391 /σ ion - K- shell ioniza)on (410 ev). Bremsstrahlung - 3% of E converted in γ- ray. Energy cutoff - E cut = 11 ev 11

13 MC simula=on* Cross section ( a 0 2 ) ! 337!! ion! ex c! 391!! K E (ev) * F. Arqueros et al. New J. Phys. 11 (2009) updated details in J. Rosado Ph.D. thesis (in press) Elas)c scapering - Individual e - - molecule collision Excita)on - E = E - <E exc > - n 337 = σ 337 /σ exc Ioniza)on - e - ejected with E s - E = E - <E ion exc > - E s - n 391 = σ 391 /σ ion - K- shell ioniza)on (410 ev). Bremsstrahlung - 3% of E converted in γ- ray. Energy cutoff - E cut = 11 ev 12

14 Novel parameteriza)on of the energy spectrum of secondaries MC simula)on d! ion de s = # % $ % &% 4" Z Ry E p ' 1+ C(E p )exp{!e s / E k } for E E 2 s + w 2 s " (E p! I) 0 for E s > (E p! I) E p ' = 1 2 m e! 2 c 2 Fully consistent with: EEDL Møller at high E s Opal (exp.) at low E s σ ion (E p ) Bethe - Bloch 13

15 MC simula)on Parameteriza)on of the energy spectrum of secondaries consistent with Bethe- Bloch de /dx (MeV g -1 cm 2 ) de dx = N air 0 E dep { E 0 dep + E s }! ion (E 0 )! = E exc ion exc + E exc! ion + I Bethe-Bloch Predictions Extended Opal of the model E (ev) 14

16 Geometry MC simula)on Generic simula)on: Medium: sphere R of air (P, T) Primary electron forced to interact at the center Detailed simula)on: Geometry e - beam features Field of view 15

17 Results: Energy deposi=on de dx = N air de dep /dx (MeV g -1 cm 2 ) { E 0 dep + E dep }! ion (E 0 ) de dx E;PR E (ev) generic simula)on ( ) 0.01 Bethe- Bloch hpa cm infinito <E dep > (ev/sec) low E secondaries high E secondaries P R (hpa cm) 1 GeV 200 ev Generic simula)ons: E dep weakly dependent of PR. Detailed simula)ons: E dep weakly dependent of fine geometrical details. E dep from generic simula=ons equals those of detailed simula=on for R size of the collision chamber Results 16

18 Energy deposi=on cross check Results GEANT4 has been implemented for comparisons with our MC simula)on using simple geometries e - air 17

19 Energy deposi=on cross check Results de dep /dx (MeV g -1 cm 2 ) e - 1.8% Air 1013 hpa 10 cm GEANT4 ~2.5% (our implementa)on) This MC algorithm E (MeV) de dep dx versus E Comparison of our detailed MC with other simula=ons - GEANT4 (our implementa)on) - GEANT4 (MACFLY) - GEANT4 (AIRFLY electrons) Systema=c difference: E dep (MC) E dep (GEANT4) 2% 18

20 Energy deposi=on cross check Results de dep /dx (MeV g -1 cm 2 ) MeV e - (our implementa)on) GEANT4 Our MC X- rays escaping Air 10 cm 15 hpa ~2% (de /dx ) dep 1.41P (de /dx ) dep 1.39P P (hpa) de dep dx versus P Comparison of our detailed MC with other simula=ons: - GEANT4 (our implementa)on) - GEANT4 (AIRFLY*) Very good agreement in hpa * Astropart Phys. 28 (2007) 41 19

21 Energy deposi=on cross check Results 2.15 FLASH collision chamber E = 28.5 GeV de dep dx versus P Comparison of our detailed MC with other simula=ons: - EGS4 (FLASH*) de dep /dx (MeV g -1 cm 2 ) FLASH This work 5% Some discrepancy < 5% This work (dens. corr. at fixed P) P (hpa) * Astropart Phys. 29 (2008) 77 20

22 Results: Fluorescence Results Photons (vv ) per meter without quenching! 0 vv' (E) = N {! vv' (E)+! vv' (E, P, R)! ion (E)} α 337 (fot/sec) α 337 (fot/sec) P R (hpa cm) E (ev) Average #ph per secondary electron 1 GeV 200 ev hpa cm infinito Y Y 337 Fluorescence yield without quenching Photons/MeV Photons/MeV Y 0 vv' = 0! vv' de / dx P R (hpa cm) 1 kev 1 MeV 1 GeV E (ev) hpa cm infinite

23 Fluorescence emission cross- check Results 20 kev low pressure Rosado et al. Intensidad relativa 337 nm Pa 8Pa Experimental Simulada y (mm) Intensidad relativa 391nm Pa 8Pa Experimental Simulada y (mm) 22

24 Fluorescence intensity vs. pressure P measurement*! vv' (E) = N 1 1+ P / P v ' {! vv' (E)+! vv' (E, P, R)! ion (E) } additional P dependence Results Neglec=ng the effect of secondary electrons in ε vv give rise to systema=c errors in the measurement of P * F. Arqueros et al. New J. Phys. 11 (2009)

25 Photons/m Fluorescence intensity vs. pressure P measurement* 1! vv' (E) = N 1+ P / P v ' Nagano et al : P' = 155 hpa PW: P' = 129 hpa 337 nm N P (hpa) {! vv' (E)+! vv' (E, P, R)! ion (E) } Photons/m Nagano et al : P' = 5.5 hpa PW: P' = 3.3 hpa 391 nm N P (hpa) Nagano s data of ε vv (P) have been re- analyzed including the α vv (P) dependence from our MC *updated results in J. Rosado Ph.D. thesis (in press) additional P dependence Results 24

26 Fluorescence intensity vs. pressure P measurement* Results Photons/m Nagano et al : P' = 19.2 hpa PW: P' = 14.6 hpa 337 nm air Photons/m Nagano et al : P' = 5.0 hpa PW: P' = 3.3 hpa 391 nm air P (hpa) P (hpa) AIR P 337 (hpa) P 391 (hpa) Nagano AIRFLY Nagano corrected Discrepancies between Nagano and AIRFLY are reduced significantly when corrected for this effect *updated results in J. Rosado Ph.D. thesis (in press) 25

27 Fluorescence yield versus Energy Results 0 Y 337 Photons/MeV % MeV keV 1MeV hpa cm GeV 10GeV E (ev) 1.5% < 0.1% 1 MeV Y constant for E > 1 kev Y dependence is even smaller for Y 391 Experimental tests show Y independent of E within 26

28 Fluorescence yield versus PR Results Photons/MeV % < 0.1% Y MeV P R (hpa cm) Y strongly dependent on PR in the vicinity of the electron track (PR < 100 hpa 100 μm) 27

29 Theore=cal value of the air- fluorescence yield Results Y 337 = 1 0 Y P / P 337! = 6.3 ph/mev 1013 hpa 293K! P Y 337 from AIRFLY* from our MC simulation Uncertain=es in our calcula=ons: Energy deposit 2% Fluorescence emission 20 % Fluorescence yield 20 % Average value of experimental results** * Astropart Phys. 28 (2007) 41 Y 337 = 5.57 ph/mev ** talk of J. Rosado 28

30 Conclusions Fluorescence emission and energy deposi)on in air is reasonably well understood. Our simula)on in agreement with GEANT4 (2%). Some disagreement (< 5%) with EGS4- FLASH. FY independent of E supported by theory at the level of < 1.5% (1MeV 100 GeV). Theore)cal absolute FY in good agreement with experiments. Systema)c errors when the effect of secondaries is neglected. Detailed simula)ons provide the necessary correc)on factors. When applied, agreement between experiments improves: - Energy deposi)on/absolute FY (see talk of J. Rosado) - P values in ε(p) measurements, e.g., Nagano vs AIRFLY 29

31 Thanks 30