PoS(ICRC2021)420 International th 12–23 July 2021 July 12–23 37 SICS CONFERENCE SICS CONFERENCE Berlin | Germany Berlin Berlin | Germany Cosmic Ray Conference Ray Cosmic ICRC 2021 THE ASTROPARTICLE PHY ICRC 2021 THEASTROPARTICLE PHY https://pos.sissa.it/ ONLINE ∗ [email protected] International Cosmic Ray Conference (ICRC 2021) Presenter ∗ th Faculty of Physics and Applied Informatics,Pomorska University 149/153, of 90-236 Lodz, Łódź, Poland. E-mail: Extensive Air Showers (EAS) inducedvery by steep cosmic cosmic ray ray particles energy spectrum ofdetectors dominate very and the low small secondary energies shower particle arrays. due fluxsearch to measured Such for by the potentially arrays single interesting connected spatial in correlations extended betweenon showers, networks the which can may nature be shed of new used ultra light to by high-energy small cosmic local rays. arrays requires Quantitative a interpretation differentoperating methodology of in than showers the that recorded used ’knee’ by regionmethod ordinary for big integrating and EAS cosmic above. ray arrays spectra over energies We ofof interest present primary and summing ’small nuclei over mass EAS in spectra generator’, arbitraryfluxes semi-analytical and detector particle configurations. density spectra are Results given. on the EAS electron and muon Copyright owned by the author(s) under the terms of the Creative Commons © Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 37 July 12th – 23rd, 2021 Online – Berlin, Germany Tadeusz Wibig CORSIKA below the knee PoS(ICRC2021)420 Tadeusz Wibig 2 The idea of small autonomous Extensive Air Shower (EAS) experiments was first explicitly Building further similar facilities for higher and higher energy cosmic ray measurements is In many countries attempts are being made to introduce such projects in schools to stimulate The mere fact of the simultaneous appearance of some signals in several detectors is not The minimum number of detectors in one station is of course 2, as it was in the famous Small showers surely pose fundamental problems of interpretation. It is of course impossible to presented by Linsley in 1885 [1]tens in the and context hundreds of of synchronization square of kilometersso large to detector small arrays record that covering showers of only the giantbeen highest instruments realized energies can to whose some produce fluxes extent are meaningful practicallyas results in the Pierre in triggering Auger a systems Observatory of reasonable or the Telescopeto time. Array. largest measure The EAS practically complex It instruments the linkage has such UHECR of fluxes local of triggers allowed one particle per square kmpractically per unjustified century. today. Fornew the techniques measurements are necessary, of suchon above Greisen–Zatsepin–Kuzmin as by cut-off satellite dozens or orhas hundreds radio been of measurements, an scientists which increased from are interestscientific many in being curiosity small-scale countries. and worked EAS develop their experiments interest On in designed science.important the to Small role satisfy other local in young (school) hand, education. EAS people’s arrays recently They can playof are there an learning one about of nuclear the physics, very modern few high-energyfor possibilities physics, high and of school physics tangible of students "hands-on" elementary for type particles whomits such image knowledge as is something generally very given distant, only mysterioussecret and indirectly, knowledge, thus unattainable modern for creating magic. the This average mortal, leads to assomething the a perception potentially kind of dangerous, of science which and it physics in would particular notResistance as and hurt protests to against oppose nuclear when power the plants opportunity are appears. an obvious manifestation ofinterest this. in cosmic ray physics.name In some: some HiSPARC [2] this in has the already Netherland,[5],3], [ WALTA, been NALTA, SKALTA, ALTA, [4], done CHICOS, SALTA, CZELTA, on [6], a CROP, CosMO smallersuch [7] or small or larger arrays scale, Maze are to 8,9]. [ notsimple a From triggering, serious a monitoring technical and problem. point recording deviceidea of A and view, of few the typical such problem scintillation is projects detectors solved.system, is connected the However, to since cost to the of popularize a appropriate such equipment arrays, for one and school preferably starts to to playfascinating, combine a although them significant role. it into may one befact, big interesting or to rather from some. aor set It of even starts such months to facts, or be fromthe really years, a interesting surrounding registration finally from that reality. something lasts such starts continuously a are To for to days, needed go emerge weeks, and from which such direct iscomprehensible tools measurement documentation actually and should to knowledge user about be its instructions. provided interpretation, to appropriate students tools andexperiment teachers of together Auger with and clear Mazeproject in and 1938 [2]. [10, 11] and Forhowever, the as stable number it operation of is 3 now andabout in detectors the full the size seems of stations control to the of shower, be over we theand should more background higher HiSPARC have secure. more coincidence and detectors events. to random However, By study to the optimizing4 coincidences, try frequency performance detectors of and seem to double, to price say triple be we something the believe that best. stations with CORSIKA below the knee PoS(ICRC2021)420 21 Tadeusz Wibig 3 From a fundamental physics point of view, it might be very interesting to combine many Analysis of data from small arrays requires specific methods. Methodological limitations do An obvious element necessary to simulate the passage of shower through the atmosphere CORSIKA allows one to do so. There is no obstacle to try to determine the chance to observe The first and undoubtedly most important parameter of a shower is its size which the CORSIKA (the more, the better)in instruments real into time. one networkGerasimova-Zatsepin and effect Observation search [12, of]13 for pairs existence thenuclei. in of existence the The of large cosmic cosmic correlations showers ray flux mass at atThe composition the distant observation in highest this of locations energies area other of could still correlations heavy the remains indicate could Cosmic a Ray via suggest mystery Ensembles waiting the the sought to existence by be of the solved. more CREDO Collaboration. exotic objects, suchnot as allow to use typical forof cosmic EAS ray registrations, experiment in methods any of case, is processing based data. on The computer interpretation simulations. is a model describingThe the modeling high of energy strong particledeveloped interactions collision a has and long a the time longnew secondary ago history. data. particle and production. All are Thethrough models constantly model the on being needs Earth’s the refined to atmosphere. market be andelectromagnetic today Complementing implemented improved cascades were them with into and with the the descriptions aprocesses geometrical release of much simulating structure other of the better of development more known of the formalism andthis EAS. of purpose transport less Today, one is important of the processes the CORSIKAKASCADE most leads program[14, 16, experiment[ widely15] to 17]. used developed programs over 30developed for and Since years is ago then now in this used Karlsruhe also program for for the has simulations at been the significantly highest extended observed energies and (even up to 10 a charged particle remaining fromGeV. The a chance of proton seeing initiated anything cascade isparticles starting surely is very large with small, indeed. the but energy we should of, recall say, that 10 the flux of such CORSIKA below the knee localize the shower axes. Besides, withat such higher a particle small number densities of on detectorsquestionable detector anyway. (3 sites For or 3 (which 4) – could localization 4 be even detectorsto the set determine up case in of the small larger directions distances showers) (aboutevent-by-event of would 10 analysis be m) arrival does it of not is also showers. give unrealistic the any In frequency meaningful the of results. absence observations of of Whatstudy how various direction we the coincidences. and can frequency of axis sensibly registration The measure position, conducted changes measurement with is by time, times which groups will can allow be ofday/night a us variability, students, basis to and for dependence such various of studies as variousray "everyday variability flux. life" quantities as As on far a the as we observed functionrates know, cosmic no on of one the has cosmic atmospheric yet ray investigated flux. the parameters, dependence of the COVID-19 infection eV). But small local arrayscosmic need ray to energy be spectrum.The simulated low-energya with end few energies of GeV/n, at the which the spectrum is other isenergies primarily end of truncated due 1 of around to GeV the energies are solar of very nota modulation. steep capable shower at of Of all. causing course, what The we atomicchance products might of nuclei of call reaching the with the a interactions kinetic earth’s Extensive initiated surface. Air by Shower, such or particles even would have no realistic PoS(ICRC2021)420 Fe Fe D E eV [ ] p Tadeusz Wibig E p Fe electrons muons Dispersion of the logarithm of elec- p independent proton showers would Fe 56 p Figure 2: tron and muoninitiated numbers by in protons and CORSIKA by ironspectively showers nuclei according shifted to re- theof superposition the model shower development.respective scales Symbols, are lines like and in Figure 1. D 4 Fe N Fe eV E [ ] p Fe p E eV, the dependence is definitely power-law with different indices for 16 muon size eV to 10 p Fe 11 electron size Average electron and muon numbers in p It has been known for many years that the transverse distributions of particles in extensive air Fig. 1 shows the average values obtained from the simulations for primary protons, and for the . In the picture of simple superposition, the dispersion of N 56 correspond to the expected dispersionthe for simulation iron calculations with induced the showers. CORSIKA programwith As for the proton can correspondingly initiated shifted be showers values do seen, for iron not thesolution, showers. overlap points the The results lines from in of Fig. our ‘fast 2 represent small our shower proposed generator’. Figure 1: CORSIKA showers initiatedcles - by scales protons onclei shifted the (solid respectively according left to cir- and themodel superposition bottom) (empty and circles by -top). iron scales nu- on the Lines rightsmall shower show and generator”: on the solid the forfor results protons iron and obtained initiated dashed showers. by our “fast iron nuclei. First of all, itseveral is times worth 10 to notice, that practically in the whole shown energy range from CORSIKA below the knee program provides. We can defineelectrons the or muons size at separately the as observation electron level. and muon size as the number of muon and electron size. According toof the single picture nucleons of and simple a superposition shower nucleusshowers. initiated is This by, treated for assumption as example, a is an set quite ironin natural nucleus and Fig. is to the a same large 1.Both as extentassumption 56 of correct, proton is as these correct, we observations can but see (ofof this for EAS, the example, is which CORSIKA not is results) entirely indispensable forshowers, and indicate carrying is exactly that out the true. correct the size calculations of superposition Another ofinitiating the important fluxes them. fluctuations of characteristic of particles the Fig. in shower small size size distributions 2 at as shows small the a energies of dispersionEnergy function scales particles of of for which the the iron are energies logarithm showers (top) ofscales of correspond for the the√ to proton protons electron the induced and (a) same showers iron energy and (bottom). nuclei per muon initiating nucleon Ordinate (b) as for showers. the iron respective showers (right) is scaled down by PoS(ICRC2021)420 m m [ ] [ ] x r eV b) and iron Tadeusz Wibig 14 eV eV 14 14 distribution of electrons ) c) iron 10 f) iron 10 H × , logarithmic dispersion of G i ( eV (a), and 10 y r m # [ ] n h 12 m m [ ] [ ] x r independent nucleon (proton) subshowers  eV eV 14 14 5 e) proton 10 b) proton 10 y r m [ ] n m m [ ] [ ] spread of the size of the iron shower. This indicates the existence of a eV c) (for b) and c) only 100 particles are plotted). Bottom histograms d), e) and x r 14 56 √ eV 12 Examples of showers generated by our small shower generator. The proton 10 a) d) Next, we have to verify a simple superposition model which allows to eliminate from our We have determined average number of particles in the shower The simplest introduction of correlations among y r m [ ] n descriptions the mass ofabove, this the model primary works well particle forcomparing average as the shower dispersion sizes. an (logarithmic) We of independent have theThe noticed variable. total observed a number dispersion significant of for particles discrepancy As iron for is protons weof greater and the have iron than nuclei. mass expectation shown obtained number by scaling by the square root the actual size, and age parameter andand "Molière unit" hard of NKG (muon) function, components separately for of softmass, (electron) CORSIKA and showers incoming as angle. a function of primary particle energy, its showers are well described by a simple formula proposedby by Greisen theoretical]. [18 considerations Its and validity was numerical confirmed by calculations Kamata with and respect Nishimura to [19], electromagnetic(NKG) hence cascades function its commonly accepted name: Nishimura-Kamata-Greisen f) show radial distributions of particles in these showers, respectively. (filled circles) and mouns (emptyshower circles) with for energy proton of shower 10 of energies 10 with the same energy per nucleonidentical they are actual supposed size. to mimic This is to decreases assume the that number some of of them independent have compounds, thus increasing the correlation between the ’subshower components’. Figure 3: CORSIKA below the knee PoS(ICRC2021)420 -2

] ] ] m [ ] 21 22 23 [ [ [ ρ Tadeusz Wibig detector, each observed value 2 Shower particle density spectra ob- ) -1 ρ s Figure 4: tained using our small showercompared generator (circles) with measurements [20, 22, 23]. [ ] f( 6 ) 39 . 1 in 1950 = W et al. )[18]. 3 . 1 = W , for example the one mea- W − d )[22], Norman in 1956 ( )[20, 21], Broadbent . The actual integer number of identical subshowers in each nucleus induced shower  47 . 425 . 1 1 All this with the modified superposition approach is already sufficient to formulate a simple If we measure the number of particles observed on a 1m The results of the modified superposition model are shown in Fig. 2 for electrons and muons. It is known that the main source of shower size fluctuations is the height of the first interaction, With our fast small shower generator one can It allows to compare predictions not only with = = W W carry out the multidimensional Monte Carlogration inte- to obtain the showerserved particle with a density single ob- small detector.the The integrationis result shown of in Fig.with measured 4 results in comparison listedsee, above. the agreement is As very we good. can [23], or Greisen in 1960 ( algorithm generating small EAS that willExamples resemble of the showers EAS generated generated in by this the way CORSIKA are program. shown in Fig. 3. As can be seen, in theenough region agreement where with the CORSIKA shower simulations. sizes are As sufficiently wenumber have large, said, of we for have particles very obtained small a in showers good the singlefrom integer the showers Poisson and distribution the have combination a dominant of role. the physical spread with thethe effect CORSIKA showers which itwith is based experimental on, results, but e.g.,ticle the density shower spectrum. par- since at least It the has middleform of been of the the last measured spectrum century. found agreedpower The law with formula a simple sured by Cocconi, Loverdo and Tongiorgi in 1946 ( fluctuates according to a binomial distribution. ( which it is related to the crossassume section that of the the interaction, average number it is of reasonableof identical and sub-shower wounded theoretically components justified nucleons is to in proportional the toatmosphere. the interaction number of Of the course, cosmic wenucleus ray are nucleus only with talking the about atomic the nucleus wounded nucleon of of the the beam, cosmic ray CORSIKA below the knee dispersion as we wish to. corresponds to a different distribution ofare the primary shown particle in energy. Fig. Theregistration results of of single the 5. muons calculation is several These timesopposite, higher the results than cases rate lead of of to simultaneous registrationof registration of some more single of than important electrons, more one and than conclusions: electron one and muon the for are primary example, much energy rarer required rate than is of much those higher. PoS(ICRC2021)420 , eV [ ] OG9.4-9

E Tadeusz Wibig e µ 4-fold 2-fold 3-fold 4-fold Distributions of primary energies single 3-fold 2-fold single 1m detectors fired with electrons (solid × Figure 6: which are responsible for4 events on 1m 1, 2,lines) 3, and by and muons (dashed lines). (E) φ 7 4 eV [ ] 3 e µ E 2 detector of 1, 2, 2 5 4 International Cosmic Ray Conference (ICRC1985) La Jolla, US 2 3 Cℎ 1 Mini and Super Mini Arrays for the Study of Highest Energy Cosmic Rays Primary particle energy spectra lead- 1 Proceedings, 19 434. Figure 5: ing to the observation in a 1 m 3, 4 and 5muons (dashed particles: lines). electrons (solid lines) and As it was mentioned, the main application of the small shower generator is to assist in the Examples of such results are presented in Fig. 6. We developed the "small shower generator", which can be used as a semianalytical method for Using our small shower generator, it is possible to perform fast integrations of secondary (E) φ [1] Linsley, J., interpretation of data fromintegrated networks small of shower local stations. arrays,of For either four example, identical for let detectors us educational assume locatedanswer purposes that the not such question or far with stations from what would for energy consist eachdistribution use of one other. the should in primary associate Small a particle, given shower or type generator more of precisely will coincidence. with help what to energy Conclusions the calculation of secondary particle fluxprovided at by the CORSIKA sea level and and otherthrough to Monte-Carlo the mimic Earth’s the programs atmosphere. exact which shower More generation fully details simulate are given a in shower [24]. passing particle fluxes at sea levelwell and as predict the single registrations detectors. madedeeper by analysis These of small predictions, the school local when local measurements and EAS confrontedshower the arrays with properties generator as of also the the allows detectors measured themselves. the values, Thesize count allow small and rate number a in of small detectors to EAS be arrays optimalised to in be this estimated respect. and theReferences detector CORSIKA below the knee PoS(ICRC2021)420 , 864. 63 AIP Confer- Proceedings, , , Dissertation report KZKA- Tadeusz Wibig 157. 63. 10 349. 085001. 10 , 846. 33 70 45 IEEE Transactions on Nuclear , Nuclear Instruments and Methods in , , 93. 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