PoS(ICRC2017)086 http://pos.sissa.it/ eric Cascade: Electron del. A quasi-analytical performed using GEANT 4 simu- and good agreement between Monte for events with arbitrary incidence is allows one to calculate atmospheric s based on pre-computed with high- sing full Monte Carlo simulation of here, explicitly considering all physical ed. atory (Oulu unit), University of ciences, St. Petersburg, Russia. Petersburg, Russia ive Commons onal License (CC BY-NC-ND 4.0). ∗ [email protected] [email protected] [email protected] [email protected] [email protected] lation tool PLANETOCOSMICS with NRLMSISEapproach, which 00 allows one atmospheric to mo compute thealso ionization presented. yields It is compared with MonteCarlo Carlo simulations simulations and quasi-analytical approach is achiev processes involved in production. The simulations were precision ionization yield functions,electron which propagation are and interaction obtained in the u Earth’s atmosp ionization induced by precipitating electrons. The model i Precipitation Induced Ionization) is presented. The model A new model of the CRAC family, CRAC:EPII (Cosmic Ray Atmosph Speaker. ∗ Copyright owned by the author(s) under the terms of the Creat c 35th International Cosmic Ray Conference -10-20 ICRC July, 2017- 2017 Bexco, Busan, Korea Attribution-NonCommercial-NoDerivatives 4.0 Internati Oulu, Finland. E-mail: Alexander Mishev Anton Artamonov Space Climate Research Unit, University ofE-mail: Oulu, Finland. Genady Kovaltsov Ioffe Physical-Technical Institute of Russian AcademyE-mail: of S Irina Mironova St. Petersburg State University, Institute ofE-mail: Physics, St. Ilya Usoskin Space Climate Research Unit; Sodankylä Geophysical Observ Computation of electron precipitation atmospheric ionization: updated model CRAC-EPII Space Climate Research Unit, University ofE-mail: Oulu, Finland.

PoS(ICRC2017)086 ) n as E , x x (2.1) (2.2) ( Y . (about 200 km K 2 Alexander Mishev g/cm 9 − 10 NRLMSISE 00 atmospheric × , averaged per primary particle km above the sea level (a.s.l.), x a yield function [18]. The ion computation of ionization induced y protons with the atmosphere are e involved in the atmospheric ion- and X-rays, which are absorbed be- rgy range of precipitating electrons f the atmosphere the impact ioniza- al atmospheric processes affected by dK cally it’s upper polar part. Effects due part of the atmosphere dominates the of the product of the primary particle 00 keV. However, the contribution of ) electric circuit and minor constituents urces of ionization below 100 km. At oduction rate q(x) at a given depth y particles with energy different regions of the h on (henceforth Bremsstrahlung). at depth s are considered elsewhere. ( ) . The ionization yield function al zone [3]. However, occasionally rela- x x he additional Bremsstrahlung ionization. ρ E ) ∂ , ∂ ral zone as well as in middle latitudes [4, 5]. osmic rays (GCRs), solar energetic particles x K om radiation belts, auroral electrons. In this into account Bremsstrahlung. ( , tion ion h E E ( ∂ Y 1 ) K )= ( J E , x Z ( Y )= h ). An example of ionization yields for electrons is shown in ( 2 q =35 eV is the average energy necessary for production of an io ion E , and E is the energy deposition in atmospheric layer E ∂ In this study, the propagation and interaction of high energ The majority of studies are focused at heights of about 60–80 The precipitating electrons ionize the atmosphere, specifi Different types and populations of high energy particles ar convoluted with a primary particle spectrum gives the ion pr which correspond to precipitating electronsrelativistic of electron about precipitation 100–4 is not discussed nor t simulated using the PLANETOCOSMICS code [16].model We [17]. employ the Here,production we rate use in a the previously atmospherespectrum is developed and obtained formalism the as pre-computed of an yield integral function defined as: Here, we present a model based on Monte Carlo simulations for 2. CRAC:EPII model to electron precipitation are usuallytivistic observed electron in precipitation the can occur auror also in sub-auro due to various mechanisms [6, 7,the 8, 9, impact 10, ionization 11]. as There well arein as sever the processes Earth’s related atmosphere to [12, global 13,tion 14, is 15]. governed by In the thesecondary direct upper ionization ionization, part mostly while o due in to the Bremsstrahlung lower radiati by relativistic electron precipitation explicitly taking In general, electrons precipitate into the atmosphere from ization [1, 2]. The energeticaltitudes particles above 100 (EPs) km are dominate the the mainlow. contribution Energetic so of precipitating solar particles UV include galactic c Computation of electron precipitation atmospheric ioniza 1. Introduction (SEPs), precipitating protons, relativistic electronswork fr we focus on relativistic electrons, while other source where where J(K) is the differential energy spectrum of the primar Fig.1 (isotropic incidence) and Fig.2 (various incidence) with kinetic energy a.s.l.) to the sea level (1033 g/cm pair in air [19]. Thebetween computations 20 were keV carried and out 500 in MeV. the and ene at atmospheric depths from 6.5 PoS(ICRC2017)086 (3.1) is the ionization Alexander Mishev ) K , x ( Y ncidence and putation of vertically derived α cos / , h 10 MeV energy for isotropic and x α = events with arbitrary incidence, details ′ x cidence of monoenergetic electrons in the cos for a monoenergetic electrons with energy ) / ) K tion , K ′ , ′ x ( x ( 2 α Y Y )= K , x ( α Y is calculated: α is the rescaled atmospheric depth, calculated as ′ x On the basis of a quasi-analytical approach, based on re-com and with angle of incidence Figure 2: Ionization yelds vs. altitude [km] of electron wit various angles of incidence as denoted in the legend. 3. Computation of ionization induced by EPs with arbitrary i ionization yields, we can compute theare given ionization elsewhere yields [20]. for The ionization yields Figure 1: Ionization yields vs. altitude due to isotropic in energy range 100 keV–100 MeV, as denoted in the legend. Computation of electron precipitation atmospheric ioniza K where PoS(ICRC2017)086 . , φ φ 2 d the α (3.4) (3.5) (3.6) (3.7) (3.2) (3.3) and allows cos , details α x F d α cos where . Therefore: ) Alexander Mishev ) α φ , φ term), defined as a , φ α ) ( α d h is the ionization yield f ( ( v α f φ 1 leads to: ρ 0 Y 0 si-analytical approach is d R J π α π cos / 2 is unit flux and the angular 0 d and R =1 )= 0 φ α cos α f J φ d = 4) The shapes of the ionization d , α A α cos α α cos nd α d ) , α / arth’s atmosphere. One can see the α les. φ ikes exist due to large fluctuations of r a hard electron spectrum from [23], K x ferential ionization function cos , cos ( cos 1. The flux of electrons within a solid = ) , leads to: spectrum of primary electrons is shown for particles with arbitrary angular dis- J ′ d cos α ) the CRAC:EPII model at depth ach other at depths greater than 5 g/cm d cos n yields, specifically at depths below 1 φ α x ) ( ) = h d , where , o see that: f n α =0, hence ( ) α ) K K ) n α φ , ρ , ′ K ( K ) d K x , x cos ( f cos tion sin ′ , ( ( 0 K α ) x ) f ) x 1 v J ( ( ( d Y Y φ K π α v F + α , , 1 ( 3 4 α A Y ) 0 x Y f n 1 α ) ( 0 Z K ( 1 R 0 sin α , f K 2 )= R x Y ( 2 ) (the integrand of Eq. 2.2, but is a function only on the zenith angle ( / )= 2 0 1 K f / π J K 0 ( ) α π F )= ( Y is: 1 Z − ( )= F φ 0 0 R f K π , x J Z K 2 , π , α 0 x 2 )= π 0 ( x ( 2 Z R ( f K 0 )= f , 1 A iso Z is the response of the atmosphere, the ionization yields, to K x Y Y ) ( ( ) h I ( )= K dF ρ , K x , ( x ( Y )= is f K Y φ , x d ( α I in a way that d ) α φ , sin α ( = f is the rescaled atmospheric depth, calculated as ′ Ω x d , which is explicitly considered in the yield function (Fig. 2 The differential ionization function The yield function In the case of axial symmetry which in case of isotropic incidence (distribution) A good agreement between Monte Carlo simulations and the qua The corresponding ionization yield function distribution is normalized to 1 i.e. but different in the region ofthe the computed upper energy deposit atmosphere, and where the sp lack of secondary partic angle given elsewhere[21, 22]. Let the intensity of electrons is Computation of electron precipitation atmospheric ioniza yields for electrons with vertical incidence computed with are the the zenith and azimuth angles of incident electrons a g/cm mono-energetic unit flux ofessential primary particles contribution entering of the Bremsstrahlung E in the ionizatio yield functions as a function of the altitude are similar to e where achieved (Fig.3) Accordingly the total flux of electrons is Hence the ion production rate at depth function for electrons with vertical incidence. It is easy t product of the ionization yield functionin (Fig.4) Figure and a 5 given for several atmosphericthe depths. details Here, of we computation conside are given elsewhere [21]. The dif tribution PoS(ICRC2017)086 2 2

2

5g/cm 10g/cm 15g/cm 6 Alexander Mishev 10 5 10 y 1 MeV, while right hand denote th various angle of incidence and the computed data points. ical approach Eq. (4) and PLANE- nergy above 20 keV. One can see that uce ionization, which strongly depends uce ionization strongly depends on the trons with vertical incidence at several 4 10 tion

4 E E [keV] 3 10 2 10 1 10 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 10 10 10 10 10 10 10

10 10 10 10 10 10

Ionization yield function [ion pairs cm pairs [ion function yield Ionization g ]

2 -1 Figure 4: Ionization yield function for precipitating elec depths as denoted in the legend. The curves are smoothed over one to estimate the most effective energyon of the primaries atmospheric to ind depth. Here,the the most integration is effective over energy the of e precipitating electrons to ind Figure 3: Comparison of ionization rates due to electrons wi energy as denoted in theTOCOSMICS. legend, The left computed hand with panels quasi-analyt denoteelectrons with electrons energy with 10 energ MeV. Computation of electron precipitation atmospheric ioniza PoS(ICRC2017)086 5 10 2 2 2 Alexander Mishev flattens, because of F 5g/cm 10g/cm 15g/cm 2157, Center of Excellence C:EPII, which allows one to reasing the altitude (increasing tions of propagation and interaction SMICS code. The model allows one y ionization model CRAC. A conve- phere, specifically in the stratosphere elativistic and high energy precipitat- is dominated by electrons with energy ed. onization yields is presented. A good 2 is governed by particles with energy of ons. ization yields for particles with arbitrary 2 tion 5 for precipitating electrons at several depths as denoted Energy [keV] Energy F the differential ionization function 2 4 10 0 2000 6000 8000

4000

10000

keV] s [g F

1 − Here, we have presented an upgraded full numerical model CRA This work was supported by the Academy of Finland (project 27 Figure 5: Differential ionization function Computation of electron precipitation atmospheric ioniza atmospheric depth. The ionization at depth of about 5 g/cm in the legend. of about 10 MeV, accordingly at depth of about 10 g/cm the diminishing number of high energy precipitating electr 4. Conclusion compute the ion production in the Earth’sing atmosphere electrons. due The to model r is basedof on precipitating a electrons full with Monte the Carlo air simula to using perform the computations PLANETOCO of ion production inover the the whole Globe. atmos In fact, thenient model quasi-analytical is approach an for extension computation of of cosmic the ra ion ReSoLVE). incidence, based on re-computation of vertically derived i agreement of the approach with direct simulations is achiev Acknowledgements about 200 MeV. 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A11 6802–6804. electron precipitation from the radiation belts relativistic proton impact in air Physics precipitating electrons: Yield function and applications Comparison of new Monte Carlo model with parametrization dr (2011), no. 7 D07307. the interaction of cosmic rays with20 the Earth’s atmosphere of atmospheric ionization induced by electronscrac-epii with non-ve Statistical comparisons and scientific issues (2002), no. A12 1468. practical applications and Solar-Terrestrial Physics electron precipitation events as observed in the long-dura of Atmospheric and Solar-Terrestrial Physics [20] A. Artamonov, I. Mironova, G. Kovaltsov, A. Mishev, E. P Computation of electron precipitation atmospheric ioniza [15] P. Verronen, C. Rodger, M. Clilverd and S. Wang, [21] A. Artamonov, A. Mishev and I. Usoskin, [22] A. Artamonov, A. Mishev and I. Usoskin, [16] L. Desorgher, E. Flückiger, M. Gurtner, M. Moser and R. B [19] H. Porter, C. Jackman and A. Green, [17] J. Picone, A. Hedin, D. 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