Accepted 10 October 2013Available online 30 October 2013
of electric or magnetic elds that are intentionally generated to clearly separate electrons from positive
JaE;s;u; tdtds$brdudE; (1)where C counting rate (counts/s), T duration of the observationstarting from time t t0, a detection efciency for the ath par-ticle species, Ja differential particle ux of the ath particle species[cm2 s1 sr1 E1], ds element of surface area of the detector
which a remains a(E), and time-s Ja J0(E), thees to the following
E S U
The bracketed quantity in Equation (2) often depends only onthe geometry of the detector relative to the guiding structure of theinstruments, such as a collimator, aperture, or bafe, and isconventionally dened as the geometric factor. For circular orrectangular apertures, the geometric factor has been previouslycalculated with the assumption that particles pass through theinstruments on a straight trajectory [1e3]. To properly interpret thecollected measurements, it is important to account for the
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Contents lists availab
Current Applied Physics 14 (2014) 132e138E-mail address: firstname.lastname@example.org (J. Seon).effective dimensions of the detector facing a certain solid angle inspace, as well as the efciency of the detectors as a function ofparticle energy. The general expression by Sullivan  gives thefollowing relation for the counting rate from the detector:
angles, and particle energies.In the case of ideal detector responses, for
constant over the domain of u, a and t, i.e., aindependent isotropic incoming particle uxeexpression for the detector counting rates reducsimpler form:
264 Z ds$br$ Z du
375J0EdE:incident uxes of charged particles critically depends on the which respectively represent the surface area of the detectors, solidGeometric factorInstrument responseCharged particle detectorGeant4
In general, the counting rate of an1567-1739/$ e see front matter 2013 Elsevier B.V.http://dx.doi.org/10.1016/j.cap.2013.10.013calculates the trajectory of scattered and unscattered charged particles under the inuence of thecalculated elds. The propagation of charged particles through the elds, their interaction with the in-struments, and energy deposition into the detectors are calculated with Geant4, whereas the electric ormagnetic elds are solved with SIMION. To geometrically model the shielding distribution of the in-strument, a novel method is introduced for interfacing with the sophisticated mechanical designsavailable from computer-aided design tools. A description of this computational method is provided,along with the results for a representative example. The calculation applied to the example clearlydemonstrates the necessity of proper accounting of interaction mechanisms such as scattering or sec-ondary emission. This procedure will demonstrate a precise method for calculating the geometric factorthat allows estimation of the uxes of incident charged particles.
2013 Elsevier B.V. All rights reserved.
tor that responds to the
[cm2], u element of solid angle [sr], br unit vector in the di-rection u, and E energy of the particles [keV], respectively. Theintegration corresponds to all relevant domains of S, U, and E,Received in revised form8 October 2013 ions. The method rst solves the distribution of electric or magnetic elds near the detectors, and thenReceived 20 April 2013A computational method for calculating the geometric factors of an instrument detecting charged par-ticles in the energy range of about 5e500 keV is presented. The method takes into account the presenceComputational method for calculating ginstruments detecting charged particlesrange with deecting electric eld
S. Park, J.H. Jeon, Y. Kim, J. Woo, J. Seon*
School of Space Research, Kyung Hee University, 1, Seocheon-dong, Giheung-gu, Yong-In
a r t i c l e i n f o
a b s t r a c t
journal homepage: wwAll rights reserved.metric factors ofthe 5e500 keV energy
eong-Gi 446-701, Republic of Korea
le at ScienceDirect
the method for interfacing the CAD with Geant4 that has beensuggested by Kim et al.  (Fig. 1).
As a model instrument to further explain the present method,an instrument design of a conventional solid-state detector with anapplied electric eld in front of the detector is employed . Themodel instrument includes an electric eld because this feature isexpected to be desirable in future instruments. Traditionally, apermanent magnet has been placed in front of the detector toseparate electrons from the measured ions (See, for example ,and references therein), but this may electromagnetically disturbneighboring devices; such a concern is especially important if theinstrument is to be deployed on a small satellite. To reduce theamount of incident and scattered light striking the detector, theaperture of the instrument is assumed to have a collimator with aset of blackened optical bafes. The shape of the entrance apertureis a rectangle with a size 39.52 mm 3.10 mm, corresponding to aeld-of-view of 65.9 18.2 relative to the detector plane posi-tioned at the other side of the collimator. Interior to the collimatoris a parallel plate electric eld that serves as a deector, bending thetrajectories of electrons and positive ions in opposite directions. Aset of knife-edge plates is inserted along the edges of the collimatorto suppress secondary electrons generated at the wall surfaces.There are thirty knife-edge plates stacked along the direction of thecollimator. The size of each plate is 41.66 mm 3.18 mm and
lied Physics 14 (2014) 132e138 133scattering of electrons off the structures of the instruments or thedetectors. Laboratory experiments on monoenergetic electron ir-radiations and the subsequent detection of electrons by semi-conductors [4e7] strongly indicate that backscattering of electronsfrom the collimators and detectors must be considered for properdata analysis. If signicant scatterings indeed occur, this rendersinvalid the geometrical factor previously obtained assumingstraight particle trajectories. The scattering also induces un-certainties in the energy measurements because only a fraction ofincident electron energies may be deposited within the detectors,yielding a long low-energy wing in the distribution of themeasured electron energies.
Modern in situ observations of charged particles in space havefound that the space environment in the vicinity of the Earth islled with charged particles, often trapped by Earths magneticelds . Later observations further showed that these regions ofaccessible space are dynamically lled with charged particles thatare diverse in energy , species  and origin . Numerousobservations have been made, but the clear determination of en-ergies from electrons and positive ions still remains a challengingtask, even in recent spaceborne experiments. For example,contamination of electron measurements by protons [12,13] andcontamination of protonmeasurements by electrons  have bothbeen reported in the energy range of the present study. Contami-nation from electrons can be partially reduced by applying appro-priate magnetic elds  or electric elds during the passage ofthe particles from the aperture to the detector. On the other hand,contamination from protons is often mitigated by applying a thickdead layer over the active volume of detectors, a strategy madepossible by the greater stopping powers of protons and heavy ionsrelative to electrons (See, for example ).
Therefore, any numerical method to calculate the geometricfactor of modern instruments should include 1) direct acceptanceof mechanical drawings of the instruments for precise modelingand processing of actual instrument designs, 2) consideration of theeffect of particle scatterings off the considered instrument, 3)consideration of any applied electromagnetic elds used to segre-gate positive ions and electrons, 4) calculation of particle trajectoryacross the applied elds, and lastly 5) calculation of energy depo-sition within the detectors. There have been several investigationsthat utilized various numerical methods to calculate the geomet-rical factors of instruments operating in energy ranges near that ofthe present study [17e22], but to our understanding, none of theseinvestigations has satised all the aforementioned requirementssimultaneously. The purpose of this paper is to describe a numericalmethod that simultaneously satises such requirements. The nu-merical method is given in Section 2; Section 3 applies the methodto a representative instrument design. Section 4 presents ourconclusions.
2. Numerical method
In the present work, Geant4 (Version 9.3)  with PENELOPEphysics model was used to calculate the geometric factor. Thephysics model includes Compton scattering, photoelectric effectand bremsstrahlung processes in the energy range of the presentstudy. Geant4 provides two ways to model instrumental data foruse in simulations: one is to manually input the instrument ge-ometry within the Geant4 simulation code, and the other is to inputa le containing the instruments geometrical information in theGeometrical Description Markup Language (GDML) format, aformat based on Extensible Markup Language (XML) . It isdesirable to nd the method to adapt the latter because the in-strument design is often carried out with a computer-aided design
S. Park et al. / Current App(CAD) tool in parallel with this simulation. In this study, we adaptthickness 56 mm.