the neutron, gamma-ray, x-ray spectrometer (ngxs): a compact instrument for making combined...

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The neutron, gamma-ray, X-ray spectrometer (NGXS): A compact instrument for making combined measurements of neutrons, gamma-rays, and X-rays David J. Lawrence a,n , William C. Feldman b , Robert E. Gold a , John O. Goldsten a , Ralph L. McNutt a a Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA b Planetary Science Institute, Tucson, AZ 85719, USA article info Article history: Received 22 December 2011 Received in revised form 5 June 2012 Accepted 21 June 2012 Available online 20 July 2012 Keywords: Neutrons Gamma rays X-rays abstract The Neutron, Gamma ray, and X-ray Spectrometer (NGXS) is a compact instrument designed to detect neutrons, gamma-rays, and hard X-rays. The original goal of NGXS was to detect and characterize neutrons, gamma-rays, and X-rays from the Sun as part of the Solar Probe Plus mission in order to provide direct insight into particle acceleration, magnetic reconnection, and cross-field transport processes that take place near the Sun. Based on high-energy neutron detections from prompt solar flares, it is estimated that the NGXS would detect neutrons from 15 to 24 impulsive flares. The NGXS sensitivity to 2.2 MeV gamma rays would enable a detection of 50–60 impulsive flares. The NGXS is estimated to measure 120 counts/s for a GOES C1-type flare at 0.1 AU, which allows for a large dynamic range to detect both small and large flares. & 2012 IAA. Published by Elsevier Ltd. All rights reserved. 1. Introduction The Neutron, Gamma ray, and X-ray Spectrometer (NGXS) is a compact instrument designed to detect neu- trons, gamma-rays, and hard X-rays. The original goal of NGXS was to detect and characterize neutrons, gamma rays, and x-rays from the Sun as part of the Solar Probe Plus (SP þ ) mission in order to provide direct insight into particle acceleration, magnetic reconnection, and cross-field trans- port processes that take place near the Sun via energetic solar flare processes [1]. In addition to measuring neutrons and gamma rays from large solar flare events, NGXS measurements could also be used to characterize new types of energetic solar events and understand the seed popula- tion of energetic particles [2]. To make the requisite observations on a highly mass-constrained mission, appro- priate trades were made between the sensor size and mass versus the types of measurables, their energy ranges, and detection sensitivity. This paper describes the design and implementation of the NGXS as well as its detection sensitivity in an environment rich in ener- getic particles. 2. NGXS overview The NGXS instrument is configured as two sensor heads that operate independently while sharing a com- mon electronics box (Fig. 1). The Neutron Spectrometer (NS) and Gamma-Ray Spectrometer (GRS) are combined to enable coincidence techniques that actively reject background charged particles. Effective background rejec- tion is critical because flare-produced neutrons and gamma rays will often be accompanied by large fluxes of energetic ions and electrons. The GRS detector is embedded within the NS detector to achieve almost full 4p active shielding; only those events in anti-coincidence (AC) with the NS detector are accepted. Background Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/actaastro Acta Astronautica 0094-5765/$ - see front matter & 2012 IAA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actaastro.2012.06.017 n Corresponding author. E-mail address: [email protected] (D.J. Lawrence). Acta Astronautica 93 (2014) 524–529

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Contents lists available at ScienceDirect

Acta Astronautica

Acta Astronautica 93 (2014) 524–529

0094-57

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/actaastro

The neutron, gamma-ray, X-ray spectrometer (NGXS): Acompact instrument for making combined measurements ofneutrons, gamma-rays, and X-rays

David J. Lawrence a,n, William C. Feldman b, Robert E. Gold a, John O. Goldsten a,Ralph L. McNutt a

a Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USAb Planetary Science Institute, Tucson, AZ 85719, USA

a r t i c l e i n f o

Article history:

Received 22 December 2011

Received in revised form

5 June 2012

Accepted 21 June 2012Available online 20 July 2012

Keywords:

Neutrons

Gamma rays

X-rays

65/$ - see front matter & 2012 IAA. Publishe

x.doi.org/10.1016/j.actaastro.2012.06.017

esponding author.

ail address: [email protected] (D.J

a b s t r a c t

The Neutron, Gamma ray, and X-ray Spectrometer (NGXS) is a compact instrument

designed to detect neutrons, gamma-rays, and hard X-rays. The original goal of NGXS

was to detect and characterize neutrons, gamma-rays, and X-rays from the Sun as part of

the Solar Probe Plus mission in order to provide direct insight into particle acceleration,

magnetic reconnection, and cross-field transport processes that take place near the Sun.

Based on high-energy neutron detections from prompt solar flares, it is estimated that the

NGXS would detect neutrons from 15 to 24 impulsive flares. The NGXS sensitivity to

2.2 MeV gamma rays would enable a detection of �50–60 impulsive flares. The NGXS is

estimated to measure �120 counts/s for a GOES C1-type flare at 0.1 AU, which allows for a

large dynamic range to detect both small and large flares.

& 2012 IAA. Published by Elsevier Ltd. All rights reserved.

1. Introduction

The Neutron, Gamma ray, and X-ray Spectrometer(NGXS) is a compact instrument designed to detect neu-trons, gamma-rays, and hard X-rays. The original goal ofNGXS was to detect and characterize neutrons, gamma rays,and x-rays from the Sun as part of the Solar Probe Plus(SPþ) mission in order to provide direct insight into particleacceleration, magnetic reconnection, and cross-field trans-port processes that take place near the Sun via energeticsolar flare processes [1]. In addition to measuring neutronsand gamma rays from large solar flare events, NGXSmeasurements could also be used to characterize new typesof energetic solar events and understand the seed popula-tion of energetic particles [2]. To make the requisiteobservations on a highly mass-constrained mission, appro-priate trades were made between the sensor size and

d by Elsevier Ltd. All right

. Lawrence).

mass versus the types of measurables, their energyranges, and detection sensitivity. This paper describesthe design and implementation of the NGXS as well asits detection sensitivity in an environment rich in ener-getic particles.

2. NGXS overview

The NGXS instrument is configured as two sensorheads that operate independently while sharing a com-mon electronics box (Fig. 1). The Neutron Spectrometer(NS) and Gamma-Ray Spectrometer (GRS) are combinedto enable coincidence techniques that actively rejectbackground charged particles. Effective background rejec-tion is critical because flare-produced neutrons andgamma rays will often be accompanied by large fluxesof energetic ions and electrons. The GRS detector isembedded within the NS detector to achieve almost full4p active shielding; only those events in anti-coincidence(AC) with the NS detector are accepted. Background

s reserved.

Fig. 1. Views of the combined NS/GRS sensor and the miniature XRS

sensor showing active materials. The GRS detector (BGO) is surrounded

by the NS detector (BC-454) to achieve almost full 4p shielding against

charged particles. The single PMT readout maximizes detector volume

and minimizes attenuating materials. A passive collimator that sits atop

the XRS excludes background outside the solar disk.

Fig. 2. Laboratory results demonstrate clean separation of gamma ray

and neutron signals from prototype sensor using pulse shape discrimi-

nation. Phoswich signal fraction is defined as the ratio of a short signal

integration to a long signal integration and discriminates between the

fast plastic signals that are dominated by neutrons and slow BGO signals

that are dominated by gamma-rays.

D.J. Lawrence et al. / Acta Astronautica 93 (2014) 524–529 525

rejection for the NS is accomplished by identifying neu-trons with a time-correlated two-pulse sequence in coin-cidence with an associated gamma ray detected in theGRS—an effective triple-coincidence measurement. TheNS/GRS detector combination is read out with a singlephotomultiplier tube (PMT) in a phoswich arrangementthat maximizes the sensitive detector volume whileminimizing the amount of attenuating materials andphotodetector mass. ‘Phoswich’ is a shortened term forphosphor sandwich, and refers to scintillator light readoutarrangements where multiple scintillators are read outwith a single PMT and signal separation is achieved viapulse time and shape discrimination [3]. A separate CdTeX-ray Spectrometer (XRS) provides high-energy resolu-tion measurements of the hard X-ray region down to thelow-energy limit of 20 keV. The estimated total mass ofthe NGXS is 2.6 kg, and its estimated power is 3 W.

The inner GRS sensor uses a bismuth germanate (BGO)scintillator (+3.8�3.8 cm long) similar to GRS instru-ments flown on the Near Earth Asteroid Rendezvous(NEAR), Lunar Prospector (LP), and Dawn missions [4–6].BGO is well understood and offers the highest photopeakefficiency of any scintillator, which is critical whenmeasuring short-duration bursts of high-energy gammarays. Its energy resolution of 6% at 2 MeV [7] is more thanadequate to resolve the 2.2 MeV H neutron capture line.The GRS covers 0.1–10 MeV with 512 energy channels.Both integral (all events) and AC spectra are reported.

The outer NS sensor uses a +9.7�9.7 cm long well-shaped boron-loaded scintillator (BC-454) similar to thoseused successfully on the LP, Mars Odyssey (MO), Dawn, andMESSENGER neutron instruments [5,6,8,9]. Boratedplastic scintillators are sensitive to fast neutrons(0.5–20 MeV) and produce a unique two-pulse sequence.An initial prompt pulse caused by energy loss of recoilprotons in the scintillator provides a measure of the incidentneutron energy with an energy resolution o50%. A delayedneutron capture pulse unambiguously identifies a neutronevent via its energy from the 10B(n,a) reaction along with its2 ms characteristic time delay from the prompt pulse.Detection of both valid pulse types provides a natural meansof rejecting charged particles and locally induced gammarays. Additional background rejection is achieved by furtherrequiring detection of the coincident 478 keV 10B(n,a)gamma-ray in the GRS, as has been demonstrated withthe LP and MESSENGER GRS instruments.

Signals from the NS and GRS sensors are both measuredwith a single PMT and the risetime difference between thefast BC-454 and slow BGO scintillators allows straightfor-ward digital electronic separation of the signals. Excellentsignal separation has been demonstrated in laboratory testsusing neutrons and electrons with prototype sensors (Figs. 1and 2). For incident neutrons below 0.5 MeV, the NS countsthe number of capture-only type interactions, which pro-vides a measure of lower energy primary neutrons as wellas neutrons that down-scatter in the spacecraft beforestriking the detector.

The XRS detector, optimized to cover the 20–200 keVenergy range, is a pre-packaged assembly similar to theSi-PIN detector flown on NEAR. The 3�3�1 mm3 CdTedetector is mounted on a two-stage thermoelectric cooler

(TEC) in a sealed vacuum can with a beryllium window.An external collimator made of copper tungsten stronglysuppresses the charged-particle background by restrictingthe field-of-view (FOV) to the solar disk at 9.5 Rs, alongwith margins for pointing and alignment.

3. Neutron sensitivity calculations

3.1. Neutron fluences

We scale measured neutron count rates to the neutronfluences calculated by Hua and Lingenfelter [10] (here-after abbreviated H and L) and Murphy et al. [11] (Fig. 3).These studies provide energy dependent fluences in unitsof (neutrons ster�1 MeV�1 Np

�1), where Np indicates the

number of flare protons greater than 30 MeV. We notethat these fluences assume the neutrons are created in an

Fig. 3. Neutron fluences used in this study as calculated for Np¼1030

and at a distance of 1 Rs.

Fig. 4. Neutron fluences propagated to distances 9–215 Rs from the

surface of the Sun.

Fig. 5. Integral number of flares greater than Np as a function of Np. over

the life of the Solar Probe mission.

D.J. Lawrence et al. / Acta Astronautica 93 (2014) 524–529526

impulsive flare scenario where the emitted neutrons arecreated on the Sun from an impulse instead of over anextended period of hours. However, this study does notaccount for other neutron-generating events on the Sunthat may scale differently than calculated by the aboveauthors.

To convert these fluences of H and L [10] and Murphyet al. [11] into more convenient units, we scaled them toNp¼1030, and to neutrons cm�2 MeV�1 using the factor:1030=4pR2

S ¼ 1:6� 107, for Rs¼7�1010 cm. Fig. 3 showsthe fluence spectrum for three different examples from Hand L [10] and Murphy et al. [11]. The total fluences persteradian for Np¼1030 at the solar surface for the threedifferent fluence models are: FTot, H and L, Fig.10¼1.0�1026

n ster�1; FTot, H and L, Fig. 8b¼7.2�1026 n ster�1; FMurphy

et al.¼2.9�1026 n ster�1. According to Shih et al. [12], aflare with Np¼1030 is roughly equivalent to an M7 flare.

To determine the total neutron counts as a function ofenergy and distance, the fluence at one Rs needs to bepropagated to different distances as a function of energy.The fluence from Fig. 3 needs to be multiplied by twofactors: (1) Rs2/D2; and, (2) e-(t/t) where t is the propaga-tion time for a neutron with a given energy E to travelfrom the Sun to D, and t is the neutron mean life of 886 s.Fig. 4 shows these propagated fluences for the H and A,Fig. 8b fluence given in Fig. 3. There is a significant dropoff for lower energy neutrons due to the exponentialfactor and an additional drop off for the 1/D2 factor.

3.2. Number of flares per flare size

Shih et al. [12] provide data for 26 solar flares mea-sured by RHESSI, where they measured the flux of the2.2 MeV neutron capture line. With these measurements,they used model calculations to estimate Np for each ofthose flares. Fig. 5 shows the integral number of flaresgreater than Np, INp

, (where Np is scaled in units of 1030

protons with energy greater than 30 MeV) and scaled by afactor of 2(7/4) to account for the seven year SPþ missioncompared to the four years of RHESSI data, as well as afactor of two to account for the fact that RHESSI only seesthe Sun for 50% of its observing time. With the fit of INp

to

log (Np), the differential number of flares in a log unit ofNp is 9.46 flares per log (Np). No account has been madefor varation of flare occurrence with solar cycle.

3.3. Probability to observe flares

Assuming a 2015 launch date, Fig. 6 shows theSPþspacecraft calculated time per distance bin, D, wherethe D bins start at 9 Rs and have a width of 6 Rs out to213 Rs. The maximum amount of time is spent around150 Rs, which is the orbit of Venus. With the timescalculated in Fig. 6, and knowing the number of flaresper log (Np) bin per hour, NFlare,hour(Np)¼9.46 flares perlog (Np)/(7 years�365�24)¼1.54�10�4 flare per hourper log (Np) bin, the probable number of detected flares ina given log (Np) bin as a function of distance D is:P(D,Np)¼NFlare,hour� TimeRs. Fig. 6 shows this probablenumber of flares as a function of Rs.

3.4. NS efficiency

Fig. 7 shows a plot of efficiency versus energy fordetector models and measurements. The black data points

Fig. 6. SPþtime spent in a given Rs bin as a function of distance from

the Sun (left axis) and corresponding probable flare detections in a given

log (Np) bin size (right axis).

Fig. 7. Plot of efficiency versus energy for various detector models and

configurations.

D.J. Lawrence et al. / Acta Astronautica 93 (2014) 524–529 527

show an MCNPX calculation of the efficiency for 10B(n,a)capture reactions in the MESSENGER NS. The circles showmeasured efficiencies from Drake et al. [13] for a BC454rod that has the same volume as the MESSENGER NS, butdifferent shape. Using MCNPX calculations, we havedetermined that the fast neutron efficiency scales as thevolume of the sensor. Therefore, the measurementsshould be a reasonable check on the modeled values.The measurements of [13] show a similar shape with themodeled values, but are low by a factor of two. We do notyet have a full understanding of the reason for thisdiscrepancy, so to be conservative, we use the MCNPXcalculated efficiencies divided by two to match the valuesfrom [13].

3.5. Total counting rate, signal-to-noise, and

total detected flares

With all the above information, the total neutroncounts, as a function of flare size, can be determined

using the relation

CTotalðD,NpÞ ¼

Z 50 MeV

EI ¼ 1:5 MeVNpeAðEIÞFðEI ,DÞdEIþCback

where F(EI,D) is the energy dependent fluence as a func-tion of distance, D, from the spacecraft to the Sun (hereusing the H and L Fig. 8b fluence), and eA is the incident,energy dependent efficiency area product of the neutronsensor. The left part of Fig. 8 shows the total counts versusD for flares of various sizes and are color-coded based onthe probability of detecting a given flare.

The total background counts are Cback¼cbackDt, wherecback is the background counting rate, and Dt correspondsto the interval of time elapsed between the arrival of thehigh-energy neutrons of 50 MeVand the arrival of lowenergy neutrons of 1.5 MeV. For the MESSENGER detector,cback�0.5 cps for En4�1 MeV [2]. Here, we scale theMESSENGER background to the smaller sized NGXS neu-tron sensor. The dashed line in Fig. 8 (left) shows the totalbackground counts as a function of distance for energiesfrom 1.5 to 50 MeV.

To determine if a flare is detected, the signal-to-noise,Sn(D,Np) is calculated using the following:

SnðD,NpÞ ¼CTotalðD,NpÞ�CBackðD,NpÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

CBackðD,NpÞp

Fig. 8 (right) shows a contour plot of Sn(D,Np). A 3sdetection (i.e., signal-to-noise of three) can be made for aflare size of 0.3�1030 at the closest distance of 10 Rs.

As a summary plot, Fig. 9 shows the detected numberof flares versus detector volume, V. For larger volumesensors, there are an increasing number of detected flares,but it only scales as V0.24, which is a relatively weakdependence. For the SPþ detector, the detected numberof flares is 24. For the fluence model of Murphy et al. [11],the total number of detected flares is 15.

4. Gamma-ray sensitivity calculations

We calculate the gamma-ray sensitivity in a similarway as was done for the neutrons. For the GRS, we used astandard calculated efficiency of 0.2 at 2.2 MeV. The areaof the detector is 11.3 cm2. Thus, the effective area is2.26 cm2.

For background counts, we scale from Lunar Prospec-tor cruise data [7], which was also a space-based BGOsensor (Fig. 10). The size of the LP-GRS is 54 cm2, with anefficiency at 2.2 MeV of �0.4. The scaling to the SPþ BGOsensor is then (0.4�54)/(0.2�11.3)¼9.5. During the LPcruise, the counting rate at 2.2 MeV is 3.67 cps. Theequivalent background counting rate for the SPþ sensoris 0.38 cps.

From [12], the estimated number of counts in theSPþGRS can be determined using

CTotal ¼n2:2eAD2

oDt

D2

where n2.2 is the number of photons per cm2 from [12],e is the sensor efficiency, A is the sensor area, Dt is thetime over which the total fluence is measured, D is thespacecraft distance from the Sun, and Do is 1 AU, where

Fig. 8. (Left) Total counts versus spacecraft distance from the Sun. Each line shows the number of counts for a flare size in terms of number of protons, Np,

greater than 30 MeV ranging from 0.03 to 8000 in units of 1030. The color-coding shows the probability of detecting a flare during the seven year

SPþmission. The dashed orange line shows the total background counts for neutron energies from 1.5 to 100 MeV, assuming a background counting rate

of 0.5 cps. (Right) Contour plots of signal-to-noise as a function of flare size versus spacecraft-to-Sun distance.

Fig. 9. Number of detected neutron flares versus sensor volume.

Fig. 10. Counting rate of the LP-GRS during the 3-day cruise prior to

reaching the Moon. The vertical lines show the region around the

2.2 MeV gamma-ray line. The total counting rate is 3.67. After scaling

for the SPþconfiguration, the equivalent counting rate is 0.38 cps.

D.J. Lawrence et al. / Acta Astronautica 93 (2014) 524–529528

the RHESSI measurements were made. As an intermediateDt given in [12], we used 1 h. When the total counts andprobabilities are added up, there is a total of 50–60 flaresthat would be detected using the assumptions stated above.

5. X-ray sensitivity calculations

For the XRS, we scaled the dynamic range to havesensitivity for a wide range of flare sizes ranging frommoderately small C1 to large M and X class flares.The driving requirement for this dynamic range is obtainingstatistically significant sensitivity for the smaller flares. Wedetermine the sensitivity of the XRS using RHESSI data asreported by Saint-Hilaire et al. [14] from 172 hard X-raypeaks during 53 solar flares that exhibited a double-foot-print structure. Saint-Hilaire et al. [14] found a correlationbetween a solar flare maximum GOES 1–8 A flux and thetotal hard X-ray flux F50 ¼ AFaGOESwhere A¼4.7�103 anda¼0.8. For a C1 flare, FGOES¼10�6, so that F50¼0.0745photons cm�2 s�1 keV�1. Also from [14], a typical spectralindex for hard X-rays is g¼3.3, where FX-ray¼CE�g. SettingFX-ray¼F50, C¼3�104. Integrating the X-ray flux from 20 to200 keV, one obtains

FTotal ¼CE�gþ1

�gþ1

�����200

20

¼ 13:2photons

cm2 s

If we assume 100% efficiency for the 3�3 mm2 CdTedetector from 20 to 200 keV, we obtain a counting rate of1.18 cts/s. Finally, we factor in the distance from 1 to0.1 AU, and we get a total of 118 cts/s for energies from 20to 200 keV for a C1 flare at 0.1 AU.

6. Summary

Based on high-energy neutron detections from promptsolar flares, it is estimated that the NGXS would detectneutrons from 15 to 24 impulsive flares. The NS would

D.J. Lawrence et al. / Acta Astronautica 93 (2014) 524–529 529

have more than doubled the total number of detectedneutron flares from all space-based missions to date [15],as well as detected extended neutron events similar to thetype observed by the MESSENGER NS on 31 December,2007 [2]. The GRS sensitivity to 2.2 MeV gamma rayswould enable a detection of �50–60 impulsive flares.The XRS is estimated to measure �120 counts/s for aGOES C1-type flare at 0.1 AU, which allows for a largedynamic range to detect both small and large flares. Whileoriginally designed for the SPþmission, the NGXS canprovide robust measurements of neutrons, gamma rays,and X-rays for a wide variety of mass constrained missionscenarios where charged particle rejection is needed.

Acknowledgements

The authors thank two anonymous reviewers fordetailed and helpful reviews. This work was supportedby internal development funding from JHU/APL.

References

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[2] William C. Feldman, et al., Evidence for extended acceleration ofsolar-flare ions from 1–8 MeV solar neutrons detected with theMESSENGER neutron spectrometer, J. Geophys. Res. http://dx.doi.org/10.1029/2009JA014535.

[3] Glenn F. Knoll, Radiation detection and measurement, 3rd edition,John Wiley and Sons, 2000.

[4] J.O. Goldsten, et al., The X-ray/gamma-ray spectrometer on theNear Earth Asteroid Rendezvous mission, Space Sci. Rev. 82 (1997)169–216.

[5] W.C. Feldman, et al., The gamma-ray, neutron, and alpha-particlespectrometers for the Lunar Prospector Mission, J. Geophys. Res. http://dx.doi.org/10.1029/2003JE002207.

[6] T.H. Prettyman, et al., Dawn’s gamma ray and neutron detector,Space Sci. Rev. 163 (2011) 371–459.

[7] D.J. Lawrence, et al., Gamma-ray measurements from Lunar Pro-spector: time series data reduction for the gamma-ray spectro-meter, J. Geophys. Res. http://dx.doi.org/10.1029/2003 JE002206.

[8] W.C. Feldman, et al., Fast neutron flux spectrum aboard Marsodyssey during cruise, J. Geophys. Res. http://dx.doi.org/10.1029/2001JA000295.

[9] John O. Goldsten, et al., The MESSENGER gamma-ray and neutronspectrometer, Space Sci. Rev. http://dx.doi.org/10.1007/s11214-007-9262-7.

[10] X.M. Hua, R.E. Lingenfelter, Solar flare neutron production andaccelerated ion angular distribution, Astrophys. J. 323 (1987)779–794.

[11] R.J. Murphy, et al., Using gamma-ray and neutron emission todetermine solar flare accelerated particle spectra and compositionand the conditions within the flare magnetic loop, Astrophys. J.Suppl. Ser. 168 (2007) 167–194.

[12] A.Y. Shih, R.P. Lin, D.M. Smith, RHESSI observations of the propor-tional acceleration of relativistic 40.3 Mev electrons and430 Mev protons in solar flares, Astrophys. J. 698 (2009) L152.

[13] D.M. Drake, W.C. Feldman, C. Hurlbut, New electronically blackneutron detectors, Nucl. Instrum. Methods A247 (1986) 576–582.

[14] P. Saint-Hilaire, S. Krucker, R.P. Lin, A statistical survey of hard X-ray spectral characteristics of solar flares with two footprint, Sol.Phys. 250 (2008) 53–73.

[15] X.. Hua, et al., Angular and energy-dependent neutron emission fromsolar flare magnetic loops, Astrophys. J. Suppl. 140 (2002) 563.