Proton and helium nuclei differential spectra were gathered with a balloon borne magnet spectrometer. The data were fitted to the assumption that the differential flux can be represented by a power law in rigidity. In the rigidity range 10 to 25 GV/c the spectral indices were found to be -(2.74 plus or minus 0.04) for protons and -(2.71 plus or minus 0.05) for helium nuclei. A brief discussion is given by systematic errors

Badhwar, G. D.

Daniel, R. R.

Golden, R. L.

Horan, S.

Kimbell, B.

Lacy, J. L.

Stephens, S. A.

Zipse, J. E.

English

NASA Technical Reports Server

OG 4.i-i
I
Absolute Rigidity Spectrum o_ Protons
and Helium Nuclei Above 10 8V/c
R. L. Golden, S. Horan, B. Kimbell
Department of Electrical and Computer Engineering
New Mexico State University
Las Cruces, NM 88003
USA
G. D. Badhwar, J. L. Lacy, J. E. Zipse
NASA, Johnson Space Center
Houston, TX 77058
USA
R. R. Daniel, S. A. Stephens
Tata Institute of Fundamental Research
Homi 0 Bhabha Road
Bombay, India 400 005
Abstract
Proton and helium nuclei differential spectra were gathered with
a balloon borne magnet spectrometer. The data were fitted to the
assumption that the differential flux can be represented by a
power law in rigidity. In the rigidity range 10-25 GV/c the
spectral indices were found to be -(2.74! 0.04) for protons and
-(2.71_ 0.05) for helium nuclei.
2m Introduction. The absolute rigiditiy spectra of protons
and Helium nuclei have become particularly important due to the
recent measurements of secondaries of these particles. The
recent publication of the absolute e- spectrum necessitated a
very careful analysis of the detection efficiencies and
sensitivities of the New Mexico State University magnetic
spectrometer. The maximum detectable momentum for the 1976 flight
(reported here) was 80 8V/c. During the analysis, it was found
that magnet spectrometer measurements in general are subject to
systematic errors that affect the spectrai index but not the
absolute flux at low energies. In this paperl we present a brief
discussion of the systematic errors, and spectral indices for
protons and helium nuclei in the rigidity range i0-25 GV/c.
Absolute fluxes will be presented at the conference.
2m Data Anal_sis. The apparatus is described in detail in
references (I) and (2). It was comprised of (top to bottom): a
gas Cherenkov counter (G) with a proton Cherenkov threshold of 40
GV/c (rigidity); two plastic scintillators ($1 and $2); 8
multiwire proportional counters (MWPC); and a lead-scintillator
shower counter consisting of 7 layers each containing 1 radiation
length of lead (P1-P7). The MWPC provide 8 readouts on the x
axis (axis of bending) and 4 readouts on the (orthogonal) y axis.
All phototubes were pulse-height analyzed. Data readout was
initiated for all occurences of an SI*PI*P7 and/or an SI*PI*P7*G
coincidence. The geometric factor of the instrument was 324 _ 5
cm^2-str and the live-time fraction was 0.80. The data were
.. 
1 
bsolute ig dity pectrum f rotons 
d elium uclei bove  BV/c 
. . Bolden, . oran, . imbell 
epartment f lectrical and omputer ngineering 
ew exico tate niversity 
as ruces,  03 
SA 
. . adhwar, . . acy, . . ipse 
ASA, J hnson pace enter 
ouston, T  77058 
SA 
. . aniel, . . tephens 
ata stitute f undamental esearch 
omi- habha oad 
ombay, I dia 00 5 
bstract 
 .1 1 
roton d elium uclei i ferential ectra ere athered ith 
a all on orne agnet s ectrometer. he ata ere fitt d t  t e 
assumption t at t e ifferential fl x can be represented by a 
power la  in ri idity. In t e ri idity range 10-25 V/c the 
ectral i di ces ere f nd t  e - (2. 74 ± O. 04) f r rotons d 
(2.71~ . 5) r elium uclei. 
1~ ! i~Q~Y£i!Qn~ he solute ri iditiy s ectra f rotons 
and elium nuclei have become articularly i portant due to the 
cent easur ments f condaries f t ese articles. he 
r cent ublication f t e solute - s ectrum ecessitated a 
ery areful nalysis f t e etection fficiencies a d 
sensitivities f t e ew exico tate niversity agnetic 
spectrometer. The aximum etectable omentum for t e 1976 fli ht 
(reported here) was 80 GV/c. During the analysis, it was found 
t at agnet spectrometer easurements in general are subject to 
systematic errors t at affect the spectralin~ex but not the 
absolute flux at lo  energies. In t is paper we present a brief 
iscussion f t e s stematic rrors, a d ectral i dices f r 
rotons a d elium uclei i  t e ri idity r nge 1 -25 V/c. 
bsolute fl xes ill e resented t t e onf rence. 
~ Q~i~ e ~l~§!§~ he p ratus i  escribed i  etail i  
r ferences (1) a d ( ). It as mprised f (t  t  ttom): a 
as herenkov c unter ( ) ith a roton herenkov t reshold f 40 
V/c (rigidity>; t o lastic scintillators (S1 and S2); 8 
ultiwire proportional counters ( WPC); and a lead-scintillator 
shower counter conSisting of 7 layers each containing 1 radiation 
l ngth f lead ( 1-P7). he PC rovide 8 readouts on t e x 
a is (axis of bending) and 4 readouts on t e (orthogonal) y axis. 
ll phototubes ere pulse-height analyzed. ata readout as 
itiated r ll ccurences f  1*P1*P7 d/or  1*P1*P7*G 
incidence. he eometriC f ctor f t e i strument as 24 t 5 
A 2-str d e e-time ction Was . 0. he ata ere 
https://ntrs.nasa.gov/search.jsp?R=19850025694 2020-03-20T18:05:24+00:00Z
OG 4.1-1
2
gathered on a balloon flight from Palestine, Texas on May 20,
1976. The data gathering period lasted 6.4 x 10^4 seconds at an
average altitude of 5.8 gm*cm^-2. Data for the spectral analysis
were selected from the flight tapes by requiring the following:
(1) The charge of the particle (as determined from $1 and
$2) correspond to 0.0-1.8 charge units for protons or 1.8-2.7
charge units for helium.
(2) All MWPC readouts be valid and that the measured
trajectory fit to a continuous track with a chi-square of 30 in
the x axis, and 8 in the y axis.
Failure of particles to pass the above criteria was
dominated by criterion 2. Each MWPC is only about 90% efficient.
The measured efficiency for passing criterion 2 was 33% for
protons and 24% for helium nuclei.
3. Results. Figures la and lb
show the proton and helium data
gathered during the flight. The
plots show number of events vs IA
magnetic deflection (1/magnetic
rigidity), measured in c/GV. i0000
The central part (deflection =
0) of each plot represents the
highest rigidities. Moving 6000
toward the right corresponds to
lower rigidities. The decline
in number of particles to the
right of 0.12 c/GV is due to the 2000
combined effects of solar
modulation and the geomagnetic
cutoff. _ /_
The data in Figure 1 have IB
been analyzed by fitting them to i000 HeUum
the assumption that the
differential flux is a power law j
_n rigidity. Other factors _-_7_
which enter the fit are: the 600
resolution function of the
instrument, solar modulation, ]
and the exact location of the
zero-deflection point. The 200
zero-deflection point in Figure I I
1 was determined by operating 0.0 0.1 0.2 0.3
the instrument with the magnet
off just prior to the flight. Figure I. DeFlect;on spectra
The center of the deflection
t
distribution gathered with the
magnet off is taken as the zero-
deflection point, and the
distribution of deflections is
taken as the resolution function
for the instrument. Figure 2
shows the resolution function.
 . -1 
2 
athered  a all on li ht fr  alestine, exas n ay 0, 
976. he ata athering eriod l sted .4  0A 4 conds t  
erage ltitude f .8 g *cmA -2. ata f r t e s ectral nalysis 
ere selected fro  t e fli ht tapes by requiring t e f llowing: 
( ) he arge f t e article ( s etermined fr  S1 d 
82) c rrespond t  .0-1.8 arge nits f r rotons r .8-2.7 
arge nits r elium. 
) l WPC adouts e alid d at e easured 
tr jectory it t  a ontin ous tr ck ith a hi~square f 0 i  
e  xis, d   e  xis. 
ailure f articles t  a s t e ove riteria as 
ominated  riterion . ach WPC i  nly bout 907. fficient. 
he easured fficiency r a sing riterion  as 7. r 
rotons d 7. r elium uclei. 
~L B§§y!t§L igures l  d l  
ow e roton d elium ata 
athered uring e li ht. he 
plots show number of events vs 
agnetic eflection l/ agnetic 
i idity), easured i  /6V. 
he entral art ( eflection  
) f ach lot r presents t e 
ighest id ties. oving 
t ard e ht o responds  
l er i idities. he ecline 
 -number f articles  e 
i ht f . 2 / V  ue  e 
mbined ffects f lar 
odulation a d t e eomagnetic 
cutoff. 
he ata i  igure 1 ave 
10000 
0 
2000 
been analyzed by fitting them to 1000 
t e ssumption t at t e 
differential flux is a power la  
~n rigidity. Other factors 
hi ch nter e it re: e  
solution nction f e 
instrument, solar odulation, 
d e act cation f e 
ero-d flection oint. he 
ero-d flection oint i  igure 
1 as determined by operating 
t e i strument ith t e agnet 
ff j st rior t  t e fLight. 
he enter f e eflection 
istribution ath red ith e 
agnet f  t ken s e ero-
eflection oint, d t e 
istribution f eflections  
en s e solution nction 
f r t e i strument. igure  
ows e solution nction. 
200 
0 
Figure 1. 
l  
Protons 
1 2  
eflection spectra. 
.. 
OG 4.i-i
3
300 - Figure 2
ResoLu±ion
Func±lon
Se00 -
o
o
100 -
-0.I0 -0.05 0.00 0.05 0.10
De£tec%lon (c/GV)
One of the most serious sources of possible systematic
error for spectral indices is a change in the zero-deflection
point between the calibration and the flight. It was hoped to
turn the magnet off at the end of the flight for another
calibration, but the instrument operation ended abruptly due to
battery failure and the calibration was not performed. A cross-
check was made however, by using the G-on protons and helium
gathered during the flight. These two samples were fit assuming
the proton Cherenkov threshold of 40 GV/c (helium threshold of 80
GV/c). Since the Cherenkov thresholds are near the upper limit
of the instrument to resolve the deflection, the dominant factor
in the fits was the offset of the zero-deflection point. The
offset was determined to be -(0.002z0.002) c/GV. In order to
minimize the effects of the offset error, solar modulation and
possible changes in the resolution function, we limit our
analyses to the deflection range 0 1-0.04 c/GV (10-25 GV/c
rigidity). Further, we have used a solar modulation of 600 MeV,
which was determined using the data below 10 GV/c. Under these
circumstances we find _ =-(2.74z0.04_ for protons and - (2.71±O. 05)
for helium nuclei. The uncertainty in the proton spectral index
is dominated by the offset uncertainty, and statistics dominates
the uncertainty for helium nuclei.
References
(1) Golden, R. L. et al. (197G), Nuc. Instr. and Meth. !_8,
179.
. (2) Golden, R. L. et al. (1984),. Ap. J. _@Z, 622.
.. 
11\ 
of> 
300 
§ 200 
o 
u 
100 
-0.10 
3 
-0.05 0.00 0.05 
Deflection (c/GV) 
0.10 
Figure 2 
Resolution 
Function 
OG 4.1-1 
One of the most serious sources of possible systematic 
error for spectral indices is a change in the zero-deflection 
point between the calibration and the flight. It was hoped to 
turn the magnet off at the end of the flight for another 
calibration, but the instrument operation ended abruptly due to 
battery failure and the calibration was not performed. A cross-
check was made however, by using the G-on protons and helium 
gathered during the flight. These two samples were fit assuming 
the proton Cherenkov threshold of 40 GV/c (helium threshold of 80 
GV/c). Since the Cherenkov thresholds are near the upper limit 
of the instrument to resolve the deflection, the dominant factor 
in the fits was the offset of the zero-deflection point. The 
offset was determined to be -(0.002±0.002) c/GV. In order to 
minimize the effects of the offset error, solar modulation and 
possible changes in the resolution function, we limit our 
analyses to the deflection range 0.1-0.04 c/GV (10-25 GV/c 
rigidity). Further, we have used a solar modulation of 600 MeV, 
which was determined using the data below 10 GV/c. Under these 
circumstances we find~ =-(2.74t O.04) for protons and-(2.71±0.05) 
for h~lium nuclei. The uncertainty in the proton spectral index 
is dominated by the offset uncertainty, and statistics dominates 
the uncertainty for helium nuclei. 
(1) Golden, R. L. et ala 
179. 
(1978) , Nuc. Instr. and Met'h. !1§, 
(2) Golden, R. L. et ala (1984), Ap. J. ~~Z, 622 • 


Absolute rigidity spectrum of protons and helium nuclei above 10 GV/c

Absolute rigidity spectrum of protons and helium nuclei above 10 GV/c

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