General Spectrum Fitting for Energetic Particles

We propose a general fitting formula of energy spectrum of suprathermal particles, J=AE-&#946;1[1+(E/E0)&#945;](&#946;1-&#946;2)/&#945;, where J is the particle flux (or intensity), E is the particle energy, A is the amplitude coefficient, E0 represents the spectral break energy, &#945; (>0) describes the sharpness of energy spectral break around E0, and the power-law index &#946;1 (&#946;2) gives the spectral shape before (after) the break. &#160;When &#945; tends to infinity (zero), this spectral formula becomes a classical double-power-law (logarithmic-parabola) spectrum. When both &#946;2 and E0 tend to infinity, this formula can be simplified to an Ellison-Ramaty-like equation. Under some other specific parameter conditions, this formula can be transformed to a Kappa or Maxwellian function. Considering &#160;the uncertainties both in particle intensity and energy, we fit this general formula well to the representative energy spectra of various suprathermal particle phenomena including solar energetic particles (electrons, protons, &#160;3He and heavier ions), shocked particles, anomalous cosmic rays, hard X-rays, solar wind suprathermal particles, etc. Therefore, this general spectrum fitting formula would help us to comparatively examine the energy spectrum of different suprathermal particle phenomena and understand their origin, acceleration and transportation.

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2–20 keV X-ray sky background

Symposium - International Astronomical Union ◽

10.1017/s0074180900004460 ◽

1970 ◽

Vol 37 ◽

pp. 309-314 ◽

Cited By ~ 1

Author(s):

E. A. Boldt ◽

U. D. Desai ◽

S. S. Holt ◽

P. J. Serlemitsos

Keyword(s):

Energy Spectrum ◽

Lower Energy ◽

X Rays ◽

X Ray ◽

Collisional Energy ◽

The North ◽

Spectral Break ◽

Diffuse Background ◽

Image Position ◽

North Galactic

The diffuse background of 2–20 keV X-rays over a band of the sky extending from Scorpius to the North galactic pole is found to be isotropic to within 5%, with a spectrum given bywheren= (1.35 ±0.100.07).A comparison with spectra at higher energies indicates that the lower energy spectrum is flatter, corresponding to an apparent unit change in spectral index within the band 20–80 keV. A spectral break in this energy region has been discussed in connection with the collisional energy loss lifetime for metagalactic protons that radiate X-rays via inverse bremsstrahlung collisions with the ambient electrons of the intergalactic medium (Boldt and Serlemitsos, 1969; Hayakawa, 1970).

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Energy spectrum of diffuse primary X rays up to 180 keV

Canadian Journal of Physics ◽

10.1139/p68-270 ◽

1968 ◽

Vol 46 (10) ◽

pp. S461-S465 ◽

Cited By ~ 17

Author(s):

J. A. M. Bleeker ◽

J. J. Burger ◽

A. J. M. Deerenberg ◽

A. Scheepmaker ◽

B. N. Swanenburg ◽

...

Keyword(s):

Energy Spectrum ◽

Power Law ◽

Plastic Scintillator ◽

Geomagnetic Latitude ◽

Cosmic Ray ◽

Rotating Disk ◽

The Other ◽

X Rays ◽

X Ray ◽

Good Agreement

Two balloon flights with identical X-ray detectors were carried out in the summer of 1966, one from De Bilt, the Netherlands (geomagnetic latitude 53 °N), and the other from Taiyomura, Japan (geomagnetic latitude 25 °N). The detector consists of a NaI(Tl) crystal, 12.5 mm thick and 50 mm in diameter, surrounded by an effective collimator-shield and a plastic scintillator guard counter. The rotating disk incorporated enables the separation of "forward" X rays from the cosmic-ray-induced background. The results of the flights are in very good agreement with each other. In view of the rather large difference in geomagnetic latitude in these two flights, this agreement supports the celestial origin of the primary X rays observed. The energy spectrum between 20 and 180 keV can be expressed by a power law:[Formula: see text]

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The Acceleration of Energetic Particles at Coronal Shocks and Emergence of a Double Power-law Feature in Particle Energy Spectra

The Astrophysical Journal ◽

10.3847/1538-4357/ab3848 ◽

2019 ◽

Vol 883 (1) ◽

pp. 49 ◽

Cited By ~ 4

Author(s):

Xiangliang Kong ◽

Fan Guo ◽

Yao Chen ◽

Joe Giacalone

Keyword(s):

Power Law ◽

Energetic Particles ◽

Particle Energy ◽

Energy Spectra

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The Energy Spectrum of Solar Energetic Electron Events

10.5194/egusphere-egu2020-1944 ◽

2020 ◽

Author(s):

Linghua Wang ◽

Zixuan Liu ◽

Haobo Fu ◽

Sam Krucker

Keyword(s):

Energy Spectrum ◽

Spectral Index ◽

Power Law ◽

Average Power ◽

Energetic Electron ◽

High Energies ◽

Spectral Break ◽

Peak Flux ◽

Crucial Information ◽

Statistical Survey

Solar energetic electron events (SEEs) are one of the most common particle acceleration phenomena occurring at the Sun, and their energy spectrum likely reflects the crucial information on the acceleration. Here we present a statistical survey of the energy spectrum of 160 SEEs measured by Wind/3DP with a clear velocity dispersion at energies of ~1-200 keV from January 1995 through December 2016, utilizing a general spectrum formula proposed by Liu et al. (2000). We find that among these 160 SEEs, 144 (90%) have a power-law (or power-law-like) spectrum bending down at high energies, including 108 (67.5%) double-power-law events, 24 (15%) Ellison-Ramaty-like events and 12 (7.5%) log-parabola events, while 16 (10%) have a power-law spectrum extending to high energies. The average power-law spectral index &#946;1&#160;is 2.1&#177;0.4 for double-power-law events, 1.7&#177;0.8 for Ellison-Ramaty-like events, and 2.8&#177;0.11 for single-power-law events. For the 108 double-power-law events, the spectral break energy E0&#160;ranges from 2 keV to 165 keV, with an average of 71&#177;79 keV, while the average spectral index &#946;2&#160;at energies above E0is 4.4&#177;2.3. E0&#160;shows a positive correlation with the electron peak flux at energies above ~40 keV, while &#946;1&#160;has a negative correlation with the electron peak flux at energies above ~15 keV. &#160;

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Spectral Tomography for 3D Element Detection and Mineral Analysis

Minerals ◽

10.3390/min11060598 ◽

2021 ◽

Vol 11 (6) ◽

pp. 598

Author(s):

Jose R. A. Godinho ◽

Gabriel Westaway-Heaven ◽

Marijn A. Boone ◽

Axel D. Renno

Keyword(s):

Energy Spectrum ◽

3D Imaging ◽

X Rays ◽

3D Images ◽

Characterization Methods ◽

X Ray ◽

Additional Information ◽

Mineral Phases ◽

Spectral Computed Tomography

This paper demonstrates the potential of a new 3D imaging technique, Spectral Computed Tomography (sp-CT), to identify heavy elements inside materials, which can be used to classify mineral phases. The method combines the total X-ray transmission measured by a normal polychromatic X-ray detector, and the transmitted X-ray energy spectrum measured by a detector that discriminates between X-rays with energies of about 1.1 keV resolution. An analysis of the energy spectrum allows to identify sudden changes of transmission at K-edge energies that are specific of each element. The additional information about the elements in a phase improves the classification of mineral phases from grey-scale 3D images that would be otherwise difficult due to artefacts or the lack of contrast between phases. The ability to identify the elements inside the minerals that compose ore particles and rocks is crucial to broaden the application of 3D imaging in Earth sciences research and mineral process engineering, which will represent an important complement to traditional 2D imaging mineral characterization methods. In this paper, the first applications of sp-CT to classify mineral phases are showcased and the limitations and further developments are discussed.

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Synchrotron Emission from Particles Having A Truncated Power-law Energy Spectrum

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/168.2.379 ◽

1974 ◽

Vol 168 (2) ◽

pp. 379-397 ◽

Cited By ~ 3

Author(s):

L. J. Gleeson ◽

M. P. C. Legg ◽

K. C. Westfold

Keyword(s):

Energy Spectrum ◽

Power Law ◽

Synchrotron Emission

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On the single-particle-energy spectrum of a Λ particle in nuclear matter

Canadian Journal of Physics ◽

10.1139/p70-348 ◽

1970 ◽

Vol 48 (23) ◽

pp. 2804-2808 ◽

Cited By ~ 7

Author(s):

K. F. Chong ◽

Y. Nogami ◽

E. Satoh

Keyword(s):

Energy Spectrum ◽

Nuclear Matter ◽

Single Particle ◽

Short Range ◽

Particle Energy ◽

Pair Approximation ◽

Single Particle Energy ◽

Short Range Repulsion ◽

Separable Potentials ◽

Independent Pair

The single-particle-energy spectrum of a Λ particle in nuclear matter is examined in the independent-pair approximation, by assuming nonlocal separable potentials for the ΛN interaction. Effects of short-range repulsion in the ΛN interaction on the Λ binding are also examined in terms of separable potentials of rank two.

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