New Method to Calculate the Time Variation of the Force Field Parameter

Galactic cosmic rays (CRs) entering the heliosphere are affected by interplanetary magnetic fields and solar wind disturbances resulting in the modulation of the CR total flux observed in the inner heliosphere. The so‐called force field model is often used to compute the galactic CR spectrum modulated by the solar activity due to the fact that it characterizes this process by only one parameter (the modulation potential, ϕ). In this work, we present two types of an empirical simplification (ES) method used to reconstruct the time variation of the modulation potential (Δϕ). Our ES offers a simple and fast alternative to compute the Δϕ at any desired time. The first ES type is based on the empirical fact that the dependence between Δϕ and neutron monitor (NM) count rates can be parameterized by a second‐degree polynomial. The second ES type is based on the assumption that there is a inverse relation between Δϕ and NM count rates. We report the parameters found for the two types, which may be used to compute Δϕ for some NMs in a very fast and efficient way. In order to test the validity of the proposed ES, we compare our results with Δϕ obtained from literature. Finally, we apply our method to obtain the proton and helium spectra of primary CRs near the Earth at four randomly selected times.

[1]  I. Usoskin,et al.  Heliospheric modulation of cosmic rays during the neutron monitor era: Calibration using PAMELA data for 2006–2010 , 2017, 1705.07197.

[2]  L. Derome,et al.  Neutron monitors and muon detectors for solar modulation studies: 2. ϕ time series , 2016, 1607.01976.

[3]  A. Lara,et al.  Solar Event Simulations using the HAWC Scaler System , 2015, 1508.07285.

[4]  A. V. Karelin,et al.  Force-field parameterization of the galactic cosmic ray spectrum : Validation for Forbush decreases , 2015 .

[5]  H. S. Ahluwalia,et al.  Sunspot numbers, interplanetary magnetic field, and cosmic ray intensity at earth: Nexus for the twentieth century , 2013 .

[6]  A. V. Karelin,et al.  TIME DEPENDENCE OF THE e− FLUX MEASURED BY PAMELA DURING THE 2006 JULY–2009 DECEMBER SOLAR MINIMUM , 2013, 1512.01079.

[7]  A. V. Karelin,et al.  Measurements of cosmic-ray proton and helium spectra with the PAMELA calorimeter , 2013 .

[8]  R. Caballero-Lopez,et al.  Cosmic‐ray yield and response functions in the atmosphere , 2012 .

[9]  V. Malvezzi,et al.  PAMELA Measurements of Cosmic-Ray Proton and Helium Spectra , 2011, Science.

[10]  I. Buchvarov,et al.  Model approximation of cosmic ray spectrum , 2011 .

[11]  G. Bazilevskaya,et al.  Solar modulation parameter for cosmic rays since 1936 reconstructed from ground-based neutron monitors and ionization chambers , 2011 .

[12]  B. Heber,et al.  On the importance of the local interstellar spectrum for the solar modulation parameter , 2010 .

[13]  I. Usoskin A History of Solar Activity over Millennia , 2008, Living Reviews in Solar Physics.

[14]  G. Bazilevskaya,et al.  Cosmic Ray Induced Ion Production in the Atmosphere , 2008 .

[15]  Kalevi Mursula,et al.  Heliospheric modulation of cosmic rays: Monthly reconstruction for 1951–2004 , 2005 .

[16]  R. Caballero-Lopez,et al.  Galactic cosmic ray modulation: Effects of the solar wind termination shock and the heliosheath , 2004 .

[17]  C. Steenberg,et al.  Validity of the Force-Field Equation to Describe Cosmic Ray Modulation , 2003 .

[18]  R. Mewaldt,et al.  Solar minimum spectra of galactic cosmic rays and their implications for models of the near-Earth radiation environment , 2001 .

[19]  J. Lockwood,et al.  Voyager and Pioneer spacecraft measurements of cosmic ray intensities in the outer heliosphere: Toward a new paradigm for understanding the global solar modulation process: 1. Minimum solar modulation (1987 and 1997) , 2001 .

[20]  J. Clem,et al.  Neutron Monitor Response Functions , 2000 .

[21]  W. Axford,et al.  The compton-getting effect , 1968 .

[22]  R. Caballero-Lopez,et al.  Limitations of the force field equation to describe cosmic ray modulation , 2004 .

[23]  P. O'Neill Badhwar–O’Neill galactic cosmic ray model update based on advanced composition explorer (ACE) energy spectra from 1997 to present , 2004 .

[24]  Eugene N. Parker,et al.  THE PASSAGE OF ENERGETIC CHARGED PARTICLES THROUGH INTERPLANETARY SPACE , 1965 .