A Survey on High-energy Protons Response to Geomagnetic Storm in the Inner Radiation Belt
Abstract. RBSPA observations suggest that the inner radiation belt high energy proton fluxes drop significantly during the storm main phase and recover in parallel to as the SYM-H index [Xu et al., 2019]. A natural problem arises: are these storm‐time proton flux variations in response to the magnetic field modifications adiabatic? Based on Liouville's theorem and conservation of the first and third adiabatic invariants, the fully adiabatic effects of high energy protons in the inner radiation belt have been quantitatively evaluated. Two case studies show that theoretically calculated, adiabatic flux decreases are in good agreement with RBSPA observations. Statistical survey of 67 geomagnetic storms which occurred in 2013–2016 has been conducted. The results confirm that the fully adiabatic response constitutes the main contribution 90 % to the changes in high energy protons in inner radiation belt during the storm main and recovery phases. It indicates that adiabatic invariants of the inner belt high energy protons are well preserved for majority of storms. Phase space density results also support adiabatic effect controls the varication of high energy protons especially for small and medium geomagnetic storms. Non-adiabatic effects could play important role for the most intense storms with fast changes in magnetic configuration.
Zhaohai He et al.
Zhaohai He et al.
Zhaohai He et al.
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This paper claims to show that adiabatic effects dominate the changes in proton fluxes in the outer part of the proton radiation belts (sometimes referred to as the inner zone).
A first (more minor point compared to my latter concerns) is that much of the cited literature concerns changes in the proton betls that are more long-lasting. For example, losses due to field line curvature scattering are true losses as opposed to temporary (adiabatic) changes. This paper does not contradict those other studies. It has a different objective.
The major problems with this paper are that (a) the methodology is not presented with enough detail to understand how the authors actually analyzed the data and (b) the methodology itself appears responsible for the results that are presented.
Specifically, the authors present formulas that they claim quantify the changes in flux due to adibatict processes that preserve mu and L. Those are listed in equations 1-4 which represent the flux during the storm (subscript m) as a function of flux prior to the storm (subscript p). The two are related by three variables: Energy, L-shell, and Magnetic field strength. The variables during and prior to the storm are represented by _p and _m.
The first problem is that the equations that relate E_m to E_p and L_m to L_p are not given so the quantities in figure 3 cannot be verified.
The second problem is that figure 3 plots E_p, L_p, and j_p as a function of time for fixed values of L_m and E_m. Surely it should be the other way around. For a given pre-storm condition (_p) the quantities during the storm (_m) are a function of time. It is not at all helpful to present it in terms of the "pre-storm" conditions vary as a function of time during the storm.
The third, and biggest, problem is that the relationship between all of the variables (e.g. L_p to L_m, E_p to E_M) are all a function of B_p/B_m. Since B == B_dip +dB and dB = -symH (for symH<0) then all of the pre-storm and storm-time variables are related to one another as a function of dB == -symH. This can be seen very cleaerly in figure 3 where all predicted variables follow every bump and wiggle of symH.
For true calculations of adiabatic effects the radial gradients of PSD are critical (as is the second invariant which is ignored here). For example, a flat radial gradient produces no change in flux when B changes. This analysis simply samples the fluxes (j_p) at different values of L and E that are related to an arbitrarily-chosen value of L_m and E_m where the relationship is defined by symH. It is a totology to conclude that adiabatic changes (defined by dB == -symH) "explain" the flux variations.
The brief discussion of phase space density in section 3.3 does not contain enough information to know what the authors have done or what is being plotted in figure 6. Is the PSD at fixed third invariant (L*)? If so, what L*? It is currently impossibe to know if the PSD results support the preceding conclusions or not.