Providing knowledge of the satellite-killer electrons in near-Earth space using a near real-time data driven space weather model based on ULF-wave radial diffusion.
Background
Enhancements in the flux of relativistic electrons in the Earth’s outer radiation belt can cause sudden damage to sensitive spacecraft electronic components, and can pose a serious health hazard for astronauts. For example, an enhancement in the flux of radiation belt electrons is believed to be responsible for the temporary loss of Telsat, Canada’s Anik E-1 communications satellite and the permanent loss of its sister satellite, Anik E-2. Understanding the conditions which cause these enhancements in the flux of radiation belt electrons, and being able to forecast when they are likely to occur, will enable satellite companies to power down the radiation sensitive components reducing the possible damage resulting from these relativistic electrons. Due to their importance for space-based technology one of the major objectives of NASA’s multi-billion dollar LWS Geospace program is to create the scientific understanding needed to model the physical processes responsible for the acceleration, transport and loss of these radiation belt particles. In addition, one of the primary CGSM scientific objectives is “to elucidate the fundamental processes that cause the energization, transport, and loss of magnetospheric particles”, such as these radiation belt electrons.
Although much is known, there are still many unanswered questions, particularly concerning the basic physical processes that determine the dynamics of the radiation belts. For example, two physical processes which have received a lot of attention are:
- cyclotron resonance wave-particle interactions with VLF waves, which lead primarily to energy and pitch-angle transport
- drift-resonance wave-particle interactions with ULF perturbations, which lead to radial diffusion
It is generally accepted that both of these processes play important roles in radiation belt dynamics, however their relative contributions are not well understood quantitatively. Recent work has shown that even when VLF local electron energization process are ignored, the transport of relativistic electrons from L=7 into the radiation belt region can be simulated by solving the radial diffusion equation with a relatively simple Kp-dependent electron loss term.
Figure 1 illustrates how large scale variations in the flux of relativistic electrons in the outer radiation belt can be accurately simulated by solving the radial diffusion equation
Here, 
represents the phase space density (PSD) of the electrons, 
is the McIlwain parameter, 
is the electron life-time, given empirically as a function of Kp (=3/Kp in days) and 
is the radial diffusion coefficient, (Shprits et al. 2005). The outer boundary condition for the results shown in Figure 1 has been taken from a measurement of the electron flux at L=7 and the top two panels illustrate how the evolution of this flux by radial diffusion has the same large scale features as the flux measured by the CRRES satellite (see Shprits et al. (2005) for more details).
The greatest difficulty in modelling the ULF driven radial diffusion of radiation belt electrons is to accurately determine the diffusion coefficient, , due to both the wave magnetic field 
and the wave electric field 
where
(see Brizzard and Chan, 2004). Here, 
, represents the magnetic field at the Earth’s surface and 
is the Earths radius. 
, 
and 
are the electrons charge, first adiabatic invariant, and the relativistic correction factor. The parameters 
and 
are the magnetic and electric field power spectral densities in the magnetospheric equatorial plane evaluated at frequencies, 
, which satisfied the drift-resonance condition
where m is the azimuthal wavenumber and 
is the azimuthal drift speed of the electron. In order to directly determine the parameters and would require simultaneous global measurements of the waves electric and magnetic fields in space.
Several different methods have been used to estimate , both directly using measurements of the wave fields, and indirectly from observations of the particles diffusion. By assuming a constant , fixed for all time independent of wave activity particle observations over long time intervals (months) have been used to obtain an indirect estimate for (Frank, 1965;Newkirk and Walt, 1968; Lanzerotti et al., 1970, Lyons and Williams, 1975, West et al., 1981; Selesnick et al., 1997). Holzworth and Mozer, (1979) used direct balloon measurements of the wave electic field at L=6 to obtain a Kp-dependent Satellite observations of the wave magnetic power spectral densities at L=4 and L=6.6 have been used to estimate . Brautigam et al., (2005), used the CRRES observations of wave electric field from L=3.0 to L=7.0 to obtained as a function of and Kp. However, these authors state that “given that it is the global structure and variability of the electric and magnetic fields that control the radiation belt particle populations, it will remain near impossible to disentangle the various competing acceleration and loss mechanisms until we can better define what those fields are doing through the deployment of multi-satellite constellations in coordination with ground stations”.
The radiation belt simulation illustrated in Figure 1 (Shprits et al., 2005), was produced using the Brautigam and Albert 2000 as an empirical function of Kp. Only diffusion due to the waves’ magnetic field was considered and the effect of radial diffusion by the waves’ electric field was ignored.
For this space weather forecast, ground-based magnetometer networks are used in conjunction with techniques for mapping the ground wave fields into the wave electric and magnetic fields in space (see e.g., Ozeke, et al., 2007) to obtain the required and diffusion coefficients that control the radiation belt dynamics. Using these diffusion coefficients the diffusion equationis solved in order to produce near real time online simulations of the radiation belt dynamics.