scholarly journals Machine-learning based discovery of missing physical processes in radiation belt modeling

2021 ◽  
Author(s):  
Enrico Camporeale ◽  
George Wilkie ◽  
Alexander Drozdov ◽  
Jacob Bortnik
Keyword(s):  
Diffusion Equation ◽  
Radiation Belt ◽  
Radiation Belts ◽  
Artificial Satellites ◽  
Observation Data ◽  
Physical Processes ◽  
Drift Diffusion ◽  
Time Prediction ◽  
Ill Posed ◽  
Physical Insight

Abstract Real-time prediction of the dynamics of energetic electrons in Earth's radiation belts incorporating incomplete observation data is important to protect valuable artificial satellites and to understand their physical processes. Traditionally, reduced models have employed a diffusion equation based on the quasi-linear approximation. Using a Physics-Informed Neutral Network (PINN) framework, we train and test a model based on four years of Van Allen Probe data. We present a recipe for gleaning physical insight from solving the ill-posed inverse problem of inferring model coefficients from data using PINNs. With this, it is discovered that the dynamics of ``killer electrons'' is described more accurately instead by a drift-diffusion equation. A parameterization for the diffusion and drift coefficients, which is both simpler and more accurate than existing models, is presented.

Evaluating the effect of wave-particle cross diffusion in radiation belts modelling using an innovative and robust numerical scheme

2020 ◽  
Author(s):  
Nour Dahmen ◽  
Vincent Maget ◽  
Francois Rogier
Keyword(s):  
Numerical Scheme ◽  
Radiation Belt ◽  
Particle Interaction ◽  
Radiation Belts ◽  
Physical Processes ◽  
Density Profiles ◽  
Cross Diffusion ◽  
Numerical Resolution ◽  
The Earth ◽  
Physical Representation

<p>The last decade has shown the prime importance of wave-particle interaction for the accurate modelling of the dynamics of energetic electrons trapped in the Earth’s radiation belts, as well as for other planets, such as Jupiter or Saturn. They have been therefore added in the sum of physical processes modeled in radiation belt codes such as Salammbô, with conclusive results. However, this upgrade of the physical representation is not straightforward and comes at the price of degrading the numerical resolution. In particular, computational instabilities and odd phase space density profiles are observed, impacting the code’s accuracy and its physical relevance. This challenging issue requires the development of a numerical scheme which supports in particular wave-particle cross diffusion terms. Thus, we will present in this talk the new dedicated numerical scheme we have developed and implemented in Salammbô. Then we will focus on quantifying the effect of wave-particle cross diffusion terms on the dynamics of highly energetic trapped electrons, in presenting results for real case storms.</p>

Real-Time Prediction of Ocean Observation Data Based on Transformer Model

2021 ◽  
Author(s):  
Wenqing Chang ◽  
Xiang Li ◽  
Huomin Dong ◽  
Chunxiao Wang ◽  
Zhigang Zhao ◽  
...  
Keyword(s):  
Real Time ◽  
Observation Data ◽  
Time Prediction ◽  
Transformer Model

On the effect of ULF waves on the outer radiation belt during geomagnetic storms

2021 ◽  
Author(s):  
Christopher Lara ◽  
Pablo S. Moya ◽  
Victor Pinto ◽  
Javier Silva ◽  
Beatriz Zenteno
Keyword(s):  
Relativistic Electron ◽  
Radiation Belt ◽  
Geomagnetic Storms ◽  
Cumulative Effect ◽  
Radiation Belts ◽  
Ulf Waves ◽  
Relativistic Electrons ◽  
Relative Role ◽  
Outer Radiation Belt ◽  
Ulf Wave

<p>The inner magnetosphere is a very important region to study, as with satellite-based communications increasing day after day, possible disruptions are especially relevant due to the possible consequences in our daily life. It is becoming very important to know how the radiation belts behave, especially during strong geomagnetic activity. The radiation belts response to geomagnetic storms and solar wind conditions is still not fully understood, as relativistic electron fluxes in the outer radiation belt can be depleted, enhanced or not affected following intense activity. Different studies show how these results vary in the face of different events. As one of the main mechanisms affecting the dynamics of the radiation belt are wave-particle interactions between relativistic electrons and ULF waves. In this work we perform a statistical study of the relationship between ULF wave power and relativistic electron fluxes in the outer radiation belt during several geomagnetic storms, by using magnetic field and particle fluxes data measured by the Van Allen Probes between 2012 and 2017. We evaluate the correlation between the changes in flux and the cumulative effect of ULF wave activity during the main and recovery phases of the storms for different position in the outer radiation belt and energy channels. Our results show that there is a good correlation between the presence of ULF waves and the changes in flux during the recovery phase of the storm and that correlations vary as a function of energy. Also, we can see in detail how the ULF power change for the electron flux at different L-shell We expect these results to be relevant for the understanding of the relative role of ULF waves in the enhancements and depletions of energetic electrons in the radiation belts for condition described.</p>

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

scholarly journals Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 539-544
Author(s):  
K. Banoo ◽  
F. Assad ◽  
M. S. Lundstrom
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Momentum Space ◽  
Bulk Silicon ◽  
Rigorous Solution ◽  
Drift Diffusion ◽  
The Boltzmann Equation ◽  
And Diffusion ◽  
Multi Mode

We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

scholarly journals A radiation belt of energetic protons located between Saturn and its rings

Science ◽  
2018 ◽  
Vol 362 (6410) ◽  
pp. eaat1962 ◽  
Author(s):  
E. Roussos ◽  
P. Kollmann ◽  
N. Krupp ◽  
A. Kotova ◽  
L. Regoli ◽  
...  
Keyword(s):  
Radiation Belt ◽  
Cosmic Ray ◽  
High Energy ◽  
Radiation Belts ◽  
Exchange Reactions ◽  
Dipole Magnetic Field ◽  
Imaging Instrument ◽  
Multiple Charge ◽  
Strong Dipole ◽  
Dense Atmosphere

Saturn has a sufficiently strong dipole magnetic field to trap high-energy charged particles and form radiation belts, which have been observed outside its rings. Whether stable radiation belts exist near the planet and inward of the rings was previously unknown. The Cassini spacecraft’s Magnetosphere Imaging Instrument obtained measurements of a radiation belt that lies just above Saturn’s dense atmosphere and is decoupled from the rest of the magnetosphere by the planet’s A- to C-rings. The belt extends across the D-ring and comprises protons produced through cosmic ray albedo neutron decay and multiple charge-exchange reactions. These protons are lost to atmospheric neutrals and D-ring dust. Strong proton depletions that map onto features on the D-ring indicate a highly structured and diverse dust environment near Saturn.

Quasi solution of a backward space fractional diffusion equation

2019 ◽  
Vol 27 (6) ◽  
pp. 795-814 ◽  
Author(s):  
Amir Hossein Salehi Shayegan ◽  
Ali Zakeri
Keyword(s):  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Linear Equations ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
The Finite Element Method ◽  
System Of Linear Equations ◽  
Solution Approach ◽  
Space Fractional Diffusion Equation ◽  
Ill Posed

Abstract In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation. To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible initial data. In addition, in order to approximate the quasi solution, the finite element method is used. Since the obtained system of linear equations is ill-posed, we apply TSVD regularization. Finally, three numerical examples are given. Numerical results reveal the efficiency and applicability of the proposed method.

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