update hybrid simulation

docs/blog/phd/2024_pre/justfile

@@ -16,4 +16,4 @@ process-tex file:
 
 process-texs:
    just process-tex proposal_EMIC.tex
-   just rm_bib proposal_SWD.tex
+   just process-tex proposal_SWD.tex

docs/blog/phd/2024_pre/proposal_EMIC.tex

@@ -170,20 +170,16 @@ \section{Abstract}\label{abstract}
 \section{Background and Motivation}\label{background-and-motivation}
 
 \paragraph{Interactions of Waves with Radiation Belt Electrons}\label{interactions-of-waves-with-radiation-belt-electrons}
-
 Relativistic electron fluxes in Earth's inner magnetosphere are greatly affected by electron scattering to the atmosphere via resonant interactions with whistler-mode and electromagnetic ion cyclotron (EMIC) waves \citep{millanReviewRadiationBelt2007, summersTimescalesRadiationBelt2007a}. Near the loss-cone, electron scattering rates for EMIC waves at such energies are much larger than for whistler-mode waves \citep{glauertCalculationPitchAngle2005}. Thus, EMIC wave-driven electron precipitation is considered a key contributor to relativistic electron losses at energies exceeding the minimum energy for cyclotron resonance with such waves, \(E_{\min}\sim 0.5-1\) MeV \citep{summersRelativisticElectronPitchangle2003, summersTimescalesRadiationBelt2007}. Numerical simulations of the outer radiation belt dynamics \citep{maModelingInwardDiffusion2015} and data-model comparisons \citep{angelopoulosEnergeticElectronPrecipitation2023} have demonstrated that EMIC waves can scatter relativistic electrons efficiently and deplete their fluxes quickly in the outer radiation belt.
 For energies below ultra-relativistic energies (below several MeV) and for typical plasma characteristics, EMIC wave-driven electron scattering mostly affects low pitch-angle electrons \citep[equatorial \(\alpha_{eq}<30^\circ\), see][]{kerstenElectronLossesRadiation2014}. Therefore, additional high pitch-angle electron scattering by whistler-mode waves is required to assist EMIC waves in the precipitation of the main, near-equatorial, (trapped) electron population \citep{mourenasFastDropoutsMultiMeV2016}. A combination of electron scattering by whistler-mode and EMIC waves at the same \(L\)-shell (even if at different MLT) can result in a very effective electron flux depletion \citep{mourenasFastDropoutsMultiMeV2016, drozdovDepletionsMultiMeVElectrons2022}. Verification of this electron loss mechanism requires a combination of satellites near the equator (to measure the waves and equatorial pitch-angle electron fluxes) and at low-altitude (to measure precipitating electron fluxes).
 
 \paragraph{Effects of Wave-particle Resonant Interactions}\label{effects-of-wave-particle-resonant-interactions}
-
 EMIC waves are generated by anisotropic ion populations from plasma sheet injections \citep{Jun19:emic}. These injections also create anisotropic ``seed'' electrons \citep{Miyoshi13,Jaynes15:seedelectrons}, the free energy source for whistler-mode chorus waves \citep{Tao11,Fu14:radiation_belts,Zhang18:whistlers&injections}. Such chorus waves can effectively accelerate the same seed electrons to relativistic energies \citep{miyoshiRebuildingProcessOuter2003, thorneRapidLocalAcceleration2013, mourenasApproximateAnalyticalSolutions2014, allisonLocalHeatingRadiation2020}. Therefore, there is a competition between electron acceleration by whistler-mode waves \citep[supported by direct adiabatic heating during injections, see, e.g.][]{sorathiaModelingDepletionRecovery2018} and electron precipitation by EMIC and chorus waves, and this competition should ultimately shape the energy spectrum of radiation belt electrons after a series of plasma sheet injections. Several recent publications indicate that the electron energy spectrum may have an upper limit corresponding to a balance between electron injections and precipitation loss, controlled by whistler-mode waves \citep{oliferTaleTwoRadiation2021, oliferNaturalLimitSpectral2022}. The existence of such an upper limit has been predicted by \citet{kennelLimitStablyTrapped1966}, and reevaluated for relativistic electrons by \citet{summersLimitStablyTrapped2009} and \citet{summersLimitingEnergySpectrum2014}. Several of its main assumptions have been verified using ELFIN data \citep{mourenasCheckingKeyAssumptions2024}. The Kennel-Petschek upper limit is based on the idea that injected electrons generate whistler-mode waves (with exponentially higher wave power for electron fluxes above the flux limit) that ultimately scatter these same injected electrons into the atmosphere. The competition between linearly increasing anisotropic electron fluxes and exponentially faster electron losses into the atmosphere due to exponentially increasing wave growth, leads to a stationary solution in the diffusion (Fokker-Planck) equation describing electron flux dynamics. Inclusion of EMIC wave-driven loss into this balance reduces the upper limit of the electron flux at high energy \citep{mourenasExtremeEnergySpectra2022}.
 
 \paragraph{Role of EMIC Waves in Space Weather}\label{role-of-emic-waves-in-space-weather}
-
 Understanding the interactions between EMIC waves and radiation belt electrons is crucial for predicting space weather effects, particularly since these interactions can lead to rapid changes in radiation belt configurations, posing risks to satellites and other space-based technologies (Baker et al., 2004; Horne et al., 2005). The 2003 Halloween storm provided a clear example of how enhanced EMIC wave activity correlated with significant radiation belt electron flux decreases, highlighting the importance of including these waves in predictive models (Turner et al., 2012).
 
 \paragraph{Gaps in Current Understanding}\label{gaps-in-current-understanding}
-
 Despite significant advances, there remain substantial gaps in our understanding of what roles these coexistent waves with concurrent processes (plasma sheet injections) play in modifying these interactions with energetic particles. The proposed study aims to bridge these gaps by combining observational data analysis with theoretical modeling efforts.
 
 \section{Proposed Data and Detailed Analysis Approach}\label{proposed-data-and-detailed-analysis-approach}
@@ -246,7 +242,7 @@ \section{Figures}\label{figures}
 
 \centering{
 
-\includegraphics[width=0.6\textwidth,height=\textheight]{figures/fig1_orbit_multi_mission_conjunctions.png}
+\includegraphics[width=0.67\textwidth,height=\textheight]{figures/fig1_orbit_multi_mission_conjunctions.png}
 
 }
 
@@ -281,7 +277,6 @@ \section{Figures}\label{figures}
 \newpage{}
 
 
-  \bibliography{../../../../files/references.bib,../../../../../share/bibliography/research.bib}
 
 
 \bibliography{files/Anton.addon.bib,files/Anton.full.bib,files/research.bib}

docs/blog/phd/2024_pre/proposal_SWD.qmd

@@ -65,17 +65,17 @@ This PhD research focuses on three main objectives:
 
 - Determination of discontinuities: We will implement Liu's [@liuMagneticDiscontinuitiesSolar2022] method to identify discontinuities in the solar wind which has better compatibility for the discontinuities with minor field changes, and is more robust to the situation encountered in the outer heliosphere. We also will use the minimum or maximum variance analysis (MVA) analysis [@sonnerupMinimumMaximumVariance1998; @sonnerupMagnetopauseStructureAttitude1967] to determine the main (most varying) magnetic field component, $B_l$, and medium variation component, $B_m$. @fig-examples shows several examples of solar wind discontinuities detected by different spacecraft.
 
-- Comparative analysis: Analyze discontinuity occurrence rate and properties across different radial distances to determine spatial trends, untangle the temporal effect due to  solar variability.
+<!-- - Comparative analysis: Analyze discontinuity occurrence rate and properties across different radial distances to determine spatial trends, untangle the temporal effect due to  solar variability. -->
 
-Two promising approaches are proposed to study the evolution of solar wind discontinuities: The first approach involves studying conjunction events, where spacecraft are either contemporaneously aligned along the same spiral field line—thereby measuring solar wind emitted from the same region on the solar surface—or where spacecraft are positioned such that they measure the same solar wind plasma. This second alignment is determined by the difference in radial distance, $\delta R$, corresponding to the solar wind travel time, $\tau = \delta R / V_{sw}$. An example of this approach is demonstrated in @fig-alignment, where plasma and magnetic field measurements from the Parker Solar Probe (PSP) and the Advanced Composition Explorer (ACE) display similar trends in magnetic field magnitude, plasma density, velocity, and temperature during the alignment period. This period corresponds to April 6-7, 2019 for PSP and April 7-9, 2019 for ACE. Further validation is provided by using the statistical plasma expansion model [@perroneRadialEvolutionSolar2019], where the plasma properties measured by PSP and projected to the ACE location show good agreement with the actual ACE measurements, as illustrated in @fig-evolution. This confirms the validity of the alignment approach for studying solar wind discontinuities.
+Two promising approaches are proposed to study the evolution of solar wind discontinuities: The first approach involves studying conjunction events, where spacecraft are either contemporaneously aligned along the same spiral field line—thereby measuring solar wind emitted from the same region on the solar surface—or where spacecraft are positioned such that they measure the same solar wind plasma [@velliUnderstandingOriginsHeliosphere2020]. This second alignment is determined by the difference in radial distance, $\delta R$, corresponding to the solar wind travel time, $\tau = \delta R / V_{sw}$. An example of this approach is demonstrated in @fig-alignment, where plasma and magnetic field measurements from the Parker Solar Probe (PSP) and the Advanced Composition Explorer (ACE) display similar trends in magnetic field magnitude, plasma density, velocity, and temperature during the alignment period. This period corresponds to April 6-7, 2019 for PSP and April 7-9, 2019 for ACE. Further validation is provided by using the statistical plasma expansion model [@perroneRadialEvolutionSolar2019], where the plasma properties measured by PSP and projected to the ACE location show good agreement with the actual ACE measurements, as illustrated in @fig-evolution. This confirms the validity of the alignment approach for studying solar wind discontinuities.
 
 The second approach leverages big data collected over many years to compare solar wind discontinuities observed by different spacecraft at various radial distances. Due to the Sun's rapid rotation, solar wind plasma emitted from a single region on the solar surface sweeps across the entire heliosphere within a solar rotation period of 27 days. By utilizing solar wind measurements at 1 AU from STEREO, ARTEMIS, and WIND, and comparing these with data from Juno and PSP, it is possible to differentiate the effects of temporal variations in solar wind from those due to spatial variations (associated with radial distance from the Sun) in the occurrence rate and characteristics of discontinuities. An example of such a comparison for the occurrence rate is shown in @fig-rate, where the number of discontinuities measured per day by different spacecraft missions is plotted.
 
 In the proposed study, we will extend this comparison to the properties of discontinuities, such as their thickness, strength (current density), and orientation, to understand how these features evolve with radial distance from the Sun and how this properties are related to the local plasma properties. This will provide insights into the physical mechanisms that govern the formation and evolution of solar wind discontinuities as they propagate through the heliosphere.
 
 **Hybrid and PIC Simulation:**
 
-The proposed study will employ a two-tiered simulation strategy to thoroughly investigate the formation and evolution of solar wind discontinuities. Initially, hybrid simulations will be utilized to model the nonlinear ion dynamics that are fundamental in the development of these discontinuities. This will be followed by a full kinetic Particle-in-Cell (PIC) simulation aimed at exploring the electron dynamics associated with these discontinuities. These simulations will be enriched with real solar wind parameters to create realistic scenarios for the examination of discontinuity development. Here we demonstrate the simulation setup using Hybrid simulation, where we successfully reproduced the formation of a rotational discontinuity in the solar wind, as shown in @fig-hybrid.
+The proposed study will employ a two-tiered simulation strategy to thoroughly investigate the formation and evolution of solar wind discontinuities. Initially, hybrid simulations will be utilized to model the nonlinear ion dynamics that are fundamental in the development of these discontinuities. This will be followed by a full kinetic Particle-in-Cell (PIC) simulation aimed at exploring the electron dynamics associated with these discontinuities. These simulations will be enriched with real solar wind parameters to create realistic scenarios for the examination of discontinuity development. Here we demonstrate the simulation setup using Hybrid simulation, where we successfully reproduced the formation of a rotational discontinuity in the solar wind from an initial oblique Alfvén wave, as shown in @fig-hybrid.
 
 Further in-depth analysis will focus on the evolution of particle velocity distributions over space and time to gain insights into their interactions with discontinuities. This includes studying the pressure balance across discontinuities and delving into the physical mechanisms responsible for energy transfer processes. Such a comprehensive study will not only enhance our understanding of particle dynamics in the presence of discontinuities but also illuminate the broader implications for solar wind physics.
 
@@ -126,7 +126,9 @@ The number of discontinuities measured by Juno per day coincides with the discon
 
 ::: {#fig-hybrid}
 
-Formation of a rotational discontinuity in the solar wind, reproduced using hybrid simulation. The magnetic field components $B_x$, $B_y$, and $B_z$ are shown in the top panel, while the ion velocity distribution function is displayed in the bottom panel.
+![](figures/fig_hybrid.png)
+
+Formation of a rotational discontinuity in the solar wind, reproduced using hybrid simulation. The magnetic field components $B_x$, $B_y$, $B_z$, magnetic field magnitude $|{\mathbf B}|$ are shown in different colors, with each panel corresponding to different times in the simulation normalized by the ion cyclotron period.
 :::