Magnetized Plasma Sheath Dynamics & Kinetic Ensemble Trajectories

Explore kinetic trajectories in screened potentials and magnetic fields. Models Maxwellian electron gyration, zero-FLR orbit collapse, and dual-species plasma ensemble transport.

https://youtu.be/RNZYeZoJvNY

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🍃Cyclotron Gyration & Plasma Screening Dynamics

Emphasizes electron Larmor radius gyration and energy-dependent particle deflection across electrostatic potential thresholds.

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🍄Deliverables 25

Magnetized Plasma Sheath Dynamics & Kinetic Ensemble Trajectories

https://payhip.com/b/BacMg

Documents

Computational and numerical models (Sheath.md)
Snippets
Conceptual guide (The Great Atomic Race.md)

Exploration Frontiers

Kinetic Motion & Single-Particle Dynamics $\rightarrow$ Radial Electrostatic Sheath Potential
Magnetized Plasma & Drift Physics $\rightarrow$ Axial Magnetic Field Alignment & Cross-Field Drifts
Species & Mass Ratio Effects $\rightarrow$ Directional Injection Streams (Unmagnetized Ions)
Macroscopic Ensemble & PIC Simulations $\rightarrow$ Radially Inward Core Collection Sinks

flowchart LR
    %% Custom Styling Definitions
    classDef inject fill:#1e293b,stroke:#38bdf8,stroke-width:2px,color:#f8fafc;
    classDef boundary fill:#312e81,stroke:#818cf8,stroke-width:2px,color:#f8fafc;
    classDef decision fill:#78350f,stroke:#f59e0b,stroke-width:2px,color:#fef3c7;
    classDef electron fill:#0c4a6e,stroke:#38bdf8,stroke-width:2px,color:#f0f9ff;
    classDef ion fill:#4c1d95,stroke:#c084fc,stroke-width:2px,color:#faf5ff;
    classDef sink fill:#064e3b,stroke:#34d399,stroke-width:2px,color:#ecfdf5;

    %% PHASE 1: Injection and Inflow
    subgraph Phase1 [Phase 1: Ensemble Injection and Inflow - Domain 3 and 4]
        A(["Macro-Particle Injection<br>Electrons e⁻ vs Ions X⁺"]):::inject
        B["Directional Inflow Stream<br>Linear parallel trajectories r > λ_D"]:::inject
        A --> B
    end

    %% PHASE 2: Debye Boundary Crossing
    subgraph Phase2 [Phase 2: Debye Boundary Crossing - Domain 1]
        C{"Cross Screening Threshold<br>r = λ_D"}:::boundary
        B --> C
    end

    %% PHASE 3: Field Interactions and Dynamics
    subgraph Phase3 [Phase 3: Screened Field and Magnetized Dynamics - Domain 1, 2, and 3]
        D["Maintain Linear Momentum<br>Ignore B_z field - High Mass / Low q/m"]:::ion
        E{"Check B_z Alignment<br>Low Mass / High q/m"}:::decision
        
        F{"Check E_k vs |qΦ_0|<br>Unmagnetized B_z = 0"}:::decision
        G["Repulsive Deflection<br>Backscattering E_k < |qΦ_0|"]:::electron
        H["Barrier Penetration<br>Penetrate to Core E_k ≥ |qΦ_0|"]:::electron

        I["Lorentz Acceleration<br>Cyclotron Gyration B_z ≠ 0"]:::electron
        J["Azimuthal E×B Drift<br>Concentric Orbital Equilibrium"]:::electron

        C -- "Ions X⁺" --> D
        C -- "Electrons e⁻" --> E
        
        E -- "B_z = 0" --> F
        F -- "E_k < |qΦ_0|" --> G
        F -- "E_k ≥ |qΦ_0|" --> H
        
        E -- "B_z ≠ 0" --> I
        I --> J
    end

    %% PHASE 4: Core Attraction and Collection
    subgraph Phase4 [Phase 4: Core Attraction and Sink Collection - Domain 1, 3, and 4]
        K["Attractive Potential Well Φ(r)<br>Inward Radial Acceleration"]:::ion
        L(["Central Core Sink Boundary<br>Absorption at r = r_sink"]):::sink
        M["Record Flux Collection<br>Macroscopic Tallies"]:::sink

        D --> K
        K --> L
        H --> L
        L --> M
    end

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https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/magnetized-plasma-sheath-dynamics-and-kinetic-ensemble-trajectories </aside>

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