Simulating Plasma Filamentation: Drift-Diffusion Models and Dynamic Trajectory Pursuit

Explore computational drift-diffusion models for plasma filamentation, simulating ionized tendril paths, barrier navigation, and dynamic target pursuit.

https://youtu.be/KMcU_mOwZug

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🍃Dynamic Drift-Diffusion Models for Electrical Streamer Propagation

Highlight the core physics of random-walk diffusion coupled with bias-driven drift toward grounded targets.

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🍄Deliverables 29

Simulating Plasma Filamentation: Drift-Diffusion Models and Dynamic Trajectory Pursuit

https://payhip.com/b/BacMg

Documents

Computational Models
Snippets
The governing principles of plasma trajectory dynamics

Exploration Frontiers

2D Planar Random Walk $\rightarrow$ 3D Volumetric Tracking
Heuristic Drift Vector $\rightarrow$ Poisson Potential Solver
Homogeneous Medium $\rightarrow$ Permittivity Gradients
Independent Single Paths $\rightarrow$ Dynamic Splitting Logic
Non-Interacting Tendrils $\rightarrow$ Space-Charge Repulsion
Static Block Barrier $\rightarrow$ Moving Boundary Detection

flowchart TD
    %% Custom Styling Definitions
    classDef startNode fill:#0284c7,stroke:#0369a1,stroke-width:2px,color:#ffffff,font-weight:bold,rx:8px,ry:8px;
    classDef processNode fill:#f0f9ff,stroke:#0284c7,stroke-width:1.5px,color:#0f172a,rx:6px,ry:6px;
    classDef transitionNode fill:#fffbeb,stroke:#f59e0b,stroke-width:1.5px,color:#78350f,stroke-dasharray:4 4,rx:6px,ry:6px;
    classDef targetNode fill:#f0fdf4,stroke:#16a34a,stroke-width:1.5px,color:#14532d,rx:6px,ry:6px;

    subgraph Current_Exploration["⚡ Current Exploration: Modified Random Walk with Drift-Diffusion"]
        direction TB
        A["<b>Particle Start</b><br/><i>Electrode Core</i>"]:::startNode --> B{"<b>Early Phase</b><br/>Diffusion Dominated"}:::processNode
        B -->|Adds Random Angular Offset| C["Paths Wander, Loop & Spread Widely"]:::processNode
        C -->|Heading Error Corrections Accumulate| D["<b>Late Phase</b><br/>Drift Dominated"]:::processNode
        D -->|Forces Bias toward Grounding Point| E["Paths Snap into Narrow Cluster"]:::processNode
        E --> F["<b>Capture Transition</b><br/><i>Grounded Target</i>"]:::startNode
    end

    subgraph Transitions["🔀 Key Extensions / Transitions"]
        direction TB
        T1["3D Path Modeling & Volumetric Tracking"]:::transitionNode
        T2["Coupled Potential Field (E = -∇Φ)"]:::transitionNode
        T3["Spatial Permittivity Variations (εᵣ)"]:::transitionNode
        T4["Dynamic Splitting & Persistence"]:::transitionNode
        T5["Multi-Agent Mutual Repulsion / Space-Charge"]:::transitionNode
        T6["Dynamic Moving Boundary & Obstacle Avoidance"]:::transitionNode
    end

    subgraph Potential_Orientation["🎯 Potential Orientation: Enhanced Physical & Multi-Agent Models"]
        direction TB
        G1["Realistic 3D Streamer Breakdown Visualization"]:::targetNode
        G2["Coupled Physical Drift via Poisson Solver"]:::targetNode
        G3["Modeling Realistic Dielectric Interfaces"]:::targetNode
        G4["Simulation of Realistic Branching Networks"]:::targetNode
        G5["Simulating Space-Charge Repulsion Effects"]:::targetNode
        G6["Optimal Grounding & Collision Detection"]:::targetNode
    end

    Current_Exploration ==>|Volumetric Tracking| T1 --> G1
    Current_Exploration ==>|Poisson Field Coupling| T2 --> G2
    Current_Exploration ==>|Dielectric Interfaces| T3 --> G3
    Current_Exploration ==>|Branching Dynamics| T4 --> G4
    Current_Exploration ==>|Space-Charge Shielding| T5 --> G5
    Current_Exploration ==>|Boundary Avoidance| T6 --> G6

    style Current_Exploration fill:#f0f9ff,stroke:#0284c7,stroke-width:2px;
    style Transitions fill:#fffbe6,stroke:#d97706,stroke-width:2px;
    style Potential_Orientation fill:#f0fdf4,stroke:#16a34a,stroke-width:2px;

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