Plasma Physics Programs
Interactive simulations for computational plasma physics ā particle motion, wave phenomena, and kinetic instabilities
These Python programs run directly in your browser using Pyodide (WebAssembly Python). The first run downloads the Python environment (~15MB). Click "Run" to execute!
Charged Particle Motion
Boris pusher algorithm for charged particle gyration and EĆB drift in uniform fields
Click Run to execute the Python code
First run will download Python environment (~15MB)
Key Equations of Plasma Physics
Fundamental Plasma Parameters
Debye Length:
$$\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^2}}$$
Plasma Frequency:
$$\omega_{pe} = \sqrt{\frac{n_e e^2}{\varepsilon_0 m_e}}$$
Cyclotron Frequency:
$$\omega_c = \frac{|q|B}{m}$$
Larmor Radius:
$$r_L = \frac{m v_\perp}{|q| B}$$
Vlasov Equation
$$\frac{\partial f}{\partial t} + \vec{v} \cdot \nabla f + \frac{q}{m}(\vec{E} + \vec{v} \times \vec{B}) \cdot \frac{\partial f}{\partial \vec{v}} = 0$$
Collisionless kinetic equation for the distribution function \( f(\vec{x}, \vec{v}, t) \)
Langmuir Wave Dispersion
$$\omega^2 = \omega_{pe}^2 + 3k^2 v_{th}^2$$
Landau damping rate:
$$\gamma_L \approx -\sqrt{\frac{\pi}{8}} \frac{\omega_{pe}}{(k\lambda_D)^3} \exp\!\left(-\frac{1}{2k^2\lambda_D^2}\right)$$
Magnetohydrodynamics
MHD Momentum:
$$\rho\frac{d\vec{v}}{dt} = -\nabla p + \vec{J} \times \vec{B}$$
Alfven Speed:
$$v_A = \frac{B}{\sqrt{\mu_0 \rho}}$$
Magnetic Pressure:
$$p_B = \frac{B^2}{2\mu_0}$$
Plasma Beta:
$$\beta = \frac{2\mu_0 n k_B T}{B^2}$$
Guiding Center Drifts
E x B Drift
$$\vec{v}_E = \frac{\vec{E} \times \vec{B}}{B^2}$$
Grad-B Drift
$$\vec{v}_{\nabla B} = \frac{m v_\perp^2}{2qB^3} \vec{B} \times \nabla B$$
Curvature Drift
$$\vec{v}_R = \frac{m v_\parallel^2}{qB^2} \frac{\vec{R}_c \times \vec{B}}{R_c^2}$$