Plasma Physics Course

Total: 8 parts covering plasma fundamentals through advanced topics

Part VII: Space & Astrophysical Plasmas

Over 99% of visible matter in the universe is in the plasma state. From the solar wind to accretion disks around black holes, plasma physics governs the most spectacular phenomena in the cosmos. This part applies the MHD, kinetic, and wave theories developed earlier to real astrophysical systems.

Governing Framework

Astrophysical plasmas are governed by ideal MHD coupled to gravity. The fundamental equations are:

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 \qquad \text{(mass continuity)}$$
$$\rho\frac{D\mathbf{v}}{Dt} = -\nabla p + \mathbf{J}\times\mathbf{B} - \rho\nabla\Phi \qquad \text{(momentum)}$$
$$\frac{\partial \mathbf{B}}{\partial t} = \nabla\times(\mathbf{v}\times\mathbf{B}) + \eta\nabla^2\mathbf{B} \qquad \text{(induction)}$$

Two key dimensionless numbers characterize astrophysical flows:

$$\beta = \frac{p}{B^2/2\mu_0} \quad \text{(plasma beta)}, \qquad R_m = \frac{v L}{\eta} \quad \text{(magnetic Reynolds number)}$$

Most astrophysical plasmas have Rm ≫ 1 (flux-frozen) and span a wide range of β (from β ≪ 1 in pulsar magnetospheres to β ≫ 1 in stellar interiors).

Chapters

Ch 1. Solar Wind

Parker's hydrodynamic model, critical point analysis, Parker spiral, Weber-Davis MHD wind

$$\frac{v}{c_s}\left(\frac{v^2}{c_s^2}-1\right)\frac{dv}{dr} = \frac{2c_s^2}{r} - \frac{GM}{r^2}$$

Ch 2. Earth's Magnetosphere

Chapman-Ferraro model, bow shock, reconnection, radiation belts, Dungey cycle

$$R_{MP} = R_E\left(\frac{B_0^2}{2\mu_0 \rho v_{sw}^2}\right)^{1/6}$$

Ch 3. Aurora & Precipitation

Field-aligned currents, Knight relation, auroral emissions, ionospheric coupling

$$j_\parallel = \frac{n_e e^2}{2\pi m_e}\frac{e\Delta\Phi}{k_B T_e}$$

Ch 4. Stellar Plasmas

Solar corona, coronal heating, stellar structure, stellar winds and mass loss

$$\frac{dp}{dr} = -\frac{\rho G M(r)}{r^2}$$

Ch 5. Accretion Disks

Shakura-Sunyaev α-disk, MRI, Eddington luminosity, AGN and X-ray binaries

$$L_{Edd} = \frac{4\pi G M m_p c}{\sigma_T}$$

Ch 6. Cosmic Rays

Fermi acceleration (1st & 2nd order), diffusive shock acceleration, Hillas criterion

$$\frac{\Delta E}{E} = \frac{4}{3}\frac{v_s}{c}$$

Astrophysical Plasma Parameters

Environmentn [m−3]T [eV]B [T]βRm
Solar corona101410010−3~0.011012
Solar wind (1 AU)107105×10−9~1109
Magnetosheath107502×10−8~5107
Magnetotail1051032×10−8~0.01109
ISM (warm)10513×10−10~11018
Accretion disk102210210−2~101010
Pulsar magnetosphere101810610810−121020
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