University:
Boston University
Course:
CAS AS 311 | Planetary Physics
Academic year:

2024
Views:

345

Pages:

17
Author:

Brenden Trevino

Outline I. Introduction to Turbulence II. Measurements of Turbulence in the Solar Wind. III. Magnetohydrodynamics (MHD) IV. Alfven Waves, the Origin of the Solar Wind, and Solar Probe Plus V. Introduction to phenomenological theories of MHD turbulence. Magnetohydrodynamics (MHD) • In order to understand the power spectra seen in the solar wind, we need a theoretical framework for analyzing fluctuations on these lengthscales and timescales. • In the solar wind near Earth, phenomena occurring at large length scales (exceeding ≈300 km) and long time scales (e.g., exceeding ≈10 s) can be usefully described within the framework of a fluid theory called magnetohydrodynamics (MHD). • In MHD, the plasma is quasi-neutral, and the displacement current is neglected in Maxwell’s equations (since the fluctuation frequencies are small). Ideal, Adiabatic MHD velocity magnetic field density pressure ratio of specific heats (The phrase “ideal MHD” means that dissipative terms involving viscosity and resistivity have been neglected. I’ll come back to these terms later.) Ideal, Adiabatic MHD “continuity equation” mass conservation Ideal, Adiabatic MHD Newton’s 2nd law Ideal, Adiabatic MHD adiabatic evolution. the specific entropy [∝ln(p/ργ)] of a fluid element does not change in time. (An alternative, simple approximation is the isothermal approximation, in which p = ρcs2, with the sound speed cs = constant. More generally, this equation is replaced with an energy equation that includes thermal conduction and possibly other heating and cooling mechanisms.) Ideal, Adiabatic MHD Ohm’s Law for a perfectly conducting plasma Ideal, Adiabatic MHD • Magnetic forces: magnetic pressure and magnetic tension • Frozen-in Law: magnetic field lines are like threads that are frozen to the plasma and advected by the plasma Waves: small-amplitude oscillations about some equilibrium wavelength λ = 2π/k decreasing λ ⇔ increasing k energy cascades to small λ, or equivalently to large k As an example, let’s look at MHD Waves in “lowbeta” plasmas such as the solar corona. Plasma Waves at Low Beta fast magnetosonic wave Alfven wave slow magnetosonic wave magnetic field lines magnetic tension magnetic pressure thermal pressure (like a wave propagating on a string) undamped weakly damped strongly damped Plasma Waves at Low Beta Alfven wave fast magnetosonic wave slow magnetosonic wave magnetic tension magnetic pressure thermal pressure undamped damped ← weakly “Alfven speed” strongly damped Plasma Waves at Low Beta Alfven wave fast magnetosonic wave magnetic tension magnetic pressure undamped weakly damped slow magnetosonic wave thermal pressure strongly damped sound speed cs = (γp/ρ)1/2 Plasma Waves at Low Beta Alfven wave fast magnetosonic wave magnetic tension magnetic pressure virtually undamped in collisionless plasmas like the solar wind damped in collisionless plasmas (weakly at β<<1, strongly at β≈1) slow magnetosonic wave thermal pressure strongly damped in collisionless plasmas Properties of Alfven Waves (AWs) Properties of Alfven Waves (AWs) (Belcher & Davis 1971) Properties of Alfven Waves (AWs) What role do AWs and AW turbulence plan in the solar wind? One possibility: AW turbulence may be one of the primary mechanisms responsible for generating the solar wind. Let’s take a closer look at how this might work.