Fluids and Plasmas in Astrophysics

Code:

AST379

Acronym:

AST379

Keywords
Classification	Keyword
OFICIAL	Astronomy

Instance: 2012/2013 - 2S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	First Degree in Astronomy

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	2	Plano de Estudos a partir de 2008	3	-	7,5	-
M:AST	0	Plano de Estudos do Mestrado em Astronomia	1	-	7,5	-

Teaching language

Portuguese

Objectives

In the first part of the course, we will introduce the fundamental tools and concepts in fluid mechanics and some applications of this theory to physics and astrophysics. In the second part, this approach will be extended to the study of plasmas and particular emphasis on the orbital theory of plasmas and on magnetohydrodynamics (MHD) will be devoted. At the end of the course, some examples of applications of MHD to the sun and to other astronomical objects will be treated.

Learning outcomes and competences

Being able to understand a number of phenomena associated with the behaviour of neutral fluids either in the ideal limit or considering the effects of viscosity. Being able to understand the behaviour of plasmas and some of the phenomena associated with them either in the limit without collisions or in the limit dominated by collisions.

Working method

Presencial

Program

PART 1: FLUIDS

1. Introduction Fluids and plasmas in Physics and Astrophysics

2. Ideal fluid Properties Derivation of macroscopic equations of hydrodynamics. The equation of continuity. The equation of motion - Euler's equation. The energy equation. The condition for absence of convection. The flow of energy and the flow of momentum. Barotropic and incompressible fluids. The conservation of motion. The Kelvin's vorticity theorem. The Bernoulli principle for stationary flows. Hydrostatics. Forces on submerged solid surfaces. Modelling the solar corona. Potential flow. Flow around a cylinder Stream function.

3. Viscous fluids Properties. Tangential stresses in a Newtonian fluid. The Navier-Stokes equations. Energy dissipation in incompressible fluids. Flow between two parallel planes subjects, in a circular tube and between two rotating cylinders. Factors of scale and the Reynolds number. Viscous flows around solid bodies. Boundary layers. Accretion disks in astrophysics: dynamics of accretion disks; stationary solutions.

4. Linear theory of waves and instabilities The philosophy of the analysis of disturbances. Convective instability and internal gravity waves: the Schwarzschild criterion. Rayleigh-Benard convection cells and Benard convection (for information). Surface gravity waves. Disturbances in the separation between two fluids: the Rayleigh-Taylor instability; Kelvin-Helmholtz instability. Jeans instability and the process of star formation. Oscillations in stars. Helioseismology.

PART 2: PLASMAS

5. Plasma physics: plasma orbital theory, dynamics of multiple charged particles and processes without collisions in plasmas. Approaches used in the theory of plasmas Orbits of motion of particles in a plasma. Effect of a perpendicular force, gradient and curvature. Larmor radius and frequency. Magnetic mirrors. Particle acceleration in astrophysics. Van Allen Belt. Cosmic rays. Basic properties of plasmas. Different types of plasma. Electrical neutrality in a plasma. Shielding and the Debye length. The plasma parameter. Oscillations in plasmas. The plasma frequency. Electromagnetic waves in hot and cold plasmas.

6. Magnetohydrodynamics (MHD) Fundamental equations. The plasma equations. The equation of induction and its consequences. Magnetohydrostatics. Applications to Fusion and Tokamaks. Applications to the solar atmosphere. Magnetohydrodynamic waves. Alfvén waves and magnetoacoustic waves. Magnetoconvection and sunspots. The buoyancy of magnetic flux tubes. The Parker instabilityof the magnetic field. The magnetic field as a carrier of angular momentum, magnetic braking and magnetized winds.

7. Magnetic topologies Application to magnetic reconnection and solar flares.

8. Dynamo theories Origin of magnetic fields in astronomy. Cowling's theorem. The solar dynamo.

Mandatory literature

Arnab Rai Choudhuri ;The physics of fluids and plasmas : an introduction for astrophysicists, Cambridge University Press, 1998. ISBN: 0-521-55543-4

Complementary Bibliography

Landau & Lifshitz; Fluid Mechanics. 2nd edition, Butterworth-Heinemann, 1987. ISBN: 978-0750627672
F. Shu; The Physics of Astrophysics Volume II: Gas Dynamics, University Science books, 2009. ISBN: 978-1891389672

Teaching methods and learning activities

Expository methods in theoretical lectures (T). In theoretical-practical classes (TP) resolution of exercises by the students.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Test 1	Teste	2,00	50,00	2013-04-11
Test 2	Teste	2,00	50,00	2013-06-04
	Total:	-	100,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Theoretical classes	Frequência das aulas	42	2013-06-04
Theoretical Pratical classes	Frequência das aulas	21	2013-06-04
Individual work	Estudo autónomo	139,5	2013-06-04
	Total:	202,50

Eligibility for exams

The student has frequency to the course if he/she misses no more than 1/4 of the planned theoretical-practical classes (TP's).

Calculation formula of final grade

Continuous evaluation with 2 assessment tests: T1 <= 10, T2 <= 10 Final Mark = T1+T2, which is the note of the normal exam epoch (1st sit). Evaluation by final exam: If the student chooses not to undergo continuous evaluation he/she must inform the lecturer (by email) until the normal exam date and, in this case, Final Mark = Exam Mark (without consultation, marked up to 20).

Classification improvement

It is possible to improve grades only through the resit exam (without consultation, marked up to 20).

Observations

This course runs simultaneously with Elasticity and Fluid Dynamics (F308). For this reason, a student cannot register simultaneously on these two courses.