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Fluids and Plasmas in Astrophysics

Code: AST3005     Acronym: AST3005

Classification Keyword
OFICIAL Astronomy

Instance: 2018/2019 - 1S Ícone do Moodle

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

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
L:B 0 Official Study Plan 3 - 6 56 162
L:CC 1 Plano de estudos a partir de 2014 2 - 6 56 162
L:F 15 Official Study Plan 2 - 6 56 162
L:G 0 study plan from 2017/18 3 - 6 56 162
L:M 0 Official Study Plan 2 - 6 56 162
L:Q 0 study plan from 2016/17 3 - 6 56 162

Teaching Staff - Responsibilities

Teacher Responsibility
João José de Faria Graça Afonso Lima

Teaching - Hours

Theoretical classes: 2,50
Theoretical and practical : 1,50
Type Teacher Classes Hour
Theoretical classes Totals 1 2,50
João José de Faria Graça Afonso Lima 2,50
Theoretical and practical Totals 1 1,50
João José de Faria Graça Afonso Lima 1,50

Teaching language



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




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. 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.


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. Magnetohydrodynamic waves. Alfvén waves and magnetoacoustic waves.

7. Applications of MHD: 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. Magnetic reconnection and application solar flares. Dynamo theories and 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
Eric Priest; Magnetohydrodynamics of the Sun, Cambridge University Press. ISBN: 0521854717
J. Monteiro Moreira, J. Machado da Silva, J. Brochado Oliveira; Elasticidade e dinâmica dos fluidos, U.Porto, 2015. ISBN: 978-989-746-067-8

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
James Ward Brown, Ruel V. Churchill; "Complex variables and applications", McGraw-Hill, 1996. ISBN: 0071140654

Teaching methods and learning activities

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


Physical sciences > Physics > Classical mechanics > Fluid dynamics
Physical sciences > Astronomy > Astrophysics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation Weight (%)
Teste 100,00
Total: 100,00

Amount of time allocated to each course unit

designation Time (hours)
Estudo autónomo 106,00
Frequência das aulas 56,00
Total: 162,00

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, minimum note in each test 7/20.
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).


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