Magnetic fields play an important role in many objects in the
universe, from the Sun with its spots and the magnetically heated
corona visible during a solar eclipse, to pulsars and the spectacular
'jets' from black holes and protostars. The behaviour of the magnetic
field in these objects, however, is very different from experience at
home or in physics class, since in astrophysical objects magnetic
field lines are 'tied' to an ionized gas. The theory for such magnetic
fields, called magnetohydrodynamics (MHD), is explained in a concise
textbook published
online.
It emphasizes understanding of MHD
by visualization of the flows and forces as they take place in a
magnetized fluid. To this end, the text also includes a number of
small video clips of basic MHD flows.
In physical processes where magnetic fields are present, one generally
also has electric fields, currents and charge
densities. Mathematically speaking, one has to deal with the full set
of Maxwell's equations plus the equations of motion for the particles
making up the plasma - the domain of plasma physics. Luckily, for most
flows seen in astronomical objects, however, this complexity is rarely
necessary. The electrical conductivity of an ionized gas makes MHD an
extremely accurate approximation. Compared with ordinary fluid
mechanics, only the magnetic field needs to be included explicitly in
the theory. The other electromagnetic quantities can be evaluated
afterwards; they are neither needed for a proper description, nor of
much use for physical understanding. Thanks to this simplification it
has become possible to include magnetic fields realistically in
numerical simulations, for example of extragalactic jets (Fig. 1).
The price to be paid is that we have to give up some of our intuitions
about the way electric and magnetic fields work. Our experience is
dominated by processes taking place in the Earth's electrically
insulating atmosphere (in copper wires, batteries, induction coils
etc.). Most astrophysical processes on the other hand happen in an
ionised gas, such as in a star, the solar wind, or the intergalactic
medium.
Because of the strong coupling between the magnetic field and the
electrically conducting gas, MHD flows behave more or less like
visco-elastic but otherwise ordinary fluids. This makes MHD an
eminently visualizable theory (for an example see the video clip
in Fig. 2), which also motivates the approach used
in the textbooklet. The first chapter (only 36 pages) is a concise
introduction including exercises. The exercises are important as
illustrations of the points made in the text (especially the less
intuitive ones). Almost all are mathematically unchallenging, though
some do require a background in undergraduate physics. This is the
'essential' part. The supplement in chapter 2 contains further
explanations, more specialized topics and occasional connections to
topics somewhat outside the scope of MHD.
