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# The Plasma Beta -

If the magnetic field is now included then we can anticipate the importance of the Lorentz force by considering the magnitude of the terms in (3.1).
1. When ther is no magnetic field then pressure gradient and gravitational force balance gives

Thus, we can neglect gravity and the exponential decrease of the pressure with height if .

2. Compare the Lorentz force with the pressure gradient force so that

Hence, we may neglect the pressure gradient term if

and we may alternatively neglect the Lorentz force if

We define the ratio of the gas pressure to the magnetic pressure as

so that
 (3.7)

Example 3.2.1   If , so that we may neglect gravity and so that we may also neglect the gas pressure, then (3.1) reduces to the low plasma approximation
 (3.8)

and the magnetic field is called force-free''.

Example 3.2.2
1. Coronal active regions where the magnetic field is closed.

This gives kg m and pascals. Therefore, the plasma beta is

Thus, is small in the corona.

2. Coronal holes have a weaker magnetic field strength and a lower temperature. Typically we take

Thus, in a coronal hole the plasma beta has a typical value of

and is even smaller than the active region value.

To a good approximation the magnetic field in the solar corona is force-free since the plasma beta is much smaller than unity. This is not the case in the convection zone where the plasm beta is usually much larger than unity. The next few sections will consider different force free equilibria.

Next: Potential Fields Up: Magnetohydrostatic Equilibria Previous: Hydrostatic Pressure Balance
Prof. Alan Hood
2000-01-11