# Plasma instabilities in fusion reactors

1. Dec 4, 2014

### ak33m98

I know that fusion experiments are difficult due to the fact the plasma seldom stays stable for long, but what exactly causes this plasma instability and are they any formulas to possibly predict the destabilisation of the plasma?

2. Dec 4, 2014

3. Dec 4, 2014

### the_wolfman

In magnetic confinement, the most disruptive instabilities are driven by steep pressure gradients or strong plasma currents.

There are a number of laws (both empirical and theoretical) that are used to predict stability/instability. There are also a number of numerical tools that are used to analyze stability.

Some examples:
Suydam Criteria
Mercier Criteria
Greenwald Limit
Troyon Limit

4. Dec 4, 2014

### ak33m98

Thanks for that link, but a lot of what it speaks about and refers to are out of my scope of knowledge, if you could point me in the direction of any introductory books/writings on the matter it would be greatly appreciated

5. May 1, 2015

### amchugh89

perturbation theory - define a small perturbation z (just a little displacement), then stick that into the Magnetohydrodynamic momentum equation (mdu/dt = pressure gradient) where pressure a sum of kinetic (P=nKT) and magnetic pressure (magnetic field lines actually repel eachother, and are 'tied' to the plasma in ideal MHD theory).

Anyway you get something like mz'' = F(z), which is the same as mx''=F(x), with z being the small perturbation displacement. F(z) is very long and complicated, but has a mathematical property of self-adjointedness that basically leads you to know that the w in z=z0*exp(-iwt), which is one of many modes (solutions) to the mz'' = F(z) is either purely real (the displacement leads to oscillation, and the plasma is stable to that mode) or purely imaginary (exponential growth, not stable) - so you can look for marginal stability conditions where w=0. mw^2z=0=F(z), which simplifies things. This is the normal mode analysis. There is also an energy pronciple, where you look for solutions to a pertubation energy (not momentum) equation, where again your x is the perturbation z. Then if dW>0 it's stable, if not, plasmas f***ed. Now I might have some details wrong.

Ch 6 of Gurnett Introduction to Plasma Physics is good
But I think Freidberg's Theory of Fusion Systems and MHD books are the standards for this

Last edited: May 2, 2015